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

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

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

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

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

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

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

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

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

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

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

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