Performance Evaluation of Hypervisors: A Comprehensive Benchmarking Study on VMware, Xen, and KVM - Satalino, Michael; Wu, Hao; Pang, Yulei (2026 3rd International Conference on Computer and Multimedia Technology (ICCMT), 2026)
This research presents a comparative performance analysis of three prominent hypervisor architectures—KVM, Xen, and VMware Workstation—to evaluate their scalability and resource efficiency under increasing virtual machine (VM) densities. Utilizing a standardized benchmarking framework, this study quantifies performance regressing across CPU throughput (GFLOPS), memory bandwidth, disk I/O, and initialization latency. The experiment results reveal that architectural design significantly dictates scalability limits: KVM’s kernel-integrated Type-1 model achieved the highest efficiency, maintaining a near-native CPU baseline and superior I/O resilience at peak density. In contrast, Xen’s microkernel architecture demonstrated stable but lower throughput due to Domain 0 (Dom0) management overhead, while VMware’s Type-2 hosted model exhibited the most acute performance degradation. These results demonstrate that while hosted hypervisors are suitable for low-density personal use, kernel-level integration is a mechanical necessity for maintaining performance in high-concurrency server environments. This work provides a reproducible methodology and critical data for system architects and researchers seeking to optimize resource orchestration in distributed and parallel systems.
Keywords: Central Processing Unit; Cloud Computing; Hardware; Hypervisor Benchmarking; Information rates; KVM; Management information base; Measurement; Memory; Performance Evaluation; Throughput; VMware; Virtual machine monitors; Virtual machines; Virtualization; Xen; dept.csc; dept.mat

Hypergeometric decomposition of Delsarte K3 pencils - Davis, Rachel; Dukes, Jessamyn; Ribeiro, Thais; Orvis, Eli; Salerno, Adriana; Sturman, Leah; Whitcher, Ursula (Research in the Mathematical Sciences, 2026)
Abstract We study five pencils of projective quartic Delsarte K3 surfaces. Over finite fields, we give explicit formulas for the point counts of each family, written in terms of hypergeometric sums. Over the complex numbers, we match the periods of the corresponding family with hypergeometric differential operators and series. We also obtain a decomposition of the incomplete L -function of each pencil in terms of hypergeometric L -series and Dedekind zeta functions. This gives an explicit description of the hypergeometric motives geometrically realized by each pencil.
Keywords: Basic hypergeometric series; Generalized hypergeometric function; Hypergeometric distribution; Hypergeometric function; Pencil (optics); Point (geometry); Quartic function; dept.mat

Change the journal title to reflect evolving focus - Choi, Kyong; Lee, Yujin; Lee, Younhee; hwang, jihyun (Mathematics Education Research and Practice, 2025)
Research in Mathematics Education.This change reflects the journal's expanding scope, integrating both theoretical and practical aspects of mathematics education in alignment with growing interdisciplinary and applied academic trends.In this editorial, we discuss revised scope of MERP and invite contributions from a diverse range of researchers and practitioners
Keywords: Field (mathematics); Focus (optics); Range (aeronautics); Scope (computer science); dept.mat

Incorporating changeable attitudes toward vaccination into compartment models for infectious diseases - Jiang, Yi; Kurianski, Kristin; Lee, Jane; Ma, Yanping; Cicala, Daniel; Ledder, Glenn (Mathematical Biosciences & Engineering, 2025)
We develop a mechanistic model that classifies individuals both in terms of epidemiological status (SIR) and vaccination attitude (Willing or Unwilling/Unable), with the goal of discovering how disease spread is influenced by changing opinions about vaccination. Analysis of the model identifies the existence and stability criteria for both disease-free and endemic disease equilibria. The analytical results, supported by numerical simulations, show that attitude changes induced by disease prevalence can destabilize endemic disease equilibria, resulting in limit cycles.
Keywords: Computer science; Disease; Econometrics; Endemic disease; Environmental health; Epidemic model; Epidemiology; Immunology; Infectious disease (medical specialty); Limit (mathematics); Machine learning; Mathematics; Medicine; Pathology; Stability (learning theory); Vaccination; dept.mat

MaPP Challenge : Giving a Taste of Contemporary Mathematics Research to Secondary Students in a Puzzle‑Based Outreach Program - Lee, Younhee; Carrigan, Braxton; Clontz, Steven; Couch, P.; Jones, Cadavious; Noble, Abby; Owens, Andrew; Pang, Yulei (Mathematics Outreach: Examples and Impact from Across the Globe, 2026)
Keywords: Community‑driven; Event (particle physics); Focus (optics); Focus group; Outreach; Perception; Taste; contemporary mathematics; dept.mat; fostering positive mathematical identity; inclusive mathematical outreach program; puzzle‑ based outreach

Rings with q-torsionfree canonical modules - Endo, Naoki; Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Iai, Shin-Ichiro; Kobayashi, Toshinori; Matsuoka, Naoyuki; Takahashi, Ryo (Commutative Algebra, 2025)
Let A be a Noetherian local ring with canonical module KA. We characterize A when KA is a torsionless, reflexive, or q-torsionfree module for an integer q ≥ 3. If A is a Cohen–Macaulay ring, H.-B. Foxby proved in 1974 that the A-module KA is q-torsionfree if and only if the ring A is q-Gorenstein. With mild assumptions, we provide a generalization of Foxby’s result to arbitrary Noetherian local rings admitting the canonical module. In particular, since the reflexivity of the canonical module is closely related to the ring being Gorenstein in low codimension, we also explore quasinormal rings, introduced by W. V. Vasconcelos. We provide several examples as well. ©2025 Walter de Gruyter GmbH,Berlin/Boston.
Keywords: Algebra over a field; Canonical module; Class (philosophy); Cohen–Macaulay ring; Gorenstein ring; Representation (politics); Set (abstract data type); dept.mat; q-Gorenstein ring; q-torsionfree module; quasinormal ring

Hilbert coefficients and Sally modules: a survey of Vasconcelos’ contributions - Hong, Jooyoun; Morey, Susan (Commutative Algebra, 2025)
Keywords: Chern numbers; Data collection; Field (mathematics); Hilbert coefficients; Hilbert functions; Hilbert polynomials; Sally modules; Work (physics); dept.mat; multiplicity

Degrees: Vasconcelos contributions - Ghezzi, Laura; Hong, Jooyoun (De Gruyter Proc. Math., 2025)
A degree of a module M is a numerical measure of information carried by M. We highlight some of Vasconcelos’ outstanding contributions to the theory of degrees, bridging commutative algebra and computational algebra. We present several degrees he introduced and developed, including arithmetic degree, jdeg, homological degree, cohomological degrees, canonical degree, and bicanonical degree. For the canonical and bicanonical degrees, we discuss recent developments motivated by our joint works [25, 19, 9]. ©2025 Walter de Gruyter GmbH,Berlin/Boston.
Keywords: Multiplicity; arithmetic degree; bicanonical degree; canonical degree; canonical ideal; cohomological degree; dept.mat; homological degree; jdeg

Toward Resolving Kang and Park’s Generalization of the Alder–Andrews Theorem - Sturman, Leah; Swisher, Holly (La Matematica, 2026)
Keywords: Alder–Andrews theorem; Alder’s conjecture; Conjecture; Generalization; Inequality; Kang-Park conjecture; Partition (number theory); Rogers–Ramanujan identities; Type (biology); d-distinct partitions; dept.mat

Skolem Number of Kagome Lattice Graphs - Carrigan, Braxton; Martone, Max (Theory and Applications of Graphs, 2025)
A proper Skolem labelling of a graph G is a function assigning a positive integer to each vertex of G such that any two vertices assigned the same integer are that distance apart in the graph. The Skolem number of a graph is smallest number n such that there exists a proper Skolem labelling only using the positive integers less than or equal to n. In this paper, we will begin by proving the Skolem number for another family of subgraphs of the hexagonal lattice and then prove the Skolem number for two families of subgraphs of the Kagome Lattice. © 2025 Georgia Southern University. All rights reserved.
Keywords: dept.mat

On Tight 6-Cycle Decompositions of Complete 3-Uniform Multi-Hypergraphs - Bandell, Jessica A.; Bunge, Ryan C.; Darrow, Brian D.; El-Zanati, Saad I.; Mountain, Claire E.; Neiburger, Levi (Springer Proceedings in Mathematics and Statistics, 2025)
The λ-fold complete 3-uniform hypergraph on v vertices has the edge multiset consisting of λ copies of each 3-element subset of its vertex set. A tight 6-cycle, denoted TC6, is a hypergraph with vertex set {a,b,c,d,e,f} and edge set {{a,b,c},{b,c,d},{c,d,e},{d,e,f},{e,f,a},{f,a,b}}. We give necessary and sufficient conditions on v for the existence of a TC6-decomposition of the λ-fold complete 3-uniform hypergraph on v vertices for any positive integer λ. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
Keywords: 3-uniform; Combinatorics; Computer science; Decomposition; Hypergraph; Mathematics; Multi-hypergraph; dept.mat

A note on the skewness of a graph - Pinciu, Val; Soss, William (Congr. Numer, 2016)
Keywords: dept.mat

Identifying which clients will cancel their insurance policy machine learning methods - Narain, K.; Pang, Y. (Proceedings - 2024 IEEE 48th Annual Computers, Software, and Applications Conference, COMPSAC 2024, 2024)
Using the 2013 data set provided by Insurance Inc., logistic regression and linear discriminant analysis models were created along with data visualizations to find out which factors recorded in the data set and the state of those factors causes a client to cancel their policy. The factors that impact whether a client will cancel are those that directly pertain to the policy. For example, the coverage type and the premium the client is paying for the policy impacts the probability the client will cancel their policy. Factors that go into forming the policy and have a relationship between one another such as age and premium, also impact the probability that a client will cancel their policy. The credit status of a client, whether it is low, medium, or high, and the type of coverage they have, has the most impact on a client's inevitability to cancel. If a client's credit score is classified as low, then that client is has a high probability of cancelling their policy according to the LDA (Linear Discriminant Analysis) classifier and logistic regression model. Likewise, if a client has coverage type B, the probability that they will cancel their policy is higher. The sales channel used to sell a client a policy also impacts the probability they will cancel. According to the LDA classifier and the logistic regression model, if a client was sold a policy over the phone, they are more likely to cancel. © 2024 IEEE.
Keywords: Gaussian Distribution; Linear Discriminant Analysis (LDA) Classifier; Logistic Regression; Naive Bayes Classifier; dept.mat

Language Learning Outcomes in on Ground Vs. Online Settings: Comparison and Correlation - Tu, I Ju; Bartlett, Andrew (American Journal of Distance Education, 2024)
While the effectiveness of online instruction has been well established, there remains a limited understanding of the correlation between language skills and performance across various instructional sections. This study investigates the language proficiency outcomes of college students in online and on-ground language instruction, focusing on four essential language skills: Reading, Writing, Listening, and Speaking. Data were collected from students enrolled in third-semester language courses in French, German, Italian, and Spanish during the Spring semesters of 2019 and 2021 with on-ground and online instruction respectively in a public university in the United States. Descriptive statistics, the Kruskal-Wallis test, and pairwise correlation analysis were used to analyze the students’ performance in both modalities. The results indicate that students generally outperformed in the online modality, demonstrating a significantly higher positive correlation range compared to on-ground instruction. This finding suggests that multi-modality language instruction has the potential to foster more integrated and cohesive language proficiency development. The implications firstly show the positive correlation range in the online modality indicates that college instructors may be more capable of implementing effective online teaching methods due to various reasons. Secondly, college students’ potential for self-directed learning in the online setting may contribute to their enhanced outcomes. However, the study also reveals challenges for less taught languages, such as the need for additional support in terms of resource curation and networking opportunities for instructors.
Keywords: dept.mat; peer-reviewed

Reactive axillary lymph nodes after COVID-19 mRNA vaccination: Comparison of mRNA vs. attenuated whole-virus vaccines - Adin, M.E.; Isufi, E.; Wu, J.; Pang, Y.; Nguyen, D.; Simsek Has, D.; Caner, C.; Aboueldaha, N.; Mossa-Basha, M.; Pucar, D. (Nuclear Medicine Communications, 2024)
Objective To compare the incidence and natural course of reactive axillary lymph nodes (RAL) between mRNA and attenuated whole-virus vaccines using Deauville criteria. Methods In this multi-institutional PET-CT study comprising multiple vaccine types (Pfizer-BioNTech/Comirnaty, Moderna/Spikevax, Sinovac/CoronaVac and Janssen vaccines), we evaluated the incidence and natural course of RAL in a large cohort of oncological patients utilizing a standardized Deauville scaling system (n=522; 293 Female, Deauville 3-5 positive for RAL). Univariate and multivariate analyses were conducted to evaluate the predictive value of clinical parameters (absolute neutrophil count [ANC], platelets, age, sex, tumor type, and vaccine-to-PET interval) for PET positivity. Results Pfizer-BioNTech/Comirnaty and Moderna vaccines revealed similar RAL incidences for the first 20 days after the second dose of vaccine administration (44% for the first 10 days for both groups, 26% vs. 20% for 10-20 days, respectively for Moderna and Pfizer). However, Moderna recipients revealed significantly higher incidences of RAL after 20 days compared to Pfizer-BioNTech/Comirnaty, with nodal reactivity spanning up to the 9th week post-vaccination (15% vs. 4%, respectively P<0.001). No RAL was observed in patients who received either a single dose of J&J vaccine or two doses of CroronaVac. Younger patients showed increased likelihood of RAL, otherwise, clinical/demographic parameters were not predictive of RAL (P=0.014 for age, P>0.05 for additional clinical/demographic parameters). Conclusion RAL based on strict PET criteria was observed with mRNA but not with attenuated whole-virus vaccines, in line with higher immunogenicity and stronger protection offered by mRNA vaccines. © 2024 Wolters Kluwer Health. All rights reserved.
Keywords: COVID-19; CoronaVac; Janssen; axillary lymph node; dept.mat; mRNA vaccine; peer-reviewed

Identification of adipogenic and osteogenic differentiation using transfer learning of ResNet-18 - Mai, M.; Luo, S.; Wang, S.; Pang, Y. (Proceedings - 22nd IEEE International Conference on Machine Learning and Applications, ICMLA 2023, 2023)
Human mesenchymal stem cells (hMSCs) have great potential in cell-based therapies and regenerative medicine due to their self-renewal and multipotency. hMSCs can be differentiated into several cell types, including adipocytes and osteblast. Conventional approaches for determining adipocyte formation include staining of lipid droplets (i.e., oil-red-O) during adipogenesis, which is time-consuming and uneconomical. Thus, there is an emerging need for a more effective and accurate approach to the prediction of adipogenic differentiation. Here, by combining live-cell imaging with a deep learning method, we developed a convolutional neural network-based approach to precisely predict lipid droplet formation during adipogenic differentiation of hMSCs. © 2023 IEEE.
Keywords: Adipogenic differentiation; CNN; Deep learning; ResNet; Transfer learning; adipogenisis; computer vision; convolution; dept.mat; hMSCs; human mesenchymal stem cells; osteogenic differentiation

Embracing bilingualism: L1 retention amidst L2 acquisition - Sorokina, A.; Mugno, R. (Language Learning Journal, 2024)
In L1 attrition research, it's recognized that a previously acquired language can transform under the influence of a newly acquired one. However, the precise L1-L2 relationship is intricate and warrants further study. Some research suggest that L2 mastery might reduce L1 proficiency, while others show that both languages can be maintained. Age of onset and L1 use are the factors that have been discussed in the debate surrounding L1 attrition. The study aims to contribute to the ongoing discussion by examining L1 and L2 proficiency of Russian-English bilingual speakers (N = 35). The participants with comparable L2 proficiency but various degrees of L1 attrition who arrived at different ages and differed in their frequency of L1 use were recruited for the study. This diverse group provided an ideal quality sample for investigating the role of age of onset and L1 use, as well as the interplay between L1 and L2. By comparing L1 and L2 lexical diversity, syntactic complexity, and fluency, the study revealed that higher L2 proficiency was not associated with lower levels of L1 proficiency, suggesting that L1 retention is possible amidst L2 acquisition. L1 use played a more significant role in the L1 maintenance of these bilingual individuals. © 2024 Association for Language Learning.
Keywords: L1 attrition; L1 maintenance; L1 use; age of onset; bilingualism; dept.mat; dept.wll; peer-reviewed

Best Darn Statistics Workbook Ever - Hauselt, William J.; Mugno, Raymond (Kendall Hunt Publishing, 2021)
Keywords: dept.mat; dept.psy

