相关论文: One step RSB scheme for the rate distortion functi…
Dynamics under which a system of Ising spins relaxes to a stationary state with Bolzmann-Gibbs measure and which do not fulfil the condition of detailed balance are irreversible and asymmetric. We revisit the problem of the determination of…
Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple…
In this paper, we present a convergence rate analysis for the inexact Krasnosel'skii-Mann iteration built from nonexpansive operators. Our results include two main parts: we first establish global pointwise and ergodic iteration-complexity…
This paper investigates the rate-distortion function, under a squared error distortion $D$, for an $n$-dimensional random vector uniformly distributed on an $(n-1)$-sphere of radius $R$. First, an expression for the rate-distortion function…
One-bit compressive sensing (CS) is an advanced version of sparse recovery in which the sparse signal of interest can be recovered from extremely quantized measurements. Namely, only the sign of each measurement is available to us. In many…
Reachability analysis provides formal guarantees for performance and safety properties of nonlinear control systems. Here, one aims to compute the backward reachable set (BRS) or tube (BRT) -- the set of states from which the system can be…
In several areas of optics and photonics like wave propagation, digital holography, holographic microscopy, diffraction imaging, biomedical imaging and diffractive optics, the behavior of the electromagnetic waves has to be calculated with…
This paper revisits the rate-distortion theory from the perspective of optimal weak transport, as recently introduced by Gozlan et al. While the conditions for optimality and the existence of solutions are well-understood in the case of…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
We provide a scheme for exploring the reconstruction limit of compressed sensing by minimizing the general cost function under the random measurement constraints for generic correlated signal sources. Our scheme is based on the statistical…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
In this short note, we present supporting evidence for the replica symmetric approach to the random bond q-state Potts models. The evidence is statistically strong enough to reject the applicability of the Parisi replica symmetry breaking…
Sequential rate-distortion (SRD) theory provides a framework for studying the fundamental trade-off between data-rate and data-quality in real-time communication systems. In this paper, we consider the SRD problem for multi-dimensional…
We construct a general framework for deriving error bounds for conic feasibility problems. In particular, our approach allows one to work with cones that fail to be amenable or even to have computable projections, two previously challenging…
Some interesting recent advances in the theoretical understanding of neural networks have been informed by results from the physics of disordered many-body systems. Motivated by these findings, this work uses the replica technique to study…
We provide the first examples of two-step replica symmetry breaking (2-RSB) models for the spherical mixed p-spin glass at zero temperature. Precisely, we show that for a certain class of mixtures, the Parisi measure at zero temperature is…
The one-bit compressed sensing framework aims to reconstruct a sparse signal by only using the sign information of its linear measurements. To compensate for the loss of scale information, past studies in the area have proposed recovering…
The Renyi entropy is a generalisation of the Shannon entropy that is sensitive to the fine details of a probability distribution. We present results for the Renyi entropy of the totally asymmetric exclusion process (TASEP). We calculate…
This paper addresses the inverse problem of identifying the linear velocity coefficient in a linear system governed by two Benjamin-Bona-Mahony-type equations, which model the displacement of water waves propagating along the surface of a…
In this paper, we employ the thoughts and methodologies of Shannon's information theory to solve the problem of the optimal radar parameter estimation. Based on a general radar system model, the \textit{a posteriori} probability density…