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Crystallography of honeycomb formation under geometric frustration

Proceedings of the National Academy of sciences of the United States of America 2022年第48期119卷 e2205043119-e2205043119页

作者： Fard, Golnar Gharooni Zhang, Daisy Jiménez, Francisco López Peleg, Orit Department of Computer Science University of Colorado Boulder 80309 CO United States Department of Computer Science Princeton University 08544 NJ United States Ann and H.J. Smead Department of Aerospace Engineering Sciences University of Colorado Boulder 80309 CO United States Department of Physics University of Colorado Boulder 80309 CO United States Department of Applied Math University of Colorado Boulder 80309 CO United States Department of Ecology and Evolutionary Biology University of Colorado Boulder 80309 CO United States BioFrontiers Institute University of Colorado Boulder 80309 CO United States Santa Fe Institute Santa Fe 87501 NM United States

As honeybees build their nests in preexisting tree cavities, they must deal with the presence of geometric constraints, resulting in nonregular hexagons and topological defects in the comb. In this work, we study how bees adapt to their environment in order to regulate the comb structure. Specifically, we identify the irregularities in honeycomb structure in the presence of various geometric frustrations. We 3D-print experimental frames with a variety of constraints imposed on the imprinted foundations. The combs constructed by the bees show clear evidence of recurring patterns in response to specific geometric frustrations on these starter frames. Furthermore, using an experimental-modeling framework, we demonstrate that these patterns can be successfully modeled and replicated through a simulated annealing process, in which the minimized potential is a variation of the Lennard-Jones potential that considers only first-neighbor interactions according to a Delaunay triangulation. Our simulation results not only confirm the connection between honeycomb structures and other crystal systems such as graphene, but also show that irregularities in the honeycomb structure can be explained as the result of analogous interactions between cells and their immediate surroundings, leading to emergent global order. Additionally, our computational model can be used as a first step to describe specific strategies that bees use to effectively solve geometric mismatches while minimizing cost of comb building. Copyright © 2022 the Author(s). Published by PNAS.

关键词： behavioral assays collective behavior honey bees honeycomb math.matical modelling

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Graph Fourier MMD for Signals on Graphs

Graph Fourier MMD for Signals on Graphs

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International Conference on Sampling Theory and Applications (SampTA)

作者： Samuel Leone Aarthi Venkat Guillaume Huguet Alexander Tong Guy Wolf Smita Krishnaswamy Applied Math Program New Haven Connecticut Computational Biology & Bioinformatics Program Yale University New Haven Connecticut Dept. of Math. & Stat Mila - Quebec AI Institute Université de Montréal Montreal Canada Dept. of Comp. Sci. & Oper. Res. Mila-Quebec AI Institute Université de Montréal Montreal Canada Department of Computer Science Department of Genetics Yale University New Haven Connecticut

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little attention has been given to computing such distances for distributions on graphs. However, there has been a marked increase in data that either lies on graph (such as protein interaction networks) or can be modeled as a graph (single cell data), particularly in the biomedical sciences. Thus, it becomes important to find ways to compare signals defined on such graphs. Here, we propose Graph Fourier MMD (GFMMD), a novel distance between distributions and signals on graphs. GFMMD is defined via an optimal witness function that is both smooth on the graph and maximizes the difference in expectation between the pair of distributions on the graph. We find an analytical solution to this optimization problem as well as an embedding of distributions that results from this method. We also prove several properties of this method including scale invariance and applicability to disconnected graphs. We showcase it on graph benchmark datasets as well on single cell RNA-sequencing data analysis. In the latter, we use the GFMMD-based gene embeddings to find meaningful gene clusters. We also propose a novel type of score for gene selection called gene localization score which helps select genes for cellular state space characterization.

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Fairness and Bias in Robot Learning

arXiv

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arXiv 2022年

作者： Londoño, Laura Hurtado, Juana Valeria Hertz, Nora Kellmeyer, Philipp Voeneky, Silja Valada, Abhinav Department of Computer Science University of Freiburg Germany Dep. International Law and Ethics of Law University of Freiburg Germany School of Business Informatics and Math. University of Mannheim Germany Department for Neurosurgery University Medical Center Freiburg Germany

Machine learning has significantly enhanced the abilities of robots, enabling them to perform a wide range of tasks in human environments and adapt to our uncertain real world. Recent works in various machine learning domains have highlighted the importance of accounting for fairness to ensure that these algorithms do not reproduce human biases and consequently lead to discriminatory outcomes. With robot learning systems increasingly performing more and more tasks in our everyday lives, it is crucial to understand the influence of such biases to prevent unintended behavior toward certain groups of people. In this work, we present the first survey on fairness in robot learning from an interdisciplinary perspective spanning technical, ethical, and legal challenges. We propose a taxonomy for sources of bias and the resulting types of discrimination due to them. Using examples from different robot learning domains, we examine scenarios of unfair outcomes and strategies to mitigate them. We present early advances in the field by covering different fairness definitions, ethical and legal considerations, and methods for fair robot learning. With this work, we aim to pave the road for groundbreaking developments in fair robot learning. Copyright © 2022, The Authors. All rights reserved.

