A theory is called κ-categorical, or categorical in power κ, if it has one model up to isomorphism of cardinality κ. Morley’s Categoricity Theorem states that if a theory of first order logic is categorical in some uncountable power κ, then it is categorical in every uncountable power. We provide an elementary exposition of this theorem, by showing that a theory is categorical in some uncountab...

We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of Lω1,ω). Theorem: Let T be any complete first-order theory in a countable language with an atomic model. If the pseudo-minimal types are not dense, then there are 2א1 pairwise non-isomorphic atomic models of T , each of size א1.

where Ḣ 1 (Ω) is the closure of C ∞ 0 (Ω) in the Sobolev space H 1 1 (Ω) of functions in L(Ω) with one derivative in L. The purpose of this paper is the study of the dependence of λ1,Ω under regular perturbations by diffeomorphisms of Ω, i.e. we want to compute the first variation, the so-called shape derivative, of the functional Ω → λ1,Ω. General results about the stability of λ1,Ω under pert...

The problem of computing the moment generating function of the first passage time T to a > 0 or −b < 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T .

A novel approach which employs principles of higher order logic analyses was developed to systematically correlate phylogenetic data with phenotype profiles by identification of phenotype specific patterns of presence of multiple proteins. For example, for most genomes expressing trait A, the presence of protein C presumes the presence of protein B, while for other genomes (not expressing the t...

Occurrence If you have asthma, you're not alone . . . Asthma is the sixth most common chronic condition in our nation, affecting between 12 and 17 million people. In children, asthma usually occurs by age 5 (several studies show that 50 to 80% of children with asthma develop symptoms before their 5 birthday). Adults usually develop asthma in their 30s, but even older adults can contract the dis...

This paper performs the first investigation into depth for large-scale human action recognition in video where the depth cues are estimated from the videos themselves. We develop a new framework called depth2action and experiment thoroughly into how best to incorporate the depth information. We introduce spatio-temporal depth normalization (STDN) to enforce temporal consistency in our estimated...

The notion of acceptability is a counterpart of the phenomenon observed in our daily argumentation and originates from an old saying, “The one who has the last word laughs best”, as stated by Dung. It is an empirical social truth or wisdom that has been evolved in various cultural sphere over generations and considered useful by people. It is remarkable and suggestive that Dung’s theory of argu...