Related papers: An Extended Small-Gain Theorem

We study a topological generalization of ideal co-maximality in topological rings and present some of its properties, including a generalization of the Chinese remainder theorem. Using the hyperspace uniformity, we prove a stronger version…

This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain…

This paper studies the distributed L2-gain control problem for continuous-time large-scale systems under Round-Robin communication protocol. In this protocol, each sub-controller obtains its own subsystem's state information continuously,…

The small object argument is a method for transfinitely constructing weak factorization systems originally motivated by homotopy theory. We establish a variant of the small object argument that is enriched over a cofibrantly generated weak…

Restriction is a natural quasi-order on $d$-way tensors. We establish a remarkable aspect of this quasi-order in the case of tensors over a fixed finite field -- namely, that it is a well-quasi-order: it admits no infinite antichains and no…

We establish a number of "concatenation theorems" that assert, roughly speaking, that if a function exhibits "polynomial" (or "Gowers anti-uniform", "uniformly almost periodic", or "nilsequence") behaviour in two different directions…

The fluctuation theorems have remained one of the cornerstones in the study of systems that are driven far out of equilibrium, and they provide strong constraints on the fraction of trajectories that behave atypically in light of the second…

The binary radix expansion of a real number can be used to code the outcome of any series of coin tosses, a fact that provides an intriguing link between number theory, measure theory and statistical physics. Inspired by this fact, a…

We establish asymptotic gain along with input-to-state practical stability results for disturbed semilinear systems w.r.t. the global attractor of the respective undisturbed system. We apply our results to a large class of nonlinear…

Following the seminal work of Zames, the input-output theory of the 70s acknowledged that incremental properties (e.g. incremental gain) are the relevant quantities to study in nonlinear feedback system analysis. Yet, non-incremental…

We give a generalization of Kung's theorem on critical exponents of linear codes over a finite field, in terms of sums of extended weight polynomials of linear codes. For all i=k+1,...,n, we give an upper bound on the smallest integer m…

Strong student models can learn from weaker teachers: when trained on the predictions of a weaker model, a strong pretrained student can learn to correct the weak model's errors and generalize to examples where the teacher is not confident,…

We introduce the Vector Fitting algorithm for the creation of reduced-order models from the sampled response of a linear time-invariant system. This data-driven approach to reduction is particularly useful when the system under modeling is…

A theorem is derived which (i) provides a new class of subfactors which may be interpreted as generalized asymptotic subfactors, and which (ii) ensures the existence of two-dimensional local quantum field theories associated with certain…

In this short note we give counterexamples to several results related to extension theorems published recently.

We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…

Statistical mechanics is generalized on the basis of an additive information theory for incomplete probability distributions. The incomplete normalization $\sum_{i=1}^wp_i^q=1$ is used to obtain generalized entropy $S=-k\sum_{i=1}^wp_i^q\ln…

We observe that successive applications of known results from the theory of positive systems lead to an {\it efficient general algorithm} for positive realizations of transfer functions. We give two examples to illustrate the algorithm, one…

We obtain the following embedding theorem for symbolic dynamical systems. Let $G$ be a countable amenable group with the comparison property. Let $X$ be a strongly aperiodic subshift over $G$. Let $Y$ be a strongly irreducible shift of…

We study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance,…