Skolem Number of Subgraphs on the Triangular Lattice - Carrigan, Braxton; Green, Garrett (Communications on Number Theory and Combinatorial Theory, 2021)
Keywords: dept.mat; peer-reviewed

Morphology-based deep learning approach for predicting adipogenic and osteogenic differentiation of human mesenchymal stem cells (hMSCs) - Mai, Maxwell; Luo, Shuai; Fasciano, Samantha; Oluwole, Timilehin Esther; Ortiz, Justin; Pang, Yulei; Wang, Shue (Frontiers in Cell and Developmental Biology, 2023)
Human mesenchymal stem cells (hMSCs) are multipotent progenitor cells with the potential to differentiate into various cell types, including osteoblasts, chondrocytes, and adipocytes. These cells have been extensively employed in the field of cell-based therapies and regenerative medicine due to their inherent attributes of self-renewal and multipotency. Traditional approaches for assessing hMSCs differentiation capacity have relied heavily on labor-intensive techniques, such as RT-PCR, immunostaining, and Western blot, to identify specific biomarkers. However, these methods are not only time-consuming and economically demanding, but also require the fixation of cells, resulting in the loss of temporal data. Consequently, there is an emerging need for a more efficient and precise approach to predict hMSCs differentiation in live cells, particularly for osteogenic and adipogenic differentiation. In response to this need, we developed innovative approaches that combine live-cell imaging with cutting-edge deep learning techniques, specifically employing a convolutional neural network (CNN) to meticulously classify osteogenic and adipogenic differentiation. Specifically, four notable pre-trained CNN models, VGG 19, Inception V3, ResNet 18, and ResNet 50, were developed and tested for identifying adipogenic and osteogenic differentiated cells based on cell morphology changes. We rigorously evaluated the performance of these four models concerning binary and multi-class classification of differentiated cells at various time intervals, focusing on pivotal metrics such as accuracy, the area under the receiver operating characteristic curve (AUC), sensitivity, precision, and F1-score. Among these four different models, ResNet 50 has proven to be the most effective choice with the highest accuracy (0.9572 for binary, 0.9474 for multi-class) and AUC (0.9958 for binary, 0.9836 for multi-class) in both multi-class and binary classification tasks. Although VGG 19 matched the accuracy of ResNet 50 in both tasks, ResNet 50 consistently outperformed it in terms of AUC, underscoring its superior effectiveness in identifying differentiated cells. Overall, our study demonstrated the capability to use a CNN approach to predict stem cell fate based on morphology changes, which will potentially provide insights for the application of cell-based therapy and advance our understanding of regenerative medicine.
Keywords: dept.mat

Briefly Recalling Some Antecedents of Standards-Based Reform and Standardized Assessment in American Mathematics Education - Darrow, Brian (Journal of Mathematics Education at Teachers College, 2023)
Keywords: dept.mat; peer-reviewed

A review of machine learning applications in life cycle assessment studies - Romeiko, Xiaobo Xue; Zhang, Xuesong; Pang, Yulei; Gao, Feng; Xu, Ming; Lin, Shao; Babbitt, Callie (Science of The Total Environment, 2023)
Life Cycle Assessment (LCA) is a foundational method for quantitative assessment of sustainability. Increasing data availability and rapid development of machine learning (ML) approaches offer new opportunities to advance LCA. Here, we review current progress and knowledge gaps in applying ML techniques to support LCA, and identify future research directions for LCAs to better harness the power of ML. This review analyzes forty studies reporting quantitative assessment with a combination of LCA and ML methods. We found that ML approaches have been used for generating life cycle inventories, computing characterization factors, estimating life cycle impacts, and supporting life cycle interpretation. Most of the reviewed studies employed a single ML method, with artificial neural networks (ANNs) as the most frequently applied approach. Both supervised and unsupervised ML techniques were used in LCA studies. For studies using supervised ML, training datasets were derived from diverse sources, such as literature, lab experiments, existing databases, and model simulations. Over 70 % of these reviewed studies trained ML models with less than 1500 sample datasets. Although these reviewed studies showed that ML approaches help improve prediction accuracy, pattern discovery and computational efficiency, multiple areas deserve further research. First, continuous data collection and compilation is needed to support more reliable ML and LCA modeling. Second, future studies should report sufficient details regarding the selection criteria for ML models and present model uncertainty analysis. Third, incorporating deep learning models into LCA holds promise to further improve life cycle inventory and impact assessment. Finally, the complexity of current environmental challenges calls for interdisciplinary collaborative research to achieve deep integration of ML into LCA to support sustainable development.
Keywords: Life cycle assessment; Machine learning; Model selection; Prediction; Sustainability; dept.mat; peer-reviewed

Inter-Pass Motion Correction for Whole-Body Dynamic PET and Parametric Imaging - Guo, Xueqi; Wu, Jing; Chen, Ming-Kai; Liu, Qiong; Onofrey, John A.; Pucar, Darko; Pang, Yulei; Pigg, David; Casey, Michael E.; Dvornek, Nicha C.; Liu, Chi (IEEE Transactions on Radiation and Plasma Medical Sciences, 2023)
Whole-body dynamic fluoro-D-glucose (FDG)-positron emission tomography (PET) imaging through continuous-bed-motion (CBM) mode multi-pass acquisition protocol is a promising metabolism measurement. However, inter-pass misalignment originating from body movement could degrade parametric quantification. We aim to apply a non-rigid registration method for inter-pass motion correction in whole-body dynamic PET. 27 subjects underwent a 90-min whole-body FDG CBM PET scan on a Biograph mCT (Siemens Healthineers), acquiring 9 over-the-heart single-bed passes and subsequently 19 CBM passes (frames). The inter-pass motion correction was executed using non-rigid image registration with multi-resolution, B-spline free-form deformations. The parametric images were then generated by Patlak analysis. The overlaid Patlak slope Ki and y-intercept Vb images were visualized to qualitatively evaluate motion impact and correction effect. The normalized weighted mean-squared Patlak fitting errors (NFEs) were compared in the whole body, head, and hypermetabolic regions of interest (ROIs). In Ki images, ROI statistics were collected and malignancy discrimination capacity was estimated by the area under the receiver operating characteristic curve (AUC). After the inter-pass motion correction was applied, the spatial misalignment appearance between Ki and Vb images was successfully reduced. Voxel-wise normalized fitting error maps showed global error reduction after motion correction. The NFE in the whole body ( p \,\,= 0.0013), head ( p \,\,= 0.0021), and ROIs ( p \,\,= 0.0377) significantly decreased. The visual performance of each hypermetabolic ROI in Ki images was enhanced, while 3.59% and 3.67% average absolute percentage changes were observed in mean and maximum Ki values, respectively, across all evaluated ROIs. The estimated mean Ki values had substantial changes with motion correction ( p \,\,= 0.0021). The AUC of both mean Ki and maximum Ki after motion correction increased, possibly suggesting the potential of enhancing oncological discrimination capacity through inter-pass motion correction.
Keywords: dept.mat; peer-reviewed

Autonomic modulation, spontaneous baroreflex sensitivity and fatigue in young men after COVID-19 - Latchman, Peter L; Yang, Qin; Morgenthaler, Diane; Kong, Lingsong; Sebagisha, J.; Melendez, Luke; Green, Cheryl A.; Bernard, Stanley; Mugno, Raymond; De Meersman, Ronald (Physiological research, 2023)
Impaired autonomic modulation and baroreflex sensitivity (BRS) have been reported during and after COVID-19. Both impairments are associated with negative cardiovascular outcomes. If these impairments were to exist undetected in young men after COVID-19, they could lead to negative cardiovascular outcomes. Fatigue is associated with autonomic dysfunction during and after COVID-19. It is unclear if fatigue can be used as an indicator of impaired autonomic modulation and BRS after COVID-19. This study aims to compare parasympathetic modulation, sympathetic modulation, and BRS between young men who had COVID-19 versus controls and to determine if fatigue is associated with impaired autonomic modulation and BRS. Parasympathetic modulation as the high-frequency power of R-R intervals (lnHFR-R), sympathetic modulation as the low-frequency power of systolic blood pressure variability (LFSBP), and BRS as the -index were measured by power spectral density analysis. These variables were compared between 20 young men who had COVID-19 and 24 controls. Independent t-tests and Mann-Whitney U tests indicated no significant difference between the COVID-19 and the control group in: lnHFR-R, P=0.20; LFSBP, P=0.11, and -index, P=0.20. Fatigue was not associated with impaired autonomic modulation or BRS. There is no difference in autonomic modulations or BRS between young men who had COVID-19 compared to controls. Fatigue did not seem to be associated with impaired autonomic modulation or impaired BRS in young men after COVID-19. Findings suggest that young men might not be at increased cardiovascular risk from COVID-19-related dysautonomia and impaired BRS.
Keywords: Autonomic Nervous System; Baroreflex; Blood Pressure; COVID-19; Cardiovascular System; Heart Rate; Humans; Male; dept.hms; dept.mat; dept.nur; dept.pch; dept.ss; peer-reviewed

Indigenous Mathematics of Native North Americans. - DeCesare, Rich (2007)
Keywords: dept.mat; faculty_collection; sabbatical_report

(Research into Expectations of College Mathematics Instructors) - Nowlan, Robert A. (1994)
Keywords: dept.mat; faculty_collection; sabbatical_report

Discrete Mathematics. - Gulati, Bodh R. (1992)
Keywords: dept.mat; faculty_collection; sabbatical_report

Integration of the Use of Computer Technology in Teaching Mathematics. - Bass, Helen (1991)
Keywords: dept.mat; faculty_collection; sabbatical_report

Study of Symbolic Computation Systems (Computer Algebra Systems) - Meck, Michael (1990)
Keywords: dept.mat; faculty_collection; sabbatical_report

Surviving Political Campaigns, Politicians, and Politics: Laugh Smile Learn Get Angry Curse - Nowlan, Robert A. (Outskirts Press, 2016)
Keywords: Politics and culture; United States; United States; Political campaigns; dept.mat; faculty_collection

The American Presidents from Polk to Hayes: What They Did, What They Said & What Was Said About Them - Nowlan, Robert A. (Outskirts Press, 2016)
Keywords: 19th century; Biography; United States; Politics and government; Presidents; United States; dept.mat; faculty_collection

Sabbatical leave report: Spring 2014 - Brin, Leon (2014)
Wrote the online, open source numerical analysis textbook "Tea Time Numerical Analysis" hosted at github.com. Report describes the process of writing, publishing the text. Includes information about review process and statement of success towards goals.
Keywords: dept.mat; faculty_collection; sabbatical_report

Sabbatical leave follow-up reports - Hong, Jooyoun (Production: Spring 2014 ; Mathematics., 2014)
The sabbatical leave was spent on research on Hibbert coefficients of ideals and integral closures of ideals, resulting in submission for publication, as co-author, of articles, Specialization and integral closure, to the Journal of the London Mathematical Society, and Hilbert polynomials of j-transforms, to the Mathematical Proceedings of the Cambridge Philosophical Society. Two research visits, to Purdue University and to Maiji University in Japan, facilitated work on these publications and laid foundation for new projects, already in progress, on normality of ideals and reduction numbers of ideals.
Keywords: dept.mat; faculty_collection; sabbatical_report

Tea Time Numerical Analysis - Brin, Leon (2013)
Keywords: dept.mat; faculty_collection

A Gentle Introduction to the Art of Mathematics: Version 3.1 - Fields, Joseph (Joseph E. Fields, 2013)
Keywords: Mathematics; Textbooks; dept.mat; faculty_collection

The American presidents, Washington to Tyler: what they did, what they said, what was said about them, with full source notes - Nowlan, Robert A. (McFarland & Co., 2012)
"Through current day, only forty-three men have held the office of the President of the United States, and some have been sanctified and some reviled. This historical work addresses the careers of the first ten presidents, men who made vital contributions not only to the office of the presidency, but to the course of the fledgling nation"--Provided by publisher.
Keywords: 1789-1815; United States; 1815-1861; Biography; United States; Politics and government; Presidents; United States; dept.mat; faculty_collection

Open Problems in the Area of Computational Geometry. - Pinciu, Valeriu (2012)
Dr. Pinciu engaged in collaborative research with T.S. Michael from the U.S. Naval Academy focusing on visibility problems, known as art gallery (polygon interior), fortress (polygon exterior), and prison yard (polygon interior and exterior) problems. The outcome resulted in two conference presentations and an article accepted for publication, with additional presentations and another article to follow.
Keywords: dept.mat; faculty_collection; sabbatical_report

A Gentle Introduction to the Art of Mathematics: Version 2.0 - Fields, Joseph (Lulu, 2010)
Keywords: Mathematics; Textbooks; dept.mat

Born This Day: A Book of Birthdays and Quotations of Prominent People Through the Centuries - Nowlan, Robert A. (McFarland & Co., 2007)
"For each date, a diverse dozen speakers were chosen based on prominence; the quality of the quotation; the uniqueness of the speaker with relation to gender, time period, nationality and vocation; and conflicting social, political, religious or philosophical background. Includes a quotation from each person that allows a glimpse of their personality"--Provided by publisher.
Keywords: Quotations, English; Birthday books; Literary calendars; dept.mat; faculty_collection

A Dictionary of Quotations in Mathematics - Nowlan, Robert A. (McFarland, 2002)
Keywords: Mathematics; Quotations, maxims, etc; dept.mat; faculty_collection

Doing Statistics for Business with Excel: Data, Inference, and Decision Making - Pelosi, Marilyn K.; Sandifer, Theresa M. (Wiley, 2002)
Keywords: Commercial statistics; Statistics; Industrial management; Statistical methods; dept.mat; faculty_collection

The Films of the Nineties: A Complete, Qualitative Filmography of Over 3000 Feature-Length English Language Films, Theatrical and Video-Only, Released Between January 1, 1990, and December 31, 1999 - Nowlan, Robert A. (McFarland, 2001)
Keywords: Catalogs; Motion pictures; dept.mat; faculty_collection

A Dictionary of Quotations and Proverbs About Cats and Dogs - Nowlan, Robert A.; Nowlan, Gwendolyn Wright (McFarland, 2001)
Keywords: Cats; Quotations, maxims, etc; Quotations, maxims, etc; Dogs; dept.ils; dept.mat; faculty_collection

A Dictionary of Quotations About Communication - Nowlan, Robert A.; Nowlan, Gwendolyn Wright (McFarland, 2000)
Keywords: Quotations; Quotations, English; dept.ils; dept.mat; faculty_collection

Born This Day: A Book of Birthdays and Quotations of Prominent People Through the Centuries - Nowlan, Robert A. (McFarland, 1996)
Keywords: Quotations, English; Birthday books; Literary calendars; dept.mat; faculty_collection

We'll Always Have Paris: The Definitive Guide to Great Lines from the Movies - Nowlan, Robert A.; Nowlan, Gwendolyn Wright (HarperCollins Publishers, 1995)
Keywords: Motion pictures; Quotations, maxims, etc; dept.ils; dept.mat; faculty_collection

Finite Mathematics with Applications to the Business and Social Sciences - Gulati, Bodh R. (Kendall/Hunt Pub. Co., 1994)
Keywords: Mathematics; dept.mat; faculty_collection

Film Quotations: 11,000 Lines Spoken on Screen, Arranged by Subject, and Indexed - Nowlan, Robert A. (McFarland, 1994)
Keywords: Motion pictures; Quotations, maxims, etc; dept.mat; faculty_collection

The Films of the Eighties: A Complete, Qualitative Filmography to Over 3400 Feature-Length English Language Films, Theatrical and Video-Only, Released Between January 1, 1980, and December 31, 1989 - Nowlan, Robert A.; Nowlan, Gwendolyn Wright (McFarland & Co., 1991)
Keywords: Catalogs; Motion pictures; dept.ils; dept.mat; faculty_collection

Movie Characters of Leading Performers of the Sound Era - Nowlan, Robert A. (American Library Association, 1990)
Keywords: Biography; Characters and characteristics in motion pictures; Dictionaries; Dictionaries; Film adaptations; Dictionaries; Motion picture actors and actresses; dept.mat; faculty_collection

Cinema Sequels and Remakes, 1903-1987 - Nowlan, Robert A. (McFarland & Co., 1989)
Keywords: Film remakes.; Film sequels.; dept.mat; faculty_collection

College Algebra and Trigonometry with Applications - Gulati, Bodh R. (Allyn and Bacon, 1986)
Keywords: Algebra; Trigonometry; dept.mat; faculty_collection

College Algebra with Applications - Gulati, Bodh R. (Allyn and Bacon, 1986)
Keywords: Algebra; dept.mat; faculty_collection

The College of Trivial Knowledge - Nowlan, Robert A. (Quill, 1983)
Keywords: FAQs.; dept.mat; faculty_collection

