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HOW MANY DIRECTIONS DETERMINE A SHAPE AND OTHER SUFFICIENCY RESULTS FOR TWO TOPOLOGICAL TRANSFORMS

Transactions of the American Mathematical Society Series B 2022年第32期9卷 1006-1043页

作者： Curry, Justin Mukherjee, Sayan Turner, Katharine Department of Mathematics and Statistics University at Albany SUNY Albany 12222 NY United States Departments of Statistical Science Mathematics Computer Science Biostatistics & Bioinformatics Duke University Durham 27708 NC United States Center for Scalable Data Analytics and Artificial Intelligence Universität Leipzig Germany Max Planck Institute for Mathematics in the Natural Sciences Leipzig Germany Mathematical Sciences Institute Australian National University Canberra Australia

In this paper we consider two topological transforms that are pop-ular in applied topology: the Persistent Homology Transform and the Euler Characteristic Transform. Both of these transforms are of interest for their mathematical properties as well as their applications to science and engineer-ing, because they provide a way of summarizing shapes in a topological, yet quantitative, way. Both transforms take a shape, viewed as a tame subset M of R^d, and associates to each direction v ∈ S^d−1 a shape summary obtained by scanning M in the direction v. These shape summaries are either persistence diagrams or piecewise constant integer-valued functions called Euler curves. By using an inversion theorem of Schapira, we show that both transforms are injective on the space of shapes, i.e. each shape has a unique transform. Moreover, we prove that these transforms determine continuous maps from the sphere to the space of persistence diagrams, equipped with any Wasserstein p-distance, or the space of Euler curves, equipped with certain L^p norms. By making use of a stratified space structure on the sphere, induced by hyperplane divisions, we prove additional uniqueness results in terms of distributions on the space of Euler curves. Finally, our main result proves that any shape in a certain uncountable space of PL embedded shapes with plausible geometric bounds can be uniquely determined using only finitely many directions. © 2022 by the author(s) under Creative Commons Attribution 3.0 License (CC BY 3.0).

关键词： Euler calculus persistent homology statistical shape analysis

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From mechanism to medicine: The progress and potential of epigenetics in osteoarthritis

Osteoarthritis and Cartilage Open

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Osteoarthritis and Cartilage Open 2025年第3期7卷 100621-100621页

作者： Roberts, Jack B. Rockel, Jason S. Mulders, Rick Capellini, Terence D. Appleton, C. Thomas Phanstiel, Douglas H. Lories, Rik Geurts, Jeroen Ali, Shabana Amanda Bhutani, Nidhi Stone, Laura Cruz-Almeida, Yenisel Jurisica, Igor Boer, Cindy G. Ramos, Yolande F.M. Rice, Sarah J. Kapoor, Mohit Biosciences Institute Newcastle University Newcastle upon Tyne United Kingdom Division of Orthopedics Osteoarthritis Research Program Schroeder Arthritis Institute University Health Network and Krembil Research Institute University Health Network Toronto ON Canada Department of Medical Biophysics and Computer Science University of Toronto Toronto ON Canada Department of Biomedical Data Sciences Section Molecular Epidemiology Leiden University Medical Center Leiden Netherlands Department of Human Evolutionary Biology Harvard University Cambridge MA United States Bone and Joint Institute and Department of Medicine Schulich School of Medicine and Dentistry Western University London Canada Curriculum in Bioinformatics and Computational Biology University of North Carolina Chapel Hill NC United States Laboratory of Tissue Homeostasis and Disease Skeletal Biology and Engineering Research Centre Department of Development and Regeneration KU Leuven Leuven Belgium Division of Rheumatology University Hospitals Leuven Leuven Belgium Rheumatology Department of Musculoskeletal Medicine Lausanne University Hospital and University of Lausanne (CHUV-UNIL) Lausanne Switzerland Bone and Joint Center Henry Ford Health + Michigan State University Health Sciences Detroit MI United States Department of Orthopaedic Surgery Stanford School of Medicine Stanford CA United States Department of Anesthesiology School of Medicine University of Minnesota Minneapolis MN United States Pain Research and Intervention Center of Excellence (PRICE) at the University of Florida Gainesville FL United States Department of Internal Medicine Genomics Medicine Center Erasmus MC University Medical Center Rotterdam Netherlands Department of Laboratory Medicine and Pathobiology University of Toronto Toronto ON Canada Department of Surgery University of Toronto Toronto ON Canada

