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Public Goods With Punishment and Abstaining in Finite and Infinite Populations

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Biological Theory 2008年第2期3卷 114-122页

作者： Hauert, Christoph Traulsen, Arne De Silva née Brandt, Hannelore Nowak, Martin A. Sigmund, Karl Program for Evolutionary Dynamics Department of Organismic and Evolutionary Biology and Department of Mathematics Harvard University Cambridge MA United States Department of Mathematics University of British Columbia Vancouver BC Canada Max-Planck-Institute for Evolutionary Biology Plön Germany Department of Finance Vienna University of Economics and Business Administration Vienna Austria Faculty of Mathematics University of Vienna Vienna Austria International Institute for Applied Systems Analysis Laxenburg Austria

The evolution and maintenance of cooperation in human and animal societies challenge various disciplines ranging from evolutionary biology to anthropology, social sciences, and economics. In social interactions, cooperators increase the welfare of the group at some cost to themselves whereas defectors attempt to free ride and neither provide benefits nor incur costs. The problem of cooperation becomes even more pronounced when increasing the number of interacting individuals. Punishment and voluntary participation have been identified as possible factors to support cooperation and prevent cheating. Typically, punishment behavior is unable to gain a foothold in a population, while volunteering alone can efficiently prevent deadlocks in states of mutual defection but is unable to stabilize cooperation. The combined effects of the two mechanisms have surprisingly different consequences in finite and infinite populations. Here we provide a detailed comparison of the two scenarios and demonstrate that driven by the inherent stochasticity of finite populations, the possibility to abstain from social interactions plays a pivotal role, which paves the way for the establishment of cooperation and punishment. © 2008, Konrad Lorenz Institute for Evolution and Cognition Research.

关键词： cooperation evolutionary game theory public goods games punishment social dilemmas voluntary participation

Thermodynamic analysis of mixed convective peristaltic propulsion of MoS2 nanomaterials in H2O-(CH2OH)2 hybrid base liquid with variable thermophysical characteristics

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ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik 2025年第5期105卷

作者： Akbar, Yasir Wang, Zhongling Huang, Shiping Alam, Mohammad Mahtab Iqbal, Jamshaid School of Interdisciplinary Science Beijing Institute of Technology Beijing China School of Materials Science and Engineering South China University of Technology Guangzhou China School of Civil Engineering and Transportation South China University of Technology Guangzhou China Department of Basic Medical Sciences College of Applied Medical Science King Khalid University Abha Saudi Arabia Department of Mathematics COMSATS University Islamabad Islamabad Pakistan

The present mathematical model endeavors to undertake a rigorous thermodynamic analysis concerning the peristaltic transport of a (Formula presented.) (50%–50%) nanofluid having variable thermophysical characteristics. The analysis takes into account important aspects, such as nanoparticles geometries, mixed convection, variable thermal conductivity, an induced magnetic field (IMF), a porous medium, and variable viscosity. The investigation also explores the role of entropy generation in the context of thermodynamics and heat transfers, aiming to detect and mitigate system inefficiencies and irreversibility. The novelty of the present study is to explore a thermodynamic analysis for the peristaltic transport of an incompressible nanofluid containing (Formula presented.) nanomaterials within a (Formula presented.) (50%–50%) hybrid base fluid flowing through a symmetric channel. To simplify the governing transport equations, the lubrication approach is employed, leading to a system of nonlinear equations that are numerically solved. Notably, the research underscores the potential to minimize entropy generation by increasing the thermal conductivity parameter. Furthermore, the study reveals that the Bejan number exhibits a declining trend as the permeability parameter reaches higher values. An intensification in the magnetic Reynolds number is found to enhance the magnitude of the axial-induced magnetic field along the channel wall, reflecting the impact of magneto-hydrodynamic interactions within the nanofluid. Lastly, the research shows that spherical-shaped nanoparticles result in the highest nanofluid flow, while platelet-shaped nanoparticles lead to the lowest flow, highlighting the significant influence of nanoparticle geometry on fluid dynamics in the nanofluid. © 2025 Wiley-VCH GmbH.

关键词： Heat convection

Epitaxial Growth Following Crystal Nucleation in Laser-Quenched Si Films on SiO2

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MRS Online Proceedings Library 2015年第1期1770卷 67-72页

作者： Wong, Vernon K. Chitu, A. M. Limanov, A. B. Im, James S. Program in Materials Science and Engineering Department of Applied Physics and Applied Mathematics Columbia University New York USA

We have investigated the solidified microstructure of nucleation-generated grains obtained via complete melting of Si films on SiO2 at high nucleation temperatures. This was achieved using a high-temperature-capable hot stage in conjunction with excimer laser irradiation. As predicted by the direct-growth model that considers (1) the evolution in the temperature of the solidifying interface and (2) the subsequent modes of growth (consisting of amorphous, defective, and epitaxial) as key factors, we were able to observe the appearance of “normal” grains that possess a single-crystal core area. These grains, which are in contrast to previously reported flower-shaped grains that fully make up the microstructure of the solidified films obtained via irradiation at lower preheating temperatures (and amongst which these “normal” grains emerge), indicate that epitaxial growth of nucleated crystals must have taken place within the grains. We discuss the implications of our findings regarding (1) the validity of the direct-growth model, (2) the nature of the heterogeneous nucleation mechanism, and (3) the alternative explanations and assumptions that have been previously employed in order to explain the microstructure of Si films obtained via nucleation and growth within the complete melting regime.

