fragility curves represent the probabilities that structural damages, under various levels of seismic excitation, will exceed the specified damage states by means of earthquake intensity damage relations. conceptual aspects related to seismic vulnerability, damage and risk evaluation are discussed first, together with a short review of the most widely used possibilities for the seismic evaluati...

In this paper we propose a unified methodology for computing the set VK(I) of complex (K = C) or real (K = R) roots of an ideal I ⊆ R[x], assuming VK(I) is finite. We show how moment matrices, defined in terms of a given set of generators of the ideal I, can be used to (numerically) find not only the real variety VR(I), as shown in the authors’ previous work, but also the complex variety VC(I),...

Given a sequence of n arbitrary events in a probability space we as sume that the individual probabilities as well as some or all joint probabilities of up to m events are known where m n Using this information we give lower and upper bounds for the probability of the union The bounds are obtained as optimum values of linear programming problems or objective function values corre sponding to fe...

The study of Artificial Neural Networks started with the analysis of linear neurons. It was then discovered that networks consisting only of linear neurons cannot describe non-linear phenomena. As a result, most currently used neural networks consist of non-linear neurons. In this paper, we show that in many cases, linear neurons can still be successfully applied. This idea is illustrated by tw...

We propose a well-posed Maxwell-type boundary condition for the linear moment system in half-space. As reduction of Boltzmann equation, equations are available to model Knudsen layers near solid wall, where proper conditions should be prescribed. Utilizing an orthogonal decomposition, we separate part with damping term from and then impose new class on it. Due condition, show that half-space va...

We show how to compute lower bounds for the maximum possible Bayes error if the class-conditional distributions must satisfy moment constraints. Our approach makes use of Curto and Fialkow’s solutions for the truncated moment problem. We also give an upper bound that follows from related work by Lanckreit et al., Bertsimas and Popescu, and Marshall and Olkin. Index Terms Bayes error, maximum en...