Related papers: The restricted isometry property for time-frequenc…
We present a theory and accompanying importance sampling method for computing rate constants in spatially inhomogenious systems. Using the relationship between rate constants and path space partition functions, we illustrate that the…
In this paper we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of…
We discuss a model for studying the statistical properties of the impedance ($Z$) and scattering ($S$) matrices of open electromagnetic cavities with several transmission lines or waveguides connected to the cavity. In this paper, we mainly…
We propose a general method for constructing a minimal cover of high-dimensional chaotic attractors by embedded unstable recurrent patterns. By minimal cover we mean a subset of available patterns such that the approximation of chaotic…
This article treats global uniform exponential stability (GUES) of discrete-time switched linear systems under restricted switching. Given admissible minimum and maximum dwell times, we provide sufficient conditions on the subsystems under…
We discuss the properties of a large number N of one-dimensional (bounded) locally periodic potential barriers in a finite interval. We show that the transmission coefficient, the scattering cross section $\sigma$, and the resonances of…
The analysis sparsity model is a very effective approach in modern Compressed Sensing applications. Specifically, redundant analysis operators can lead to fewer measurements needed for reconstruction when employing the analysis…
The Restricted Isometry Property (RIP) introduced by Cand\'es and Tao is a fundamental property in compressed sensing theory. It says that if a sampling matrix satisfies the RIP of certain order proportional to the sparsity of the signal,…
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
This paper develops a unified finite-time theory for the ordinary least squares estimation of possibly unstable and even slightly explosive vector autoregressive models under linear restrictions, with the applicable region $\rho(A)\leq…
We analyse universal statistical properties of phase shifts and time delays for open chaotic systems in the crossover regime of partly broken time-reversal invariance. In particular, we find that the distribution of the time delay shows…
First this report presents a restricted set of finite transducers used to synthesise structural time-series constraints described by means of a multi-layered function composition scheme. Second it provides the corresponding synthesised…
For Gamma a finite, connected metric graph, we consider the space of configurations of n points in Gamma with a restraint parameter r dictating the minimum distance allowed between each pair of points. These restricted configuration spaces…
We study the mixing time of systematic scan Glauber dynamics Ising model on the complete graph. On the complete graph $K_n$, at each time, $k \leq n$ vertices are chosen uniformly random and are updated one by one according to the uniformly…
We study singularly perturbed systems that exhibit input-to-state stability (ISS) with fixed-time properties in the presence of bounded disturbances. In these systems, solutions converge to the origin within a time frame independent of…
We prove that any Markov chain that performs local, reversible updates on randomly chosen vertices of a bounded-degree graph necessarily has mixing time at least $\Omega(n\log n)$, where $n$ is the number of vertices. Our bound applies to…
Although frames, which are a generalization of bases, are important tools used in signal processing, their potential in other fields of engineering and applied mathematics (e.g. acoustics) has not been fully explored yet. Gabor frames, that…
We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (biorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of isolated resonances, we apply…
Recently, many works have focused on the characterization of non-linear dimensionality reduction methods obtained by quantizing linear embeddings, e.g., to reach fast processing time, efficient data compression procedures, novel…
This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…