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The Black-White Pixels Ratio in Medial Temporal Lobe Brain Structure in Transcranial B-Images as a Measurable Marker of Alzheimer’s Disease Probability: The Reproducibility Overview

The Black-White Pixels Ratio in Medial Temporal Lobe Brain S...

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International Conference on Software, Telecommunications and computer Networks (SoftCOM)

作者： Jiri Blahuta Tomas Soukup Lukas Pavlik Computer Science and Applied Math. Moravian Business College Olomouc Olomouc Czech Republic Computer Science and Informatics Silesian University in Opava Opava Czech Republic

ISBN: (数字)9789532900996

ISBN: (纸本)9781728175386

The objective of the presented study is to introduce analysis the black-white pixels ratio in medial temporal lobe (MTL) brain structure in digitized transcranial B-images using our developed software B-MODE Assist. This ratio could be a significant marker related to the echogenicity grade. In B-image, the MTL is stable anechogenic structure but increased echogenicity of surrounding cortex is detectable in the case of MTL atrophy; the atrophy predicts Alzheimer's Disease. Within this study, a set of 97 B-images is used. There are two key goals of this pilot study; verify the reproducibility of the ratio between two observers and to show that the ratio is not much different in the case of original image in comparison with a magnified segment and using constant brightness increasing; the ratio should be independent on image resolution and brightness. To select medial temporal lobe structure, a 20mm square-shaped Region of Interest is used. The correlation coefficient r=0.69 was achieved between two independent, non-experienced observers. The error does not exceed 28 % between 2 non-experienced observers and does not exceed 12 % between the measurements from the same observer. Also, the variance and the range were computed. Achieved results have been judged by an experienced sonographer. In the future, the ratio could be an effective value to determine the MTL atrophy based on the ratio value and possibility to create a rule-based expert system which should help evaluate probability of Alzheimer's Disease based on the cortex echogenicity grade. In general, this approach could be a reliable way to detect risk of Alzheimer's Disease using neurosonological imaging.

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Beyond circular-arc graphs - recognizing lollipop graphs and medusa graphs

arXiv

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arXiv 2022年

作者： Çağirici, Deniz Ağaoğlu Çağirici, Onur Derbisz, Jan Hartmann, Tim A. Hliněný, Petr Kratochvíl, Jan Krawczyk, Tomasz Zeman, Peter Masaryk University Brno Czech Republic Toronto Metropolitan University Toronto Canada Theoretical Computer Science Department Faculty of Mathematics and Computer Science Jagiellonian University Kraków Poland RWTH Aachen University Aachen Germany Department of Applied Mathematics Faculty of Mathematics and Physics Charles University Prague Czech Republic Institut de Mathématiques University of Neuchâtel Switzerland

In 1992 Biró, Hujter and Tuza introduced, for every fixed connected graph H, the class of H-graphs, defined as the intersection graphs of connected subgraphs of some subdivision of H. Such classes of graphs are related to many known graph classes: for example, K2-graphs correspond to interval graphs, K3-graphs correspond to circular-arc graphs, the union of T-graphs, where T ranges over all trees, correspond to chordal graphs. Recently, quite a lot of research has been devoted to understanding the tractability border for various computational problems, such as recognition or isomorphism testing, in classes of H-graphs for different graphs H. In this work we undertake this research topic, focusing on the recognition problem. Chaplick, Töpfer, Voborník, and Zeman showed an XP-algorithm testing whether a given graph is a T-graph, where the parameter is the size of the tree T. In particular, for every fixed tree T the recognition of T-graphs can be solved in polynomial time. Tucker showed a polynomial time algorithm recognizing K3-graphs (circular-arc graphs). On the other hand, Chaplick at al. showed also that recognition of H-graphs is NP-hard if H contains two different cycles sharing an edge. The main two results of this work narrow the gap between the NP-hard and P cases of H-graphs recognition. First, we show that recognition of H-graphs is NP-hard when H contains two different cycles. On the other hand, we show a polynomial-time algorithm recognizing L-graphs, where L is a graph containing a cycle and an edge attached to it (L is called a lollipop and L-graphs are called lollipop graphs). Clearly, the class of lollipop graphs extends the class of circular-arc graphs. Our work leaves open the recognition problems of M-graphs for every unicyclic graph M different from a cycle and a lollipop. Other results of this work, which shed some light on the cases that remain open, are as follows: • recognition of M-graphs, where M is a fixed unicyclic graph, admits a polynom