Objective: Osteoarthritis (OA) is a chronic, degenerative disease of the articular joints. The disease presents an enormous clinical and economic burden globally, due in part to the lack of disease modifying therapies. For over a decade, OA researchers have been working to determine epigenetic mechanisms underlying the disease to better understand pathology, identify biomarkers of progression, and pinpoint novel targets for therapeutic intervention. Design: This article presents a summary of the 3rd International Workshop on the Epigenetics of Osteoarthritis held in Toronto, Ontario, Canada, in September 2024. The purpose of this meeting was to gather the international community to discuss the status of OA epigenetic research and share expertise on innovative techniques for future. Results: Since the two previous meetings, there has been increasing adoption of advanced single-cell and spatial sequencing technologies and bioinfomatic analyses. Furthermore, investigations of multiple joint tissues has highlighted the shifting paradigm from OA as a cartilage centric disease to the consideration of all joint tissues. Conclusions: The workshop provided a unique opportunity for early-career researchers to expand their network, and for all participants to discuss new or improved approaches to advance the field, including international consortia and data sharing. The highlights and outcomes from this OA epigenetics workshop are described in this report. © 2025 The Authors

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Cholesterol allosteric modulation of the oxytocin receptor

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Biophysical Journal 2025年

作者： Marlow, Brennica Vogel, Alexander Kuenze, Georg Pankonin, Maik Reinhardt, Franziska Stadler, Peter F. Hildebrand, Peter W. Meiler, Jens Center for Structural Biology Vanderbilt University Nashville TN United States Institute for Drug Discovery Medical Faculty Leipzig University Leipzig Germany Center for Scalable Data Analytics and Artificial Intelligence ScaDS.AI Leipzig University Leipzig Germany Interdisciplinary Center for Bioinformatics Leipzig University Leipzig Germany Chemical and Physical Biology Program Vanderbilt University Nashville TN United States Department of Chemistry Vanderbilt University Nashville TN United States Institute of Medical Physics and Biophysics Medical Faculty Leipzig University Leipzig Germany Bioinformatics Group Institute of Computer Science Interdisciplinary Center of Bioinformatics Leipzig University Leipzig Germany Max-Planck-Institute for Mathematics in the Sciences Leipzig Germany Institute of Theoretical Chemistry University of Vienna Wien Austria Facultad de Ciencias Universidad National de Colombia Sede Bogota Colombia Santa Fe Institute New Mexico Santa Fe Mexico

G-protein coupled receptors are critical components in cellular signaling, mediating various physiological responses to external stimuli. Here, we investigate the intricate relationship between cholesterol and the oxytocin receptor (OXTR), focusing on the binding mechanisms and the allosteric cross talk of bound cholesterol to the orthosteric ligand binding pocket. Utilizing molecular docking and molecular dynamics simulations, we identify cholesterol binding sites both on the agonist-bound and antagonist-bound state, which show differing distributions and residence times of the cholesterol molecules. Importantly, both methods converge on several key sites, demonstrating strong predictive overlap. Notably, one such site, and several sites detected by our molecular dynamics approach, also coincide with electron density observed in an experimental cryo-EM map, providing orthogonal validation for computational predictions. Allosteric network analysis uncovers the distinct pathways through which cholesterol may affect ligand-mediated receptor signaling, highlighting the significance of one site on the extracellular leaflet between TM4 and TM5, and two sites on the intracellular leaflet between TM2, TM3, and TM4 and between TM4 and TM5 in transmitting allosteric signals to the orthosteric pocket. These findings provide insights into the impact of cholesterol on OXTR function, emphasizing specific binding sites and signaling paths for further experimental exploration. © 2025 Biophysical Society