Algebra and Trigonometry: Precalculus Mathematics - Gulati, Bodh R. (Allyn and Bacon, 1982)
Keywords: Algebra; Trigonometry; dept.mat; faculty_collection

College Algebra - Gulati, Bodh R. (Allyn and Bacon, 1982)
Keywords: Algebra; dept.mat; faculty_collection

A Mathematical Panorama: Topics for the Liberal Arts - Berlinghoff, William P.; Gulati, Bodh R.; Grant, Kerry E. (D.C. Heath, 1980)
Keywords: Mathematics; dept.mat; faculty_collection

College Mathematics with Applications to the Business and Social Sciences - Gulati, Bodh R. (Harper & Row, 1978)
Keywords: Mathematics; Business mathematics; Social sciences; Methodology; dept.mat; faculty_collection

Finite Mathematics: An Introduction - Gulati, Bodh R. (Harper & Row, 1975)
Keywords: Mathematics; dept.mat; faculty_collection

Geometry for Teachers - Nowlan, Robert A.; Washburn, Robert M. (1973)
Keywords: Geometry; dept.mat; faculty_collection

Mathematics; the Art of Reason - Berlinghoff, William P. (Heath, 1968)
Keywords: Mathematics; dept.mat; faculty_collection

Residual intersections and core of modules - Costantini, Alessandra; Fouli, Louiza; Hong, Jooyoun (Journal of Algebra, 2023)
We introduce the notion of residual intersections of modules and prove their existence. We show that projective dimension one modules have Cohen-Macaulay residual intersections, namely they satisfy the relevant Artin-Nagata property. We then establish a formula for the core of orientable modules satisfying certain homological conditions, extending previous results of Corso, Polini, and Ulrich on the core of projective one modules. Finally, we provide examples of classes of modules that satisfy our assumptions.
Keywords: Core; Reductions; Residual intersections; dept.mat; peer-reviewed

Application of Time Series Analysis Methods to Assess the impact of COVID-19 on Carbon Dioxide Emission Reduction in Connecticut - Kiernan, Katherine A.; Wu, Hao; Mugno, Ray; Pang, Yulei (2022 IEEE International Conference on Big Data (Big Data), 2022)
The primary goals of this study are to determine if the datasets of positive COVID-19 test cases and CO2 emissions from Connecticut over the span of March 24th, 2020-October 31, 2021 are in any ways correlated. With climate change a prominent issue facing the entire world today, it is important to explore methods of providing records of past patterns of greenhouse gas emissions in order to inform decision making that could reduce future ones. Autoregressive integrated moving average (ARIMA) modeling is also implemented in this paper to provide forecasting based on CO2 emissions in CT starting from 2019. The most significant results from this paper are as follows: the CO2 emission data of transportation sectors including ground transportation, domestics aviation, and international aviation and weekly COVID-19 positive test cases data has a strong relationship during the first 28 weeks of the pandemic with a correlation of -86.34%. The CO2 emissions experienced on average a -22.96% change of pre-pandemic vs during initial quarantine conditions and at most a - 44.48% change when comparing the pre-pandemic mean to the during initial quarantine minimum value. Lastly, the ARIMA model found to have the lowest Akaike information criterion (AIC) was ARIMA (4,0,4). In conclusion, in the event of a collective global pandemic and lockdown conditions, less traveling resulting in a correlated decrease of CO2 emissions. This means that perhaps concentrated efforts on reducing unnecessary travel could help mitigate the levels of carbon dioxide emissions as a more long-term solution to climate change opposed to the pandemic’s short-term example.
Keywords: ARIMA; CO2 emission; COVID-19; Carbon dioxide; Change points detection; Climate change; Correlation coefficient; Decision making; Greenhouse effect; Pandemics; Time series analysis; dept.csc; dept.mat

A norm functor for quadratic algebras - Biesel, Owen (Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2022)
Given commutative, unital rings $$\mathcal {A}$$and $$\mathcal {B}$$with a ring homomorphism $$\mathcal {A}\rightarrow \mathcal {B}$$making $$\mathcal {B}$$free of finite rank as an $$\mathcal {A}$$-module, we can ask for a “trace” or “norm” homomorphism taking algebraic data over $$\mathcal {B}$$to algebraic data over $$\mathcal {A}$$. In this paper we we construct a norm functor for the data of a quadratic algebra: given a locally-free rank-2 $$\mathcal {B}$$-algebra $$\mathcal {D}$$, we produce a locally-free rank-2 $$\mathcal {A}$$-algebra $$\textrm{Nm}_{\mathcal {B}/\mathcal {A}}(\mathcal {D})$$in a way that is compatible with other norm functors and which extends a known construction for étale quadratic algebras. We also conjecture a relationship between discriminant algebras and this new norm functor.
Keywords: 11R11; 13B02; 13B40; 13C10; 14B25; Algebra of finite rank; Norm functor; Quadratic algebra; Ring extension; dept.mat; Étale algebra

Generalization of bi-canonical degrees - Brennan, J.; Ghezzi, L.; Hong, J.; Vasconcelos, W. V. (São Paulo Journal of Mathematical Sciences, 2023)
We discuss invariants of Cohen-Macaulay local rings that admit a canonical module $$ω$$. Attached to each such ring R, when $$ω$$is an ideal, there are integers–the type of R, the reduction number of $$ω$$–that provide valuable metrics to express the deviation of R from being a Gorenstein ring. In (Ghezzi et al. in JMS 589:506–528, 2017) and (Ghezzi et al. in JMS 571:55–74, 2021) we enlarged this list with the canonical degree and the bi-canonical degree. In this work we extend the bi-canonical degree to rings where $$ω$$is not necessarily an ideal. We also discuss generalizations to rings without canonical modules but admitting modules sharing some of their properties.
Keywords: 13A99; Bi-canonical degree; Canonical module; Primary 13H15; Secondary 13H10; dept.mat; peer-reviewed

Deformations of reducible SL(n, C) representations of fibered 3-manifold groups - Kozai, K. (Osaka Journal of Mathematics, 2022)
Let Mφ be a surface bundle over a circle with monodromy φ: S → S. We study deformations of certain reducible representations of π1(Mφ)intoSL(n, C), obtained by composing a reducible representation into SL(2, C) with the irreducible representation SL(2, C) → SL(n, C). In particular, we show that under certain conditions on the eigenvalues of φ∗, the reducible representation is contained in a (n + 1 + k)(n − 1) dimensional component of the representation variety, where k is the number of components of ∂Mφ . This result applies to mapping tori of pseudo-Anosov maps with orientable invariant foliations whenever 1 is not an eigenvalue of the induced map on homology, where the reducible representation is also a limit of irreducible representations. © 2022, Osaka University. All rights reserved.
Keywords: dept.mat; ⛔ No DOI found

An isoperimetric inequality involving conformal mapping - Berlinghoff, W.P.; Reid, J.D. (Proceedings of the American Mathematical Society, 1977)
This paper characterizes quasi-pure projective (q.p.p.) and quasi-pure injective (q.p.i.) p-groups, and hence characterizes all such (abelian) torsion groups. A p-group is q.p.i. if and only if it is the direct sum of a divisible group and a torsion complete group. A nonreduced p-group is q.p.p. if and only if it is the direct sum of a divisible group and a bounded group; a reduced p-group is q.p.p. if and only if it is a direct sum of cyclic groups. © 1977 American Mathematical Society.
Keywords: Abelian group; Direct sum of cyclic groups; Pure exact sequence; Quasi-injective; Quasi-projective; Torsion complete; dept.mat

On two level symmetrical factorial designs - Kounias, E.G.; Gulati, B.R. (Annals of the Institute of Statistical Mathematics, 1972)
Keywords: dept.mat

Correction note to "on maximal (k,t)-sets" - Gulati, B.R. (Annals of the Institute of Statistical Mathematics, 1971)
Keywords: dept.mat

A study of H-spaces via left translations - Nowlan, R.A. (Pacific Journal of Mathematics, 1971)
H-spaces are examined by studying left translations, actions and a homotopy version of left translations to be called homolations. If (F, m) is an H-space, the map s: F-→FF given by s(x) = Lx, i.e. s(x) is left translation by x, is a homomorphism if and only if m is associative. In general, s is an An-map if and only if (F, m) is an An+1 space. The action r: FF × F → F is given by r(φ, x) = φ(x). The map s respects the action only of left translations. In general, s respects the action of homolations up to higherorder homotopies. Each homolation generates a family of maps to be called a homolation family. Denoting the set of all homolation families by H∞(F), s: F -→ FF factors through F → H∞(F) and this latter map is a homotopy equivalence. © 1971 Pacific Journal of Mathematics.
Keywords: dept.mat

Nonnegativity results for generalized q-binomial coefficients - Fishel, S. (Discrete Mathematics, 1995)
Let q be a prime number. The number of subgroups of order qk in an abelian group G of order qn and type λ is a polynomial in q, [kλ′]q. In 1987, Lynne Butler showed that the first difference, [kλ′] - [k - 1λ′], has nonnegative coefficients as a polynomial in q, when 2k ≤ |λ|. We generalize the first difference to the rth difference, and give conditions for the nonnegativity of its coefficients. © 1995.
Keywords: dept.mat

Quadruple covers of algebraic varieties - Hahn, D.W.; Miranda, R. (Journal of Algebraic Geometry, 1999)
Let X and Y be varieties over a field k; π : X → Y is a quadruple cover of Y if π*script O signX is a locally free, rank 4 script O signY-algebra. If char k ≠ 2, we see that π*script O signX splits as script O signY ⊕ε where ε is a locally free rank 3 sheaf over script O signY, which is locally the "trace zero" module. For each y ∈ Y, we therefore have a rank 4 associative, commutative algebra over script O signY,y. We find that these algebras are parametrized by an affine cone over the Grassmanian G(2, 6) with vertex corresponding to the algebra k[x, y, z]/(x, y, z)2. We then show that a quadruple cover with trace zero module ε over a variety Y is determined by a totally decomposable section η ∈ H0(∧2S2 E* ⊗ ∧3 E). We then examine the case in which the section η has no zeros. Here, each rank 4 algebra may be associated to a pencil of conics. As a special case of this, we look at the work of G. Casnati and T. Ekedahl on Gorenstein covers, and we show that their analysis is the subcase where the pencil of conics has length 4 base locus. Finally, we study the case in which the trace zero module ε is split. In this context, Galois covers, which are covers induced by the action of a group of order 4 on the covering variety X, are also studied.
Keywords: dept.mat; ⛔ No DOI found

Art gallery theorems for guarded guards - Michael, T.S.; Pinciu, V. (Computational Geometry: Theory and Applications, 2003)
We prove two art gallery theorems in which the guards must guard one another in addition to the gallery. A set G of points (the guards) in a simple closed polygon (the art gallery) is a guarded guard set provided (i) every point in the polygon is visible to some point in G; and (ii) every point in G is visible to some other point in G. We prove that a polygon with n sides always has a guarded guard set of cardinality ⌊(3n-1)/7⌋ and that this bound is sharp (n5); our result corrects an erroneous formula in the literature. We also use a coloring argument to give an entirely new proof that the corresponding sharp function for orthogonal polygons is ⌊n/3⌋ for n≤6; this result was originally established by induction by Hernández-Peñalver. © 2003 Elsevier B.V.
Keywords: Art gallery theorems; Visibility in polygons; dept.mat

Polynomial identities of matrices with the symplectic involution: The low degrees - D'Amour, A.; Racine, M. (Communications in Algebra, 2004)
The *-polynomial identities of minimal degree of Mn(F) are determined for n = 2, 4, * the symplectic involution. Copyright © 2004 by Marcel Dekker, Inc.
Keywords: *-Polynomial identity; Polynomial identity; Symplectic involution; dept.mat

Full ideals - Hong, J.; Lee, H.; Noh, S.; Rush, D.E. (Communications in Algebra, 2009)
Contractedness of m-primary integrally closed ideals played a central role in the development of Zariski's theory of integrally closed ideals in two-dimensional regular local rings (R, m). In such rings, the contracted m-primary ideals are known to be characterized by the property that I: m = I: x for some x ∈ m\m2. We call the ideals with this property full ideals and compare this class of ideals with the classes of m-full ideals, basically full ideals, and contracted ideals in higher dimensional regular local rings. The m-full ideals are easily seen to be full. In this article, we find a sufficient condition for a full ideal to be m-full. We also show the equivalence of the properties full, m-full, contracted, integrally closed, and normal, for the class of parameter ideals. We then find a sufficient condition for a basically full parameter ideal to be full. © Taylor & Francis Group, LLC.
Keywords: Basically full ideal; Contracted ideal; Full ideal; Ideal with Rees property; Integrally closed ideal; dept.mat; m-Full ideal

Tiling polyhedra with tetrahedra - Bezdek, A.; Carrigan, B. (2012)
When solving an algorithmic problem involving a polyhedron in R 3, it is common to start by partitioning the given polyhedron into simplier ones. The most common process is called triangulation and it refers to partitioning a polyhedron into tetrahedra in a face-to-face manner. In this paper instead of triangulations we will consider tilings by tetrahedra. In a tiling the tetrahedra are not required to be attached to each other along common faces. We will construct several polyhedra which can not be triangulated but can be tiled by tetrahedra. We will also revisit a nontriangulatable polyhedron of Rambau and a give a new proof for his theorem. Finally we will identify new families of non-tilable, and thus non-triangulable polyhedra.
Keywords: Algorithmic problems; Common process; Computational geometry; Theorem proving; Triangulation; dept.mat; ⛔ No DOI found

The mathematics for middle school teachers program at Western Oregon University - Beaver, C.; Harrington, R.; Kruczek, K. (Resources for Preparing Middle School Mathematics Teachers, 2013)
Introduction: Although there is some common pedagogical ground for all teachers of mathematics, there is a fundamental difference in the topics and depth of content knowledge required for students preparing to teach elementary, middle, or high school mathematics. The middle school teacher preparation program at Western Oregon University (WOU) seeks to develop foundational content for middle school teachers while exploring best practices such as active learning, appropriate use of technology, and hands-on exploration. WOU offers many courses specifically for middle school teachers that are designed to develop mathematical maturity and content knowledge while connecting the subject matter to the middle school curriculum and standards. This article describes the structure of WOU's middle school mathematics program and the courses designed specifically for middle school mathematics teachers. We point out the difference in the mathematical preparation and requirements for middle school mathematics teachers compared to elementary teachers and high school mathematics teachers and explain the licensure requirements for middle school mathematics teachers in Oregon. Background and Philosophy of the Program: Western Oregon University's math curriculum for K–8 teacher preparation was among ten programs singled out as meeting critical coursework needs by the National Council on Teacher Quality [5]. The teacher preparation program as a whole was named the 2010 recipient of the Christa McAuliffe Award for Excellence in Teacher Education by the American Association of State Colleges and Universities (AASCU). © 2013 by The Mathematical Association of America (Incorporated).
Keywords: dept.mat

Visual College Algebra for Teachers - Burton, L.J.; Kruczek, K.T. (Resources for Preparing Middle School Mathematics Teachers, 2013)
At Western Oregon University, we offer a College Algebra for Teachers course using the Visual Algebra for College Students [3] materials that we wrote and class tested. Visual Algebra is designed to help middle school teachers gain a deep understanding of basic algebraic skills. Students visually show algebra using a concrete model (algebra pieces), verbally describe the meaning of each algebra piece move, symbolically connect the ideas to standard algebraic algorithms and procedures, and graphically connect the ideas of the visual models and symbolic work. Overall, students think deeply about topics, do not rely on rote memorization or rote rules, and understand ideas so well that they can easily describe, model, and teach core algebraic ideas to their middle grade students in a variety of ways. This allows our future teachers to meet the needs of the different learning styles in their classrooms. Visual Algebra takes students through modeling integer operations with black and red tiles to modeling linear and quadratic patterns with tiles and variable algebra pieces, looking at the general forms of the patterns and then connecting all the ideas to symbolic manipulation, creating data sets, graphing, and finding intercepts and points of intersection. Ideas are then extended to higher order polynomial functions and then to modeling complex number operations with black, red, yellow, and green tiles. Throughout the course, students are able to relate what they learned using visual methods to the standard methods and algorithms they will see every day in their classroom. For example, after factoring quadratic equations using visual methods, students learn factoring by grouping and factoring using the “ac” method. © 2013 by The Mathematical Association of America (Incorporated).
Keywords: dept.mat

Academic Freedom and Tenure: National Louis University (Illinois) - Grant, K.E.; Simpson, P.A.; Zannoni, D.C. (Academe, 2013)
Keywords: dept.mat; ⛔ No DOI found