关键词： Polynomial approximation

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A new trigonometric kernel function for support vector machine

arXiv

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arXiv 2022年

作者： Hafshejani, Sajad Fathi Moaberfard, Zahra Department of Applied Mathematics Shiraz University of Technology Modarres Boulevard Fars Shiraz71557-13876 Iran Department of Math and Computer Science University of Lethbridge 4401 University Dr W LethbridgeABT1K 3M4 Canada

In the last few years, various types of machine learning algorithms, such as Support Vector Machine (SVM), Support Vector Regression (SVR), and Non-negative Matrix Factorization (NMF) have been introduced. The kernel approach is an effective method for increasing the classification accuracy of machine learning algorithms. This paper introduces a family of one-parameter kernel functions for improving the accuracy of SVM classification. The proposed kernel function consists of a trigonometric term and differs from all existing kernel functions. We show this function is a positive definite kernel function. Finally, we evaluate the SVM method based on the new trigonometric kernel, the Gaussian kernel, the polynomial kernel, and a convex combination of the new kernel function and the Gaussian kernel function on various types of datasets. Empirical results show that the SVM based on the new trigonometric kernel function and the mixed kernel function achieve the best classification accuracy. Moreover, some numerical results of performing the SVR based on the new trigonometric kernel function and the mixed kernel function are presented. Copyright © 2022, The Authors. All rights reserved.

关键词： Support vector machines

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MIXUP-BASED DEEP METRIC LEARNING APPROACHES FOR INCOMPLETE SUPERVISION

arXiv

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arXiv 2022年

作者： Buris, Luiz H. Pedronette, Daniel C.G. Papa, Joao P. Almeida, Jurandy Carneiro, Gustavo Faria, Fabio Augusto Institute of Science and Technology Universidade Federal de São Paulo Brazil Depart. of Statistics Applied Math. and Computing São Paulo State University Brazil Department of Computing São Paulo State University Brazil Department of Computing Federal University of São Carlos Brazil Australian Institute for Machine Learning The University of Adelaide Australia

Deep learning architectures have achieved promising results in different areas (e.g., medicine, agriculture, and security). However, using those powerful techniques in many real applications becomes challenging due to the large labeled collections required during training. Several works have pursued solutions to overcome it by proposing strategies that can learn more for less, e.g., weakly and semi-supervised learning approaches. As these approaches do not usually address memorization and sensitivity to adversarial examples, this paper presents three deep metric learning approaches combined with Mixup for incomplete-supervision scenarios. We show that some state-of-the-art approaches in metric learning might not work well in such scenarios. Moreover, the proposed approaches outperform most of them in different datasets. Copyright © 2022, The Authors. All rights reserved.

关键词： Deep learning

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Harmful information spreading and its impact on vaccination campaigns modeled through fractal-fractional operators

arXiv

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arXiv 2025年

作者： Akgül, Ali Usman, Auwalu Hamisu Conejero, J. Alberto Department of Electronics and Communication Engineering Saveetha School of Engineering SIMATS Tamilnadu Chennai India Siirt University Art and Science Faculty Department of Mathematics Siirt56100 Turkey Department of Computer Engineering Biruni University Topkapı Istanbul34010 Turkey Near East University Mathematics Research Center Department of Mathematics Near East Boulevard Nicosia/Mersin 10 MersinPC: 99138 Turkey Dept. Mathematics Faculty of Science King Mongkut’s University of Technology Thonburi Bangkok Thailand Bangkok10140 Thailand Dept. Math. Sci. Faculty of Physical Sciences Bayero University Kano Nigeria Instituto de Matemática Pura y Aplicada Universitat Politècnica de València Spain

Despite the huge efforts to develop and administer vaccines worldwide to copewith the COVID-19 pandemic, misinformation spreading through fake news in mediaand social networks about vaccination safety, make that people refuse to bevaccinated, which harms not only these people but also the whole population. In this work, we model the effects of harmful information spreading inimmunization acquisition through vaccination. Our model is posed for severalfractional derivative operators. We have conducted a comprehensive foundationanalysis of this model for the different fractional derivatives. Additionally,we have incorporated a strength parameter that shows the combined impact ofnonlinear and linear components within an epidemiological model. We have usedthe second derivative of the Lyapunov function to ascertain the detection ofwave patterns within the vaccination *** Codes 26A33, 34A08, 35R11 Copyright © 2025, The Authors. All rights reserved.