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Uniform Consistency of Generalized Fréchet Means

arXiv

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arXiv 2024年

作者： Aveni, Andrea Mukherjee, Sayan Department of Statistical Science Duke University United States Center for Scalable Data Analytics and Artificial Intelligence Department of Computer Science Universität Liepzig Germany Max Planck Institute for Mathematics in the Natural Sciences Duke University Departments of Statistical Science Mathematics Computer Science and Biostatistics & Bioinformatics United States

We study a generalization of the Fréchet mean on metric spaces, which we call φ-means. Our generalization is indexed by a convex function φ. We find necessary and sufficient conditions for φ-means to be finite and provide a tight bound for the diameter of the intrinsic mean set. We also provide sufficient conditions under which all the φ-means coincide in a single point. Then, we prove the consistency of the sample φ-mean to its population analogue. We also find conditions under which classes of φ-means converge uniformly, providing a Glivenko-Cantelli result. Finally, we illustrate applications of our results and provide algorithms for the computation of φ-*** Codes 0F05, 60F15, 60D05, 62E20, 62F10, 58K05 © 2024, CC BY.

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Modeling the Percentage of NEET in Indonesia with Spatial Cauchy Regression through the Bayesian Analysis Approach

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IAENG International Journal of Applied Mathematics 2024年第7期54卷 1288-1295页

作者： Rantini, Dwi Fakhruzzaman, Muhammad Noor Ningrum, Ratih Ardiati Othman, Fazidah Choir, Achmad Syahrul Ramadan, Arip Alya, Najma Attaqiya Putri, Elfira Rahma Pratama, Muhammad Alfian Engineering Department Data Science Technology Study Program Faculty of Advanced Technology and Multidiscipline Universitas Airlangga Indonesia Engineering Department Data Science Technology Study Program Faculty of Advanced Technology andMultidiscipline Universitas Airlangga Indonesia Department of Computer System and Technology Faculty of Computer Science and Information Technology University of Malaya Malaysia Statistical Computing StudyProgram Politeknik Statistika STIS Indonesia Information System Study Program School of Industrial and System Engineering Telkom University Indonesia

Indonesia has entered a period of demographic bonus. Human resources must be optimized. The number of children who do not in employment, education or training (NEET) in each province needs attention. Several factors that could contribute to the decline in the NEET percentage are literacy rates and the number of adolescents with computer skills. Increasing these two factors is believed to be able to reduce the percentage of NEET in every province in Indonesia. To find out the relationship between these two factors and how much influence they have on the percentage of NEET, this research is modeled by Cauchy regression and includes spatial effects. The results of the analysis show that the best model is when the spatial effect is modeled by Fernandez Steel Skew Normal conditionally autoregressive (FSSN CAR). This result is seen from the smallest value of the Watanabe Akaike Information Criterion (WAIC) in this model, which is 190.5. The parameter estimated shows that the higher the literacy rate and the number of adolescents with computer skills, the lower the percentage of NEET in each province in Indonesia. The results of this research can be useful for the Indonesian government to increase the number of educational facilities related to these two factors. © (2024), (International Association of Engineers). All rights reserved.

关键词： Bayesian CAR Cauchy Education NEET

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Comparison of Decision Tree and Support Vector Machine for Predicting Jakarta Air Quality Index

Comparison of Decision Tree and Support Vector Machine for P...

