Related papers: Confluence and Convergence in Probabilistically Te…
We show that degrees containing a complete extensions of arithmetic have the random join property: they are the supremum of any random real they compute, with another random real. The same is true for the truth-table and weak truth-table…
In this paper we attack the Erdos-Straus conjecture by means of the structure of its solutions, extending and improving the results of a previous paper. Using previous results and supported by the works of Elsholtz and Tao and Monks and…
This note deals with the relationship between the abscissas of simple, uniform and absolute convergence for the Dirichlet series $f(s) = \sum_{n=1}^\infty a_n n^{-s}$, when the coefficients $a_n$ are either multiplicative or completely…
In this paper, by providing a class of coherence measures in finite dimensional systems, a sufficient and necessary condition for the existence of coherence transformations that convert one probability distribution of any pure states into…
Assuming that the absence of perturbations guarantees weak or strong convergence to a common fixed point, we study the behavior of perturbed products of an infinite family of nonexpansive operators. Our main result indicates that the…
Let $\{A_{i,n}\}$ be a triangular array of elements in a Banach algebra, whose norms do not grow too fast, and whose row averages converge to $A$. Let $\sigma \in S(n)$ be a permutation drawn uniformly at random. If the array only contains…
Condensation is the phenomenon whereby one of a sum of random variables contributes a finite fraction to the sum. It is manifested as an aggregation phenomenon in diverse physical systems such as coalescence in granular media, jamming in…
Answer set programming (ASP) is a logic programming formalism used in various areas of artificial intelligence like combinatorial problem solving and knowledge representation and reasoning. It is known that enhancing ASP with function…
We investigate a slight weakening of the classical property of strong approximation, which we call almost strong approximation, for connected reductive algebraic groups over global fields with respect to special sets of valuations. While…
This work studies the question of learning probabilistic deterministic automata from language models. For this purpose, it focuses on analyzing the relations defined on algebraic structures over strings by equivalences and similarities on…
A nearly unstable sequence of stationary spatial autoregressive processes is investigated, when the sum of the absolute values of the autoregressive coefficients tends to one. It is shown that after an appropriate norming the least squares…
Approximate Bayesian computation (ABC) has gained popularity in recent years owing to its easy implementation, nice interpretation and good performance. Its advantages are more visible when one encounters complex models where maximum…
The almost sure convergence of ergodic averages in Birkhoff's pointwise ergodic theorem is known to fail in the finitely additive setting. We introduce a natural reformulation of almost sure convergence suitable for finitely additive…
This is an announcement of a series of upcoming works on boundary regularity for area minimizing currents, one of which is in collaboration with Reinaldo Resende. The setting we consider is that of an area minimizing current with a smooth…
The vast majority of convergence rates analysis for stochastic gradient methods in the literature focus on convergence in expectation, whereas trajectory-wise almost sure convergence is clearly important to ensure that any instantiation of…
This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
Confluence denotes the property of a state transition system that states can be rewritten in more than one way yielding the same result. Although it is a desirable property, confluence is often too strict in practical applications because…
We introduce a system of monadic affine sized types, which substantially generalise usual sized types, and allows this way to capture probabilistic higher-order programs which terminate almost surely. Going beyond plain, strong…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
We present an equational inference system for finite-state expressions, and prove that the system is sound and complete with respect to divergence preserving branching congruence, closing a problem that has been open since 1993. The…