Related papers: An Extended Small-Gain Theorem

Evolution of arbitrary stochastic system was considered in frame of phase transition description. Concept of Reynolds parameter of hydrodynamic motion was extended to arbitrary complex system. Basic phase parameter was expressed through…

This paper studies the graph-theoretic conditions for stability of positive monotone systems. Using concepts from input-to-state stability and network small-gain theory, we first establish necessary and sufficient conditions for the…

We generalize the dual notions of "expansion" and "collapse" so they can be applied to arbitrary metric spaces. We also expand the theory to allow for infinitely many such moves. Those tools are then employed to prove a variety of…

In this paper, we develop Terence Tao's harmonic analysis method and apply it to restricted sumsets. The well known Cauchy-Davenport theorem asserts that if $A$ and $B$ are nonempty subsets of $Z/pZ$ with $p$ a prime, then $|A+B|\ge…

In this paper, we introduce a compositional scheme for the construction of finite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on small-gain type reasoning. In…

We derive an upper bound for the expected gain of informed traders in the Glosten-Milgrom model with finite horizon, fully analogous to a generalized second law of thermodynamics. This result extends that obtained by Touzo et al. a couple…

The small-world property is known to have a profound effect on the navigation efficiency of complex networks [J. M. Kleinberg, Nature 406, 845 (2000)]. Accordingly, the proper addition of shortcuts to a regular substrate can lead to the…

If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…

We present a generalization of Warning's Second Theorem to polynomial systems over a finite local principal ring with suitably restricted input and output variables. This generalizes a recent result with Forrow and Schmitt (and gives a new…

Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…

The purpose of this note is to present my understanding of Tim Austin's proof of the multiple ergodic theorem for commuting transformations, emphasizing on the use of joinings, extensions and factors. The existence of a sated extension,…

We prove a general transfer theorem for multivariate random sequences with independent random indexes in the double array limit setting. We also prove its partial inverse providing necessary and sufficient conditions for the convergence of…

The formal consideration of the concept of interaction in thermodynamic analysis makes it possible to deduce, in the broadest terms, new results related to the coevolution of interacting systems, irrespective of their distance from…

In this paper, we address the distributed prescribed-time convex optimization (DPTCO) for a class of networked Euler-Lagrange systems under undirected connected graphs. By utilizing position-dependent measured gradient value of local…

In this paper we define contractive and nonexpansive properties for adapted stochastic processes $X_1, X_2, \ldots $ which can be used to deduce limiting properties. In general, nonexpansive processes possess finite limits while contractive…

This work considers distributed sensing and transmission of sporadic random samples. Lower bounds are derived for the reconstruction error of a single normally or uniformly-distributed finite-dimensional vector imperfectly measured by a…

We introduce the homogeneous and piecewise multilinear extensions and the eigenvalue problem for locally Lipschitz function pairs, in order to develop a systematic framework for relating discrete and continuous min-max problems. This also…

We revisit the classical dissipativity theorem of linear-quadratic theory in a generalized framework where the quadratic storage is negative definite in a p-dimensional subspace and positive definite in a complementary subspace. The…

This note provides a theorem showing, under suitable technical assumptions, that if a system S adapts to a class of external signals U, in the sense of egulation against disturbances or tracking signals in U, then S must ecessarily contain…

This article is the last of the series of articles where we reprove the foundational ideas of abstract six-functor formalisms developed by Liu-Zheng. We prove the theorem of partial adjoints, which is a simplicial technique of encoding…