Related papers: Chain-dependent Conditions in Extremal Set Theory
We investigate the relative information content of six measures of dependence between two random variables $X$ and $Y$ for large or extreme events for several models of interest for financial time series. The six measures of dependence are…
This paper continues studies of non-intersection properties of finite collections of sets initiated 40 years ago by the extremal principle. We study elementary non-intersection properties of collections of sets, making the core of the…
Model transformations operate on models conforming to precisely defined metamodels. Consequently, it often seems relatively easy to chain them: the output of a transformation may be given as input to a second one if metamodels match.…
Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…
In the study of quantum nonlocality, one obstacle is that the analytical criterion for identifying the boundaries between quantum and postquantum correlations has not yet been given, even in the simplest Bell scenario. We propose a…
We study the extremes for a class of a symmetric stable random fields with long range dependence. We prove functional extremal theorems both in the space of sup measures and in the space of cadlag functions of several variables. The limits…
We investigate the task of controlling ensembles of initial and terminal state vectors of parameter-dependent linear systems by applying parameter-independent open loop controls. Necessary, as well as sufficient, conditions for ensemble…
Let $T$ be a (first order complete) dependent theory, ${\mathfrak{C}}$ a $\bar\kappa$-saturated model of $T$ and $G$ a definable subgroup which is abelian. Among subgroups of bounded index which are the union of $<\bar\kappa$ type definable…
We show that classical chaining bounds on the suprema of random processes in terms of entropy numbers can be systematically improved when the underlying set is convex: the entropy numbers need not be computed for the entire set, but only…
A collection of sets is {\em intersecting} if every two members have nonempty intersection. We describe the structure of intersecting families of $r$-sets of an $n$-set whose size is quite a bit smaller than the maximum ${n-1 \choose r-1}$…
Let $\mathcal{F}\subseteq{[n]\choose k}$ be a $t$-intersecting family. Define the $t$-covering number $\tau_t(\mathcal{F})$ of $\mathcal{F}$ as the minimum size of a subset $S$ of $[n]$ with $|S\cap F|\geqslant t$ for each…
For a left-compressed intersecting family \A contained in [n]^(r) and a set X contained in [n], let \A(X) = {A in \A : A intersect X is non-empty}. Borg asked: for which X is |\A(X)| maximised by taking \A to be all r-sets containing the…
In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…
There is much more known about the family of superstable theories when compared to stable theories. This calls for a search of an analogous "super-dependent" characterization in the context of dependent theories. This problem has been…
In statistical physics, the challenging combinatorial enumeration of the configurations of a system subject to hard constraints (microcanonical ensemble) is mapped to a mathematically easier calculation where the constraints are softened…
Given a finite set satisfying condition $\mathcal{A}$, the subset selection problem asks, how large of a subset satisfying condition $\mathcal{B}$ can we find? We make progress on three instances of subset selection problems in planar point…
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…
A balanced pattern of order $2d$ is an element $P \in \{+,-\}^{2d}$, where both signs appear $d$ times. Two sets $A,B \subset [n]$ form $P$-pattern, which we denote by $\operatorname{pat}(A,B) = P$, if $A\triangle B = \{j_1,\ldots…
Dependent pattern matching is a key feature in dependently typed programming. However, there is a theory-practice disconnect: while many proof assistants implement pattern matching as primitive, theoretical presentations give semantics to…