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44th Annual Allerton Conference on Communication, Control, and Computing 2006

作者： Winkler, Stephan Tatikonda, Sekhar Program in Applied Mathematics Yale University CT06520 United States Department of Electrical Engineering Yale University CT06520 United States

ISBN: (纸本)9781604237924

We survey conditions for rapid mixing of certain Markov chains, called Gibbs samplers, and uniqueness of certain probability measures with prescribed finite dimensional conditional distributions, called Gibbs measures. By Tatikonda and Jordan's [1] sufficiency result, these criteria translate into conditions for convergence of the Sum-Product algorithm. The basic idea, which goes back to Dobrushin [2], is to show that the transition kernels (in the Gibbs sampler case) or the prescribed conditional distributions (in the Gibbs measure case) act as contractions on spaces of functions or measures, provided they are weakly influenced by neighboring sites. The contributions of this paper are as follows: We compare various notions of influence, unifying notation and terminology currently scattered across a large body of literature. We survey, generalize and extend existing proof techniques which fall in three broad categories: analytic arguments, coupling arguments, and arguments using path coupling. In particular, we extend all arguments from single sites to finite blocks and from total variation to Wasserstein distance;we introduce new matrix methods;we answer an open question by Weitz [3];and we provide evidence to support the superiority of path coupling, addressing a question raised by Sokal [4] regarding the dual relationship of analytic and coupling techniques.

关键词： Surveys

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Spike-time reliability of layered neural oscillator networks

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AIP Conference Proceedings 2013年第1期1510卷 207-209页

作者： K. K. Lin E. Shea-Brown L.-S. Young Department of Mathematics and Program in Applied Mathematics the University of Arizona USA Department of Applied Mathematics the University of Washington USA Courant Institute of Mathematical Sciences New York University USA

If a network of neurons is repeatedly driven by the same fluctuating signal, will it give the same response each time? If so, the network is said to be reliable. Reliability is of interest in computational neuroscience because the degree to which a network is reliable constrains its ability to encode information in precise temporal patterns of spikes. This note outlines how the question of reliability may be fruitfully formulated and studied within the framework of random dynamical systems theory. A specific network architecture, that of a single-layer network, is examined. For the type of single-neuron dynamics and coupling considered here, single-layer networks are found to be very reliable. A qualitative explanation is proposed for this phenomenon.

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Adaptive governance in the water-energy-food-ecosystem nexus for sustainable community sanitation

World Development Sustainability

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World Development Sustainability 2025年 6卷

作者： Sofiyah, Evi Siti Sianipar, Imelda Masni Juniaty Rahman, Ari Caesarina, Naila Putri Suhardono, Sapta Suryawan, I Wayan Koko Lee, Chun-Hung Department of Environmental Engineering Faculty of Infrastructure Planning Universitas Pertamina Jalan Sinabung II Terusan Simprug Jakarta 12220 Indonesia Department of International Relations Faculty of Social Science and Political Science Universitas Kristen Indonesia Jakarta 13630 Indonesia Environmental Sciences Study Program Faculty of Mathematics and Natural Sciences Universitas Sebelas Maret Surakarta 57126 Indonesia Department of Natural Resources and Environmental Studies College of Environmental Studies and Oceanography National Dong Hwa University Hualien 97401 Taiwan Center for Environmental Solution (CVISION) Universitas Pertamina Jalan Sinabung II Terusan Simprug Jakarta 12220 Indonesia Center for Interdisciplinary Research on Ecology and Sustainability College of Environmental Studies and Oceanography National Dong Hwa University Hualien 97401 Taiwan

As the intensity of global environmental challenges increases, so does the need to understand and strengthen the resilience of interconnected systems. This research underscores the crucial role of adaptive governance in navigating the complexities of the Water-Energy-Food-Ecosystem nexus, particularly under the pressures of changing climatic conditions. The study conducts an in-depth analysis of adaptive capacities by identifying critical components such as assets, flexibility, organization, learning, and agency as fundamental elements of adaptive governance in sanitation practices. Data were collected through structured questionnaires and analyzed using binary probit and logit models to examine how these attributes influence community engagement in sanitation. Descriptive analysis was also used to summarize respondent characteristics and attribute distributions. © 2025 The Author(s)

关键词： Adaptive governance Community engagement Environmental sustainability Sanitation resilience Water-energy-food-ecosystem nexus

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Optimum classical beam-position sensing

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Physical Review applied 2024年第4期22卷 L041004页

