Yao's formula is one of the basic tools in any situation where one wants to estimate the number of blocks to be read in answer to some query. We show that such situations can be modelized by probabilistic urn models. This allows us to fully characterize the distribution probability of the number of selected blocks under uniformity assumptions, and to consider extensions to non-uniform block pro...

Probabilistic numerical methods aim to model numerical error as a source of epistemic uncertainty that is subject to probabilistic analysis and reasoning, enabling the principled propagation of numerical uncertainty through a computational pipeline. In this paper we focus on numerical methods for integration. We present probabilistic (Bayesian) versions of both Markov chain and Quasi Monte Carl...

In this article, we propose a Partition ofUnity Refinement (PUR)method to improve the local approximations of elliptic boundary value problems in regions of interest. The PUR method only needs to refine the local meshes and hanging nodes generate no difficulty. The mesh qualities such as uniformity or quasi-uniformity are kept. The advantages of the PUR include its effectiveness and relatively ...

Quasi-Monte Carlo integration is said to be better than Monte-Carlo integration since its error bound can be in the order of O(N (1 )) instead of the O(N 0:5) probabilistic bound of classical Monte-Carlo integration if the integrand has finite variation. However, since in computer graphics the integrand of the rendering equation is usually discontinuous and thus has infinite variation, the supe...

Quasi-Borel spaces are a new mathematical structure that supports higher-order probability theory, first-order iteration, and modular semantic validation of Bayesian inference algorithms with continuous distributions. Like a measurable space, a quasi-Borel space is a set with extra structure suitable for defining probability and measure distributions. But unlikemeasurable spaces, quasi-Borel sp...

New concepts are defined, in particular the quasi-question or vertex with an outgoing arc of zero probability. A quasi-questionnaire is a probabilistic homogeneous (rooted) tree with quasiquestions. It is shown that every instantaneous code is a quasi-questionnaire with precise restrictive conditions; it may also be a questionnaire, without an arc of zero probability. Also, an approximation is ...

Given positive integers n and k, a k-term quasi-progression of diameter n is a sequence (x1, x2, ..., xk) such that d ≤ xj+1−xj ≤ d+n, 1 ≤ j ≤ k−1, for some positive integer d. Thus an arithmetic progression is a quasi-progression of diameter 0. Let Qn(k) denote the least integer for which every coloring of {1, 2, ..., Qn(k)} yields a monochromatic k-term quasi-progression of diameter n. We obt...

The original definition of a topological space given by Hausdorff used neighborhood systems. Lattice-valued maps appear in this context when you identify a topology with a monoid in the Kleisli category of the filter monad on SET. H?hle’s notion of a lattice-valued topology [2] uses the same idea and it’s inspired in the classical lattice-valued topologies. Ltopological spaces are motivated by ...

Loosely speaking, an interactive proof is said to be zeroknowledge if the view of every “efficient” verifier can be “efficiently” simulated. An outstanding open question regarding zero-knowledge is whether constant-round concurrent zero-knowledge proofs exists for nontrivial languages. We answer this question to the affirmative when modeling “efficient adversaries” as probabilistic quasi-polyno...