The hyperstability theory of adaptive control systems is extended to encompass plants with unmodelled dynamics and disturbances. The analysis not only shows that leakage in the adaptive law is a natural way to avoid robustness problems (which is a known result in adaptive control theory), but also provides a new adaptive law that is a sort of signal-dependent σ-modification. The proposed adapti...

Let P (x, z) = z + ∑d i=1 ai(x)z d−i be a polynomial, where ai are real analytic functions in an open subset U of R. If for any x ∈ U the polynomial z 7→ P (x, z) has only real roots, then we can write those roots as locally lipschitz functions of x. Moreover, there exists a modification (a locally finite composition of blowing-ups with smooth centers) σ : W → U such that the roots of the corre...

Let Σ be a weighted homogeneous (singular) subvariety of C . The main objective of this paper is to present a class of explicit integral formulae for solving the ∂-equation ω = ∂λ on the regular part of Σ, where ω is a ∂-closed (0, q)-form with compact support and degree q ≥ 1. Particular cases of these formulae yield L-bounded solution operators for 1 ≤ p ≤ ∞ if Σ is a homogeneous and pure dim...

In a network, each arc is assigned a weight. The weight of a path or a cycle is defined as the minimum weight of its arcs. The maximum of weights of all paths between two nodes is defined as the strength of connectedness between the nodes. In network applications, the reduction in the strength of connectedness is more relevant than the total disconnection of the graph. A graph is totally weight...

A rational and selfish environment may have an incentive to cheat the system it interacts with. Cheating the system amounts to reporting a stream of inputs that is different from the one corresponding to the real behavior of the environment. The system may cope with cheating by charging penalties to cheats it detects. In this paper, we formalize this setting by means of weighted automata and th...

We address the problem of constructing hybrid translation systems by intersecting a Hiero-style hierarchical system with a phrase-based system and present formal techniques for doing so. We model the phrase-based component by introducing a variant of weighted finite-state automata, called σ-automata, provide a self-contained description of a general algorithm for intersecting weighted synchrono...

This paper presents a performance analysis of the recently proposed σ-self-adaptive weighted recombination evolution strategy (ES) with scaled weights. The steady state behavior of this ES is investigated for the non-noisy and noisy case, and formulas for the optimal choice of the learning parameter are derived allowing the strategy to reach maximal performance. A comparison between weighted mu...

Let d∈{3,4,5,...} and a weight w∈A ∞ ρ . We consider the second-order Riesz transform T=∇ 2 L -1 associated with Schrödinger operator L=-Δ+V, where V∈RH σ σ>d 2. present three main results. First T is bounded on weighted Hardy space H w,L 1 (ℝ d ) if w enjoys certain stable property. Secondly BMO w,ρ also belongs to an appropriate doubling class. Thirdly dual of when

We consider perfect matchings of the square-octagon lattice, also known as “fortresses” [16]. There is a natural local Markov chain on the set of perfect matchings that is known to be ergodic. However, unlike Markov chains for sampling perfect matchings on the square and hexagonal lattices, corresponding to domino and lozenge tilings, respectively, the seemingly related Markov chain on the squa...