‎let $x=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the hankel matrix of size $2times n$ and let $g$ be a closed graph on the vertex set $[n].$ we study the binomial ideal $i_gsubset k[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $x$ which correspond to the edges of $g.$ we show that...

We investigate the connection between measure, capacity and algorithmic randomness for the space of closed sets. For any computable measure m, a computable capacity T may be de ned by letting T (Q) be the measure of the family of closed sets K which have nonempty intersection with Q. We prove an e ective version of Choquet's capacity theorem by showing that every computable capacity may be obta...

The study of random surfaces as a generalization of Brownian motion, led to a renewed interest after the work of A. N. Polyakov[1]. In 1984, A. Billore, D.J. Gross and E. Marinari[2] applied Monte Carlo techniques to the numerical study of free random surfaces defined as a set of a fixed number of triangles embedded in a continuum space. This method, in practice, is a simulation of a microcanon...

We recently introduced an extensional model of the pure λcalculus living in a cartesian closed category of sets and relations. In this paper, we provide sufficient conditions for categorical models living in arbitrary cpo-enriched cartesian closed categories to have H∗, the maximal consistent sensible λ-theory, as their equational theory. Finally, we prove that our relational model fulfils thes...

There are many properties of mathematical objects that satisfy what is sometimes called a 0-1 law, in the following sense. Under some natural probability measure on the set of objects, the measure of the subset of objects having the given property is either 0 or 1. In the latter case we can say that almost all the objects have the property. Familiar examples of this phenomenon are the following...

We introduce Oberwolfach randomness, a notion within Demuth’s framework of statistical tests with moving components; here the components’ movement has to be coherent across levels. We show that a ML-random set computes all K-trivial sets if and only if it is not Oberwolfach random, and indeed that there is a K-trivial set which is not computable from any Oberwolfach random set. We show that Obe...