This paper is concerned with the factorization method with a single far-field pattern to recover an arbitrary convex polygonal scatterer/source in linear elasticity. The approach also applies to the compressional (res...
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The factorization method by Kirsch (1998) provides a necessary and sufficient condition for characterizing the shape and position of an unknown scatterer by using far-field patterns of infinitely many time-harmonic pl...
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A description of the so called "particles with coupled oscillator dynamics" (PCOD) is presented which is used to model, analyze and synthesize collective motion. An oscillator model with spatial dynamics is ...
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A description of the so called "particles with coupled oscillator dynamics" (PCOD) is presented which is used to model, analyze and synthesize collective motion. An oscillator model with spatial dynamics is presented to help describe how to design steering control laws while it is being used to study biological collectives. Lastly, both engineering and biological analysis were described.
Reed-Muller (RM) codes were introduced in 1954 and have long been conjectured to achieve Shannon's capacity on symmetric channels. The activity on this conjecture has recently been revived with the emergence of po...
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Reed-Muller (RM) codes were introduced in 1954 and have long been conjectured to achieve Shannon's capacity on symmetric channels. The activity on this conjecture has recently been revived with the emergence of polar codes. RM codes and polar codes are generated by the same matrix G_m= [1/1 0/1] ^⊗m but using different subset of rows. RM codes select simply rows having largest weights. Polar codes select instead rows having the largest conditional mutual information proceeding top to down in G_m; while this is a more elaborate and channel-dependent rule, the top-to-down ordering allows Arikan to show that the conditional mutual information polarizes, and this gives directly a capacity-achieving code on any symmetric channel. RM codes are yet to be proved to have such a property, despite the recent success for the erasure channel. In this paper, we connect RM codes to polarization theory. We show that proceeding in the RM code ordering, i.e., not top-to-down but from the lightest to the heaviest rows in G_m, the conditional mutual information again polarizes. We further demonstrate that it does so faster than for polar codes. This implies that G_m contains another code, different than the polar code and called here the twin-RM code, that is provably capacity-achieving on any symmetric channel. This gives in particular a necessary condition for RM codes to achieve capacity on symmetric channels. It further gives a sufficient condition if the rows with largest conditional mutual information correspond to the heaviest rows, i.e., if the twin-RM code is the RM code. We demonstrate here that the two codes are at least similar and give further evidence that they are indeed the same.
In this paper we consider a stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniquen...
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To be used as an analysis tool, it is important that a spatial network’s construction algorithm reproduces the structural properties of the original physical embedding. One method for converting a two-dimensional (2D...
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To be used as an analysis tool, it is important that a spatial network’s construction algorithm reproduces the structural properties of the original physical embedding. One method for converting a two-dimensional (2D) point pattern into a spatial network is the Delaunay triangulation. Here, we apply the Delaunay triangulation to seven different types of 2D point patterns, including hyperuniform systems. The latter are characterized by completely suppressed normalized infinite-wavelength density fluctuations. We demonstrate that the quartile coefficients of dispersion of multiple centrality measures are capable of rank-ordering hyperuniform and nonhyperuniform systems independently, but they cannot distinguish a system that is nearly hyperuniform from hyperuniform systems. Thus, in each system, we investigate the local densities of the point pattern ρP (ri;) and of the network ρG(ni;). We reveal that there is a strong correlation between ρP (ri;) and ρG(ni;) in nonhyperuniform systems, but there is no such correlation in hyperuniform systems. When calculating the pair-correlation function and local density covariance function on the point pattern and network, the point pattern and network functions are similar only in nonhyperuniform systems. In hyperuniform systems, the triangulation has a positive covariance of local network densities in pairs of nodes that are close together;such covariance is not present in the point patterns. Thus, we demonstrate that the Delaunay triangulation accurately captures the density fluctuations of the underlying point pattern only when the point pattern possesses a positive correlation between ρP (ri;) for points that are close together. Such positive correlation is seen in most real-world systems, so the Delaunay triangulation is generally an effective tool for building a spatial network from a 2D point pattern, but there are situations (i.e., disordered hyperuniform systems) where we caution that the Delaunay triangulation would not
Many types of cells require the ability to pinpoint the location of an external stimulus from the arrival of diffusing signaling molecules at cell-surface receptors. How does the organization (number and spatial confi...
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Many types of cells require the ability to pinpoint the location of an external stimulus from the arrival of diffusing signaling molecules at cell-surface receptors. How does the organization (number and spatial configuration) of these receptors shape the limit of a cell’s ability to infer the source location? In the idealized scenario of a spherical cell, we apply asymptotic analysis to compute splitting probabilities between individual receptors and formulate an information-theoretic framework to quantify the role of receptor organization. Clustered configurations of receptors provide an advantage in detecting sources aligned with the clusters, suggesting a possible multiscale mechanism for single-cell source inference.
A stencil-adaptive SBP-SAT finite difference scheme is shown to display superconvergent behavior. applied to the linear advection equation, it has a convergence rate O(∆x4) in contrast to a conventional scheme, which ...
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We study the nonlinear Schrödinger equation with an inversesquare potential in dimensions 3 ≤ d ≤ 6. We consider both focusing and defocusing nonlinearities in the mass-supercritical and energy-subcritical regi...
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We present a deep generative model, named Monge-Ampère flow, which builds on continuous-time gradient flow arising from the Monge-Ampère equation in optimal transport theory. The generative map from the late...
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