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Co-evolution of Viral Processes and Structural Stability in Signed Social Networks

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arXiv 2021年

作者： Kalimzhanov, Temirlan Khamseh'i, Amir Haji Ali Dadlani, Aresh Kumar, Muthukrishnan Senthil Khonsari, Ahmad Nur-Sultan010000 Kazakhstan The School of Electrical and Computer Engineering College of Engineering University of Tehran Tehran*** Iran The Department of Applied Mathematics and Computational Sciences PSG College of Technology Coimbatore641004 India

Prediction and control of spreading processes in social networks (SNs) are closely tied to the underlying connectivity patterns. Contrary to most existing efforts that exclusively focus on positive social user interactions, the impact of contagion processes on the temporal evolution of signed SNs (SSNs) with distinctive friendly (positive) and hostile (negative) relationships yet, remains largely unexplored. In this paper, we study the interplay between social link polarity and propagation of viral phenomena coupled with user alertness. In particular, we propose a novel energy model built on Heider's balance theory that relates the stochastic susceptible-alert-infected-susceptible epidemic dynamical model with the structural balance of SSNs to substantiate the trade-off between social tension and epidemic spread. Moreover, the role of hostile social links in the formation of disjoint friendly clusters of alerted and infected users is analyzed. Using three real-world SSN datasets, we further present a time-efficient algorithm to expedite the energy computation in our Monte-Carlo simulation method and show compelling insights on the effectiveness and rationality of user awareness and initial network settings in reaching structurally balanced local and global network energy states. © 2021, CC BY.

关键词： Monte Carlo methods

Multilayer thin film growth on crystalline and quasicrystalline surfaces: A phase-field crystal study

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Physical Review B 2012年第24期85卷 245428-245428页

作者： Srevatsan Muralidharan Raika Khodadad Ethan Sullivan Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA and School of Mathematics Institute for Advanced Study Princeton New Jersey 08540 USA

In this paper, we explore the effects of misfit strain fields on both heterogeneous nucleation behavior and anisotropic growth of islands at submonolayer coverages and compositional patterning at complete monolayer coverage via simulations of a phase-field crystal model. In particular, deposition on top of a herringbone structure and quasicrystalline (QC) substrate are considered, the former representing a system with spatially periodic misfit strain fields arising from the presence of surface dislocations, and the latter representing a system which inherently possesses a wide range of local, aperiodic misfit patterns. In the case of single-component systems, we demonstrate that misfit strain fields lead to heterogeneous nucleation behavior and anisotropic island growth. In the case of QC substrate, a wide range of morphologies, such as coexistence of locally hexagonally ordered atomic clusters within a larger scale arrangement with overall QC symmetry and so-called “starfish” aggregates, is observed in a pure system at submonolayer coverages when the adlayer-substrate interaction strength and lattice mismatch are tuned. In the case of bulk-immiscible binary systems at complete monolayer coverage, strain-stabilized compositional domains emerge at low line tension values for both substrates. Interestingly, the compositional domains on the QC substrate inherit their symmetries at sufficiently low line tension values, while at larger line tension values, the domain structure begins to resemble the classical spinodal microstructure. Such domain structures should be readily observable in colloidal systems in which attractive interparticle and particle-substrate interactions can be tuned.

关键词： THIN films CRYSTALS NUCLEATION DISLOCATIONS in crystals MICROSTRUCTURE

High temperature structure detection in ferromagnets

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arXiv 2018年

作者： Cao, Yuan Neykov, Matey Liu, Han Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Statistics & Data Science Carnegie Mellon University PittsburghPA United States Department of Electrical Engineering and Computer Science Northwestern University EvanstonIL United States

This paper studies structure detection problems in high temperature ferromagnetic (positive interaction only) Ising models. The goal is to distinguish whether the underlying graph is empty, i.e., the model consists of independent Rademacher variables, versus the alternative that the underlying graph contains a subgraph of a certain structure. We give matching upper and lower minimax bounds under which testing this problem is possible/impossible respectively. Our results reveal that a key quantity called graph arboricity drives the testability of the problem. On the computational front, under a conjecture of the computational hardness of sparse principal component analysis, we prove that, unless the signal is strong enough, there are no polynomial time linear tests on the sample covariance matrix which are capable of testing this problem. Copyright © 2018, The Authors. All rights reserved.

关键词： Ferromagnetism

Viscosity Solutions for McKean-Vlasov Control I: one-dimensional torus

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arXiv 2022年

作者： Soner, H. Mete Yan, Qinxin Department of Operations Research and Financial Engineering Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States

An optimal control problem in the space of probability measures, and the viscosity solutions of the corresponding dynamic programming equations defined using the intrinsic linear derivative are studied. The value function is shown to be Lipschitz continuous with respect to a novel smooth Fourier-Wasserstein metric. A comparison result between the Lipschitz viscosity sub and super solutions of the dynamic programming equation is proved using this metric, characterizing the value function as the unique Lipschitz viscosity *** Codes 35Q89, 35D40, 49L25, 60G99 © 2022, CC BY-NC-ND.