引用

computer science, Information Technology and Engineering (ICCoSITE), International Conference on

作者： Musyaffa Ayman Rafif Gede Sanjaya Indrajaya Muhammad Kent Al-Ghazi Johnny Johnny Noviyanti T M Sagala Data Science Program School of Computer Sciences Bina Nusantara University Jakarta Indonesia Statistics Department School of Computer Science Bina Nusantara University Jakarta Indonesia

The people in the capital city of the Republic of Indonesia, Jakarta, have been living for years with air pollution. Air quality has been a concern for a long time due to the health risks it has on people, especially those at risk. Using classification algorithms, we would like to implement data mining for the air quality index and make predictions from our capital city, DKI Jakarta. This research aims to compare Decision Tree and Support Vector Machine in predicting Air Quality Index in DKI Jakarta in 2020. The dataset was collected from the Jakarta Open data Web, and the results of this research highlight the effectiveness of data mining techniques in predicting air quality index levels in Jakarta and emphasize the importance of selecting the appropriate classification algorithm for data mining applications. This research shows that SVM, compared to the Decision tree, has a better result with an accuracy score of 87.86%. On the other hand, Decision Tree has a score of 90.56%.

关键词： Support vector machines Urban areas Support vector machine classification Predictive models Air pollution Classification algorithms Decision trees

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Optimal Physician Shared-Patient Networks and the Diffusion of Medical Technologies

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Journal of data science 2023年第3期21卷 578-598页

作者： Ran, Xin An, Chuankai Rockmore, Daniel N. Department of Biomedical Data Science The Dartmouth Institute for Health Policy and Clinical Practice Geisel School of Medicine at Dartmouth Lebanon 03756 NH United States Department of Biomedical Data Science The Dartmouth Institute for Health Policy and Clinical Practice and the Program in Quantitative Biomedical Sciences Geisel School of Medicine at Dartmouth Lebanon 03756 NH United States Research Institute of China Investment Corporation Beijing 100010 China Department of Mathematics Department of Computer Science Hanover 03755 NH United States The Santa Fe Institute Santa Fe 87501 NM United States

Social network analysis has created a productive framework for the analysis of the histories of patient-physician interactions and physician collaboration. Notable is the construction of networks based on the data of "referral paths"- sequences of patient-specific temporally linked physician visits - in this case, culled from a large set of Medicare claims data in the United States. Network constructions depend on a range of choices regarding the underlying data. In this paper we introduce the use of a five-factor experiment that produces 80 distinct projections of the bipartite patient-physician mixing matrix to a unipartite physician network derived from the referral path data, which is further analyzed at the level of the 2,219 hospitals in the final analytic sample. We summarize the networks of physicians within a given hospital using a range of directed and undirected network features (quantities that summarize structural properties of the network such as its size, density, and reciprocity). The different projections and their underlying factors are evaluated in terms of the heterogeneity of the network features across the hospitals. We also evaluate the projections relative to their ability to improve the predictive accuracy of a model estimating a hospital's adoption of implantable cardiac defibrillators, a novel cardiac intervention. Because it optimizes the knowledge learned about the overall and interactive effects of the factors, we anticipate that the factorial design setting for network analysis may be useful more generally as a methodological advance in network analysis. © 2023 The Author(s).

关键词： bipartite network directional information factorial design implantable cardiac defibrillators optimal bipartite-unipartite projection shared-patient physician network

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Network Topology Mapping from Partial Virtual Coordinates and Graph Geodesics

arXiv

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arXiv 2017年

作者： Jayasumana, Anura P. Paffenroth, Randy Ramasamy, Sridhar Department of Electrical & Computer Engineering Colorado State University Fort CollinsCO80525 Department of Mathematical Sciences Department of Computer Science Data Science Program Worcester Polytechnic Institute WorcesterMA01609