Extremal rees Algebras - Hong, J.; Simis, A.; Vasconcelos, W.V. (Journal of Commutative Algebra, 2013)
We study almost complete intersection ideals whose Rees algebras are extremal in the sense that some of their fundamental metrics depth or relation type have maximal or minimal values in the class. The focus is on those ideals that lead to almost Cohen-Macaulay algebras, and our treatment is wholly concentrated on the nonlinear relations of the algebras. Several classes of such algebras are presented, some of a combinatorial origin. We offer a different prism to look at these questions with accompanying techniques. The main results are effective methods to calculate the invariants of these algebras. © 2013 Rocky Mountain Mathematics Consortium.
Keywords: Almost Cohen-Macaulay algebra; Almost complete intersection; Birational mapping; Castelnuovo regularity; Extremal Rees algebra; Hilbert function; Module of nonlinear relations; Rees algebra; Relation type; Sally module; dept.mat

Truck versus human: Mathematics under pressure - Field, E.; Ivison, R.; Reyher, A.; Warner, S. (College Mathematics Journal, 2014)
If you are ever faced with an oncoming truck, this paper could save your life. We investigate the optimal path that you should take from the middle of the road to the curb in order to avoid being hit by an oncoming truck. Although your instincts may tell you to run directly toward the curb, it turns out that this path, although the shortest, is not generally the safest.
Keywords: dept.mat

The art gallery theorem, revisited - Michael, T.S.; Pinciu, V. (American Mathematical Monthly, 2016)
The art gallery theorem asserts that any polygon with n vertices can be protected by at most [n/3] stationary guards. The original proof by Chvátal uses a nonroutine and nonintuitive induction. We give a simple inductive proof of a new, more general result, the constrained art gallery theorem: If V∗and E∗are specified sets of vertices and edges that must contain guards, then the polygon can be protected by at most [(n + 2|V∗| + |E∗|) /3] guards. Our result reduces to Chvátal's art gallery theorem when V∗and E∗are empty. We give a second short proof of this generalization in the spirit of Fisk's proof of the art gallery theorem using graph colorings. © THE MATHEMATICAL ASSOCIATION OF AMERICA.
Keywords: dept.mat; ⚠️ Invalid DOI

Characterization and comparison of injuries caused by spontaneous versus organized dogfighting - Intarapanich, N.P.; Touroo, R.M.; Rozanski, E.A.; Reisman, R.W.; Intarapanich, P.P.; McCobb, E.C. (Journal of the American Veterinary Medical Association, 2017)
OBJECTIVE To characterize and compare injuries found in dogs involved in spontaneously occurring dogfights with those of dogs used in illegal organized dogfighting. DESIGN Retrospective case-control study. ANIMALS 36 medium-sized dogs evaluated following spontaneous fights with a dog of the same sex and similar weight (medium dog–medium dog [MDMD] fights), 160 small dogs examined following spontaneous fights with a larger dog (big dog–little dog [BDLD] fights), and 62 dogs evaluated after being seized in connection with dogfighting law enforcement raids. PROCEDURES Demographic characteristics and injuries were recorded from medical records. Prevalence of soft tissue injuries in predetermined body surface zones, as well as dental or skeletal injuries, was determined for dogs grouped by involvement in BDLD, MDMD, and organized dogfights. The extent of injuries in each location was scored and compared among groups by 1-factor ANOVA. Patterns of injuries commonly incurred by each group were determined by use of prevalence data. RESULTS Mean extent of injury scores differed significantly among groups for all body surface zones except the eye and periorbital region. Mean scores for dental injuries and rib fractures also differed significantly among groups. Organized fighting dogs more commonly had multiple injuries, particularly of the thoracic limbs, dorsal and lateral aspects of the head and muzzle or oral mucosa, dorsal and lateral aspects of the neck, and ventral neck and thoracic region. CONCLUSIONS AND CLINICAL RELEVANCE To the authors’ knowledge, this was the first study to compare injuries incurred during spontaneous and organized dogfighting. Establishing evidence-based patterns of injury will help clinicians identify dogs injured by organized dogfighting and aid in the prosecution of this crime. © 2017, American Veterinary Medical Association. All rights reserved.
Keywords: Animals; Article; Athletic Injuries; Behavior, Animal; Bites and Stings; Case-Control Studies; Dogs; Female; Injury Severity Score; Male; Retrospective Studies; Violence; age; animal; animal behavior; bite wound; bites and stings; body surface; case control study; comparative study; dept.mat; dog; dog bite; dog breed; female; fighting; injuries; injury; injury scale; male; nonhuman; pathophysiology; prevalence; retrospective study; rib fracture; scoring system; soft tissue injury; sport injury; tooth injury; veterinary; violence

Factors affecting the acquisition of energy-efficient durable goods - Kuusela, H.; Spence, M.T. (Greener Marketing: A Global Perspective on Greening Marketing Practice, 2017)
Keywords: dept.mat

On Decomposing the Complete Symmetric Digraph into Orientations of K4-e - Bunge, R.C.; Darrow, B.D.; Dubczuk, T.M.; El-Zanati, S.I.; Hao, H.H.; Keller, G.L.; Newkirk, G.A.; Roberts, D.P. (Discussiones Mathematicae - Graph Theory, 2019)
Let D be any of the 10 digraphs obtained by orienting the edges of K4 - e. We establish necessary and sufficient conditions for the existence of a (K∗ n,D)-design for 8 of these digraphs. Partial results as well as some nonexistence results are established for the remaining 2 digraphs. © 2019 Ryan C. Bunge et al., published by Sciendo 2019.
Keywords: dept.mat; digraph decompositions; orientations of K4-e; peer-reviewed

Comparison of Support Vector Machine and Gradient Boosting Regression Tree for Predicting Spatially Explicit Life Cycle Global Warming and Eutrophication Impacts: A case study in corn production - Romeiko, X.X.; Guo, Z.; Pang, Y. (Institute of Electrical and Electronics Engineers Inc., 2019)
Agriculture ranks one of the top contributors to global warming and nutrient pollution. Quantifying life cycle environmental impacts from agricultural production serves as scientific foundation for forming effective remediation strategies. However, the methods capable of accurately and efficiently calculating spatially explicit life cycle global warming and eutrophication impacts at a fine spatial scale over a geographic region are lacking. The objective of this study was to compare two regression models for estimating spatially explicit life cycle global warming and eutrophication, with corn production in the Midwest region as a demonstrating example. The results indicated that the gradient boosting regression tree model built with monthly weather features yielded higher predictive accuracy for life cycle global warming impact and life cycle EU. Moreover, predictive accuracy was improved at the cost of simulation time. The gradient boosting regression tree model required longer training time. Additionally, all machine learning models were million times faster than the traditional process-based model and were suitable for use in computationally-intensive applications like optimization and predication. © 2019 IEEE.
Keywords: Agricultural productions; Agriculture; Big data; Environmental impact; Eutrophication; Forestry; Global warming; Learning systems; Life Cycle Assessment (LCA); Life cycle; Life cycle assessment; Life-cycle environmental impact; Machine learning; Machine learning models; Process-based modeling; Remediation strategies; Scientific foundations; Spatial assessment; Support vector machines; Support vector regression; dept.mat

Comparative assessment of shell properties in eight species of cohabiting unionid bivalves - Prezant, Robert S.; Dickinson, Gary H.; Chapman, Eric J.; Mugno, Raymond; Rosen, Miranda N.; Cadmus, Maxx B. (Freshwater Mollusk Biology and Conservation, 2022)
Freshwater unionid mussels produce a bilayered shell with the mineral proportion comprising an outer prismatic and an inner nacreous layer. The shell is the animals’ primary structural means of protection from predators and environmental challenges; therefore, variations in shell strength and properties may lead to differences in survival. Few studies have systematically assessed shell properties in unionids. A major challenge in such work is separating effects of environment from those of evolutionary history, because ultimately, both can affect shell properties. We collected eight species of unionids within a small area of the Allegheny River, Pennsylvania, that was relatively homogeneous in substratum type and other environmental characteristics. For each species, we quantified shell thickness, including thickness of the prismatic and nacreous layers, and shell micromechanical properties (microhardness and crack propagation, a measure of fracture resistance) in three regions of the shell. Shell thickness varied dramatically among species and was about five times greater in the thickest-shelled species, Pleurobema sintoxia, than in the thinnest-shelled species, Villosa iris. Because all species experienced similar environmental conditions, variation in shell thickness can be attributed largely to evolutionary history. In contrast, microhardness and crack propagation showed little variation among species. Given that micromechanical properties are similar among species, shell strength may be largely a function of thickness. These results have conservation implications, as differences in shell thickness could reflect relative vulnerability to predators and physical conditions
Keywords: dept.aa; dept.mat; peer-reviewed

Secondary Teacher Candidates’ Mathematical Modeling Task Design and Revision - Kim, Dong-Joong; Choi, Sang-Ho; Lee, Younhee; Lim, Woong (Mathematics, 2021)
The purpose of this study is to investigate secondary teacher candidates’ experience of mathematical modeling task design. In the study, 54 teacher candidates in a university-based teacher education program created modeling tasks and scoring rubrics. Next, the participants pilot-tested the tasks with students and had the opportunity to revise the original tasks and rubrics based on student responses. The data included participants’ statements, in which they described and reflected on the design and revision process of modeling tasks. The study describes six didactic revision strategies in revising modeling tasks and identifies five emerging pedagogical ideas from revising tasks and rubrics. The study also discusses the way modeling task design activities have the potential to support teacher candidates’ learning through a bottom-up modeling curriculum in teacher education.
Keywords: dept.mat; didactic revision strategy; mathematical modeling task design; peer-reviewed; secondary teacher candidates

A Comprehensive Astrometric Calibration of HST's WFPC2. I. Distortion Mapping - Casetti-Dinescu, Dana I.; Girard, Terrence M.; Kozhurina-Platais, Vera; Platais, Imants; Anderson, Jay; Horch, Elliott P. (Publications of the Astronomical Society of the Pacific, 2021)
Wide field planetary camera 2 (WFPC2) exposures are already some 20 years older than Gaia epoch observations, or future James Webb Space Telescope observations. As such, they offer an unprecedented time baseline for high-precision proper-motion studies, provided the full astrometric potential of these exposures is reached. We have started such a project with the work presented here being its first step. We explore geometric distortions beyond the well-known ones published in the early 2000 s. This task is accomplished by using the entire database of WFPC2 exposures in filters F555W, F606W and F814W and three standard astrometric catalogs: Gaia EDR3, 47 Tuc and ωCen. The latter two were constructed using Hubble Space Telescope observations made with cameras other than WFPC2. We explore a suite of centering algorithms, and various distortion maps in order to understand and quantify their performance. We find no high-frequency systematics beyond the 34th-row correction, down to a resolution of 10 pixels. Low-frequency systematics starting at a resolution of 50 pixels are present at a level of 30–50 millipix (1.4–2.3 mas) for the PC and 20–30 millipix (2–3 mas) for the WF chips. We characterize these low-frequency systematics by providing correction maps and updated cubic-distortion coefficients for each filter.
Keywords: dept.mat; dept.phy; peer-reviewed

Constructing (3, B)-sudoku pair latin squares - Carrigan, Braxton; Diaz, David; Hammer, James; Lorch, John (Australasian Journal of Combinatorics, 2022)
An (a, b)-Sudoku pair Latin square is a Latin square that is simult-aneously an (a, b)-Sudoku Latin square and a (b, a)-Sudoku Latin square. While (a, b)-Sudoku Latin squares are known to exist for any positive integers a and b, the pairs a, b for which an (a, b)-Sudoku pair Latin square exists are largely unknown. In this article we establish the existence of (a, b)-Sudoku pair Latin squares for an infinite collection of pairs (a, b). Our results show that a (3, b)-Sudoku pair Latin square can be constructed for any positive integer b. ©The author(s).
Keywords: dept.mat; peer-reviewed; ⛔ No DOI found

Portraying mathematics pre-service teachers’ experience of creating video lessons with portable interactive whiteboards through the TPACK - Bonafini, Fernanda Cesar; Lee, Younhee (The New Educator, 2021)
This study investigates how pre-service teachers use their knowledge of technology, mathematics, and pedagogy to create video lessons using portable interactive whiteboards. The TPACK framework was used to identify the different types of knowledge pre-service teachers rely on as they create their videos. Results indicate pre-service teachers’ effective use of conveyance technology, pedagogical techniques, and mathematical representations using technology. Their videos portray their process of coordinating their TPACK. Recommendations are made for teacher educators to integrate technology in activities that aim to develop pre-service teachers’ comfort and confidence with technological tools for teaching and learning. © 2021 ATE and CCNY.
Keywords: dept.mat; peer-reviewed

CT-free attenuation correction for dedicated cardiac SPECT using a 3D dual squeeze-and-excitation residual dense network. - Chen, Xiongchao; Zhou, Bo; Shi, Luyao; Liu, Hui; Pang, Yulei; Wang, Rui; Miller, Edward J.; Sinusas, Albert J.; Liu, Chi (Journal of nuclear cardiology : official publication of the American Society of Nuclear Cardiology, 2021)
Background: Attenuation correction (AC) using CT transmission scanning enables the accurate quantitative analysis of dedicated cardiac SPECT. However, AC is challenging for SPECT-only scanners. We developed a deep learning-based approach to generate synthetic AC images from SPECT images without AC. Methods: CT-free AC was implemented using our customized Dual Squeeze-and-Excitation Residual Dense Network (DuRDN). 172 anonymized clinical hybrid SPECT/CT stress/rest myocardial perfusion studies were used in training, validation, and testing. Additional body mass index (BMI), gender, and scatter-window information were encoded as channel-wise input to further improve the network performance. Results: Quantitative and qualitative analysis based on image voxels and 17-segment polar map showed the potential of our approach to generate consistent SPECT AC images. Our customized DuRDN showed superior performance to conventional network design such as U-Net. The averaged voxel-wise normalized mean square error (NMSE) between the predicted AC images by DuRDN and the ground-truth AC images was 2.01 ± 1.01%, as compared to 2.23 ± 1.20% by U-Net. Conclusions: Our customized DuRDN facilitates dedicated cardiac SPECT AC without CT scanning. DuRDN can efficiently incorporate additional patient information and may achieve better performance compared to conventional U-Net. © 2021, American Society of Nuclear Cardiology.
Keywords: adult; article; body mass; controlled study; deep learning; dept.mat; excitation; female; gender; human; male; myocardial perfusion imaging; patient information; peer-reviewed; physiological stress; qualitative analysis; quantitative analysis; single photon emission computed tomography; x-ray computed tomography

Inter-pass motion correction for whole-body dynamic parametric PET imaging - Guo, Xueqi; Wu, Jing; Chen, Ming-Kai; Onofrey, John A.; Pang, Yulei; Pigg, David; Casey, Michael E.; Dvornek, Nicha C.; Liu, Chi (The Journal of Nuclear Medicine, 2021)
Keywords: dept.mat; peer-reviewed; ⛔ No DOI found

Skolem number of cycles and grid graphs - Carrigan, Braxton; Asplund, John (Theory and Applications of Graphs, 2021)
A Skolem sequence can be thought of as a labelled path where two vertices with the samelabelarethatdistanceapart.Thisconcepthasnaturallybeengeneralizedto labellingsofothergraphs,butalwaysusingatmosttwoofanyintegerlabel.Giventhat more than two vertices can be mutually distance d apart, wedefine a new generalization of aSkolemsequenceongraphsthatwecallaproperSkolemlabelling.Thisbrings rise tothequestion;use to proper Skolemlabel a graph?"This will be known as the Skolem number of the graph. In this paper we give the Skolem number for cycles and grid graphs,while also providing other related results along the way. Published by Digital Commons@Georgia Southern, 2021. © 2021 Georgia Southern University. All rights reserved.
Keywords: dept.mat; peer-reviewed

List colorings count rokudoku-pair squares - Carrigan, Braxton; Hammer, James; Lorch, John; Lorch, Robert; Owens, Caitlin (Bulletin of the Institute of Combinatorics and its Applications, 2021)
A rokudoku-pair square is an order-6 sudoku Latin square for both 2 x 3 and 3 x 2 tiling regions simultaneously. We count the distinct rokudoku-pair squares as well as orbits under the action of a suitable group. Our arguments employ group actions and list colorings of graphs. As an application we determine which rokudoku-pair squares are based on groups. © 2021. All Rights Reserved.
Keywords: dept.mat; peer-reviewed; ⛔ No DOI found

