Related papers: Exact conditions for countable inclusion-exclusion…
We introduce the $\Sigma_1$-definable universal finite sequence and prove that it exhibits the universal extension property amongst the countable models of set theory under end-extension. That is, (i) the sequence is $\Sigma_1$-definable…
If T has only countably many complete types, yet has a type of infinite multiplicity then there is a ccc forcing notion Q such that, in any Q --generic extension of the universe, there are non-isomorphic models M_1 and M_2 of T that can be…
We introduce and prove the consistency of a new set theoretic axiom we call the \emph{Invariant Ideal Axiom}. The axiom enables us to provide (consistently) a full topological classification of countable sequential groups, as well as fully…
A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…
This paper investigates coherent-like conditions and related properties that a trivial extension might inherit from the ground ring over some classes of modules. It captures previous results dealing primarily with coherence, and also…
We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…
Given any polynomial $p$ in $C[X]$, we show that the set of irreducible matrices satisfying $p(A)=0$ is finite. In the specific case $p(X)=X^2-nX$, we count the number of irreducible matrices in this set and analyze the arising sequences…
Missing data may be disastrous for the identifiability of causal and statistical estimands. In graphical missing data models, colluders are dependence structures that have a special importance for identification considerations. It has been…
A necessary and sufficient condition is provided for the solvability of a binomial congruence with a composite modulus, circumventing its prime factorization. This is a generalization of Euler's Criterion through that of Euler's Theorem,…
In this article, we derive conditions for the existence of solutions to state-constrained continuity inclusions in Wasserstein spaces whose right-hand sides may be discontinuous in time. These latter are based on a fine investigation of the…
An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…
We consider general non-Euclidean distance measures between real world objects that need to be classified. It is assumed that objects are represented by distances to other objects only. Conditions for zero-error dissimilarity based…
Young's inequality is extended to the context of absolutely continuous measures. Several applications are included.
We introduce a new natural notion of convergence for permutations at any specified scale, in terms of the density of patterns of restricted width. In this setting we prove that limits may be chosen independently at a countably infinite…
In this article we introduce associative Look-Up Tables. With their help, pseudo sums are correctly determined. The set of limit distributions in a pseudo-summation scheme of i.i.d. random variables is described. Also, two special cases…
We prove a tight uniform continuity bound for the conditional Shannon entropy of discrete finitely supported random variables in terms of total variation distance.
We prove that it is consistent that the covering of the ideal of measure zero sets has countable cofinality.
The bounds for absolute moments of order statistics are established. Let $X_1,\dots ,X_n$ be independent identically distributed real-valued random variables and let $X_{1:n}\le \dots \le X_{n:n}$ be the corresponding order statistics. The…
We consider the question of which nonconvex sets can be represented exactly as the feasible sets of mixed-integer convex optimization problems. We state the first complete characterization for the case when the number of possible integer…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…