Related papers: An Extended Small-Gain Theorem
A generalized divergence theorem is established allowing for domains with inner boundaries. The normal trace of a rough integrand is not a Radon measure; rather, the boundary integral is expressed via a surface functional continuous with…
In this note, we derive and interpret hidden zeros of tree-level amplitudes of various theories, including Yang-Mills, non-linear sigma model, special Galileon, Dirac-Born-Infeld, and gravity, by utilizing universal expansions of tree-level…
We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution…
In this work, it is demonstrated that the usual power system dynamic model exhibits a feedforward-feedback control structure. The distinct properties of the feedforward and feedback subsystems are identified and studied using respective…
A theorem on (partial) convergence to consensus of multiagent systems is presented. It is proven with tools studying the convergence properties of products of row stochastic matrices with positive diagonals which are infinite to the left.…
We consider the problem of adaptive observer design in the settings when the system is allowed to be nonlinear in the parameters, and furthermore they are to satisfy additional feasibility constraints. A solution to the problem is proposed…
We prove two extension theorems for positive maps from operator systems into matrix algebras
The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a property has a small witness, i.e. a witness in every definable…
During the past three decades, the advantageous concept of the Green's function has been extended from linear systems to nonlinear ones. At that, there exist a rigorous and an approximate extensions. The rigorous extension introduces the…
In this note, the distributed consensus corrupted by relative-state-dependent measurement noises is considered. Each agent can measure or receive its neighbors' state information with random noises, whose intensity is a vector function of…
We propose a combinatorial and graph-theoretic theory of dropout by modeling training as a random walk over a high-dimensional graph of binary subnetworks. Each node represents a masked version of the network, and dropout induces stochastic…
The paper presents a result which relates connectedness of the interaction graphs in a multi-agent systems with the capability for global convergence to a common equilibrium of the system. In particular we extend a previously known result…
The most general form of a marginal extended perturbation in a two-dimensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surface, a line or a point for which…
We introduce the concept of efficiency of a network, measuring how efficiently it exchanges information. By using this simple measure small-world networks are seen as systems that are both globally and locally efficient. This allows to give…
A collection of converse theorems for integral quadratic constraints (IQCs) is established for linear time-invariant systems. It is demonstrated that when a system interconnected in feedback with an arbitrary system satisfying an IQC is…
Fluctuation theorem is derived for a quantum current system around a nonequilibrium steady state. It is demonstrated that the fluctuation theorem can be a part of the generalized Green-Kubo formula or a nonlinear response theory of an…
We prove a version of a general transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverse providing the necessary and sufficient…
Thanks to the test function of Bian-Guan[2], we successfully obtain a constant rank theorem for partial convex solutions of a class partial differential equations. This is the microscopic version of the macroscopic partial convexity…
It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…
Addition theorems have been indispensable tools for the reduction of quantum transition amplitudes. They are normally utilized at the start of the process to move the angular dependence within plane waves and Coulomb potentials, and the…