Comparing the performance on the MI and SAT/PSAT for the purpose of monitoring student achievement - McDonald, Michael; Pang, Yulei (International Journal of Information and Education Technology, 2021)
This paper will discuss the correlation between the SAT and the Math Inventory Test. Many school districts adopted the Math Inventory as a tool to measure student growth from grades kindergarten through high school. The Math Inventory is a computer-administered test that gives students math problems spanning from counting to high school level math. When completed, the students are given a quantile measure, much like a Lexile score for reading skill. The purpose of this study is to figure out if success on the Math Inventory is a good indicator for performing well on the SAT. For most high schools around the United States, objectives and lessons are aligned with those of the SAT. The goal of high school teachers is for students to excel on the SAT so that they can go to college, which means the tests used in middle school should be aligned with that goal. If the Math Inventory is not, then it might not be a very good use of school time and resources. Data was analyzed from the 2017-2018 school year from ten different high schools in an urban school district to determine the correlation between Math Inventory score, and the math score/sub scores of SAT/PSAT. The value of the Pearson’s correlation coefficient is used to suggest a fairly moderate positive relationship between these two variables. © 2021, International Journal of Information and Education Technology. All rights reserved.
Keywords: dept.mat; peer-reviewed

Investigating prospective teachers’ TPACK and their use of mathematical action technologies as they create screencast video lessons on iPads - Bonafini, Fernanda Cesar; Lee, Younhee (TechTrends : for leaders in education & training, 2021)
The increasing number of technological devices available in schools, aligned with curriculum guidance, set an expectation for mathematics teachers to incorporate these devices into their teaching. This qualitative study investigated prospective teachers’ use of TPACK and mathematical action technologies as they created screencast video lessons using iPads. Results showed prospective teachers’ effective use of pedagogical techniques and the screencast app as an amplifier tool, according to the amplifier-reorganizer metaphor. Half of the participants used mathematics technology to confirm and expand the results they had found without technology. The other half had mathematics technology integrated into their solution exercising the balance among TPACK components. For some, their use of the mathematical tool had the potential of expanding the mathematical repertoire of virtual students. We conclude by making recommendations for teacher educators to implement cycles of learning for pre-service teachers to design, enact, and reflect upon the creation of screencast video lessons. © 2021, Association for Educational Communications & Technology.
Keywords: dept.mat; peer-reviewed

Comparing Machine Learning Approaches for Predicting Spatially Explicit Life Cycle Global Warming and Eutrophication Impacts from Corn Production - Romeiko, Xiaobo Xue; Guo, Zhijian; Pang, Yulei; Lee, Eun Kyung; Zhang, Xuesong (Sustainability, 2020)
Agriculture ranks as one of the top contributors to global warming and nutrient pollution. Quantifying life cycle environmental impacts from agricultural production serves as a scientific foundation for forming effective remediation strategies. However, methods capable of accurately and efficiently calculating spatially explicit life cycle global warming (GW) and eutrophication (EU) impacts at the county scale over a geographic region are lacking. The objective of this study was to determine the most efficient and accurate model for estimating spatially explicit life cycle GW and EU impacts at the county scale, with corn production in the U.S.’s Midwest region as a case study. This study compared the predictive accuracies and efficiencies of five distinct supervised machine learning (ML) algorithms, testing various sample sizes and feature selections. The results indicated that the gradient boosting regression tree model built with approximately 4000 records of monthly weather features yielded the highest predictive accuracy with cross-validation (CV) values of 0.8 for the life cycle GW impacts. The gradient boosting regression tree model built with nearly 6000 records of monthly weather features showed the highest predictive accuracy with CV values of 0.87 for the life cycle EU impacts based on all modeling scenarios. Moreover, predictive accuracy was improved at the cost of simulation time. The gradient boosting regression tree model required the longest training time. ML algorithms demonstrated to be one million times faster than the traditional process-based model with high predictive accuracy. This indicates that ML can serve as an alternative surrogate of process-based models to estimate life-cycle environmental impacts, capturing large geographic areas and timeframes.
Keywords: Agriculture; Eutrophication; Global warming; Life cycle assessment; Machine learning; Midwest; Spatial assessment; United States; Zea mays; agricultural production; agriculture; crop production; dept.mat; eutrophication; global warming; life cycle analysis; life cycle assessment; machine learning; peer-reviewed; prediction; spatial analysis; spatial assessment

On maximal t-linearly independent sets - Gulati, Bodh Raj; Johnson, Bruce McK.; Koehn, Uwe (Journal of Combinatorial Theory, Series A, 1973)
Consider a finite t + r − 1 dimensional projective space PG(t + r − 1, s) over a Galois field GF(s) of order s = ϱh, where ϱ and h are positive integers and ϱ is the prime characteristic of the field. A collection of k points in PG (t + r − 1, s) constitutes an L(t, k)-set if no t of them are linearly dependent. An L(t, k)-set is maximal if there exists no other L(t, k′)-set with k′ > k. The largest k for which an L(t, k)-set exists is denoted by Mt(t + r, s). K. A. Bush [3] established that Mt(t, s) = t + 1 for t ⩾ s. The purpose of this paper is to generalize this result and study Mt(t + r, s) for t, r, and s in certain relationships.
Keywords: dept.mat; information; theoretical study

An apparently algebraic property of the integers - Berlinghoff, W P (Mathematics Magazine, 1973)
Keywords: dept.mat

Maximal sets of points in finite projective space, no t-linearly dependent - Gulati, Bodh Raj; Kounias, E G (Journal of Combinatorial Theory, Series A, 1973)
Consider a finite (t + r - 1)-dimensional projective space PG(t + r - 1, s) based on the Galois field GF(s), where s is prime or power of a prime. A set of k distinct points in PG(t + r - 1, s), no t-linearly dependent, is called a (k, t)-set and such a set is said to be maximal if it is not contained in any other (k*, t)-set with k* > k. The number of points in a maximal (k, t)-set with the largest k is denoted by mt(t + r, s). Our purpose in the paper is to investigate the conditions under which two or more points can be adjoined to the basic set of Ei, i = 1, 2, ..., t + r, where Ei is a point with one in i-th position and zeros elsewhere. The problem has several applications in the theory of fractionally replicated designs and information theory. © 1973.
Keywords: dept.mat; melampolide

3 Level Symmetrical Factorial Designs and Ternary Group Codes - Gulati, BR; Kounias, EG (Sankhya-the Indian Journal of Statistics Series A, 1973)
Keywords: dept.mat; ⛔ No DOI found

More about maximal (n, r)-sets - Gulati, Bodh Raj (Information & Computation, 1972)
Consider a finite r-dimensional projective space PG(r, s) based on the Galois field GF(s) where s is prime or power of a prime. A set of n distinct points in PG(r, s), no t linearly dependent, is said to be maximal or complete if it is not contained in any other set with n* points with n* > n. The number of points in a maximal set is denoted by mt(r + 1, s). The purpose of this paper is to improve the existing bounds for m5(r + 1, s) for r ≥ 5 and s ≥ 5 (odd). The investigation of maximal sets in certain relationships of t, r and s yields parity check matrices of (r + 1) rows and n columns with elements from GF(s) satisfying the condition that no t columns are linearly dependent. This problem has applications to coding theory and also in the theory of fractionally replicated designs. © 1972 Academic Press, Inc.
Keywords: dept.mat

On maximal (k,t)-sets - Gulati, Bodh Raj (Annals of the Institute of Statistical Mathematics, 1971)
This investigation was originally motivated by the problem of determining the maximum number of points in finite n-dimensional projective space PG(n, s) based on the Galois field GF(s) of order s=ph (where p and h are positive integers and p is the prime characteristic of the field), such that no t of these chosen points are linearly dependent. A set of k distinct points in PG(n, s), no t linearly dependent, is called a (k, t)-set for k1 >k. The maximum value of k is denoted by mt (n+1, s). The purpose of this paper is to find new upper bounds for some values of n, s and t. These bounds are of importance in the experimental design and information theory problems. © 1971 Institute of Statistical Mathematics.
Keywords: dept.mat

Orthogonal arrays of strength five - Gulati, Bodh Raj (Trabajos De Estadistica Y De Investigacion Operativa, 1971)
Keywords: dept.mat

Note on the cochran Q test - Tate, Merle W; Brown, Sara M (Journal of the American Statistical Association, 1970)
Cochran’s Q test for differences between related-sample percentages or proportions has generally been incorrectly presented in secondary sources. The most common mistake results from failure to recognize that rows containing only 1’s or only 0’s, i.e., only successes or only failures, do not affect the value of Q. The F test, however, is affected by such rows. The probabilities from the χ2 and F approximations are compared with the exact probabilities in three sets of data. A rule of thumb, based on extensive study of the distribution of 0 in small samples, is given as an aid in judging when the χ2 approximation is satisfactory for practical purposes. © Taylor & Francis Group, LLC.
Keywords: dept.mat

Statistics for special q, t-kostka polynomials - Fishel, Susanna (Proceedings of the American Mathematical Society, 1995)
Kirillov and Reshetikhin introduced rigged configurations as a new way to calculate the entries of the Kostka matrix. Macdonald defined the two-parameter Kostka matrix whose entries generalize. We use rigged configurations and a formula of Stembridge to provide a combinatorial interpretation of in the case where is a partition with no more than two columns. In particular, we show that in this case, has nonnegative coefficients. © 1995 American Mathematical Society.
Keywords: dept.mat

Canonical bases for the Brauer centralizer algebra - Fishel, Susanna; Grojnowski, I (Mathematical Research Letters, 1995)
Keywords: dept.mat

Applications über alles: mathematics for the liberal arts - Aboufadel, Edward F (Primus, 1994)
This paper presents a fresh approach to a general education mathematics course. The basic idea is to turn the customary mathematics class on its head by focusing on applications first, through a reading of articles from magazines and newspapers, and then turning to the technical mathematical details. A description of the topics that were covered in my course, along with references to various publications, is given. A course such as this one is important because it conveys how mathematics is serving the goals of society. © 1994 Taylor and Francis Group, LLC.
Keywords: Applied mathematics; Coding theory; Discrete mathematics; General education courses; Geometry; Mathematics in government; Mathematics in industry; Probability; Statistics; dept.mat

Doing Statistics with OlympiaStat: Statistical Analysis Package Version 1.0: Explorations in Data Analysis Using a Spreadsheet Based Statistical Tool - Pelosi, Marilyn K.; Sandifer, Theresa M. (John Wiley & Sons, Inc., 1994)
Keywords: dept.mat

Color spreading algorithm for the retail industry - Pelosi, Marilyn K; Sandifer, Theresa M; Sandifer, C Edward (Annual Conference on Computers, 1992)
One of the problems which many companies face is the distribution of inventory from one or more centrally located distribution centers. The retail, industry, and in particular the women's clothing industry, faces the additional problem that not only does the merchandise have to be distributed but it must be distributed in such a way that every store gets a reasonable spread of colors and sizes. This research attempts to optimize the multi-criteria allocation objective by developing a computer algorithm. In order to be implemented any algorithm developed must be computationally efficient due to the size of the industry and other system related programming constraints. The algorithm which was developed not only provided a solution which was a marked improvement regarding the color spread of the merchandise but was also efficient enough to be immediately implemented on a national basis. © 1992.
Keywords: Algorithms; Garment manufacture; Multi-criteria allocation objective; Retail industry color spreading algorithm; Retail stores; Women's clothing industry; dept.mat

Adaptive urn designs for estimating several percentiles of a dose–response curve - Mugno, Raymond; Zhus, Wei; Rosenberger, William F (Statistics in Medicine, 2004)
Dose-response experiments are crucial in biomedical studies. There are usually multiple objectives in such experiments and among the goals is the estimation of several percentiles on the dose-response curve. Here we present the first non-parametric adaptive design approach to estimate several percentiles simultaneously via generalized Pó lya urns. Theoretical properties of these designs are investigated and their performance is gaged by the locally compound optimal designs. As an example, we re-investigated a psychophysical experiment where one of the goals was to estimate the three quartiles. We show that these multiple-objective adaptive designs are more efficient than the original single-objective adaptive design targeting the median only. We also show that urn designs which target the optimal designs are slightly more efficient than those which target the desired percentiles directly. Guidelines are given as to when to use which type of design. Overall we are pleased with the efficiency results and hope compound adaptive designs proposed in this work or their variants may prove to be a viable non-parametric alternative in multiple-objective dose-response studies. Copyright © 2004 John Wiley & Sons, Ltd.
Keywords: *Dose-Response Relationship, Drug; Adaptive design; Dose-Response Relationship, Drug; Dose-response experiment; Generalized Pólya urn; Guidelines; Guidelines as Topic; Likelihood Functions; Monte Carlo method; Non-parametric design; Psychophysics; United States; article; biostatistics; c-optimal design; cerebrovascular accident; clinical trial; dept.mat; dose response; experimental design; human; kinesthesia; maximum likelihood method; neurologic disease; nonparametric test; process optimization; psychophysics; sensory stimulation; statistical analysis; theoretical study; validation process

Dominating Sets for Outerplanar Graphs - Pinciu, Val (International Conference on Applied Mathematics, 2004)
Abstract:- We provide lower and upper bounds for the domination numbers and the connected domination numbers for outerplanar graphs. We also provide a recursive algorithm that finds a connected domination set for an outerplanar graph. Finally, we show that for outerplanar graphs where all bounded faces are 3-cycles, the problem of determining the connected domination number is equivalent to an art gallery problem, which is known to be NP-hard. Key-Words:- dominating sets, star forests, outerplanar graphs, art gallery 1
Keywords: dept.mat; ⛔ No DOI found

A coloring algorithm for finding connected guards in art galleries - Pinciu, Val (Springer Verlag, 2003)
In this paper we consider a variation of the Art Gallery Problem. A set of points script G sign in a polygon Pn is a connected guard set for Pn provided that is a guard set and the visibility graph of the set of guards script G sign in Pn is connected. We use a coloring argument to prove that the minimum number of connected guards which are necessary to watch any polygon with n sides is ⌊(n - 2)/2⌋. This result was originally established by induction by Hernández-Peńalver [3]. From this result it easily follows that if the art gallery is orthogonal (each interior angle is 90° or 270°), then the minimum number of connected guards is n/2 - 2. © Springer-Verlag Berlin Heidelberg 2003.
Keywords: Algorithms; Art gallery; Artificial intelligence; Coloring algorithms; Computer science; Computers; Visibility graphs; dept.mat

Connected guards in orthogonal art galleries - Pinciu, Val (Springer Verlag, 2003)
In this paper we consider a variation of the Art Gallery Problem for orthogonal polygons. A set of points in a polygon Pn is a connected guard set for Pn provided that is a guard set and the visibility graph of the set of guards in Pn is connected. The polygon P n is orthogonal provided each interior angle is 90° or 270°. First we use a coloring argument to prove that the minimum number of connected guards which are necessary to watch any orthogonal polygon with n sides is n/2-2. This result was originally established by induction by Hernández-Peñalver. Then we prove a new result for art galleries with holes: we show that n/2-h connected guards are always sufficient to watch an orthogonal art gallery with n walls and h holes. This result is sharp when n = 4h + 4. We also construct galleries that require at least n/2-h-1 connected guards, for all n and h. © Springer-Verlag 2003.
Keywords: Art gallery; Art gallery problem; Geometry; New results; Visibility graphs; Watches; dept.mat

Computer-generated fractals using iterated function systems - Stiegler, Cynthia Joy Gayda (2003)
Keywords: dept.mat

College and university academic and professional appointments - Nelson, C; Conklin, CL; Galloway, R; Grant, KE; Halpern, J; Humphreys, RM; Kalman, L; Matthews, TE; Moore, RK; Smith, LD; Wood, DD (Academe-Bulletin of the Aaup, 2002)
Keywords: dept.mat

Numerical testing of the stability of viscous shock waves - Brin, Leon Q (Mathematics of Computation, 2001)
A new theoretical Evans function condition is used as the basis of a numerical test of viscous shock wave stability. Accuracy of the method is demonstrated through comparison against exact solutions, a convergence study, and evaluation of approximate error equations. Robustness is demonstrated by applying the method to waves for which no current analytic results apply (highly nonlinear waves from the cubic model and strong shocks from gas dynamics). An interesting aspect of the analysis is the need to incorporate features from the analytic Evans function theory for purposes of numerical stability. For example, we find it necessary, for numerical accuracy, to solve ODEs on the space of wedge products.
Keywords: dept.mat

