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To Trust or Not to Trust: Evolutionary Dynamics of an Asymmetric N-player Trust Game

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arXiv 2023年

作者： Soo Lim, Ik. Masuda, Naoki School of Computing and Mathematical Sciences University of Greenwich LondonSE10 9LS United Kingdom Department of Mathematics and Computational and Data-Enabled Science and Engineering Program State University of New York Buffalo United States

Trusting others and reciprocating the received trust with trustworthy actions are fundaments of economic and social interactions. The trust game (TG) is widely used for studying trust and trustworthiness and entails a sequential interaction between two players, an investor and a trustee. It requires at least two strategies or options for an investor (e.g. to trust versus not to trust a trustee). According to the evolutionary game theory, the antisocial strategies (e.g. not to trust) evolve such that the investor and trustee end up with lower payoffs than those that they would get with the prosocial strategies (e.g. to trust). A generalisation of the TG to a multiplayer (i.e. more than two players) TG was recently proposed. However, its outcomes hinge upon two assumptions that various real situations may substantially deviate from: (i) investors are forced to trust trustees and (ii) investors can turn into trustees by imitation and vice versa. We propose an asymmetric multiplayer TG that allows investors not to trust and prohibits the imitation between players of different roles;instead, investors learn from other investors and the same for trustees. We show that the evolutionary game dynamics of the proposed TG qualitatively depends on the nonlinearity of the payoff function and the amount of incentives collected from and distributed to players through an institution. We also show that incentives given to trustees can be useful and sufficient to cost-effectively promote trust and trustworthiness among self-interested players. © 2023, CC BY.

关键词： Dynamics

N3 bias field correction explained as a Bayesian modeling method

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Lecture Notes in Computer Science (including subseries Lectu...

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2014年 8677卷 1-12页

作者： Larsen, Christian Thode Eugenio Iglesias, J. Van Leemput, Koen Department of Applied Mathematics and Computer Science Technical University of Denmark Denmark Martinos Center for Biomedical Imaging MGH Harvard Medical School United States Basque Center on Cognition Brain and Language Spain Departments of Information and Computer Science and of Biomedical Engineering and Computational Science Aalto University Finland

Although N3 is perhaps the most widely used method for MRI bias field correction, its underlying mechanism is in fact not well understood. Specifically, the method relies on a relatively heuristic recipe of alternating iterative steps that does not optimize any particular objective function. In this paper we explain the successful bias field correction properties of N3 by showing that it implicitly uses the same generative models and computational strategies as expectation maximization (EM) based bias field correction *** demonstrate experimentally that purely EM-based methods are capable of producing bias field correction results comparable to those of N3 in less computation time. © Springer International Publishing Switzerland 2014.

关键词： Bayesian networks

THE CAUCHY PROBLEM FOR BOLTZMANN BI-LINEAR SYSTEMS: THE MIXING OF MONATOMIC AND POLYATOMIC GASES

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arXiv 2023年

作者： Alonso, Ricardo J. Gamba, Irene M. Pavić-Čolić, Milana Texas A&M Division of Arts and Sciences Education City Doha Qatar AustinTX78712-1229 United States Department of Mathematics and Informatics Faculty of Sciences University of Novi Sad Trg Dositeja Obradovića 4 Novi Sad21000 Serbia Applied and Computational Mathematics RWTH Aachen University Schinkelstr. 2 Aachen52062 Germany

From a unified vision of vector valued solutions in weighted Banach spaces, this manuscript establishes the existence and uniqueness for space homogeneous Boltzmann bi-linear systems with conservative collisional forms arising in complex gas dynamical structures. This broader vision is directly applied to dilute multi-component gas mixtures composed of both monatomic and polyatomic gases. Such models can be viewed as extensions of scalar Boltzmann binary elastic flows, as much as monatomic gas mixtures with disparate masses and single polyatomic gases, providing a unify approach for vector valued solutions in weighted vector Banach spaces. Novel aspects of this work include developing the extension of a general ODE theory in vector valued weighted Banach spaces, precise lower bounds for the collision frequency in terms of the weighted Banach norm, energy identities and the consequently angular or compact manifold averaging lemmas which provide coerciveness resulting into global in time stability, a new combinatorics estimate for p-binomial forms producing sharper estimates for the k-moments of bi-linear collisional forms. These techniques enable the Cauchy problem improvement that resolves the model with initial data corresponding to strictly positive and bounded initial vector valued mass and total energy, in addition to only 2+ moment determined by the hard potential rates discrepancy, a result comparable in generality to the classical Cauchy theory of the scalar homogeneous Boltzmann *** Codes 35Q20, 76P05, 82C40 Copyright © 2023, The Authors. All rights reserved.