关键词： Intelligent robots

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Topological Entropy and Sequence Entropy for Hom Tree-Shifts on Unexpandable Trees

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Qualitative Theory of Dynamical Systems 2024年第3期23卷 108-108页

作者： Ban, Jung-Chao Chang, Chih-Hung Hu, Wen-Guei Lai, Guan-Yu Wu, Yu-Liang Department of Mathematical Sciences National Chengchi University Taipei 11605 Taiwan Math. Division National Center for Theoretical Science National Taiwan University Taipei 10617 Taiwan Department of Applied Mathematics National University of Kaohsiung Kaohsiung 81148 Taiwan College of Mathematics Sichuan University Chengdu 610064 China Department of Mathematical Sciences University of Oulu Oulu 90014 Finland

This article explores the topological entropy and topological sequence entropy of hom tree-shifts on unexpandable trees. Regarding topological entropy, we establish that the entropy, denoted as h(T_X) on an unexpandable tree, equals the entropy h(X) of the base shift X when X is a subshift satisfying the almost specification property. Additionally, we derive some fundamental properties such as entropy approximation and the denseness of entropy for subsystems. Concerning topological sequence entropy, we show that the set of sequence entropies of hom tree-shifts with a base shift is generated by an irreducible matrix A, forming a subset of logN. Precisely, these entropies correspond to the logarithms of the largest cardinalities of the periodic classes of A. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

关键词： Entropy Sequence entropy Tree-shift

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A graph-based convolutional neural network stock price prediction with leading indicators

A graph-based convolutional neural network stock price predi...

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作者： Wu, Jimmy Ming-Tai Li, Zhongcui Srivastava, Gautam Tasi, Meng-Hsiun Lin, Jerry Chun-Wei College of Computer Science and Engineering Shandong University of Science and Technology Shandong China Department of Math and Computer Science Brandon University Brandon Canada Research Centre for Interneural Computing China Medical University Taichung Taiwan Department of Management Information Systems National Chung Hsing University Taichung Taiwan Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Sciences Bergen Norway

The stock market is a capitalistic haven where the issued shares are transferred, traded, and circulated. It bases stock prices on the issue market, however, the structure and trading activities of the stock market are much more complicated than the issue market itself. Therefore, making an accurate prediction becomes an intricate as well as highly difficult task. On the other hand, because of the potential benefits of stock prediction, it attracts generation after generation of scholars as well as investors to continuously develop various prediction methods from different perspectives, a myriad of theories, a multitude of investment strategies, and different practical experiences. In this article, aiming at the task of time series (financial) feature extraction and prediction of price movements, a new convolutional novel neural network that can be called a framework to improve the prediction accuracy of stock trading is proposed. The method that is proposed is called SSACNN, a short form of stock sequence array convolutional neural network. SSACNN collects data including historical data of prices and its leading indicators (options/futures) for a stock to take an array as the input graph of the convolutional neural network framework. In our experimental results, five Taiwanese and American stocks were used as a benchmark to compare with the previous algorithms and proposed algorithm, the motion prediction performance of SSACNN has been improved significantly and proved that it has the potential to be applied in the real financial market. © 2020 John Wiley & Sons Ltd

关键词： Forecasting

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Semi-Implicit Lagrangian Voronoi Approximation for Compressible Viscous Fluid Flows

arXiv

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arXiv 2024年

作者： Kincl, Ondřej Peshkov, Ilya Boscheri, Walter Laboratory of Applied Mathematics DICAM University of Trento Trento38123 Italy 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

This paper contributes to the recent investigations of Lagrangian methods based on Voronoi meshes. The aim is to design a new conservative numerical scheme that can simulate complex flows and multi-phase problems with more accuracy than SPH (Smoothed Particle Hydrodynamics) methods but, unlike diffuse interface models on fixed grid topology, does not suffer from the deteriorating quality of the computational grid. The numerical solution is stored at particles, which move with the fluid velocity and also play the role of the generators of the computational mesh, that is efficiently re-constructed at each time step. The main novelty stems from combining a Lagrangian Voronoi scheme with a semi-implicit integrator for compressible flows. This allows to model low-Mach number flows without the extremely stringent stability constraint on the time step and with the correct scaling of numerical viscosity. The implicit linear system for the unknown pressure is obtained by splitting the reversible from the irreversible (viscous) part of the dynamics, and then using entropy conservation of the reversible sub-system to derive an auxiliary elliptic equation. The method, called SILVA (Semi-Implicit Lagrangian Voronoi Approximation), is validated in a variety of test cases that feature diverse Mach numbers, shocks and multi-phase flows. Copyright © 2024, The Authors. All rights reserved.

关键词： Topology

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On classification of 2-dimensional evolution algebras and its applications 5

On classification of 2-dimensional evolution algebras and it...

