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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.

This paper surveys and summarizes Wolmer Vasconcelos’ results surrounding multiplicities, Hilbert coefficients, and their extensions. We particularly focus on Vasconcelos’ results regarding multiplicities and Chern coefficients, and other invariants which they bound. The Sally module is an important instrument introduced by Vasconcelos for this study, which naturally relates Hilbert coefficients to reduction numbers. ©2025 Walter de Gruyter GmbH,Berlin/Boston.

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.

The Alder–Andrews Theorem, a partition inequality generalizing Euler’s partition identity, the first Rogers–Ramanujan identity, and a theorem of Schur to d-distinct partitions of n, was proved successively by Andrews in 1971, Yee in 2008, and Alfes, Jameson, and Lemke Oliver in 2010. While Andrews and Yee utilized q-series and combinatorial methods, Alfes et al. proved the finite number of remaining cases using asymptotics originating with Meinardus together with high-performance computing. In 2020, Kang and Park conjectured a “level 2” Alder–Andrews type partition inequality which relates to the second Rogers–Ramanujan identity. Duncan, Khunger, the second author, and Tamura proved Kang and Park’s conjecture for all but finitely many cases using a combinatorial shift identity. Here, we generalize the methods of Alfes et al. to resolve nearly all of the remaining cases of Kang and Park’s conjecture. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2026.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 K_i and y-intercept V_b 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 K_i 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 K_i and V_b 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 K_i images was enhanced, while 3.59% and 3.67% average absolute percentage changes were observed in mean and maximum K_i values, respectively, across all evaluated ROIs. The estimated mean K_i values had substantial changes with motion correction ( p \,\,= 0.0021). The AUC of both mean K_i and maximum K_i after motion correction increased, possibly suggesting the potential of enhancing oncological discrimination capacity through inter-pass motion correction.

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.