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Interplay between k-core and community structure in complex networks

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arXiv 2020年

作者： Malvestio, Irene Cardillo, Alessio Masuda, Naoki Department of Engineering Mathematics University of Bristol BristolBS8 1UB United Kingdom Department of Computer Science and Mathematics University Rovira i Virgili TarragonaE-43007 Spain University of Zaragoza ZaragozaE-50018 Spain Department of Mathematics University at Buffalo BuffaloNY14260-2900 United States Computational and Data-Enabled Science and Engineering Program University at Buffalo State University of New York BuffaloNY14260-5030 United States

The organisation of a network in a maximal set of nodes having at least k neighbours within the set, known as k-core decomposition, has been used for studying various phenomena. It has been shown that nodes in the innermost k-shells play a crucial role in contagion processes, emergence of consensus, and resilience of the system. It is known that the k-core decomposition of many empirical networks cannot be explained by the degree of each node alone, or equivalently, random graph models that preserve the degree of each node (i.e., configuration model). Here we study the k-core decomposition of some empirical networks as well as that of some randomised counterparts, and examine the extent to which the k-shell structure of the networks can be accounted for by the community structure. We find that preserving the community structure in the randomisation process is crucial for generating networks whose k-core decomposition is close to the empirical one. We also highlight the existence, in some networks, of a concentration of the nodes in the innermost k-shells into a small number of communities. Copyright © 2020, The Authors. All rights reserved.

关键词： Complex networks

Visualizing structure and transitions in high-dimensional biological data (vol 54, pg 781, 2019)

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NATURE BIOTECHNOLOGY 2020年第1期38卷 108-108页

作者： Moon, Kevin R. van Dijk, David Wang, Zheng Gigante, Scott Burkhardt, Daniel B. Chen, William S. Yim, Kristina van den Elzen, Antonia Hirn, Matthew J. Coifman, Ronald R. Ivanova, Natalia B. Wolf, Guy Krishnaswamy, Smita Department of Mathematics and Statistics Utah State University Logan USA Cardiovascular Research Center section Cardiology Department of Internal Medicine Yale University New Haven USA Department of Computer Science Yale University New Haven USA School of Basic Medicine Qingdao University Qingdao China Yale Stem Cell Center Department of Genetics Yale University New Haven USA Computational Biology and Bioinformatics Program Yale University New Haven USA Department of Genetics Yale University New Haven USA Department of Computational Mathematics Science and Engineering Michigan State University East Lansing USA Department of Mathematics Michigan State University East Lansing USA Applied Mathematics Program Yale University New Haven USA Department of Genetics Center for Molecular Medicine University of Georgia Athens USA Department of Mathematics and Statistics Université de Montréal Montréal Canada Mila—Quebec Artificial Intelligence Institute Montréal Canada

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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BPS2025 - Structural basis of potassium selectivity in kalium channelrhodopsins

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Biophysical Journal 2025年第3期124卷 64a-65a页

作者： Seiya Tajima Yoon Seok Kim YoungJu Jo Peter Y. Wang Joseph M. Paggi Charu Ramakrishnan Shunki Takaramoto Takashi Nagata Masae Konno Kota Katayama Hideki Kandori Ron O. Dror Keiichi Inoue Karl Deisseroth Hideaki Kato Research Center for Advanced Science and Technology The University of Tokyo Tokyo Japan Department of Bioengineering Stanford University Stanford CA USA Department of Computer Science Stanford University Stanford CA USA Cracking the Neural Code Program Stanford University Stanford CA USA The Institute for Solid State Physics The University of Tokyo Kashiwa Japan PRESTO Japan Science and Technology Agency Kawaguchi Japan Department of Life Science and Applied Chemistry Nagoya Institute of Technology Nagoya Japan OptoBioTechnology Research Center Nagoya Institute of Technology Nagoya Japan Institute for Computational and Mathematical Engineering Stanford University Stanford CA USA Howard Hughes Medical Institute Stanford University Stanford CA USA Graduate School of Arts and Sciences The University of Tokyo Tokyo Japan

Reed-Muller codes polarize

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arXiv 2019年

作者： Abbe, Emmanuel Ye, Min Mathematics Institute School of Computer and Communication Sciences Epfl Switzerland Program in Applied and Computational Mathematics Department of Electrical Engineering Princeton University United States Department of Electrical Engineering Princeton University PrincetonNJ United States

