相关论文: Variance of finite difference methods for reaction…

Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…

In this work we propose a new kind of parameterized outer estimate of the united solution set to an interval parametric linear system. The new method has several advantages compared to the methods obtaining parameterized solutions…

This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational inequalities. We establish efficient conditions for well-posedness, in the sense of robust Lipschitzian…

This paper establishes problem-specific sample complexity lower bounds for linear system identification problems. The sample complexity is defined in the PAC framework: it corresponds to the time it takes to identify the system parameters…

This paper is concerned with the large deviation principle of the stochastic reaction-diffusion lattice systems defined on the N-dimensional integer set, where the nonlinear drift term is locally Lipschitz continuous with polynomial growth…

We present a systematic mathematical analysis of the qualitative steady-state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions,…

Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the…

The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…

Numerical analysis for linear constant-coefficients Finite Difference schemes was developed approximately fifty years ago. It relies on the assumption of scheme stability and in particular -- for the $L^2$ setting -- on the absence of…

A reduced-rank mixed effects model is developed for robust modeling of sparsely observed paired functional data. In this model, the curves for each functional variable are summarized using a few functional principal components, and the…

Given a countable set of sites and a collection of flip rates at each site, we give a sufficient condition on the long-range dependancies of the flip rates ensuring the well-definedness of the corresponding spin system. This hypothesis has…

Beta regression models are a suitable choice for continuous response variables on the unity interval. Random effects add further flexibility to the models and accommodate data structures such as hierarchical, repeated measures and…

We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…

In this study, we introduce a sensitivity analysis methodology for stochastic systems in chemistry, where dynamics are often governed by random processes. Our approach is based on gradient estimation via finite differences, averaging…

For the formal verification and design of control systems, abstractions with quantified accuracy are crucial. This is especially the case when considering accurate deviation bounds between a stochastic continuous-state model and its finite…

This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…

Linear mixed models with large imbalanced crossed random effects structures pose severe computational problems for maximum likelihood estimation and for Bayesian analysis. The costs can grow as fast as $N^{3/2}$ when there are N…

Spiking activity in cortical networks is nonlinear in nature. The linear-nonlinear cascade model, some versions of which are also known as point-process generalized linear model, can efficiently capture the nonlinear dynamics exhibited by…

The focus of this paper is on linear system identification in the setting where it is known that the underlying partially-observed linear dynamical system lies within a finite collection of known candidate models. We first consider the…

Variable selection naturally arises as a useful subject when faced with data with massive predictor space. In addition to the massive dimensionality, the data may be characterized by intra-subject correlation, and cure fraction, which are…