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Optimum classical beam-position sensing

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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Deuteration removes quantum dipolar defects from KDP crystals

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npj Computational Materials 2024年第1期10卷 684-693页

作者： Bingjia Yang Pinchen Xie Roberto Car Department of Chemistry Princeton UniversityPrincetonNJ 08544USA Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ 08544USA Department of Chemistry Department of PhysicsProgram in Applied and Computational MathematicsPrinceton Materials InstitutePrinceton UniversityPrincetonNJ 08544USA

Dielectric properties of the hydrogen-bonded ferroelectric crystal KH_(2)PO_(4)(KDP)differ significantly from those of KD_(2)PO_(4)(DKDP).It is well established that deuteration affects the interplay of hydrogenbond switches and heavy ion displacements that underlie the emergence of macroscopic polarization,but a detailed microscopic model is *** show that all-atompath integral molecular dynamics simulations can predict the isotope effects,revealing the microscopic mechanism that differentiates KDP and *** tunneling generates phosphate configurations that do not contribute to the *** low temperatures,these quantum dipolar defects are substantial in KDP but negligible in *** intrinsic defects explain why KDP has lower spontaneous polarization and transition entropy than *** prominent role of quantum fluctuations in KDP is related to the unusual strength of the hydrogen bonds and should be equally important in other crystals of the KDP family,which exhibit similar isotope effects.

关键词： quantum KDP remove

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An Ant Colony Algorithm Approach to the Vehicle Routing Problem and Variants

An Ant Colony Algorithm Approach to the Vehicle Routing Prob...

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2024 Systems and Information Engineering Design Symposium, SIEDS 2024

作者： Tablada, Tulio Davis, Cleon Palumbo, Neil Johns Hopkins University Electrical and Computer Engineering Program Johns Hopkins University Applied and Computational Mathematics Program United States

ISBN: (纸本)9798350385144

In the basic vehicle routing problem (VRP), a vehicle must deliver goods from one centralized warehouse to multiple customers efficiently. Several VRP variants and constraints exist, including different product types, specific delivery times, multiple warehouses, vehicle fuel constraints, and pick-up from one location and delivery to another. This work proposes and demonstrates a flexible algorithm for solving the VRP via ant colony optimization (ACO) that can address many of the variants discussed above. ACO algorithms mimic the behavior of ants, learning optimal paths to a food source and back to the nest based on stigmergic behavior. This work compares a proposed, more flexible ACO algorithm to a traditional optimization algorithm that is implemented in the Google VRP solver. Readily available data were used to test and demonstrate results. Several VRP variants were implemented in both the (proposed) flexible ACO algorithm and the Google VRP solver. The flexible ACO algorithm performed better in terms of distance traveled versus the Google VRP solver for two variants and worse for three other cases. However, the Google VRP solver was not able to solve some of the VRP variant combinations considered here and failed when solving some backhaul datasets. Because the flexible ACO algorithm was able to better handle many case variations, it may be an attractive alternative optimization tool. © 2024 IEEE.

关键词： Ant colony optimization

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Differentiable Simulator For Dynamic & Stochastic Optimal Gas & Power Flows 63

Differentiable Simulator For Dynamic & Stochastic Optimal Ga...

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63rd IEEE Conference on Decision and Control, CDC 2024

作者： Hyett, Criston Pagnier, Laurent Alisse, Jean Goldshtein, Igal Saban, Lilah Ferrando, Robert Chertkov, Michael University of Arizona Program in Applied Mathematics & Department of Mathematics TucsonAZ United States Noga the Israel Independent System Operator Haifa Israel

ISBN: (纸本)9798350316339

In many power systems, particularly those isolated from larger intercontinental grids, reliance on natural gas is crucial. This dependence becomes particularly critical during periods of volatility or scarcity in renewable energy sources, further complicated by unpredictable consumption trends. To ensure the uninterrupted operation of these isolated gas-grid systems, innovative and efficient management strategies are essential. This paper investigates the complexities of achieving synchronized, dynamic, and stochastic optimization for autonomous transmission-level gas-grid infrastructures. We introduce a novel methodology grounded in differentiable programming, which synergizes symbolic programming, a conservative numerical method for solving gas-flow partial differential equations, and automated sensitivity analysis powered by SciML/Julia. Our methodology refines the co-optimization landscape for gas-grid systems by grounding gas dynamics in physics-adherent simulation. We demonstrate efficiency and precision of the methodology by solving a stochastic optimal gas flow problem, phrased on an open source model of Israel's gas grid model. © 2024 IEEE.

关键词： Sensitivity analysis

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Preface to the special issue dedicated to Saber Elaydi on the occasion of his 80th birthday

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Journal of Difference Equations and Applications 2024年第10期30卷 1397-1404页

作者： Cushing, Jim Michael Sasu, Adina Luminiţa Department of Mathematics Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ United States Department of Mathematics West University of Timişoara Timişoara Romania Academy of Romanian Scientists Bucharest Romania

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PARSING NEURAL DYNAMICS WITH INFINITE RECURRENT SWITCHING LINEAR DYNAMICAL SYSTEMS 12

PARSING NEURAL DYNAMICS WITH INFINITE RECURRENT SWITCHING LI...