Reed-Muller (RM) codes and polar codes are generated by the same matrix Gm= [1 0/1 1]⊗mbut using different subset of rows. RM codes select simply rows having largest weights. Polar codes select instead rows having the largest conditional mutual information proceeding top to down in Gm;while this is a more elaborate and channel-dependent rule, the top-to-down ordering has the advantage of making the conditional mutual information polarize, giving directly a capacity-achieving code on any binary memoryless symmetric channel (BMSC). RM codes are yet to be proved to have such property. In this paper, we reconnect RM codes to polarization theory. It is shown that proceeding in the RM code ordering, i.e., not top-to-down but from the lightest to the heaviest rows in Gm, the conditional mutual information again polarizes. We further demonstrate that it does so faster than for polar codes. This implies that Gmcontains another code, different than the polar code and called here the twin code, that is provably capacity-achieving on any BMSC. This proves a necessary condition for RM codes to achieve capacity on BMSCs. It further gives a sufficient condition if the rows with largest conditional mutual information correspond to the heaviest rows, i.e., if the twin code is the RM code. We show here that the two codes bare similarity with each other and give further evidence that they are likely the same. Copyright © 2019, The Authors. All rights reserved.

关键词： Forward error correction

On Phase Reduction and Time Period of Noisy Oscillators

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On Phase Reduction and Time Period of Noisy Oscillators

IEEE Annual Conference on Decision and Control

作者： Zahra Aminzare Philip Holmes Vaibhav Srivastava Department of Mathematics University of Iowa IA USA Program in Applied and Computational Mathematics Princeton Neuroscience Institute Princeton University Princeton NJ USA Electrical and Computer Engineering Michigan State University East Lansing MI USA

ISBN: (数字)9781728113982

ISBN: (纸本)9781728113999

We study phase reduction for noisy oscillator models by deriving a reduced order stochastic differential equation describing the phase evolution using the first and second order Phase Response Curves (PRCs). We discuss direct methods and ordinary differential equations for computing these PRCs, and derive approximate first and second moments of the time period of the oscillator models in terms of functions of the PRCs. We illustrate the theoretical results on a noisy Hopf bifurcation normal form, on a noisy Van der Pol oscillator, and on a noisy bursting neuron model.

关键词： Oscillators Limit-cycles Noise measurement Biological system modeling Perturbation methods Bifurcation Stochastic processes

Building Ramps and Pathways to Data science in K-12, Minority-Serving Institutions, and Two-Year Colleges

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Scatterplot 2024年第1期1卷

作者： Rachel Saidi Helen Burn Ben Baumer Jason Black Debzani Deb Zarek Drozda a Math Statistics and Data Science Department Montgomery College – Rockville Campus Rockville MD USA b Mathematics Department Highline College Des Moines Washington Des Moines WA USA c Statistical and Data Sciences Department Smith College Northampton MA USA d School of Business and Interdisciplinary Center for Creativity and Innovation (ICCI) Florida A&M University Tallahassee FL USA e Computer Science Department Center for Applied Data Science (CADS) Winston-Salem State University Winston-Salem NC USA f Data Science 4 Everyone (DS4E) Program University of Chicago Chicago IL USA

Global demand for data scientists and analysts is on a trajectory of sustained growth, underscoring the need to expand enrollment of students in data science and data analytics courses and programs. This article explores diverse pathways to data science for various groups, including high school students, those in two-year colleges, and students in small colleges and minority-serving institutions. This article identifies opportunities and challenges associated with pursuing data science for students in these sectors, including factors such as building partnerships and awareness of the field and difficulties in establishing articulation agreements between institutions. The authors, representing various organizations participating in a panel discussion at the 2023 Data science Leadership Summit of the Academic Data science Alliance (ADSA), share insights into efforts to develop nontraditional pathways, serving as a resource for schools, colleges, and organizations contemplating creation of data science programs. The panelists’ combined experience spans work with a broad range of organizations including ADSA, American mathematics Association of Two-Year Colleges, American Statistical Association, Data science for Everyone, the Department of Education, HBCU Data science Consortium, Mathematical Association of America, National Academies of science, Engineering, and Medicine, HBCU Data science Consortium, National science Foundation, and StatPREP.

关键词： Data science pathways access K-12 minority-serving institution two-year college

Topological Data Analysis of Black Hole Images

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arXiv 2022年

作者： Christian, Pierre Chan, Chi-Kwan Hsu, Anthony Özel, Feryal Psaltis, Dimitrios Natarajan, Iniyan Physics Department Fairfield University 1073 N Benson Rd FairfieldCT06824 United States Department of Astronomy University of Arizona 933 North Cherry Avenue TucsonAZ85721 United States Data Science Institute University of Arizona 1230 N. Cherry Ave. TucsonAZ85721 United States Program in Applied Mathematics University of Arizona 617 N. Santa Rita TucsonAZ85721 United States Department of Computer Science University of Arizona 1040 4th St TucsonAZ85721 United States Wits Centre for Astrophysics University of the Witwatersrand 1 Jan Smuts Avenue Braamfontein Johannesburg2050 South Africa South African Radio Astronomy Observatory Observatory Cape Town7925 South Africa

Features such as photon rings, jets, or hot spots can leave particular topological signatures in a black hole image. As such, topological data analysis can be used to characterize images resulting from high resolution observations (synthetic or real) of black holes in the electromagnetic sector. We demonstrate that persistent homology allows for this characterization to be made automatically by counting the number of connected components and one-dimensional holes. Further, persistent homology also allows for the distance between connected components or diameter of holes to be extracted from the image. In order to apply persistent homology on synthetic black hole images, we also introduce metronization, a new algorithm to prepare black hole images into a form that is suitable for topological analysis. Copyright © 2022, The Authors. All rights reserved.