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5th International Conference on math.matical Applications in Engineering 2019

作者： Ahmed, H. Bekbaev, U. Rakhimov, I. Department of Math. Faculty of Science UPM Selangor Malaysia Depart. of Math. Faculty of Science Taiz University Taiz Yemen Department of Mathematical and Natural Sciences TTPU Uzbekistan Department of Science in Engineering Faculty of Engineering IIUM Malaysia Department of Mathematics Faculty of Computer and Mathematical Sciences UiTM Malaysia V.I.Romanovskiy Institute of Mathematics Uzbekistan Academy of Science Uzbekistan

In the paper we give a complete classification of 2-dimensional evolution algebras over algebraically closed fields, we compare the list of representatives of the isomorphism classes with that of obtained earlier by the other authors. Also we describe their groups of automorphisms and derivation algebras. © Published under licence by IOP Publishing Ltd.

关键词： Algebra

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SCORE: A Second-Order Conic Initialization for Range-Aided SLAM

SCORE: A Second-Order Conic Initialization for Range-Aided S...

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IEEE International Conference on Robotics and Automation (ICRA)

作者： Alan Papalia Joseph Morales Kevin J. Doherty David M. Rosen John J. Leonard Computer Science and Artificial Intelligence Laboratory (CSAIL) Massachusetts Institute of Technology (MIT) Cambridge MA USA Department of Applied Ocean Physics & Engineering Woods Hole Oceanographic Institution Woods Hole MA USA Department of Electrical & Computer Engineering Northeastern University Boston MA USA Department of Math Northeastern University Boston MA USA

We present a novel initialization technique for the range-aided simultaneous localization and mapping (RA-SLAM) problem. In RA-SLAM we consider measurements of point-to-point distances in addition to measurements of rigid transformations to landmark or pose variables. Standard formulations of RA-SLAM approach the problem as non-convex optimization, which requires a good initialization to obtain quality results. The initialization technique proposed here relaxes the RA-SLAM problem to a convex problem which is then solved to determine an initialization for the original, non-convex problem. The relaxation is a second-order cone program (SOCP), which is derived from a quadratically constrained quadratic program (QCQP) formulation of the RA-SLAM problem. As a SOCP, the method is highly scalable. We name this relaxation Second-order COnic RElaxation for RA-SLAM (SCORE). To our knowledge, this work represents the first convex relaxation for RA-SLAM. We present real-world and simulated experiments which show SCORE initialization permits the efficient recovery of quality solutions for a variety of challenging single- and multi-robot RA-SLAM problems with thousands of poses and range measurements.

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Threshold Decision-Making Dynamics Adaptive to Physical Constraints and Changing Environment

arXiv

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arXiv 2023年

作者： Amorim, Giovanna Santos, María Park, Shinkyu Franci, Alessio Leonard, Naomi Ehrich The Dept. of Mechanical and Aerospace Engineering Princeton Univ. PrincetonNJ08544 United States Computer Electrical and Math. Science and Eng. Div. Thuwal23955-6900 Saudi Arabia The Department of Electrical Engineering and Computer Science University of Liege 10 Allée de la Découverte Liège4000 Belgium The WEL Research Institute Wavre Belgium

We propose a threshold decision-making framework for controlling the physical dynamics of an agent switching between two spatial tasks. Our framework couples a nonlinear opinion dynamics model that represents the evolution of an agent’s preference for a particular task with the physical dynamics of the agent. We prove the bifurcation that governs the behavior of the coupled dynamics. We show by means of the bifurcation behavior how the coupled dynamics are adaptive to the physical constraints of the agent. We also show how the bifurcation can be modulated to allow the agent to switch tasks based on thresholds adaptive to environmental conditions. We illustrate the benefits of the approach through a multi-robot task allocation application for trash collection. Copyright © 2023, The Authors. All rights reserved.

关键词： Dynamics

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Radial kinks in a Schwarzschild-like geometry

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Physical Review D 2024年第12期110卷 125025-125025页

作者： Jean-Guy Caputo Tomasz Dobrowolski Jacek Gatlik Panayotis G. Kevrekidis Laboratoire de Mathématiques INSA de Rouen Avenue de l’Université 76801 Saint-Etienne du Rouvray France Department of Computer Physics and Quantum Computing University of the National Education Commission in Krakow Podchora¸żych 2 30-084 Cracow Poland AGH University of Krakow Faculty of Physics and Applied Computer Science 30-059 Krakow Poland Department of Mathematics and Statistics University of Massachusetts Amherst Massachusetts 01003-4515 USA

We study the propagation of a domain wall (kink) of the ϕ4 model in a radially symmetric environment defined by a gravity source. This source introduces a Schwarzschild-like geometry. We introduce an effective model that accurately describes the dynamics of the kink center. This description works well even outside the perturbation region, i.e., even for large masses of the gravitating object. We observed that such a spherical domain wall surrounding a star-type object inevitably “collapses,” i.e., shrinks in radius toward the origin and offer an understanding of the latter phenomenology. The relevant analysis is presented for a circular domain wall and a spherical one.

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