Related papers: A conjecture on some estimates for integrals
The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary…
A simple procedure to estimate O(alpha_s^3) and O(alpha_s^4) corrections to mass-dependent observables is conjectured. The method is tested in a number of cases where the O(alpha_s^3) contribution is exactly known, and reasonable agreement…
By the example of the proof of Minkowski's conjecture on critical determinant we give a category theory framework for interval computation.
We consider the problem of function estimation in the case where an underlying causal model can be inferred. This has implications for popular scenarios such as covariate shift, concept drift, transfer learning and semi-supervised learning.…
We discuss conjectures related to the following two conjectures: (1) for each complex numbers x_1,...,x_n there exist rationals y_1,...,y_n \in [-2^{n-1},2^{n-1}] such that \forall i \in {1,...,n} (x_i=1 \Rightarrow y_i=1) \forall i,j,k \in…
We address the conjectures left by the recent article by Ferreira et al. titled ``Commuting maps and identities with inverses on alternative division rings.'' We also present an example showing the necessity of the conditions of the results…
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].
We give some results and conjectures about recurrence relations for certain sequences of binomial sums.
Comparing alternatives in pairs is a very well known technique of ranking creation. The answer to how reliable and trustworthy ranking is depends on the inconsistency of the data from which it was created. There are many indices used for…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
Interference arises when an individual's potential outcome depends on the individual treatment level, but also on the treatment level of others. A common assumption in the causal inference literature in the presence of interference is…
We derive bilateral asymptotic as well as non-asymptotic estimates for the multivariate Laplace integrals. Possible applications: Tauberian theorems for random vectors.
Much of the controversy about methods for automated decision making has focused on specific calculi for combining beliefs or propagating uncertainty. We broaden the debate by (1) exploring the constellation of secondary tasks surrounding…
Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements…
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
The Multiplicity Conjecture is a deep problem relating the multiplicity (or degree) of a Cohen-Macaulay standard graded algebra with certain extremal graded Betti numbers in its minimal free resolution. In the case of level algebras of…
In this paper we present some observations about the well-known Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also…
In this pedagogical text aimed at those wanting to start thinking about or brush up on probabilistic inference, I review the rules by which probability distribution functions can (and cannot) be combined. I connect these rules to the…
Two estimates for the inverse binary entropy function are derived using the property of information entropy to estimate combinatorics of sequences as well as related formulas from population genetics for the effective number of alleles. The…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…