关键词： Gas mixtures

Elastohydrodynamic study of actin filaments using fluorescence microscopy

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Physical Review E 1997年第2期56卷 R1330(R)-R1330(R)页

作者： D. Riveline C. H. Wiggins R. E. Goldstein A. Ott Laboratoire PhysicoChimie Curie Section de Recherche Institut Curie 11 rue Pierre et Marie Curie 75231 Paris Cedex 05 France Department of Physics Joseph Henry Laboratories Princeton University Princeton New Jersey 08544 Department of Physics and Program in Applied Mathematics University of Arizona Tucson Arizona 85721

We probed the bending of actin subject to external forcing and viscous drag. Single actin filaments were moved perpendicular to their long axis in an oscillatory way by means of an optically tweezed latex bead attached to one end of the filaments. Shapes of these polymers were observed by epifluorescence microscopy. They were found to be in agreement with predictions of semiflexible polymer theory and slender-body hydrodynamics. A persistence length of 7.4±0.2 μm could be extracted.

关键词： Elastohydrodynamics

Electron–hydrogen-atom elastic and inelastic scattering with screened Coulomb interaction around the n=2 excitation threshold

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Physical Review A 2010年第3期81卷 032707-032707页

作者： Song Bin Zhang Jian Guo Wang R. K. Janev Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics University of Science and Technology of China Hefei 230026 People’s Republic of China Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing 100088 People’s Republic of China Macedonian Academy of Sciences and Arts P. O. Box 428 1000 Skopje Macedonia

The effects of Coulomb interaction screening on electron–hydrogen-atom elastic and excitation scattering around the n=2 threshold have been investigated by using the R-matrix method with pseudostates. The elastic and excitation collision strengths show dramatic changes when the interaction screening length D varies from ∞ to 3.8 a.u., as a result of the convergence of 1,3S Feshbach resonances to the varying 2s threshold and of the transformation of 1,3P and 1D Feshbach resonances into shape-type resonances when they pass across the 2s and 2p threshold at certain critical value of D, respectively [S. B. Zhang et al., Phys. Rev. Lett. 104, 023203 (2010)]. The resonance parameters for a large number of D in the range D=∞–3.8 a.u. are presented. It is observed that the 1,3P and 1D resonance contributions to the elastic and excitation collision strengths decrease rapidly with decreasing D after the resonance passes the critical D value. The contribution of a 1Se Feshbach resonance to the elastic or excitation collision strength changes into a cusp after the resonance merges into its parent 2s state and immerses into the background with the further decrease of D.

关键词： Excited states

Immunological-based Approach for Accurate Fitting of 3D Noisy Data Points with Bézier Surfaces

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Procedia Computer Science 2013年 18卷 50-59页

作者： Akemi Gálvez Andrés Iglesias Andreina Avila Department of Applied Mathematics and Computational Sciences University of Cantabria E.T.S.I. Caminos Canales y Puertos Avda. de los Castros s/n E-39005 Santander Spain Department of Information Sciences Faculty of Sciences Toho University 2-2-1 Miyama 274-8510 Funabashi Japan

Free-form parametric surfaces are common tools nowadays in many applied fields, such as Computer-Aided Design & Manu- facturing (CAD/CAM), virtual reality, medical imaging, and many others. A typical problem in this setting is to fit surfaces to 3D noisy data points obtained through either laser scanning or other digitizing methods, so that the real data from a physical object are transformed back into a fully usable digital model. In this context, the present paper describes an immunological- based approach to perform this process accurately by using the classical free-form Bézier surfaces. Our method applies a powerful bio-inspired paradigm called Artificial Immune Systems (AIS), which is receiving increasing attention from the sci- entific community during the last few years because of its appealing computational features. The AIS can be understood as a computational methodology based upon metaphors of the biological immune system of humans and other mammals. As such, there is not one but several AIS algorithms. In this chapter we focus on the clonal selection algorithm (CSA), which explicitly takes into account the affinity maturation of the immune response. The paper describes how the CSA algorithm can be effectively applied to the accurate fitting of 3D noisy data points with Bézier surfaces. To this aim, the problem to be solved as well as the main steps of our solving method are described in detail. Some simple yet illustrative examples show the good performance of our approach. Our method is conceptually simple to understand, easy to implement, and very general, since no assumption is made on the set of data points or on the underlying function beyond its continuity. As a consequence, it can be successfully applied even under challenging situations, such as the absence of any kind of information regarding the underlying function of data.

