Related papers: A conjecture on some estimates for integrals
In 2008, M. Kaneko made several interesting observations about the values of the modular j invariant at real quadratic irrationalities. The values of modular functions at real quadratics are defined in terms of their cycle integrals along…
To interpret uncertainty estimates from differentiable probabilistic models, recent work has proposed generating Counterfactual Latent Uncertainty Explanations (CLUEs). However, for a single input, such approaches could output a variety of…
We propose an inference procedure for estimators defined by mathematical programming problems, focusing on the important special cases of linear programming (LP) and quadratic programming (QP). In these settings, the coefficients in both…
Although much has been said about parallelism in discourse, a formal, computational theory of parallelism structure is still outstanding. In this paper, we present a theory which given two parallel utterances predicts which are the parallel…
We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when…
An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.
The aim of this expository article is twofold. The first is to introduce several polynomials of one variable as well as two variables defined on the positive integers with values as congruent numbers. The second is to present connections…
After discussing two senses in which the notion of undecidability is used, we present a survey of undecidable decision problems arising in various branches of mathematics.
Calibration is a frequently invoked concept when useful label probability estimates are required on top of classification accuracy. A calibrated model is a function whose values correctly reflect underlying label probabilities. Calibration…
These lecture notes are devoted to selected topics related to the uncertainty principle in harmonic analysis. Rather than attempting a systematic treatment, we emphasize only a number of both classical and deep manifestations of this…
The random integral mappings (some type of functionals of L\'evy processes) are continuous homomorphisms between convolution subsemigroups of the semigroup of all infinitely divisible measures. Compositions of those random integrals…
We establish supercongruences for two kinds of Ap\'ery-like numbers, which involve Bernoulli numbers and Bernoulli polynomials. Conjectural supercongruences of the same type for another four kinds of Ap\'ery-like numbers are also proposed.
The inability to correctly resolve rumours circulating online can have harmful real-world consequences. We present a method for incorporating model and data uncertainty estimates into natural language processing models for automatic rumour…
A key challenge in causal inference from observational studies is the identification and estimation of causal effects in the presence of unmeasured confounding. In this paper, we introduce a novel approach for causal inference that…
In upcoming papers by Conrey, Farmer and Zirnbauer there appear conjectural formulas for averages, over a family, of ratios of products of shifted L-functions. In this paper we will present various applications of these ratios conjectures…
We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.
We present correspondences induced by some classical mappings between measures on an interval and measures on the unit circle. More precisely, we link their sequences of orthogonal polynomial and their recursion coefficients. We also deduce…
The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized…
As a consequence of the Integral Test we find a triple inequality which bounds up and down both a series with respect to its corresponding improper integral, and reciprocally an improper integral with respect to its corresponding series.
We introduce the notion of multiple extremal integrals as an extension of single extremal integrals, which have played important roles in extreme value theory. The multiple extremal integrals are formulated in terms of a product-form random…