关键词： Si thin film nucleation & growth

Continuously heterogeneous hyper-objects in cryo-EM and 3-D movies of many temporal dimensions

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arXiv 2017年

作者： Lederman, Roy R. Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Mathematics Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States

Single particle cryo-electron microscopy (EM) is an increasingly popular method for determining the 3-D structure of macromolecules from noisy 2-D images of single macromolecules whose orientations and positions are random and unknown. One of the great opportunities in cryo-EM is to recover the structure of macromolecules in heterogeneous samples, where multiple types or multiple conformations are mixed together. Indeed, in recent years, many tools have been introduced for the analysis of multiple discrete classes of molecules mixed together in a cryo-EM experiment. However, many interesting structures have a continuum of conformations which do not fit discrete models nicely;the analysis of such continuously heterogeneous models has remained a more elusive goal. In this manuscript we propose to represent heterogeneous molecules and similar structures as higher dimensional objects. We generalize the basic operations used in many existing reconstruction algorithms, making our approach generic in the sense that, in principle, existing algorithms can be adapted to reconstruct those higher dimensional objects. As proof of concept, we present a prototype of a new algorithm which we use to solve simulated reconstruction problems. Copyright © 2017, The Authors. All rights reserved.

关键词： Inverse problems

KOLMOGOROV WIDTH DECAY AND POOR APPROXIMATORS IN MACHINE LEARNING: SHALLOW NEURAL NETWORKS, RANDOM FEATURE MODELS AND NEURAL TANGENT KERNELS

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arXiv 2020年

作者： Weinan, E. Wojtowytsch, Stephan Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544

We establish a scale separation of Kolmogorov width type between subspaces of a given Banach space under the condition that a sequence of linear maps converges much faster on one of the subspaces. The general technique is then applied to show that reproducing kernel Hilbert spaces are poor L2-approximators for the class of two-layer neural networks in high dimension, and that two-layer networks with small path norm are poor approximators for certain Lipschitz functions, also in the *** Codes 68T07, 41A30, 41A65, 46E15, 46E22 Copyright © 2020, The Authors. All rights reserved.

关键词： Banach spaces

Poisson stochastic master equation unravellings and the measurement problem: a quantum stochastic calculus perspective

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arXiv 2019年

作者： Keys, Dustin Wehr, Jan Program in Applied Mathematics University of Arizona TucsonAZ85721 United States Department of Mathematics and Program in Applied Mathematics University of Arizona TucsonAZ85721 United States

The paper studies a class of quantum stochastic differential equations, modeling an interaction of a system with its environment in the quantum noise approximation. The space representing quantum noise is the symmetric Fock space over L2 (+). Using the isomorphism of this space with the space of square-integrable functionals of the Poisson process, the equations can be represented as classical stochastic differential equations, driven by Poisson processes. This leads to a discontinuous dynamical state reduction which we compare to the Ghirardi-Rimini-Weber model. A purely quantum object, the norm process, is found which plays the role of an observer (in the sense of Everett [H. Everett III, Reviews of modern physics, 29.3, 454, (1957)]), encoding all events occurring in the system space. An algorithm introduced by Dalibard et al [J. Dalibard, Y. Castin, and K. Mølmer, Physical review letters, 68.5, 580 (1992)] to numerically solve quantum master equations is interpreted in the context of unravellings and the trajectories of expected values of system observables are calculated. © 2019, CC BY.

关键词： Poisson distribution

Threshold and decay properties of transient isolated turbulent band in plane Couette flow

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applied mathematics and Mechanics(English Edition) 2019年第10期40卷 1449-1456页

作者： Jianzhou LU Jianjun TAO Weitao ZHOU Xiangming XIONG CAPT-HEDPS SKLTCS Collaborative Innovation Center of IFSA Department of Mechanics and Engineering Science College of Engineering Peking University Beijing 100871 China The Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 U. S.A.

By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growth before the eventual relaminarization at moderate Reynolds numbers. The lower bound Reynolds number of the transient-growth regime is determined as 286. The width, length, and tilt angle of the iso- lated band structure are defined based on the disturbance kinetic energy in the mid-plane, and the geometric characteristics of the band can be described with a tilted rectangle. It is illustrated that before its eventual fragmentation, the isolated turbulent band decays in a style of longitudinal contraction, where the center, width, and tilt angle of the band keep almost constant but the band length contracts with a statistically constant velocity.

关键词： plane Couette flow (PCF) subcritical transition turbulent band

Coarse-grained spectral projection (CGSP): A deep learning-assisted approach to quantum unitary dynamics

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arXiv 2020年

作者： Xie, Pinchen Weinan, E. Program in Applied and Computational Mathematics Princeton University NJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We propose the coarse-grained spectral projection method (CGSP), a deep learning-assisted approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show CGSP can extract spectral components of many-body quantum states systematically with sophisticated neural network quantum ansatz. CGSP exploits fully the linear unitary nature of the quantum dynamics, and is potentially superior to other quantum Monte Carlo methods for ergodic dynamics. Preliminary numerical results on 1D XXZ models with periodic boundary condition are carried out to demonstrate the practicality of CGSP. Copyright © 2020, The Authors. All rights reserved.

关键词： Dynamics

A BRIDGE BETWEEN VECTOR BUNDLE THEORY AND NONLINEAR SPECTRAL THEORY

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arXiv 2022年

作者： López-Gómez, Julián Sampedro, Juan Carlos Institute of Interdisciplinary Mathematics Department of Mathematical Analysis and Applied Mathematics Complutense University of Madrid Madrid28040 Spain

This paper establishes some hidden connections between the theory of generalized algebraic multiplicities, the intersection index of algebraic varieties, and the notion of orientability of vector bundles. The novel approach adopted in it facilitates the definition of several invariants closely related to the first Stiefel-Whitney fundamental class through some path integration *** Codes 47H11, 58C40, 55R50 Copyright © 2022, The Authors. All rights reserved.

关键词： Algebra