关键词： Fractals

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FURSTENBERG SYSTEMS OF PRETENTIOUS AND MRT MULTIPLICATIVE FUNCTIONS

arXiv

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arXiv 2023年

作者： Frantzikinakis, Nikos Lemańczyk, Mariusz de la Rue, Thierry University of Crete Department of Mathematics and Applied Mathematics Voutes University Campus Heraklion71003 Greece Faculty of Mathematics and Computer Science Nicolaus Copernicus University Toruń Poland Université de Rouen Normandie CNRS Laboratoire de Mathématiques Raphaël Salem Avenue de L’Université Saint Étienne du Rouvray76801 France

We prove structural results for measure preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious multiplicative functions these systems always have rational discrete spectrum and, as a consequence, zero entropy. We obtain several other refined structural and spectral results, one consequence of which is that the Archimedean characters are the only pretentious multiplicative functions that have Furstenberg systems with trivial rational spectrum, another is that a pretentious multiplicative function has ergodic Furstenberg systems if and only if it pretends to be a Dirichlet character, and a last one is that for any fixed pretentious multiplicative function all its Furstenberg systems are isomorphic. We also study structural properties of Furstenberg systems of a class of multiplicative functions, introduced by Matomäki, Radziwill, and Tao, which lie in the intermediate zone between pretentiousness and strong aperiodicity. In a work of the last two authors and Gomilko, several examples of this class with exotic ergodic behavior were identified, and here we complement this study and discover some new unexpected phenomena. Lastly, we prove that Furstenberg systems of general bounded multiplicative functions have divisible spectrum. When these systems are obtained using logarithmic averages, we show that trivial rational spectrum implies a strong dilation invariance property, called strong stationarity, but, quite surprisingly, this property fails when the systems are obtained using Cesàro *** Codes Primary: 11N37, Secondary: 37A44, 11K65 © 2023, CC BY.

关键词： Rational functions

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Solving the Families In the Wild Kinship Verification Challenge by Program Synthesis

arXiv

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arXiv 2021年

作者： Huang, Junyi Strome, Maxwell Benjamin Jenkins, Ian Williams, Parker Feng, Bo Wang, Yaning Wang, Roman Bagri, Vaibhav Cheng, Newman Drori, Iddo Department of Mathematics Columbia University United States Department of Computer Science Columbia University United States Department of Applied Physics and Math Columbia University United States Department of Electrical Engineering Columbia University United States Department of Electrical Engineering and Computer Science MIT United States

Kinship verification is the task of determining whether a parent-child, sibling, or grandparent-grandchild relationship exists between two people and is important in social media applications, forensic investigations, finding missing children, and reuniting families. We demonstrate high quality kinship verification by participating in the 2021 Recognizing Families in the Wild challenge which provides the largest publicly available dataset in the field. Our approach is among the top 3 winning entries in the competition. We ensemble models written by both human experts and a foundation model, OpenAI Codex, trained on text and code. We use Codex to generate model variants, and also demonstrate its ability to generate entire running programs for kinship verification tasks of specific relationships. © 2021, CC BY.