关键词： Viscosity

An adaptive solution strategy for Richards' equation

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arXiv 2023年

作者： Stokke, Jakob S. Mitra, Koondanibha Storvik, Erlend Both, Jakub W. Radu, Florin A. Center for Modeling of Coupled Subsurface Dynamics Department of Mathematics University of Bergen Norway Computational Mathematics Group Hasselt University Belgium Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Sciences Norway

Flow in variably saturated porous media is typically modelled by the Richards equation, a nonlinear elliptic-parabolic equation which is notoriously challenging to solve numerically. In this paper, we propose a robust and fast iterative solver for Richards’ equation. The solver relies on an adaptive switching algorithm, based on rigorously derived a posteriori indicators, between two linearization methods: L-scheme and Newton. Although a combined L-scheme/Newton strategy was introduced previously in [1], here, for the first time we propose a reliable and robust criteria for switching between these schemes. The performance of the solver, which can be in principle applied to any spatial discretization and linearization methods, is illustrated through several numerical *** Codes 65M12, 65J08, 65M50, 76Sxx © 2023, CC BY.

关键词： Nonlinear equations

Viscosity Solutions of the Eikonal Equation on the Wasserstein Space∗

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arXiv 2023年

Dynamic programming equations for mean field control problems with a separable structure are Eikonal type equations on the Wasserstein space. Standard differentiation using linear derivatives yield a direct extension of the classical viscosity theory. We use Fourier representation of the Sobolev norms on the space of measures, together with the standard techniques from the finite dimensional theory to prove a comparison result among semicontinuous sub and super solutions, obtaining a unique characterization of the value *** Codes 35D40, 35Q89, 49L12, 49L25, 60G99 © 2023, CC BY-NC-ND.

关键词： Viscosity

Design and implementation of a fully integrated compressed-sensing signal acquisition system

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Design and implementation of a fully integrated compressed-s...

International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Juhwan Yoo Stephen Becker Manuel Monge Matthew Loh Emmanuel Candès Azita Emami-Neyestanak Department of Electrical Engineering California Institute of Technology Pasadena CA USA Department of Applied and Computational Mathematics California Institute of Technology Pasadena CA USA Department of Statistics University of Stanford Stanford CA USA

Compressed sensing (CS) is a topic of tremendous interest because it provides theoretical guarantees and computationally tractable algorithms to fully recover signals sampled at a rate close to its information content. This paper presents the design of the first physically realized fully-integrated CS based Analog-to-Information (A2I) pre-processor known as the Random-Modulation Pre-Integrator (RMPI) [1]. The RMPI achieves 2GHz bandwidth while digitizing samples at a rate 12.5× lower than the Nyquist rate. The success of this implementation is due to a coherent theory/algorithm/hardware co-design approach. This paper addresses key aspects of the design, presents simulation and hardware measurements, and discusses limiting factors in performance.

关键词： Bandwidth Compressed sensing Harmonic analysis Noise Hardware Frequency estimation CMOS integrated circuits

Convex Inversion of the Entrywise Product of Real Signals with Known Signs

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Convex Inversion of the Entrywise Product of Real Signals wi...

Asilomar Conference on Signals, Systems, and Computers

作者： Alireza Aghasi Ali Ahmed Paul Hand School of Business Georgia State University Atlanta School of Electrical and Computer Engineering Information Technology University Lahore Pakistan Department of Computational and Applied Mathematics Rice University Houston TX

We consider the bilinear inverse problem of recovering two vectors, x and w, in R~L from their entrywise product. For the case where the vectors have known signs and belong to known subspaces, we introduce the convex program BranchHull, which is posed in the natural parameter space and does not require an approximate solution or initialization in order to be stated or solved. Under the structural assumptions that x and w are the members of known K and N dimensional random subspaces, we prove that BranchHull recovers x and w up to the inherent scaling ambiguity with high probability, whenever L {approx.>} K + N. This problem is motivated by applications in the sweep distortion removal task in dielectric imaging, where one of the signals is a nonnegative reflectivity, and the other signal lives in a known wavelet subspace. Additional potential applications are blind deconvolution and self-calibration.

关键词： Deconvolution Electronic mail Signal processing Calibration Task analysis Imaging

Dynamic Mode Decomposition and Sparse Measurements for Characterization and Monitoring of Power System Disturbances

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arXiv 2019年

作者： Ramos, J. Jorge Kutz, J. Nathan Graduate Program in Electrical Engineering Cinvestav Unidad Guadalajara Guadalajaram Jal Mexico Department of Applied Mathematics University of Washington SeattleWA98195 United States

We introduce the dynamics mode decomposition for monitoring wide-area power grid networks from sparse measurement data. The mathematical framework fuses data from multiple sensors based on multivariate statistics, providing accurate full state estimation from limited measurements and generating data-driven forecasts for the state of the system. Our proposed data-driven strategy, which is based on energy metrics, can be used for the analysis of major disturbances in the network. The approach is tested and validated using time domain simulations in the IEEE 118 bus system under various disturbance scenarios and under different sparse observations of the system. In addition to state reconstruction, the minimal number of sensors required for monitoring disturbances can be evaluated. Visualization techniques are developed in order to aid in the analysis and characterization of the system after disturbance. Copyright © 2019, The Authors. All rights reserved.

关键词： Time domain analysis