关键词： Black holes

Classification of datasets with imputed missing values: does imputation quality matter?

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arXiv 2022年

作者： Shadbahr, Tolou Roberts, Michael Stanczuk, Jan Gilbey, Julian Teare, Philip Dittmer, Sören Thorpe, Matthew Torné, Ramon Viñas Sala, Evis Lió, Pietro Patel, Mishal Rudd, James H.F. Mirtti, Tuomas Rannikko, Antti Sakari Aston, John A.D. Tang, Jing Schönlieb, Carola-Bibiane Selby, Ian Breger, Anna Weir-McCall, Jonathan R. Gkrania-Klotsas, Effrossyni Korhonen, Anna Jefferson, Emily Langs, Georg Yang, Guang Prosch, Helmut Preller, Jacobus Stanczuk, Jan Babar, Judith Sánchez, Lorena Escudero Wassin, Marcel Holzer, Markus Walton, Nicholas Research Program in Systems Oncology Faculty of Medicine University of Helsinki Helsinki Finland Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom Data Science & Artificial Intelligence AstraZeneca Cambridge United Kingdom Department of Mathematics University of Manchester Manchester United Kingdom Department of Computer Science and Technology University of Cambridge Cambridge United Kingdom Department of Radiology University of Cambridge Cambridge United Kingdom Clinical Pharmacology & Safety Sciences AstraZeneca Cambridge United Kingdom Department of Medicine University of Cambridge Cambridge United Kingdom Department of Pathology University of Helsinki Helsinki University Hospital Finland iCAN-Digital Precision Cancer Medicine Flagship Helsinki Finland Department of Urology University of Helsinki Helsinki University Hospital Helsinki Finland Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge United Kingdom ZeTeM University of Bremen Bremen Germany Faculty of Mathematics University of Vienna Austria Royal Papworth Hospital Cambridge Royal Papworth Hospital NHS Foundation Trust Cambridge United Kingdom Addenbrooke’s Hospital Cambridge University Hospitals NHS Trust Cambridge United Kingdom Language Technology Laboratory University of Cambridge Cambridge United Kingdom Population Health and Genomics School of Medicine University of Dundee Dundee United Kingdom Department of Biomedical Imaging and Image-guided Therapy Computational Imaging Research Lab Medical University of Vienna Vienna Austria National Heart and Lung Institute Imperial College London London United Kingdom Contextflow GmbH Vienna Austria Institute of Astronomy University of Cambridge Cambridge United Kingdom

Classifying samples in incomplete datasets is a common aim for machine learning practitioners, but is non-trivial. Missing data is found in most real-world datasets and these missing values are typically imputed using established methods, followed by classification of the now complete, imputed, samples. The focus of the machine learning researcher is then to optimise the downstream classification performance. In this study, we highlight that it is imperative to consider the quality of the imputation. We demonstrate how the commonly used measures for assessing quality are flawed and propose a new class of discrepancy scores which focus on how well the method recreates the overall distribution of the data. To conclude, we highlight the compromised interpretability of classifier models trained using poorly imputed data. All code and data used in this paper are also released publicly at [inserted upon publication]. © 2022, CC BY.

关键词： Classification (of information)

A meta-analysis of Boolean network models reveals design principles of gene regulatory networks

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arXiv 2020年

作者： Kadelka, Claus Butrie, Taras-Michael Hilton, Evan Kinseth, Jack Schmidt, Addison Serdarevic, Haris Department of Mathematics Iowa State University AmesIA50011 United States Department of Aerospace Engineering Iowa State University AmesIA50011 United States Department of Computer Science Iowa State University AmesIA50011 United States Bioinformatics and Computational Biology Program Iowa State University AmesIA50011 United States

Gene regulatory networks (GRNs) play a central role in cellular decision-making. Understanding their structure and how it impacts their dynamics constitutes thus a fundamental biological question. GRNs are frequently modeled as Boolean networks, which are intuitive, simple to describe, and can yield qualitative results even when data is sparse. We assembled the largest repository of expert-curated Boolean GRN models. A meta-analysis of this diverse set of models reveals several design principles. GRNs exhibit more canalization, redundancy and stable dynamics than expected. Moreover, they are enriched for certain recurring network motifs. This raises the important question why evolution favors these design mechanisms. Copyright © 2020, The Authors. All rights reserved.

关键词： Decision making