Multiply guarded guards in orthogonal art galleries - Michael, T S; Pinciu, Val (Springer Verlag, 2001)
We prove a new theorem for orthogonal art galleries in which the guards must guard one another in addition to guarding the polygonal gallery. A set of points G in a polygon Pn is a k-guarded guard set for Pn provided that (i) for every point x in Pn there exists a point w in G such that x is visible from w; and (ii) every point in G is visible from at least k other points in G: The polygon Pn is orthogonal provided each interior angle is 90° or 270°. We prove that for k ≥ 1 and n ≥ 6 every orthogonal polygon with n sides has a k-guarded guard set of cardinality (Formula Presented.) this bound is best possible. This result extends our recent theorem that treats the case k = 1. © Springer-Verlag Berlin Heidelberg 2001.
Keywords: Art gallery; Cardinalities; Computation theory; Geometry; dept.mat

Realistic reconfiguration of crystalline (and telecube) robots - Aloupis, Greg; Collette, Sebastien; Damian, Mirela; Demaine, Erik D; Elkhechen, Dania; Flatland, Robin; Langerman, Stefan; Orourke, Joseph; Pinciu, Val; Ramaswami, Suneeta; Sacristan, Vera; Wuhrer, Stefanie (2009)
In this paper we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2×2×2 modules. We respect certain physical constraints: each atom reaches at most unit velocity and (via expansion) can displace at most one other atom. We require that one of the atoms can store a map of the target configuration. Our algorithms involve a total of O(n 2) such atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n 2) parallel steps [8,10,4] or do not respect the constraints mentioned above [1]. In fact, in the setting considered, our algorithms are optimal, in the sense that certain reconfigurations require Ω(n) parallel steps. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configurations. © 2009 Springer-Verlag.
Keywords: Algorithms; Atoms; Novel algorithm; Physical constraints; Reconfiguration algorithm; Robotics; Robots; Target configurations; dept.mat

Exploring gender differences in the relationship between HIV/STD testing and condom use among undergraduate college students - Bontempi, Jean M Breny; Mugno, Raymond; Bulmer, Sandra Minor; Danvers, Karina; Vancour, Michele (American journal of health education, 2009)
Keywords: dept.mat; dept.pch

The signature of the chern coefficients of local rings - Ghezzi, Laura; Hong, Jooyoun; Vasconcelos, Wolmer V (Mathematical Research Letters, 2009)
This paper considers the following conjecture: If R is an unmixed, equidimensionallocal ring that is a homomorphic image of a Cohen-Macaulay local ring, then for any ideal J generated by a system of parameters, the Chern coefficient e1(J) < 0 is equivalent to R being non Cohen-Macaulay. The conjecture is established if R is a homomorphic image of a Gorenstein ring, and for all universally catenary integral domains containing fields. Criteria for the detection of Cohen-Macaulayness in equi-generated graded modules are derived. © International Press 2009.
Keywords: dept.mat; ⚠️ Invalid DOI

Leveraging summative assessment for formative purposes. - Vaden-Goad, Robert E (College Teaching, 2009)
The problem of motivation has received a great deal of attention, and many successful approaches have been developed. However, in areas such as introductory college mathematics, students often question their own potential for success. At the first sign of trouble, their fears are confirmed and many of them drop out, formally or informally. If a method could be found to improve persistence, motivational techniques would have an opportunity to succeed. In this article, the author describes a simple method to improve persistence using assessments that are normally already in place. Data are presented indicating that the method improves persistence and achievement. © 2009, Copyright Taylor & Francis Group, LLC.
Keywords: classroom assessment; dept.mat; mathematics

On the homology of two-dimensional elimination - Hong, Jooyoun; Simis, Aron; Vasconcelos, Wolmer V (Journal of Symbolic Computation, 2008)
We study birational maps with empty base locus defined by almost complete intersection ideals. Birationality is shown to be expressed by the equality of two Chern numbers. We provide a relatively effective method for their calculation in terms of certain Hilbert coefficients. In dimension 2 the structure of the irreducible ideals-always complete intersections by a classical theorem of Serre-leads by a natural approach to the calculation of Sylvester determinants. We introduce a computer-assisted method (with a minimal intervention by the computer) which succeeds, in degree ≤5, in producing the full sets of equations of the ideals. In the process, it answers affirmatively some questions raised by Cox [Cox, D.A., 2006. Four conjectures: Two for the moving curve ideal and two for the Bezoutian. In: Proceedings of Commutative Algebra and its Interactions with Algebraic Geometry, CIRM, Luminy, France, May 2006 (available in CD media)]. © 2007 Elsevier Ltd. All rights reserved.
Keywords: Almost complete intersection; Birational map; Elimination; Rees algebra; Special fiber; Sylvester determinant; dept.mat

On the fewest nets problem for convex polyhedra - Pinciu, Val (2007)
Given a convex polyhedron with n vertices and F faces, what is the fewest number of pieces, each of which unfolds to a simple polygon, into which it may be cut by slices along edges? Shephard's conjecture says that this number is always 1, but it's still open. The fewest nets problem asks to provide upper bounds for the number of pieces in terms of n and/or F. We improve the previous best known bound of F/2 by proving that every convex polyhedron can be unfolded into no more than 3F/8 non-overlapping nets. If the polyhedron is triangulated, the upper bound we obtain is 4F/11.
Keywords: Computational geometry; Convex polyhedrons; Simple polygon; Upper Bound; dept.mat; ⛔ No DOI found

Guarding the guards in art galleries - Michael, T S; Pinciu, Val (Math Horizons, 2006)
Keywords: dept.mat

Learning from others: A low‐cost–high‐impact risk/opportunity identification technique - Williams, Brendan E.; Williams, Anne S.; Williams, Katherine M. (Journal of Healthcare Risk Management, 2020)
Keywords: dept.mat; peer-reviewed

‘Is it wise to open up America again now?’ Learning from government responses to COVID-19 and economy reopen points in three Asia-Pacific countries - Yu, Jia; Pang, Yulei (British Journal of Healthcare Management, 2020)
With the continuously increasing number of new confirmed COVID-19 cases, many health experts worried about the possibility of a ‘second wave’ outbreak, which might cause more deaths and hit economies even worse. This article looks at the experiences of fighting COVID-19 from three Asia-Pacific countries and discusses whether it is a wise decision to open up America again at this time.
Keywords: dept.eco; dept.mat; peer-reviewed

William Ludlam: portrait of an eighteenth-century mathematician - Decesare, Richard (Bshm Bulletin: Journal of The British Society for The History of Mathematics, 2011)
In 1785, William Ludlam wrote a book entitled The rudiments of mathematics. After I purchased the 1790 edition of this text some years ago at an antiquarian bookstore in Connecticut, I became interested in learning more about him. Ludlam's name had appeared as a footnote in several histories of mathematics, but little else had been written about him. I began some research, simply out of curiosity. What emerged was a story of an interesting mathematician, scientist, inventor, and clergyman - and a man who often found himself in the middle of controversy and subject to personal attacks, whether deserved or not. This article is a biography of Ludlam, in which I have used his own words, as well as those of his adversaries, wherever possible. © 2011 British Society for the History of Mathematics.
Keywords: dept.mat

Parental knowledge and substance use among african american adolescents: influence of gender and grade level - Tebes, Jacob Kraemer; Cook, Emily C.; Vanderploeg, Jeffrey J.; Feinn, Richard; Chinman, Matthew J.; Shepard, Jane K.; Brabham, Tamika; Connell, Christian M. (Journal of Child and Family Studies, 2011)
Parental knowledge is defined as parental awareness and information about a child's activities, whereabouts, and associations that is obtained through parental monitoring, parental solicitation, or self-disclosure. Increased parental knowledge is generally associated with lower adolescent substance use; however, the influence of various contextual factors, such as adolescent gender and grade level is not well understood, particularly for different racial or ethnic groups. In the present study, we used Hierarchical Generalized Linear Modeling analyses to examine the longitudinal relationship of parental knowledge to adolescent substance use in the context of adolescent gender and grade level among 207 urban African American adolescents in grades 6-11. Results indicated that increased parental knowledge is associated with a concurrent lower likelihood of substance use across all types of substances examined (alcohol, tobacco, marijuana, other drug use, and any drug use), but it did not predict changes in substance use 1 year later for the entire sample. However, analyses by gender and grade level showed that for boys and middle school youth, parental knowledge was a protective factor for increases in substance use across 1 year. Findings are discussed in terms of their implications for prevention and health promotion interventions for adolescent substance use among African American youth.
Keywords: African American adolescents; Developmental differences; Gender; Parental knowledge; Substance use; dept.mat

Robert patterson: american ‘revolutionary’ mathematician - Decesare, Richard (Bshm Bulletin: Journal of The British Society for The History of Mathematics, 2016)
You will not see Robert Patterson's name mentioned in many mathematics books. While his mathematical works survive, his name is more likely to appear in American history books dealing with the Colonial period, given his associations with the most influential men of that time. In this article, we will examine his mathematical work, as well as his contributions to a newly-formed nation. Most of what we know about Robert Patterson's ancestors and life is due to his grandson, William Ewing DuBois, who wrote a family history in 1847. For other information, I have drawn upon diaries and a great many letters. All spelling and syntax are copied exactly as they appear. © 2015 British Society for the History of Mathematics.
Keywords: dept.mat

Coverage-based lossy node localization for wireless sensor networks - Bao, Forrest Sheng; Pang, Yulei; Zhou, Wujun; Jiang, Wu; Yang, Yinfei; Liu, Yang; Qian, Chen (IEEE Sensors Journal, 2016)
To ensure the function of wireless sensor networks (WSNs), nodes that fail to forward packets must be localized efficiently and then fixed or replaced promptly. The state-of-the-art work frames lossy node localization in WSNs as an optimal sequential testing problem guided by end-to-end data. It combines both the active and passive measurements to minimize the testing cost and the number of iterations. However, this hybrid approach has many limitations. Inspired by the success of coverage-based software debugging, and the similarity between software debugging and lossy node localization, we propose a coverage-based lossy node detection for WSNs. Supported by established statistic theories, this approach greatly boosts the performance. Experiments on randomly generated networks and deployed networks show that the proposed algorithm can significantly reduce testing cost and number of iterations, which are the two optimization goals of previous work. We expect to use this approach for other diagnostic problems in WSNs. © 2001-2012 IEEE.
Keywords: Chi-square test; Chi-square tests; Diagnostic problem; Lossy node localization; Lossy nodes; Network diagnosis; Number of iterations; Optimal sequential; Passive measurements; Program debugging; Sensor nodes; Statistical tests; Wireless sensor network (WSNs); Wireless sensor networks; dept.mat; network diagnosis; wireless sensor network

On nontriangulable polyhedra - Bezdek, Andras; Carrigan, Braxton (Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2016)
Triangulations of 3-dimensional polyhedron are partitions of the polyhedron with tetrahedra in a face-to-face fashion without introducing new vertices. Schönhardt (Math. Ann. 89:309–312, 1927), Bagemihl (Amer. Math. Mon. 55:411–413, 1948), Kuperberg (Personal communication 2011) and others constructed special polyhedra in such a way that clever one line geometric reasons imply nontriangulability. Rambau (Comb. Comput. Geom. 52:501–516, 2005) proved that twisted prisms over n-gons are nontriangulable. Our approach for proving polyhedra are nontriangulable is to show that partitions with tetrahedra, which we call tilings, do not exist even if the face-to-face-restriction is relaxed. First we construct a polyhedron which is tileable but is not triangulable. Then we revisit Rambau type twisted prisms. In fact we consider a slightly different class of polyhedra, and prove that these new twisted prisms are nontileable, thus are nontriangulable. We also show that one can twist the regular dodecahedron so that it becomes nontileable, which is abstracted to a new family of nontileable polyhedra, called nonconvex twisted pentaprisms. © 2015, The Managing Editors.
Keywords: Polyhedron; Tiling; Triangulation; dept.mat

Hilbert polynomials of j-transforms - Goto, Shiro; Hong, Jooyoun; Vasconcelos, Wolmer V (Mathematical Proceedings of the Cambridge Philosophical Society, 2016)
We study transformations of finite modules over Noetherian local rings that attach to a module M a graded module H(x)(M) defined via partial systems of parameters x of M. Despite the generality of the process, which are called j-transforms, in numerous cases they have interesting cohomological properties. We focus on deriving the Hilbert functions of j-transforms and studying the significance of the vanishing of some of its coefficients. Copyright © 2016 Cambridge Philosophical Society.
Keywords: dept.mat

Characterization and comparison of injuries caused by accidental and non-accidental blunt force trauma in dogs and cats - Intarapanich, Nida P; Mccobb, Emily; Reisman, Robert W; Rozanski, Elizabeth A; Intarapanich, Pichai P (Journal of Forensic Sciences, 2016)
Motor vehicle accidents (MVA) are often difficult to distinguish from non-accidental injury (NAI). This retrospective case–control study compared animals with known MVA trauma against those with known NAI. Medical records of 426 dogs and cats treated after MVA and 50 after NAI were evaluated. Injuries significantly associated with MVA were pelvic fractures, pneumothorax, pulmonary contusion, abrasions, and degloving wounds. Injuries associated with NAI were fractures of the skull, teeth, vertebrae, and ribs, scleral hemorrhage, damage to claws, and evidence of older fractures. Odds ratios are reported for these injuries. MVA rib fractures were found to occur in clusters on one side of the body, with cranial ribs more likely to fracture, while NAI rib fractures were found to occur bilaterally with no cranial–caudal pattern. Establishing evidence-based patterns of injury may help clinicians differentiate causes of trauma and may aid in the documentation and prosecution of animal abuse. © 2016 American Academy of Forensic Sciences
Keywords: animal; blunt force trauma; dept.mat; dog; forensic science; injury; motor vehicle accident; non-accidental injury; veterinary

How to guard orthogonal polygons: diagonal graphs and vertex covers - Michael, T S; Pinciu, Val (Discrete and Computational Geometry, 2016)
We extend and unify most known results about guarding orthogonal polygons by introducing the same-sign diagonal graphs of a convex quadrangulation and applying results about vertex covers for graphs. Our approach also yields new theorems and often guarantees two disjoint vertex guard sets of relatively small cardinality. For instance, an orthogonal polygon on n vertices has two disjoint vertex guard sets of cardinality at most (Formula presented.). We give new proofs of Aggarwal’s one-hole theorem and the orthogonal fortress theorem. We prove that an orthogonal polygon with n vertices and any number of holes can be protected by at most (Formula presented.) vertex guards, improving the best known bound of (Formula presented.). Also, an orthogonal polygon with n vertices and h holes can be protected by (Formula presented.) guarded guards, which is best possible when (Formula presented.). Moreover, for orthogonal fortresses with n vertices, (Formula presented.) guarded guards are always sufficient and sometimes necessary. © 2016, Springer Science+Business Media New York (outside the USA).
Keywords: Art gallery theorem; Orthogonal polygon; Vertex cover; Visibility; dept.mat

The orthogonal art gallery theorem with constrained guards - Michael, T S; Pinciu, Val (Electronic Notes in Discrete Mathematics, 2016)
Let P be an orthogonal polygon with n vertices, and let V⁎ and E⁎ be specified sets of vertices and edges of P. We prove that P has a guard set of cardinality at most ⌊(n+3|V⁎|+2|E⁎|)/4⌋ that includes each vertex in V⁎ and at least one point of each edge in E⁎. Our bound is sharp and reduces to the orthogonal art gallery theorem of Kahn, Klawe and Kleitman when V⁎ and E⁎ are empty. © 2016 Elsevier B.V.
Keywords: art gallery theorem; dept.mat; graph coloring; orthogonal polygon; polygon visibility

Early identification of vulnerable software components via ensemble learning - Pang, Yulei; Xue, Xiaozhen; Namin, Akbar Siami (Institute of Electrical and Electronics Engineers Inc., 2016)
Software components, which are vulnerable to being exploited, need to be identified and patched. Employing any prevention techniques designed for the purpose of detecting vulnerable software components in early stages can reduce the expenses associated with the software testing process significantly and thus help building a more reliable and robust software system. Although previous studies have demonstrated the effectiveness of adapting prediction techniques in vulnerability detection, the feasibility of those techniques is limited mainly because of insufficient training data sets. This paper proposes a prediction technique targeting at early identification of potentially vulnerable software components. In the proposed scheme, the potentially vulnerable components are viewed as mislabeled data that may contain true but not yet observed vulnerabilities. The proposed hybrid technique combines the supports vector machine algorithm and ensemble learning strategy to better identify potential vulnerable components. The proposed vulnerability detection scheme is evaluated using some Java Android applications. The results demonstrated that the proposed hybrid technique could identify potentially vulnerable classes with high precision and relatively acceptable accuracy and recall.
Keywords: Android applications; Artificial intelligence; Ensemble learning; Learning systems; Machine components; Mislabeled data; Prediction techniques; Prevention techniques; Software component; Software testing; Support vector machine; Support vector machines; Vulnerability; Vulnerability detection; dept.mat