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HiPoNet: A Topology-Preserving Multi-View Neural Network For High Dimensional Point Cloud and Single-Cell Data

arXiv

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arXiv 2025年

作者： Viswanath, Siddharth Madhu, Hiren Bhaskar, Dhananjay Kovalic, Jake Johnson, Dave Ying, Rex Tape, Christopher Adelstein, Ian Perlmutter, Michael Krishnaswamy, Smita Department of Computer Science Yale University New Haven United States Department of Genetics Yale University New Haven United States Department of Applied Physics Yale University New Haven United States Program in Computing Boise State University Idaho United States Cell Communication Lab Department of Oncology University College London Cancer Institute London United Kingdom Department of Mathematics Yale University New Haven United States Department of Mathematics Boise State University Idaho United States Computational Biology and Bioinformatics Program Yale University New Haven United States Wu-Tsai Institute Yale University New Haven United States Program for Applied Math Yale University New Haven United States

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionality exceeding the capabilities of existing methods for point clouds which are tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e. one on every patient), necessitating models that can process large, high-dimensional point clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric information. In contrast, HiPoNet forms higher-order simplicial complexes through learnable feature reweighting, generating multiple data views that disentangle distinct biological processes. It then employs simplicial wavelet transforms to extract multiscale features—capturing both local and global topology. We empirically show that these components preserve topological information in the learned representations, and that HiPoNet significantly outperforms state-of-the-art point-cloud and graph-based models on single cell. We also show an application of HiPoNet on spatial transcriptomics datasets using spatial co-ordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis. © 2025, CC BY.

关键词： Network topology

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An all Mach number semi-implicit hybrid Finite Volume/ Virtual Element method for compressible viscous flows on Voronoi meshes

arXiv

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arXiv 2024年

作者： Boscheri, Walter Busto, Saray Dumbser, Michael Laboratoire de Mathématiques UMR 5127 CNRS Université Savoie Mont Blanc Le Bourget du Lac73376 France Department of Mathematics and Computer Science University of Ferrara Ferrara44121 Italy Department of Applied Mathematics Universidade de Santiago de Compostela Santiago de Compostela15782 Spain Galician Center for Mathematical Research and Technology CITMAga Santiago de Compostela15782 Spain Department of Civil Environmental and Mechanical Engineering University of Trento Trento38123 Italy

We present a novel high order semi-implicit hybrid finite volume/virtual element numerical scheme for the solution of compressible flows on Voronoi tessellations. The method relies on the flux splitting of the compressible Navier-Stokes equations into three sub-systems: a convective sub-system solved explicitly using a finite volume (FV) scheme, and the viscous and pressure sub-systems which are discretized implicitly at the aid of a virtual element method (VEM). Consequently, the time step restriction of the overall algorithm depends only on the mean flow velocity and not on the fast pressure waves nor on the viscous eigenvalues. As such, the proposed methodology is well suited for the solution of low Mach number flows at all Reynolds numbers. Moreover, the scheme is proven to be globally energy conserving so that shock capturing properties are retrieved in high Mach number flows. To reach high order of accuracy in time and space, an IMEX Runge-Kutta time stepping strategy is employed together with high order spatial reconstructions in terms of CWENO polynomials and virtual element space basis functions. The chosen discretization techniques allow the use of general polygonal grids, a useful tool when dealing with complex domain configurations. The new scheme is carefully validated in both the incompressible limit and the high Mach number regime through a large set of classical benchmarks for fluid dynamics, assessing robustness and *** Codes 65M08, 65M60, 76N06 © 2024, CC BY-NC-ND.

关键词： Mach number

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The least Euclidean distortion constant of a distance-regular graph

arXiv

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arXiv 2021年

作者： Cioabă, Sebastian M. Gupta, Himanshu Ihringer, Ferdinand Kurihara, Hirotake Department of Mathematical Sciences University of Delaware NewarkDE19716-2553 United States Dept. of Mathematics: Analysis Logic and Discrete Math. Ghent University Belgium Department of Applied Science Yamaguchi University Yoshida Yamaguchi753-8511 Japan

In 2008, Vallentin made a conjecture involving the least distortion of an embedding of a distance-regular graph into Euclidean space. Vallentin's conjecture implies that for a least distortion Euclidean embedding of a distance-regular graph of diameter d, the most contracted pairs of vertices are those at distance d. In this paper, we confirm Vallentin's conjecture for several families of distance-regular graphs. We also provide counterexamples to this conjecture, where the largest contraction occurs between pairs of vertices at distance d − 1. We suggest three alternative conjectures and prove them for various families of distance-regular graphs and for distance-regular graphs of diameter 3. Copyright © 2021, The Authors. All rights reserved.

关键词： Embeddings

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