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This paper introduces a chordal decomposition approach for scalable analysis of linear networked systems, including stability, $\mathcal{H}_2$ and $\mathcal{H}_{\infty}$ performance. Our main strategy is to exploit any sparsity within these…
For any real-valued stochastic process $X$ with c\'rdl\'rg paths we define non-empty family of processes which have locally finite total variation, have jumps of the same order as the process $X$ and uniformly approximate its paths on…
We consider a class of Schrodinger equations with time-dependent smooth magnetic and electric potentials having a growth at infinity at most linear and quadratic, respectively. We study the convergence in $L^p$ with loss of derivatives,…
Consider a random graph model where each possible edge $e$ is present independently with some probability $p_e$. Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we…
Sparse view computed tomography (CT) reconstruction poses a challenging ill-posed inverse problem, necessitating effective regularization techniques. In this letter, we employ $L_p$-norm ($0<p<1$) regularization to induce sparsity and…
Merging asymptotic expansions of arbitrary length are established for the distribution functions and for the probabilities of suitably centered and normalized cumulative winnings in a full sequence of generalized St. Petersburg games,…
In this paper we propose and analyze inexact and stochastic versions of the CGALP algorithm developed in the authors' previous paper, which we denote ICGALP, that allows for errors in the computation of several important quantities. In…
Approximation of high-dimensional functions is a problem in many scientific fields that is only feasible if advantageous structural properties, such as sparsity in a given basis, can be exploited. A relevant tool for analysing sparse…
An integrator for a class of stochastic Lie-Poisson systems driven by Stratonovich noise is developed. The integrator is suited for Lie-Poisson systems that also admit an isospectral formulation, which enables scalability to…
We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…
In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance:…
Brains process information through the collective dynamics of large neural networks. Collective chaos was suggested to underlie the complex ongoing dynamics observed in cerebral cortical circuits and determine the impact and processing of…
We consider a general infinite horizon Heterogeneous Restless multi-armed Bandit (RMAB). Heterogeneity is a fundamental problem for many real-world systems largely because it resists many concentration arguments. In this paper, we assume…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
We study the problem of multivariate $L_2$-approximation of functions in a weighted Korobov space using a median lattice-based algorithm recently proposed by the authors. In the original work, the algorithm requires knowledge of the…
The high computational cost involved in modeling of the progressive fracture simulations using large discrete lattice networks stems from the requirement to solve {\it a new large set of linear equations} every time a new lattice bond is…
We study chaotic synchronization in a 5D Hindmarsh--Rose neuron model augmented with electromagnetic induction and a switchable memristive autapse. For two diffusively coupled identical neurons, we derive the transverse error dynamical…
In this paper, we establish the existence of the solutions $ (X, L)$ of reflected stochastic differential equations with possible anticipating initial random variables. The key is to obtain some substitution formula for Stratonovich…
This paper studies the expected $L_p$-discrepancy ($2 \leq p < \infty$) for stratified sampling schemes under importance sampling. We introduce a parametric family of equivolume partitions $\Omega_{\theta,\sim}$ and leverage recent exact…
A new chaotic financial system is proposed by considering ethics involvement in a four-dimensional financial system with market confidence. A five-dimensional conformable derivative financial system is presented by introducing conformable…