The chern numbers and euler characteristics of modules - Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Ozeki, Kazuho; Phuong, Tran Thi; Vasconcelos, Wolmer V (Acta Mathematica Vietnamica, 2015)
The set of the first Hilbert coefficients of parameter ideals relative to a module—its Chern coefficients—over a local Noetherian ring codes for considerable information about its structure–noteworthy properties such as that of Cohen-Macaulayness, Buchsbaumness, and of having finitely generated local cohomology. The authors have previously studied the ring case. By developing a robust setting to treat these coefficients for unmixed rings and modules, the case of modules is analyzed in a more transparent manner. Another series of integers arise from partial Euler characteristics and are shown to carry similar properties of the module. The technology of homological degree theory is also introduced in order to derive bounds for these two sets of numbers. © 2014, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.
Keywords: Buchsbaum module; Cohen-Macaulay module; Euler characteristic; Generalized Cohen-Macaulay module; Hilbert coefficient; Hilbert function; Local cohomology; Parameter ideal; Vasconcelos module; dept.mat

Ideals generated by quadrics - Hong, Jooyoun; Simis, Aron; Vasconcelos, Wolmer V (Journal of Algebra, 2015)
Our purpose is to study the cohomological properties of the Rees algebras of a class of ideals generated by quadrics. For all such ideals I⊂. R=. K[. x, y, z] we give the precise value of depth. R[. It] and decide whether the corresponding rational maps are birational. In the case of dimension d≥. 3, when K=R, we give structure theorems for all ideals of codimension d minimally generated by (d+12)-1 quadrics. For arbitrary fields K, we prove a polarized version. © 2014 Elsevier Inc.
Keywords: Associated graded ring; Castelnuovo regularity; Hilbert coefficients; Primary; Rees algebra; Relation type; Secondary; dept.mat; peer-reviewed

Diversity and anxiety: A case study on collaborative testing - Pang, Yulei; Mugno, Raymond; Xue, Xiaozhen (Institute of Electrical and Electronics Engineers Inc., 2015)
In order to reduce students' test anxiety, collaborative testing was suggested as an evaluation strategy. However, few studies have focused on testing group construction, especially when an important factor, i.e., group diversity is taken into consideration. In this paper we conducted a case study to assess the association between group diversity and test anxiety in collaborative testing. The results observed may indicate that: 1) around 20% of students suffered from test anxiety to some extent in either an individual test or a collaborative test; 2) collaborative testing could alleviate test anxiety, whereas the effect is not statistically significant; 3) there exists a moderate positive correlation between group diversity and test anxiety in collaborative testing. The results of the study may suggest limiting group diversity in collaborative testing in order to alleviate test anxiety. © 2015 IEEE.
Keywords: Collaborative testing; Evaluation strategies; Group diversity; Positive correlations; Students; Testing; collaborative testing; dept.mat; group diversity; test anxiety

Constructing collaborative learning groups with maximum diversity requirements - Pang, Yulei; Mugno, Raymond; Xue, Xiaozhen; Wang, Huaying (Institute of Electrical and Electronics Engineers Inc., 2015)
Due to the considerable advantages of collaborative learning, group work is widely used in tertiary institutions. Previous studies demonstrated that group diversity had positive influence on group work achievement. Therefore, an interesting question that arises is how to achieve maximum group diversity effectively and automatically, especially when the features to be considered are numerous and the number of students is large. In this paper we apply a multi-start algorithm composed by a greedy constructive and strategic oscillation improvement to group students. We evaluated the technique based on a small-scale case study. The results observed indicate that the multi-start algorithm-based grouping model is feasible. It improved the overall and average students diversity within group significantly, and it also enhanced students' collaborative learning outcomes compared to random grouping model. However, we did not find any evidence on monotonic positive relationship between diversity and students' learning outcomes. © 2015 IEEE.
Keywords: Collaborative learning; Education; Engineering education; Group diversity; Grouping model; Learning outcome; Multi-start algorithm; Multistart; Random grouping; Strategic oscillations; Students; Tertiary institutions; dept.mat

Debugging in parallel or sequential: an empirical study. - Pang, Yulei; Xue, Xiaozhen; Namin, Akbar Siami (Journal of Software, 2015)
Keywords: dept.mat

Predicting vulnerable software components through n-gram analysis and statistical feature selection - Pang, Yulei; Xue, Xiaozhen; Namin, Akbar Siami (Institute of Electrical and Electronics Engineers Inc., 2015)
Vulnerabilities need to be detected and removed from software. Although previous studies demonstrated the usefulness of employing prediction techniques in deciding about vulnerabilities of software components, the accuracy and improvement of effectiveness of these prediction techniques is still a grand challenging research question. This paper proposes a hybrid technique based on combining N-gram analysis and feature selection algorithms for predicting vulnerable software components where features are defined as continuous sequences of token in source code files, i.e., Java class file. Machine learning-based feature selection algorithms are then employed to reduce the feature and search space. We evaluated the proposed technique based on some Java Android applications, and the results demonstrated that the proposed technique could predict vulnerable classes, i.e., software components, with high precision, accuracy and recall. © 2015 IEEE.
Keywords: Android applications; Application programs; Artificial intelligence; Computer software; Continuous sequences; Feature extraction; Feature selection; Feature selection algorithm; Forecasting; Java programming language; Learning systems; N-gram; N-grams; Prediction techniques; Research questions; Statistical features; Vulnerability prediction; Wilcoxon test; dept.mat

Guarding polyominoes, polycubes and polyhypercubes - Pinciu, Val (Electronic Notes in Discrete Mathematics, 2015)
We consider variations of the original art gallery problem where the domain is a polyomino, a polycube, or a polyhypercube. An m-polyomino is the connected union of m unit squares called pixels, an m-polycube is the connected union of m unit cubes called voxels, and an m-polyhypercube is the connected union of m unit hypercubes in a d dimensional Euclidean space. In this paper we generalize and unify the known results about guarding polyominoes and polycubes and obtain simpler proofs. We also obtain new art gallery theorems for guarding polyhypercubes. © 2015 Elsevier B.V.
Keywords: Art gallery theorem; Polycube; Polyhypercube; Polyomino; dept.mat

A predator–prey interaction from micro to macro perspectives - Wang, Huaying; Pang, Yulei; Zhang, Luona; Martin, Clyde F (Nonlinear Dynamics, 2015)
This paper deals with predator–prey dynamics in individual and population perspectives. First, we build a discrete Markov model on predator–prey interactions in individual perspective. By shortening the time gap, from discrete time to continuous time, and increasing the number of individuals to infinity, a continuity equation on the predator–prey interactions is derived in a large population regime. Then, with the leading items of the continuity equation, that is the mean-field equation, following the approximate model, which entails qualitative analysis, we can obtain an asymptotically stable closed orbit or simply put, the parameter conditions where equilibrium point exists. These qualitative conclusions are the performance of individual microscopic interactions on macro-level groups, or can be treated as one component of microscopic models of various random statistical average results.This paper explored the accuracy and operability of the model constructed on individual level, which differs from traditional method, constructing population model directly via differential equations and difference equations. Therefore, by operating variables and data from individual behavior, it is probable for us to construct more accurate models for population dynamic. © 2014, Springer Science+Business Media Dordrecht (outside the USA).
Keywords: Asymptotically stable; Continuity equation; Continuity equations; Continuous time systems; Difference equations; Differential equations; Discrete Markov model; Individual interaction; Macro-level groups; Markov processes; Microscopic interaction; Parameter conditions; Population statistics; Predator prey systems; Qualitative analysis; Stable limit cycle; dept.mat

Parameters governing deviations from the beer-lambert-bouger law for direct transmission - Clark, Aaron S (14th Conference on Cloud Physics/14th Conference on Atmospheric Radiation/Anthony Slingo Symposium, 2014)
Keywords: dept.mat; ⛔ No DOI found

On the link between particle size and deviations from the Beer–Lambert–Bouguer law for direct transmission - Larsen, Michael L; Clark, Aaron S (Journal of Quantitative Spectroscopy & Radiative Transfer, 2014)
Ballistic photon models of radiative transfer in discrete absorbing random media have demonstrated deviations from the Beer-Lambert-Bouguer law of exponential attenuation. A number of theoretical constructs to quantify the deviation from the Beer-Lambert-Bouguer law have appeared in the literature, several of which rely principally on a statistical measure related to the statistics of the absorber spatial positions alone. Here, we utilize a simple computational model to explore the interplay between the geometric size of the absorbing obstacles and the statistics governing the placement of the absorbers in the volume. We find that a description of the volume that depends on particle size and the spatial statistics of absorbers is not sufficient to fully characterize deviations from the Beer-Lambert-Bouguer law. Implications for future further theoretical and computational explorations of the problem are explored. © 2013 Elsevier Ltd.
Keywords: Beer; Beer-Lambert-Bouguer law; Light transmission; Non-exponential transmission laws; Optical depth; Particle size; Poisson process; Poisson ratio; Stochastic media; Transmission law; dept.mat; numerical model; optical depth; particle size; radiative transfer; stochasticity

A clustering-based grouping model for enhancing collaborative learning - Pang, Yulei; Xiao, Feiya; Wang, Huaying; Xue, Xiaozhen (Institute of Electrical and Electronics Engineers Inc., 2014)
Group work is widely used in tertiary institutions due to the considerable advantages of collaborative learning. Previous studies indicated that the group diversity had positive influence on the group work achievement. Therefore, how to achieve diversity within a group effectively and automatically is an interesting question. In this paper we propose a novel clustering-based grouping model. The proposed technique first employs balanced K-means algorithm to divide the students into several size-balanced clusters, such that the students within the same cluster are more similar (in some sense) to each other than to those in other clusters, then adopts one-sample-each-cluster strategy to construct the groups. We evaluated the proposed technique based on two small-scale case studies. The result observed may indicate that the clustering-based grouping model is feasible and effective. © 2014 IEEE.
Keywords: Artificial intelligence; Case-studies; Collaborative learning; Group diversity; Grouping model; K-means; Learning systems; Novel clustering; Tertiary institutions; balanced K-means; collaborative learning; dept.mat; group diversity; k-Means algorithm

Feature selections for effectively localizing faulty events in GUI applications - Xue, Xiaozhen; Pang, Yulei; Namin, Akbar Siami (Institute of Electrical and Electronics Engineers Inc., 2014)
Due to the complex causality of failure and the special characteristics of test cases, the faults in GUI (Graphic User Interface) applications are difficult to localize. This paper adapts feature selection algorithms to localize GUI-related faults in a given program. Features are defined as the subsequences of events executed. By employing statistical feature ranking techniques, the events can be ranked by the suspiciousness of events being responsible to exhibit faulty behavior. The features defined in a given source code implementing (event handle) the underlying event are then ranked in suspiciousness order. The evaluation of the proposed technique based on some open source Java projects verified the effectiveness of this feature selection based fault localization technique for GUI applications. © 2014 IEEE.
Keywords: Artificial intelligence; Fault localization; Feature extraction; Feature selection algorithm; GUI; GUI applications; Graphic user interface; Graphical user interfaces; Java programming language; Learning systems; Open source software; Open sources; Source codes; Statistical features; Test case; User interfaces; dept.mat; faults localization; feature selection

Rank numbers of graphs that are combinations of paths and cycles - Blake, Brianna; Field, Elizabeth; Jacob, Jobby (Involve, A Journal of Mathematics, 2013)
Keywords: dept.mat

Variation of hilbert coefficients - Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Vasconcelos, Wolmer V (Proceedings of the American Mathematical Society, 2013)
For a Noetherian local ring (R, m), the first two Hilbert coefficients, e0 and e1, of the I-adic filtration of an m-primary ideal I are known to code for properties of R, of the blowup of Spec(R) along V (I), and even of their normalizations. We give estimations for these coefficients when I is enlarged (in the case of e1 in the same integral closure class) for general Noetherian local rings. © American Mathematical Society.
Keywords: dept.mat

Guarding orthogonal polygons with h holes: A bound independent of h - Michael, T S; Pinciu, Val (Fall Workshop on Computational Geometry, 2013)
Hoffmann and Kriegel showed that an orthogonal gallery with n vertices and an unspecified number of holes can be protected by at most n/3 vertex guards. We improve this bound to (17n − 8)/52.
Keywords: dept.mat; ⛔ No DOI found

Variation of the first hilbert coefficients of parameters with a common integral closure - Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Ozeki, Kazuho; Phuong, Tran Thi; Vasconcelos, Wolmer V (Journal of Pure and Applied Algebra, 2012)
A problem posed by Vasconcelos [33] on the variation of the first Hilbert coefficients of parameter ideals with a common integral closure in a local ring is studied. Affirmative answers are given and counterexamples are explored as well. © 2011 Elsevier B.V.
Keywords: Primary; Secondary; dept.mat

The homology of parameter ideals - Goto, Shiro; Hong, Jooyoun; Vasconcelos, Wolmer V (Journal of Algebra, 2012)
For a Noetherian local ring, we analyze conjectural relationships between the first Hilbert coefficient of a parameter ideal and the first partial Euler characteristic of its Koszul complex. Given their similar role as predictors of the Cohen-Macaulay property, we consider a direct comparison between them. For parameter ideals generated by d-sequences these numbers are related in an explicit formula. We then turn to study of families of parameter ideals that have the same Hilbert function. © 2012 Elsevier Inc.
Keywords: Cohen-Macaulay ring; D-sequence; Euler characteristic; Hilbert coefficient; Hilbert function; dept.mat; peer-reviewed

The equations of almost complete intersections - Hong, Jooyoun; Simis, Aron; Vasconcelos, Wolmer V (Bulletin of the Brazilian Mathematical Society, New Series, 2012)
In this paper we inject four Hilbert functions in the determination of the defining equations of the Rees algebra of almost complete intersections of finite co-length. Because three of the corresponding modules are Artinian, some of these relationships are very effective, with the novel approach opening up tracks to the determination of the equations and also to processes of going from homologically defined sets of equations to higher degrees ones. While not specifically directed towards the extraction of elimination equations, it will show how some of these arise naturally. © 2012 Sociedade Brasileira de Matemática.
Keywords: Castelnuovo-Mumford regularity; Hilbert function; Rees algebra; associated graded ring; balanced ideal; birational mapping; dept.mat; relation type; secondary elimination degree

Efficient constant-velocity reconfiguration of crystalline robots** - Aloupis, Greg; Collette, S bastien; Damian, Mirela; Demaine, Erik D.; Flatland, Robin; Langerman, Stefan; O'Rourke, Joseph; Pinciu, Val; Ramaswami, Suneeta; Sacrist, Vera; Wuhrer, Stefanie (Robotica, 2011)
In this paper, we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2 × 2 × 2 modules. We respect certain physical constraints: each atom reaches at most constant velocity and can displace at most a constant number of other atoms. We assume that one of the atoms has access to the coordinates of atoms in the target configuration. Our algorithms involve a total of O(n2) atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n2) parallel steps or do not respect the constraints mentioned above. In fact, in the settings considered, our algorithms are optimal. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configuration space, and only requires local communication. © 2011 Cambridge University Press.
Keywords: Algorithms; Atoms; Constant velocities; Control of robotic systems; Local communications; Mobile robots; Modular robots; Motion planning; Novel algorithm; Path planning; Physical constraints; Reconfiguration algorithm; Robot programming; Robotic systems; Robotics; Target configurations; dept.mat

A group with deep pockets for all finite generating sets - Warshall, Andrew D (Israel Journal of Mathematics, 2011)
We show that the discrete Heisenberg group has unbounded dead-end depth with respect to every finite generating set. We also show that, in contrast, it has bounded retreat depth. © 2011 Hebrew University Magnes Press.
Keywords: dept.mat

Cohen–Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals - Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Ozeki, Kazuho; Phuong, Tran Thi; Vasconcelos, Wolmer V (Journal of The London Mathematical Society-second Series, 2010)
The conjecture of Wolmer Vasconcelos on the vanishing of the first Hilbert coefficient e1(Q) is solved affirmatively, where Q is a parameter ideal in a Noetherian local ring. Basic properties of the rings for which e 1(Q) vanishes are derived. The invariance of e1(Q) for parameter ideals Q and its relationship to Buchsbaum rings are studied. © 2010 London Mathematical Society.
Keywords: dept.mat

The positivity of the first coefficients of normal Hilbert polynomials - Goto, Shiro; Hong, Jooyoun; Mandal, Mousumi (Proceedings of the American Mathematical Society, 2010)
Let R be an analytically unramified local ring with maximal ideal m and d = dimR > 0. If R is unmixed, then e1I (R) = 0 for every m-primary ideal I in R, where e1I (R) denotes the first coefficient of the normal Hilbert polynomial of R with respect to I. Thus the positivity conjecture on e1I(R) posed by Wolmer V. Vasconcelos is settled affirmatively. © 2010 American Mathematical Society.
Keywords: Associated graded ring; Normal Hilbert polynomial; Normal ideal; Rees algebra; dept.mat

