Related papers: Inexpressibility in Exp-Minus-Log
Exponential-constructible functions are an extension of the class of constructible functions. This extension was formulated by Cluckers-Loeser in the context of semi-algebraic and sub-analytic structures, when they studied stability under…
Itsykson and Sokolov [IS14] identified resolution over parities, denoted by $\text{Res}(\oplus)$, as a natural and simple fragment of $\text{AC}^0[2]$-Frege for which no super-polynomial lower bounds on size of proofs are known. Building on…
While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…
We denote by $\ell(n)$ the minimal length of an addition chain leading to $n$ and we define the counting function $$ F(m,r):=\#\left\{n\in[2^m, 2^{m+1}):\ell(n)\le m+r\right\}, $$ where $m$ is a positive integer and $r\ge 0$ is a real…
The authors proved that a Weyl module for a simple algebraic group is irreducible over every field if and only if the module is isomorphic to the adjoint representation for $E_{8}$ or its highest weight is minuscule. In this paper, we prove…
Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional…
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
We analyse some peculiar properties of the function of the Mittag-Leffler (M-L) type, $e_\alpha(t):= E_\alpha(-t^\alpha)$ for $0 <\alpha < 1$ and $t > 0$, which is known to be completely monotone (CM) with a non negative spectrum of…
This paper presents very simple and easy integration-free proofs in the context of Weierstrass's theory of functions, of the Maximum and Minimum Modulus Principles and Gutzmer-Parseval Inequalities for polynomials and for functions…
In this work we study a rational extension $SROEL^R T$ of the low complexity description logic SROEL, which underlies the OWL EL ontology language. The extension involves a typicality operator T, whose semantics is based on Lehmann and…
We introduce a model of register automata over infinite trees with extrema constraints. Such an automaton can store elements of a linearly ordered domain in its registers, and can compare those values to the suprema and infima of register…
We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak Konig's Lemma within the…
This paper is a mathematical investigation on Epstein semantics. One of the main tools of the present paper is the model-theoretic S-set construction introduced in (Krawczyk 2022). We use it to prove several results: 1) that each Epstein…
In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data $\omega$-words). The notion of computability is defined through Turing machines with infinite inputs which can…
Recently data trees and data words have received considerable amount of attention in connection with XML reasoning and system verification. These are trees or words that, in addition to labels from a finite alphabet, carry data values from…
Given a bounded domain $\Omega \subset {\Bbb R}^d$ with positive measure and a finite set $A=\{a^1, a^2, \dots, a^d\}$, we say that the set ${\mathcal E}(A)={\{e^{2 \pi i x \cdot a^j}\}}_{a^j \in A}$ is a complete exponential system if for…
Addition and subtraction of observed values can be computed under the obvious and implicit assumption that the scale unit of measurement should be the same for all arguments, which is valid even for any nonlinear systems. This paper starts…
We establish an irreducibility property for the characters of finite dimensional, irreducible representations of simple Lie algebras (or simple algebraic groups) over the complex numbers, i.e., that the characters of irreducible…
We show that one-dimensional Schr{\"o}dinger operators whose potentials arise by randomly concatenating words from an underlying set exhibit exponential dynamical localization (EDL) on any compact set which trivially intersects a finite set…
We investigate the convergence properties of the EM algorithm when applied to overspecified Gaussian mixture models -- that is, when the number of components in the fitted model exceeds that of the true underlying distribution. Focusing on…