关键词： Data fitting Bézier surfaces immunological approach artificial immune systems reverse engineering

Exploiting self-organized criticality in strongly stratified turbulence

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arXiv 2021年

作者： Chini, Gregory P. Michel, Guillaume Julien, Keith Rocha, Cesar B. Caulfield, Colm-Cille P. Program in Integrated Applied Mathematics University of New Hampshire DurhamNH03824 United States Department of Mechanical Engineering University of New Hampshire DurhamNH03824 United States Institut Jean Le Rond d’Alembert Sorbonne Université CNRS UMR 7190 ParisF-75005 France Department of Applied Mathematics University of Colorado BoulderCO80309 United States Department of Marine Sciences University of Connecticut StorrsCT06269 United States BP Institute Department of Applied Mathematics & Theoretical Physics Cambridge University CambridgeCB3 0WA United Kingdom

A multiscale reduced description of turbulent free shear flows in the presence of strong stabilizing density stratification is derived via asymptotic analysis of the Boussinesq equations in the simultaneous limits of small Froude and large Reynolds numbers. The analysis explicitly recognizes the occurrence of dynamics on disparate spatiotemporal scales, yielding simplified partial differential equations governing the coupled evolution of slow large-scale hydrostatic flows and fast small-scale isotropic instabilities and internal waves. The dynamics captured by the coupled reduced equations is illustrated in the context of two-dimensional strongly stratified Kolmogorov flow. A noteworthy feature of the reduced model is that the fluctuations are constrained to satisfy quasilinear (QL) dynamics about the comparably slowly-varying large-scale fields. Crucially, this QL reduction is not invoked as an ad hoc closure approximation, but rather is derived in a physically relevant and mathematically consistent distinguished limit. Further analysis of the resulting slow-fast QL system shows how the amplitude of the fast stratified-shear instabilities is slaved to the slowly-evolving mean fields to ensure the marginal stability of the latter. Physically, this marginal stability condition appears to be compatible with recent evidence of self-organized criticality in both observations and simulations of stratified turbulence. Algorithmically, the slaving of the fluctuation fields enables numerical simulations to be time-evolved strictly on the slow time scale of the hydrostatic flow. The reduced equations thus provide a solid mathematical foundation for future studies of three-dimensional strongly stratified turbulence in extreme parameter regimes of geophysical relevance and suggest avenues for new sub-grid-scale parameterizations. Copyright © 2021, The Authors. All rights reserved.

关键词： Asymptotic analysis

Optimal actuator design via Brunovsky's normal form

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arXiv 2021年

作者： Geshkovski, Borjan Zuazua, Enrique Departamento de Matemáticas Universidad Autónoma de Madrid Madrid28049 Spain Computational Mathematics Fundación Deusto Av. de las Universidades Bilbao24 48007 Spain Applied Analysis Alexander von Humboldt-Professorship Department of Mathematics Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen91058 Germany

In this paper, by using the Brunovsky normal form, we provide a reformulation of the problem consisting in finding the actuator design which minimizes the controllability cost for finite-dimensional linear systems with scalar controls. Such systems may be seen as spatially discretized linear partial differential equations with lumped controls. The change of coordinates induced by Brunovsky's normal form allows us to remove the restriction of having to work with diagonalizable system dynamics, and does not entail a randomization procedure as done in past literature on diffusion equations or waves. Instead, the optimization problem reduces to a minimization of the norm of the inverse of a change of basis matrix, and allows for an easy deduction of existence of solutions, and for a clearer picture of some of the problem's intrinsic symmetries. Numerical experiments help to visualize these artifacts, indicate further open problems, and also show a possible obstruction of using gradient-based algorithms - this is alleviated by using an evolutionary algorithm. Copyright © 2021, The Authors. All rights reserved.

关键词： Inverse problems

Observation of sequential spin flips in quantum rings

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Physical Review B 2011年第16期84卷 165320-165320页

作者： E. Räsänen A. Mühle M. Aichinger R. J. Haug Nanoscience Center Department of Physics University of Jyväskylä FI-40014 Jyväskylä Finland Institut für Festkörperphysik Leibniz Universität Hannover Appelstr. 2 D-30167 Hannover Radon Institute for Computational and Applied Mathematics (RICAM) A-4040 Linz Austria

We observe strong signatures of spin flips in quantum rings exposed to external magnetic fields in the Coulomb blockade regime. The signatures appear as a pattern of lines corresponding to local reduction of conductance, and they cover a large range of magnetic fields and number of electrons. The sequence of lines, as well as other features in the conductance, can be captured by many-electron calculations within density-functional theory. The calculations show that most lines in the pattern correspond to sequential spin flips between filling factors 2 and 1. We believe that the ability to probe individual spin flips provides an important step toward precise spin control in quantum ring devices.

关键词： MAGNETIC fields ELECTRONS DENSITY functionals COULOMB functions PHYSICS