作者： Wenhua He Christos N. Gagatsos Dalziel J. Wilson Saikat Guha Wyant College of Optical Sciences Department of Electrical and Computer Engineering Program in Applied Mathematics

Beam-displacement measurements are widely used in optical sensing and communications; however, their performance is affected by numerous intrinsic and extrinsic factors, including beam profile, propagation loss, and receiver architecture. Here we present a framework for designing a classically optimal beam-displacement transceiver, using quantum estimation theory. We consider the canonical task of estimating the position of a diffraction-limited laser beam after passing through an apertured volume characterized by Fresnel-number product DF. As a rule of thumb, higher-order Gaussian modes provide more information about beam displacement, but are more sensitive to loss. Applying quantum Fisher information, we design mode combinations that optimally leverage this trade-off, and show that a greater than tenfold improvement in precision is possible, relative to the fundamental mode, for a practically relevant DF=100. We also show that this improvement is realizable with a variety of practical receiver architectures. Our findings extend previous works on lossless transceivers, may have immediate impact on applications, such as atomic force microscopy and near-field optical communication, and pave the way towards globally optimal transceivers using nonclassical laser fields.

关键词： Classical optics Metrology Quantum Fisher information Quantum optics Quantum parameter estimation Devices Wireless communication networks Atomic force microscopy

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Wigner non-negative states that verify the Wigner entropy conjecture

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Physical Review A 2024年第1期110卷 012228-012228页

作者： Qipeng Qian Christos N. Gagatsos Program in Applied Mathematics The Department of Electrical and Computer Engineering The Wyant College of Optical Sciences The

We present further progress, in the form of analytical results, on the Wigner entropy conjecture set forth by Van Herstraeten and Cerf [Phys. Rev. A 104, 042211 (2021)] and Hertz et al. [J. Phys. A: Math. Theor. 50, 385301 (2017)]. Said conjecture asserts that the differential entropy defined for non-negative, yet physical, Wigner functions is minimized by pure Gaussian states while the minimum entropy is equal to 1+lnπ. We prove this conjecture for the qubits formed by Fock states |0〉 and |1〉 that correspond to non-negative Wigner functions. In particular, we derive an explicit form of the Wigner entropy for those states lying on the boundary of the set of Wigner non-negative qubits. We then consider general mixed states and derive a sufficient condition for the conjecture's validity. Lastly, we elaborate on the states which are in accordance with our condition.

关键词： Quantum foundations Quantum information theory

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Variational boundary conditions for molecular dynamics simulations of crystalline solids at finite temperature: Treatment of the thermal bath

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Physical Review B 2007年第10期76卷 104107-104107页

作者： Xiantao Li Weinan E Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

This paper presents a systematic approach for finding efficient boundary conditions for molecular dynamics simulations of crystalline solids. These boundary conditions effectively eliminate phonon reflection at the boundary and at the same time allow the thermal energy from the bath to be introduced to the system. Our starting point is the Mori-Zwanzig formalism [R. Zwanzig, J. Chem. Phys. 32, 1173 (1960); in Systems Far from Equilibrium, edited by L. Garrido (Interscience, New York, 1980); H. Mori, Prog. Theor. Phys. 33, 423 (1965)] for eliminating the thermal bath, but we take the crucial next step that goes beyond this formalism in order to obtain memory kernels that decay faster. An equivalent variational formulation allows us to find the optimal approximate boundary conditions, after specifying the spatial-temporal domain of dependence for the positions of the boundary atoms. Application to a one-dimensional chain, a two-dimensional Lennard-Jones system, and a three-dimensional model of α-iron with embedded atom potential is presented to demonstrate the effectiveness of this approach.

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Second-order Sigma-Delta (ΣΔ) quantization of finite frame expansions

Second-order Sigma-Delta (ΣΔ) quantization of finite frame...

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作者： Benedetto, John J. Powell, Alexander M. Yilmaz, Özgür Department of Mathematics University of Maryland College Park MD 20742 United States Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department of Mathematics University of British Columbia Vancouver BC V6T 1Z2 Canada

The second-order Sigma-Delta (ΣΔ) scheme with linear quantization rule is analyzed for quantizing finite unit-norm tight frame expansions for Rd. Approximation error estimates are derived, and it is shown that for certain choices of frames the quantization error is of order 1/N2, where N is the frame size. However, in contrast to the setting of bandlimited functions there are many situations where the second-order scheme only gives approximation error of order 1/N. For example, this is the case when quantizing harmonic frames of odd length in even dimensions. An important component of the error analysis involves extending existing stability results to yield smaller invariant sets for the linear second-order ΣΔ scheme. © 2005 Elsevier Inc. All rights reserved.