Academic freedom and tenure: Clark atlanta university - Williams, Rebecca J; Betsey, Charles L; Gasman, Marybeth; Grant, Kerry; Rabban, David M (Academe, 2010)
Keywords: dept.mat; ⛔ No DOI found

Trends in alcohol consumption among undergraduate students at a northeastern public university, 2002-2008. - Bulmer, Sandra Minor; Irfan, Syed; Mugno, Raymond; Barton, Barbara; Ackerman, Louise (Journal of American college health : J of ACH, 2010)
OBJECTIVE: This study examined alcohol consumption patterns and trends at a public university in the Northeast from 2002 to 2008., PARTICIPANTS: Stratified random sampling was used to select undergraduate students enrolled in courses during spring semesters in 2002, 2004, 2006, and 2008., METHODS: Data were collected during regularly scheduled classes for 4 measures of alcohol consumption and 5 demographic categories using the Core Alcohol and Drug Survey., RESULTS: Four groups showed significant increases in both frequency and volume of alcohol consumption-students who were female, over 21 years of age or over, living off-campus, or performing well academically. There were no decreasing trends for any demographic group. These results differ from national college health surveys, which have shown alcohol use remaining steady during this period., CONCLUSIONS: Campus-specific trend data can provide unique perspectives and guide programming efforts. These trends suggest a need for new intervention strategies on this campus.
Keywords: *Alcohol Drinking/ep [Epidemiology]; *Public Sector/sn [Statistics & Numerical Data]; *Students/sn [Statistics & Numerical Data]; *Universities/sn [Statistics & Numerical Data]; Alcohol Drinking; Alcohol consumption; College; Connecticut; Data Collection; Drinking; Female; Humans; Male; Public Sector; Risk-Taking; Statistics, Nonparametric; Students; Trends; United States; Universities; Young Adult; adult; article; dept.mat; dept.pch; drinking behavior; female; high risk behavior; human; information processing; male; nonparametric test; organization and management; peer-reviewed; statistics; student; university

Colorings, cliques and relaxations of planarity - Pinciu, Val (Matemática Contemporânea, 2019)
A conjecture by Albertson states that if χ(G) ≥ n then cr(G) ≥ cr(Kn), where χ(G) is the chromatic number of G and cr(G) is the crossing number of G. This conjecture is true for positive integers n ≤ 16, but it is still open for n ≥ 17. In this paper we consider the statements corresponding to this conjecture where the crossing number of G is replaced with the skewness µ(G) (the minimum number of edges whose removal makes G planar), the genus γ(G) (the minimum genus of the orientable surface on which G is embeddable), and the thickness θ(G) (the minimum number of planar subgraphs of G whose union is G.) We show that the corresponding statements are true for all positive integers n when cr(G) is replaced with µ(G) or γ(G). We also show that the corresponding statement is true for inﬁnitely many values of n, but not for all n, when cr(G) is replaced with θ(G).
Keywords: dept.mat; peer-reviewed; ⛔ No DOI found

Genus, skewness, thickness and coloring theorems - Pinciu, Valeriu (Southeastern International Conference on Combinatorics, Graph Theory & Computing, 2019)
Keywords: dept.mat; ⛔ No DOI found

On the minimum skewness of certain classes of graphs - Pinciu, Valeriu (BGW 2019, 2019)
Keywords: dept.mat; ⛔ No DOI found

Skewness, minimum degree and chromatic number - Pinciu, Valeriu (Congressus Numerantium, 2017)
Keywords: dept.mat; ⛔ No DOI found

A regional Kronecker product and multiple-pair latin squares - Carrigan, Braxton; Hammer, James; Lorch, John (Discrete Mathematics, 2020)
We introduce a variant of the Kronecker product, called the regional Kronecker product, that can be used to build new, larger multiple-pair latin squares from existing multiple-pair latin squares. We present applications to the existence and orthogonality of multiple-pair latin squares. © 2019 Elsevier B.V.
Keywords: Factor pair latin squares; Multiple pair latin squares; Sudoku pair latin squares; dept.mat; peer-reviewed

Conceptualizing discursive teaching capacity: A case study of a middle school mathematics teacher - Kim, Dong-Joong; Shin, Jaehong; Lee, Ji-Eun; Lim, Woong; Lee, Younhee; Choi, Sang-Ho (School Mathematics, 2019)
Keywords: dept.mat; peer-reviewed

The bi-canonical degree of a Cohen–Macaulay ring - Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Hutson, H. L.; Vasconcelos, Wolmer V. (Journal of Algebra, 2021)
This paper is a sequel to [8] where we introduced an invariant, called canonical degree, of Cohen–Macaulay local rings that admit a canonical ideal. Here to each such ring R with a canonical ideal, we attach a different invariant, called bi-canonical degree, which in dimension 1 appears also in [12] as the residue of R. The minimal values of these functions characterize specific classes of Cohen–Macaulay rings. We give a uniform presentation of such degrees and discuss some computational opportunities offered by the bi-canonical degree. © 2019 Elsevier Inc.
Keywords: dept.mat; peer-reviewed

Ten-year trends and differences in alcohol consumption among black and white female undergraduates - Barton, Barbara A; Bulmer, Sandra Minor; Mugno, Raymond; Misencik, Leann (Journal of Substance Use, 2019)
Background: Few studies have explored changing patterns of alcohol consumption among young females and differences based on race/ethnicity. Objective: This study examined differences in alcohol consumption between black and white undergraduate females and compared trends in three different measures of alcohol consumption over a 10-year period from 2004 to 2014. Methods: The CORE Alcohol and Drug Survey was used to collect data from female undergraduates attending a public university in the northeastern USA. Classes were randomly selected into the sample; class acceptance was 68% and student participation was 96%. The chi-square test examined differences between groups and the Cochrane Armitage Test for Trend assessed changes over time. Results: In 2014, for every measure of alcohol consumption examined, a significantly larger percentage of white females engaged in the behavior compared to black females. Trend analysis from 2004 to 2014 demonstrated a narrowing of this gap. Controlling for age, any alcohol use in past 30 days and binge drinking in the past 2 weeks increased significantly for black females 21 years or older. Any alcohol use in the past 30 days decreased significantly for white females under 21 years. Conclusion: These findings introduce many questions which should be explored through additional research.
Keywords: Alcohol; Article; Black person; Caucasian; United States; adult; alcohol; alcohol consumption; binge drinking; college females; dept.hhs; dept.mat; dept.pch; drinking trends; female; human; major clinical study; peer-reviewed; priority journal; race difference; undergraduate student

Finding the volume and surface area in the gut - Lim, Woong; Lee, Younhee; Lee, Ji-Eun (Australian Mathematics Educational Journal, 2019)
Keywords: dept.mat; ⛔ No DOI found

Traveling in networks with blinking nodes - Carrigan, Braxton; Hammer, James (Theory and Applications of Graphs, 2018)
Keywords: dept.mat; peer-reviewed

A maker--breaker game on the boolean hypercube with subcubes as winning sets - Kruczek, Klay; Sundberg, Eric (Integers: The Electronic Journal of Combinatorial Number Theory, 2018)
Keywords: dept.mat; peer-reviewed; ⛔ No DOI found

Developing a structural perspective and its role in connecting school algebra and abstract algebra: A factorization example - Lee, Younhee; Heid, M. Kathleen (Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers, 2018)
Keywords: dept.mat

An application of mathematics to computer programming: Connecting translation vectors, the Minkowski difference, and collision detection - Lee, Younhee; Lu, Qi; Lim, Woong (The Mathematics Teacher, 2018)
Keywords: dept.mat; peer-reviewed

Predicting students' graduation outcomes through support vector machines - Pang, Yulei; Judd, Nicolas; O'Brien, Joseph; Ben-Avie, Michael (2017 IEEE Frontiers in Education Conference (FIE), 2017)
Low graduation rate is a significant and growing problem in U.S. higher education systems. Although previous studies have demonstrated the usefulness of building statistical models for predicting students' graduation outcomes, advanced machine learning models promise to improve the effectiveness of these models, and hone in on the “difference that makes a difference” not only on the group level, but also on the level of the individual student. In this paper we propose an ensemble support vector machines based model for predicting students' graduation. Up to about 100 features, including a set of psychological-educational factors, were employed to construct the predicting model. We evaluated the proposed model using data taken from a state university's longitudinal, cohort data sets from the incoming classes of students from 2011-2012 (n=350). The experimental results demonstrated the effectiveness of the model, with considerable accuracy, precision, and recall. This paper presents the results of analysis that were conducted in order to gauge the predictive capability of a machine learning algorithm to predict on-time graduation that took into consideration students' learning and development.
Keywords: Artificial intelligence; Education computing; Forecasting; Graduation outcome; Graduation rates; Group level; Higher education; Higher education system; Kernel; Learning algorithms; Learning systems; Machine learning; Machine learning algorithms; Machine learning models; Measurement; Predicting models; Predictive capabilities; Predictive models; Seminars; Students; Support vector machine; Support vector machines; advanced machine learning models; dept.mat; ensemble support vector machines; further education; graduation outcome; higher education; higher education systems; learning (artificial intelligence); low graduation rate; machine learning; on-time graduation; psychological-educational factors; statistical analysis; statistical models; support vector machine; support vector machines

Sally modules and reduction numbers of ideals - Ghezzi, L.; Goto, S.; Hong, J.; Vasconcelos, W. V. (Nagoya Mathematical Journal, 2017)
We study the relationship between the reduction number of a primary ideal of a local ring relative to one of its minimal reductions and the multiplicity of the corresponding Sally module. This paper is focused on three goals: (i) to develop a change of rings technique for the Sally module of an ideal to allow extension of results from Cohen–Macaulay rings to more general rings; (ii) to use the fiber of the Sally modules of almost complete intersection ideals to connect its structure to the Cohen–Macaulayness of the special fiber ring; (iii) to extend some of the results of (i) to two-dimensional Buchsbaum rings. Along the way, we provide an explicit realization of the S2S_{2} -fication of arbitrary Buchsbaum rings.
Keywords: 13D40; 13H15; Primary 13H10; Secondary 13A30; dept.mat

A Clustering-Based Test Case Classification Technique for Enhancing Regression Testing - Pang, Yulei; Xue, Xiaozhen; Akbar, Akbar (Journal of Software, 2017)
Keywords: dept.mat

Further results on minimizing positive integer sequences without duplicate substrings - Carrigan, Braxton; Kagey, Peter; O’Brien, Joseph (Congressus Numerantium, 2017)
Keywords: dept.mat; ⛔ No DOI found

Minimizing positive integer sequences without duplicate substrings - Carrigan, Braxton; Kagey, Peter; O’Brien, Joseph (Geombinatorics, 2017)
Keywords: dept.mat; ⛔ No DOI found

Invariants of Cohen–Macaulay rings associated to their canonical ideals - Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Vasconcelos, Wolmer V (Journal of Algebra, 2017)
The purpose of this paper is to introduce new invariants of Cohen–Macaulay local rings. Our focus is the class of Cohen–Macaulay local rings that admit a canonical ideal. Attached to each such ring R with a canonical ideal C, there are integers–the type of R, the reduction number of C–that provide valuable metrics to express the deviation of R from being a Gorenstein ring. We enlarge this list with other integers–the roots of R and several canonical degrees. The latter are multiplicity based functions of the Rees algebra of C. © 2017 Elsevier Inc.
Keywords: Analytic spread; Canonical degree; Cohen–Macaulay type; Reduction number; Roots; dept.mat; peer-reviewed

Shoelace formula: Connecting the area of a polygon with vector cross product - Lee, Younhee; Lim, Woong (The Mathematics Teacher, 2017)
Keywords: dept.mat; peer-reviewed

Masters of mathematics: The problems they solved, why these are important, and what you should know about them - Nowlan, Robert A. (Masters of Mathematics: The Problems They Solved, Why These Are Important, and What You Should Know about Them, 2017)
The original title for this work was “Mathematical Literacy, What Is It and Why You Need it”. The current title reflects that there can be no real learning in any subject, unless questions of who, what, when, where, why and how are raised in the minds of the learners. The book is not a mathematical text, and there are no assigned exercises or exams. It is written for reasonably intelligent and curious individuals, both those who value mathematics, aware of its many important applications and others who have been inappropriately exposed to mathematics, leading to indifference to the subject, fear and even loathing. These feelings are all consequences of meaningless presentations, drill, rote learning and being lost as the purpose of what is being studied. Mathematics education needs a radical reform. There is more than one way to accomplish this. Here the author presents his approach of wrapping mathematical ideas in a story. To learn one first must develop an interest in a problem and the curiosity to find how masters of mathematics have solved them. What is necessary to be mathematically literate? It’s not about solving algebraic equations or even making a geometric proof. These are valuable skills but not evidence of literacy. We often seek answers but learning to ask pertinent questions is the road to mathematical literacy. Here is the good news: new mathematical ideas have a way of finding applications. This is known as “the unreasonable effectiveness of mathematics.”
Keywords: dept.mat

Fault localizations through feature selections - Pang, Yulei; Xue, Xiaozhen; Namin, Akbar Siami (International Journal of Software Engineering and Knowledge Engineering, 2017)
We introduce a novel application of feature ranking methods to the fault localization problem. We envision the problem of localizing causes of failures as instances of ranking program's elements where elements are conceptualized as features. In this paper, we define features as program's statements. However, in its fine-grained definition, the idea of program's features can refer to any traits of programs. This paper proposes feature ranking-based algorithms. The algorithms analyze execution traces of both passing and failing test cases, and extract the bug signatures from the failing test cases. The proposed procedure extracts possible combinations of program's elements when executed together from bug signatures. The feature ranking-based algorithms then order statements according to the suspiciousness of the combinations. When viewed as sequences, the combination of program's elements produced and traced in bug signatures can be utilized to reason about the common longest subsequence. The common longest subsequence of bug signatures represents the common statements executed by all failing test cases and thus provides a means for identifying statements that contain possible faults. Our evaluation indicates that the proposed feature-based fault localization outperforms existing fault localization ranking schemes. © 2017 World Scientific Publishing Company.
Keywords: Artificial intelligence; Computer debugging; Execution trace; Fault localization; Feature ranking; Feature-based; Fine grained; Learning systems; Novel applications; Software engineering; Test case; debugging; dept.mat; feature ranking methods; machine learning

Predicting vulnerable software components through deep neural network - Pang, Yulei; Xue, Xiaozhen; Wang, Huaying (ACM, 2017)
Vulnerabilities need to be detected and removed from software. Although previous studies demonstrated the usefulness of employing prediction techniques in deciding about vulnerabilities of software components, the improvement of effectiveness of these prediction techniques is still a grand challenging research question. This paper employed a technique based on a deep neural network with rectifier linear units trained with stochastic gradient descent method and batch normalization, for predicting vulnerable software components. The features are defined as continuous sequences of tokens in source code files. Besides, a statistical feature selection algorithm is then employed to reduce the feature and search space. We evaluated the proposed technique based on some Java Android applications, and the results demonstrated that the proposed technique could predict vulnerable classes, i.e., software components, with high precision, accuracy and recall.
Keywords: Android; Android (operating system); Android applications; Application programs; Communication channels (information theory); Computer software; Continuous sequences; Deep learning; Deep neural networks; Education; Forecasting; Java programming language; Network security; Neural network; Neural networks; Prediction techniques; Research questions; Software component; Statistical features; Stochastic gradient descent method; Stochastic systems; Vulnerability prediction; deep learning; dept.mat; neural network; vulnerability prediction

On the exact distribution of Wald’s SPRT for the negative exponential model - Starvaggi, Patrick; Khan, M K (Sequential Analysis, 2017)
In this article, we derive the joint Laplace transform of the sequential probability ratio test (SPRT) and the resulting stopped random walk process for the negative exponential model. The Laplace transform is derived by solving a related difference equation. This technique is novel because it only takes advantage of the Markov structure and does not rely on the typical martingale methods used for deriving the Laplace transform of other SPRTs. The joint Laplace transform provides the joint distribution of the SPRT and the associated stopped process, which is a new result. Even the marginal distributions were hitherto unknown. © 2017 Taylor & Francis.
Keywords: Difference equations; Exact distribution; Joint distributions; Laplace transform; Laplace transforms; Marginal distribution; Negative exponential model; Random walk process; SPRT; Sequential probability ratio test; dept.mat; sequential probability ratio test; variance