Let $X$ be a regular tame stack. If is locally of finite type over field, we prove that the essential dimension equal to its generic dimension, this generalizes previous result P. Brosnan, Z. Reichstein and second author. Now suppose $1$-dimensional local noetherian domain $R$ with fraction field $K$ residue $k$. We $\operatorname{ed}_{k}X_{k} \le \operatorname{ed}_{K}X_{K}$ if $X\to \operatorn...

How far can we go in weakening the assumptions of the general equilibrium model? Existence of equilibrium, structural stability and finiteness of equilibria of regular economies, genericity of regular economies and an index formula for the equilibria of regular economies have been known not to require transitivity and completeness of consumers’ preferences. We show in this paper that if consume...

This paper deals with two important aspects of communicat ion protocols namely specificationnand verification.We present a new variant of the Formal Description Techni que Estelle called SSL which has the semantics of a High-level Petri net model. Such a semantics enables to apply efficient proof methods in order to automatically verify communication prot ocol properties. SSL is mainly characte...

Abstract This paper addresses the following question of neural network identifiability: Does input–output map realized by a feed-forward with respect to given nonlinearity uniquely specify architecture, weights, and biases? The existing literature on subject (Sussman in Neural Netw 5(4):589–593, 1992; Albertini et al. Artificial networks for speech vision, 1993; Fefferman Rev Mat Iberoam 10(3):...

A set A is a base for Schnorr randomness if it is Turing reducible to a set R which is Schnorr random relative to A, and the notion of a base for weak 1-genericity can be defined similarly. We show that A is a base for Schnorr randomness if and only if A is a base for weak 1-genericity if and only if the halting set K is not Turing reducible to A. Furthermore, we define a set A to be high for S...

Multi-homogeneous polynomial systems arise in many applications. We provide bit complexity estimates for solving them which, up to a few extra other factors, are quadratic in the number of solutions and linear in the height of the input system under some genericity assumptions. The assumptions essentially imply that the Jacobian matrix of the system under study has maximal rank at the solution ...

This paper investigates the notion of resource bounded genericity developed by Ambos Spies Fleischhack and Huwig Ambos Spies Neis and Terwijn have recently shown that every language that is t n random over the uniform probability measure is t n generic It is shown here that in fact every language that is t n random over any strongly positive t n computable probability measure is t n generic Rou...

We study the number of nodal domains (maximal connected regions on which a function has constant sign) of the eigenfunctions of Schrödinger operators on graphs. Under certain genericity condition, we show that the number of nodal domains of the n-th eigenfunction is bounded below by n− l, where l is the number of links that distinguish the graph from a tree. Our results apply to operators on bo...

This paper presents a case study for the GraBaTs'09 tool contest. Program comprehension may bene t from graph and transformation techniques because they enable custom queries, and complex query results (i.e., graphs). However, there is one main issue to address: scalability. Software developers need tools that help them understand large code bases. For instance, the Java Development Tools from ...