关键词： Estimation

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Translation of a sphere towards a rigid plane in an Oldroyd-B fluid

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Physical Review Fluids 2024年第8期9卷 083303页

作者： Tachin Ruangkriengsin Rodolfo Brandão Bimalendu Mahapatra Evgeniy Boyko Howard A. Stone Program in Applied and Computational Mathematics Department of Mechanical and Aerospace Engineering Faculty of Mechanical Engineering

We analyze the low-Reynolds-number translation of a sphere towards or away from a rigid plane in an Oldroyd-B fluid under two scenarios: prescribing the sphere's translational velocity, and prescribing the force on the sphere. Leveraging the lubrication approximation and a perturbation expansion in powers of the Deborah number, we develop a comprehensive theoretical analysis that yields analytical approximations for velocity fields, pressures, and forces acting on the sphere. Our framework aids in understanding temporal microstructural changes as the particle-wall gap evolves over time. In particular, we show that alterations in the polymer conformation tensor in response to geometric changes induce additional forces on the sphere. For cases with prescribed velocity, we present a theoretical approach for calculating resistive forces at any order in the Deborah number and utilize a reciprocal theorem to obtain higher-order corrections based on velocity fields in the previous orders. When the sphere translates with a constant velocity, the fluid viscoelasticity decreases the resistive force at the first order. However, at the second-order correction, the direction of the sphere's movement determines whether viscoelasticity increases or decreases the resistive force. For cases with prescribed force, we show that understanding the influence of viscoelasticity on the sphere's translational velocity necessitates a more intricate analysis even at low Deborah numbers. Specifically, we introduce an ansatz for constant force scenarios, and we derive solution forms for general prescribed forces using the method of multiple scales. We find that when a sphere undergoes sedimentation due to its own weight, the fluid viscoelasticity results in a slower settling process, reducing the leading-order sedimentation rate.

关键词： Complex fluids Low Reynolds number flows Lubrication theory Polymer conformation changes Rheology

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Constructions and existence of tight fusion frames

Constructions and existence of tight fusion frames

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Wavelets XIII

作者： Casazza, Peter G. Fickus, Matthew Mixon, Dustin G. Wang, Yang Zhou, Zhengfang Department of Mathematics and Statistics Air Force Institute of Technology Wright-Patterson Air Force Base OH 45433 United States Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department of Mathematics Michigan State University East Lansing MI 48824 United States Department of Mathematics University of Missouri Columbia MO 65211 United States

ISBN: (纸本)9780819477361

Fusion frames are an emerging topic of frame theory, with applications to communications and distributed processing. However, until recently, little was known about the existence of tight fusion frames, much less how to construct them. We discuss a new method for constructing tight fusion frames which is akin to playing Tetris with the spectrum of the frame operator. When combined with some easily obtained necessary conditions, these Spectral Tetris constructions provide a near complete characterization of the existence of tight fusion frames. © 2009 SPIE.

关键词： Optical engineering

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Fuzzy petri net representation of fuzzy production propositions of a rule based system 3rd

Fuzzy petri net representation of fuzzy production propositi...

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3rd International Conference on Advances in Computing and Data Sciences, ICACDS 2019

作者： Gupta, Sakshi Kumawat, Sunita Singh, Gajendra Pratap Department of Applied Mathematics Amity School of Applied Sciences Amity University Haryana Gurgaon India Mathematical Sciences and Interdisciplinary Research Lab School of Computational and Integrative Sciences JNU New Delhi India

ISBN: (纸本)9789811399381

Petri net is a potential mathematical and graphical modelling tool, used to examine the properties of various complex discrete event and distributed systems. In this paper, a Petri net variant, called Fuzzy Petri net (FPN) has been used to represent Fuzzy Production propositions of a rule based system, where a fuzzy production proposition explains the fuzzy relation among two propositions. For this purpose, another Petri net variant, known as Boolean Petri net (BPN) is considered because of its practical significance. BPNs can be used to represent active and inactive stages of a system like switching circuits;to qualitatively describe gene regulatory interactions etc. The Fuzzy Production propositions of BPN have been represented using Fuzzy Petri net and a precedent-subsequent relation between the two fuzzy propositions of BPNs has been checked using fuzzified propositional algorithm. This relation provides an important property of BPNs based on initial marking of Petri nets and the obtained truth degree of the success node validates the belief strength of this property. © Springer Nature Singapore Pte Ltd 2019.

关键词： Petri nets

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