Related papers: State-Space Averaging Revisited via Reconstruction…
Stationary subspace analysis (SSA) is a blind source separation framework that decomposes linearly mixed multivariate data into stationary and nonstationary components. We extend SSA to spatially indexed data by introducing spatial…
Two approaches to moment matching based model reduction of aperiodically sampled data systems are given. The term "aperiodic sampling" is used in the paper to indicate that the time between two consecutive sampling instants can take its…
Balanced Singular Perturbation Approximation (SPA) is a model order reduction method for linear time-invariant systems that guarantees asymptotic stability and for which there exists an a priori error bound. In that respect, it is similar…
We consider the continuous-time setting of linear time-invariant (LTI) systems in feedback with multiplicative stochastic uncertainties. The objective of the paper is to characterize the conditions of Mean-Square Stability (MSS) using a…
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as…
We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical…
In many real-world applications data exhibits non-stationarity, i.e., its distribution changes over time. One approach to handling non-stationarity is to remove or minimize it before attempting to analyze the data. In the context of brain…
State-space models (SSMs) have recently emerged as a compelling alternative to Transformers for sequence modeling tasks. This paper presents a theoretical generalization analysis of selective SSMs, the core architectural component behind…
This work presents generalized low-rank signal decompositions with the aid of switching techniques and adaptive algorithms, which do not require eigen-decompositions, for space-time adaptive processing. A generalized scheme is proposed to…
In stationary subspace analysis (SSA) one assumes that the observable p-variate time series is a linear mixture of a k-variate nonstationary time series and a (p-k)-variate stationary time series. The aim is then to estimate the unmixing…
We present an alternative to the conventional matrix product state representation, which allows us to avoid the explicit local Hilbert space truncation many numerical methods employ. Utilising chain mappings corresponding to linear and…
We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the…
This paper extends the inverse substructuring (IS) approach to the state-space domain and presents a novel state-space substructuring (SSS) technique that embeds the dynamics of connecting elements (CEs) in the Lagrange Multiplier…
This paper addresses the problem of basis correction in the context of LSS identification from input-output data. It is often the case that identification algorithms for the LSSs from input-output data operate locally. The individually…
We report a multiscale approach of broad applicability to stochastic reconstruction of multiphase materials, including porous ones. The approach devised uses an optimization method, such as the simulated annealing (SA) and the so-called…
Spatial covariance matrix (SCM) is essential in many applications of multi-antenna systems such as massive multiple-input multiple-output (MIMO). For massive MIMO operating at millimeter-wave bands, hybrid analog-digital structure has been…
We describe a Markov latent state space (MLSS) model, where the latent state distribution is a decaying mixture over multiple past states. We present a simple sampling algorithm that allows to approximate such high-order MLSS with fixed…
The theory of sampling and the reconstruction of data has a wide range of applications and a rich collection of techniques. For many methods a core problem is the estimation of the number of samples needed in order to secure a stable and…
We present an unconditionally stable algorithm for applying matrix transfer function of a linear time invariant system (LTI) in time domain. The state matrix of an LTI system used for modeling long range dependencies in state space models…
The problem of state reconstruction and estimation is considered for a class of switched dynamical systems whose subsystems are modeled using linear differential-algebraic equations (DAEs). Since this system class imposes time-varying…