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12th International Conference on Learning Representations, ICLR 2024

作者： Geadah, Victor Pillow, Jonathan W. Program in Applied and Computational Mathematics Princeton University United States Princeton Neuroscience Institute Princeton University United States

Unsupervised methods for dimensionality reduction of neural activity and behavior have provided unprecedented insights into the underpinnings of neural information processing. One popular approach involves the recurrent switching linear dynamical system (rSLDS) model, which describes the latent dynamics of neural spike train data using discrete switches between a finite number of low-dimensional linear dynamical systems. However, a few properties of rSLDS model limit its deployability on trial varying data, such as a fixed number of states over trials, and no latent structure nor organization of states. Here we overcome these limitations by endowing the rSLDS model with a semi-Markov discrete state process, with latent geometry, that captures key properties of stochastic processes over partitions with flexible state cardinality. We leverage partial differential equations (PDE) theory to derive an efficient, semi-parametric formulation for dynamical sufficient statistics to the discrete states. This process, combined with switching dynamics, defines our infinite recurrent switching linear dynamical system (irSLDS) model class. We first validate and demonstrate the capabilities of our model on synthetic data. Next, we turn to the analysis of mice electrophysiological data during decision-making, and uncover strong non-stationary processes underlying both within-trial and trial-averaged neural activity. © 2024 12th International Conference on Learning Representations, ICLR 2024. All rights reserved.

关键词： Stochastic systems

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Bi-endomorphism induces new types of derivations on BH-algebras

Italian Journal of Pure and Applied Mathematics

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Italian Journal of Pure and applied mathematics 2024年第52期 138-152页

作者： Muangkarn, Patchara Suanoom, Cholatis Saybounheaung, Thongsouk Sriyotha, Wilaiwan Iampan, Aiyared Program of Mathematics Faculty of Science and Technology Kamphaeng Phet Rajabhat University Kamphaeng Phet62000 Thailand Science and Applied Science Center Program of Mathematics Faculty of Science and Technology Kamphaeng Phet Rajabhat University Kamphaeng Phet62000 Thailand Department of Mathematics Faculty of Natural Sciences National University of Laos Xaythany District Vientiane Laos Department of Mathematics School of Science University of Phayao 19 Moo 2 Tambon Mae Ka Amphur Mueang Phayao56000 Thailand

In this paper, we study the concepts of an (l, r) and an (r, l)-τ-derivation on a BH-algebra, which is induced by a left and a right bi-endomorphism and we provide important properties. In addition, the relationship ... 详细信息

关键词： Algebra

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System-Wide Emergency Policy for Transitioning from Main to Secondary Fuel 63

System-Wide Emergency Policy for Transitioning from Main to ...

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63rd IEEE Conference on Decision and Control, CDC 2024

作者： Pagnier, Laurent Hyett, Criston Ferrando, Robert Goldshtein, Igal Alisse, Jean Saban, Lilah Chertkov, Michael University of Arizona Graduate Interdisciplinary Program in Applied Mathematics and Department of Mathematics TucsonAZ85721 United States Noga the Israel Independent System Operator Haifa Israel

ISBN: (纸本)9798350316339

Faced with the complexities of managing natural gas-dependent power system amid the surge of renewable integration and load unpredictability, this study explores strategies for navigating emergency transitions to costlier secondary fuels. Our aim is to develop decision-support tools for operators during such exigencies. We approach the problem through a Markov Decision Process (MDP) framework, accounting for multiple uncertainties. These include the potential for dual-fuel generator failures and operator response during high-pressure situations. Additionally, we consider the finite reserves of primary fuel, governed by gas-flow partial differential equations (PDEs) and constrained by nodal pressure. Other factors include the variability in power forecasts due to renewable generation and the economic impact of compulsory load shedding. For tractability, we address the MDP in a simplified context, replacing it by Markov Processes evaluated against a selection of policies and scenarios for comparison. Our study considers two models for the natural gas system: an oversimplified model tracking linepack and a more nuanced model that accounts for gas flow network heterogeneity. The efficacy of our methods is demonstrated using a realistic model replicating Israel's power-gas infrastructure. © 2024 IEEE.

关键词： Markov processes

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Fast decisions reflect biases;slow decisions do not

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Physical Review E 2024年第2期110卷 024305-024305页

作者： Samantha Linn Sean D. Lawley Bhargav R. Karamched Zachary P. Kilpatrick Krešimir Josić Department of Mathematics Institute of Molecular Biophysics Program in Neuroscience Department of Applied Mathematics Department of Biology and Biochemistry

Decisions are often made by heterogeneous groups of individuals, each with distinct initial biases and access to information of different quality. We show that in groups of independent agents who accumulate evidence the first to decide are those with the strongest initial biases. Their decisions align with their initial bias, regardless of the underlying truth. In contrast, agents who decide last make decisions as if they were initially unbiased and hence make better choices. We obtain asymptotic expressions in the large population limit quantifying how agents' initial inclinations shape early decisions. Our analysis shows how bias, information quality, and decision order interact in nontrivial ways to determine the reliability of decisions in a group.

关键词： Social networks Diffusion & random walks Extreme event statistics First passage problems Fokker–Planck equation Langevin equation Monte Carlo methods Stochastic analysis Stochastic differential equations

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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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