For many important network types (e.g., sensor networks in complex harsh environments and social networks) physical coordinate systems (e.g., Cartesian), and physical distances (e.g., Euclidean), are either difficult to discern or inappropriate. Accordingly, Topology Preserving Maps (TPMs) derived from a Virtual-Coordinate (VC) system representing the distance to a small set of anchors is an attractive alternative to physical coordinates for many network algorithms. Herein, we present an approach, based on the theory of low-rank matrix completion, to recover geometric properties of a network with only partial information about the VCs of nodes. In particular, our approach is a combination of geodesic recovery concepts and low-rank matrix completion, generalized to the case of hop-distances in graphs. Distortion evaluated using the change of distance among node pairs shows that even with up to 40% to 60% of random coordinates missing, accurate TPMs can be obtained. TPM generation can now also be based on different context appropriate VC systems or measurements as long as they characterize each node with distances to a small set of random nodes (instead of a global set of anchors). The proposed method is a significant generalization that allows the topology to be extracted from a random set of graph geodesics, making it applicable in contexts such as social networks where VC generation may not be *** Codes 15A83 Copyright © 2017, The Authors. All rights reserved.

关键词： Sensor networks

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Med-IC: Fusing a Single Layer Involution with Convolutions for Enhanced Medical Image Classification and Segmentation

arXiv

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arXiv 2024年

作者： Islam, Md. Farhadul Zabeen, Sarah Manab, Meem Arafat Mahin, Mohammad Rakibul Hasan Mondal, Joyanta Jyoti Reza, Md. Tanzim Hasan, Md Zahidul Haque, Munima Sadeque, Farig Noor, Jannatun Research Group Department of Computer Science and Engineering School of Data and Sciences BRAC University Dhaka Bangladesh Department of Computer Science and Engineering School of Data and Sciences BRAC University Dhaka Bangladesh Biotechnology Program Department of Mathematics and Natural Sciences School of Data and Sciences BRAC University Dhaka Bangladesh Department of Computer and Information Sciences University of Delaware United States School of Law and Government Dublin City University Ireland Gina Cody School of Engineering and Computer Science Concordia University Canada

The majority of medical images, especially those that resemble cells, have similar characteristics. These images, which occur in a variety of shapes, often show abnormalities in the organ or cell region. The convolution operation possesses a restricted capability to extract visual patterns across several spatial regions of an image. The involution process, which is the inverse operation of convolution, complements this inherent lack of spatial information extraction present in convolutions. In this study, we investigate how applying a single layer of involution prior to a convolutional neural network (CNN) architecture can significantly improve classification and segmentation performance, with a comparatively negligible amount of weight parameters. The study additionally shows how excessive use of involution layers might result in inaccurate predictions in a particular type of medical image. According to our findings from experiments, the strategy of adding only a single involution layer before a CNN-based model outperforms most of the previous *** Codes 68T45 © 2024, CC BY-NC-SA.

关键词： Convolutional neural networks

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An efficient swarm intelligence approach to the optimization on high-dimensional solutions with cross-dimensional constraints, with applications in supply chain management

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Frontiers in Computational Neuroscience 2024年 18卷 1283974页

作者： Liu, Hsin-Ping Phoa, Frederick Kin Hing Chen-Burger, Yun-Heh Lin, Shau-Ping Data Science Degree Program National Taiwan University Taipei Taiwan Institute of Statistical Science Academia Sinica Taipei Taiwan Department of Computer Sciences Heriot-Watt University Edinburgh United Kingdom Institute of Biotechnology National Taiwan University Taipei Taiwan

Introduction: The Swarm Intelligence Based (SIB) method has widely been applied to efficient optimization in many fields with discrete solution domains. E-commerce raises the importance of designing suitable selling strategies, including channel- and direct sales, and the mix of them, but researchers in this field seldom employ advanced metaheuristic techniques in their optimization problem due to the complexities caused by the high-dimensional problems and cross-dimensional constraints. Method: In this work, we introduce an extension of the SIB method that can simultaneously tackle these two challenges. To pursue faster computing, CPU parallelization techniques are employed for algorithm acceleration. Results: The performance of the SIB method is examined on the problems of designing selling schemes in different scales. It outperforms the Genetic Algorithm (GA) in terms of both the speed of convergence and the optimized capacity as measured using improvement multipliers. Copyright © 2024 Liu, Phoa, Chen-Burger and Lin.

关键词： Supply chain management

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