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A classical problem of statistical inference is the valid specification of a model that can account for the statistical dependencies between observations when the true structure is dense, intractable, or unknown. To address this problem, a…

Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a…

Some of the most important results in prediction theory and time series analysis when finitely many values are removed from or added to its infinite past have been obtained using difficult and diverse techniques ranging from duality in…

Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to invariance condition of dynamical system, submitted to Applied Mathematics and Computation}] proposed a novel unified approach to study, i.e., invariance conditions,…

We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…

Machine-learning technologies for learning dynamical systems from data play an important role in engineering design. This research focuses on learning continuous linear models from data. Stability, a key feature of dynamic systems, is…

A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…

We study constrained versions of the Ingleton inequality in the entropic setting and quantify its stability under small violations of conditional independence. Although the classical Ingleton inequality fails for general entropy profiles,…

We investigate the dependence on parameters for second order difference equations with two point boundary value conditions by using a variational method in case when the corresponding Euler action functional is coercive. Some applications…

In the data-based setting, analysis and control design of dynamical systems using measured data are typically based on overlapping trajectory segments of the input and output variables. This could lead to complex designs because the system…

We establish a replacement lemma for a variational problem, which is not based on a local argument. We then apply it to a phase transition problem and obtain pointwise estimates.

We propose an estimator of the Hilbert-Schmidt Independence Criterion obtained from an appropriate modification of the usual estimator. We then get asymptotic normality of this estimator both under independence hypothesis and under the…

Incremental stability properties are considered for certain systems of forced, nonlinear differential equations with a particular positivity structure. An incremental stability estimate is derived for pairs of input/state/output…

This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets…

We consider the oscillatory integrals with parameter-dependent phases. We decompose the integrals into a leading term and a remainder term. Instead of the pointwise estimate, we use some $L^p$-estimate for the remainder term and get various…

The principle which allows to construct new physical theories on the basis of classical mechanics by reduction of the number of its axiom without engaging new postulates is formulated. The arising incompleteness of theory manifests itself…

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

An alternative approach for minimum and mode-dependent dwell-time characterization for switched systems is derived. The proposed technique is related to Lyapunov looped-functionals, a new type of functionals leading to stability conditions…