Related papers: Solovay reducibility implies S2a-reducibility
Prominent approaches to belief revision prescribe the adoption of a new belief that is as close as possible to the prior belief, in a process that, even in the standard case, can be described as attempting to minimize surprise. Here we…
The article is devoted to the resampling approach application to the reliability problems. This approach to reliability problems was first proposed by Ivnitsky (1967). Resampling is intensive statistical computer method, which is…
We show that there is a strong connection between Weihrauch reducibility on one hand, and provability in EL_0, the intuitionistic version of RCA_0, on the other hand. More precisely, we show that Weihrauch reducibility to the composition of…
This paper presents categorical formulations of Turing, Medvedev, Muchnik, and Weihrauch reducibilities in Computability Theory, utilizing Lawvere doctrines. While the first notions lend themselves to a smooth categorical presentation,…
We survey the Kolmogorov's approach to the notion of randomness through the Kolmogorov complexity theory. The original motivation of Kolmogorov was to give up a quantitative definition of information. In this theory, an object is randomness…
We define the rectangular additive convolution of polynomials with nonnegative real roots as a generalization of the asymmetric additive convolution introduced by Marcus, Spielman and Srivastava. We then prove a sliding bound on the largest…
We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., for problems in which there are first-stage feasible solutions that are not guaranteed to have a feasible…
The paper is the second of our series of notes aimed to bring back in circulation some bright ideas of early modern set theory, mainly due to Harrington and Sami, which have never been adequately presented in set theoretic publications. We…
This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for…
This paper discusses a forgotten remark of Paul L\'evy (1935), determining the asymptotic distribution of sums of i.i.d. random variables with tails $cx^{-\alpha}\psi(\log x)$, where $0<\alpha<2$ and $\psi$ is a periodic function on…
We introduce and study several notions of computability-theoretic reducibility between subsets of $\omega$ that are "robust" in the sense that if only partial information is available about the oracle, then partial information can be…
We present an approach for variational regularization of inverse and imaging problems for recovering functions with values in a set of vectors. We introduce regularization functionals, which are derivative-free double integrals of such…
We investigate the role of continuous reductions and continuous relativisation in the context of higher randomness. We define a higher analogue of Turing reducibility and show that it interacts well with higher randomness, for example with…
Monotonic convergence is established for a general class of multiplicative algorithms introduced by Silvey, Titterington and Torsney [Comm. Statist. Theory Methods 14 (1978) 1379--1389] for computing optimal designs. A conjecture of…
In this article we prove a reducibility result for the linear Schr\"odinger equation on a Zoll manifold with quasi-periodic in time pseudo-differential perturbation of order less or equal than $1/2$. As far as we know, this is the first…
In 1853 J. Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these…
For variable-length coding with an almost-sure distortion constraint, Zhang et al. show that for discrete sources the redundancy is upper bounded by $\log n/n$ and lower bounded (in most cases) by $\log n/(2n)$, ignoring lower order terms.…
The regularity theory for variational inequalities over polyhedral sets developed in a series of papers by Robinson, Ralph and Dontchev-Rockafellar in the 90s has long become classics of variational analysis. But in the available proofs of…
General extensions of an inequality due to Rogozin, concerning the essential supremum of a convolution of probability density functions on the real line, are obtained. While a weak version of the inequality is proved in the very general…
A quantitative version of the scalar lower bound under $C^0$ convergence was conjectured by Gromov. More recently, Mazurowski and Yao proved that a refined form of Gromov's conjecture holds in dimension three. Furthermore, they constructed…