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We give an alternative presentation of the ordinal notation at the strength of $\Pi^1_1-CA_0$ which allows the "uncountable" notation $\Omega$ to be interpreted "polymorphically" - that is, we allow the notation to be interpreted as…

Logic · Mathematics 2025-06-23 Henry Towsner

Electronics has changed greatly during recent decades, and some its basic concepts should be revisited. Starting from the sampling procedure, we consider some mathematical, physical and engineering aspects related to singular, mainly…

Exactly Solvable and Integrable Systems · Physics 2008-01-24 Emanuel Gluskin

This article reveals an analysis of the quadratic systems that hold multiparametric families therefore, in the first instance the quadratic systems are identified and classified in order to facilitate their study and then the stability of…

Rankings are central to decision-making in fields ranging from education to online platforms, yet classical deterministic methods such as the Borda count method or Copeland-type pairwise methods ignore uncertainty due to sampling noise or…

Methodology · Statistics 2026-05-20 Shunpu Zhang

This paper expands on existing learned models of human behavior via a measured step in structured irrationality. Specifically, by replacing the suboptimality constant $\beta$ in a Boltzmann rationality model with a function over states…

Artificial Intelligence · Computer Science 2024-04-30 Osher Lerner

The paper concerns the study of criticality of Lagrange multipliers in variational systems that has been recognized in both theoretical and numerical aspects of optimization and variational analysis. In contrast to the previous developments…

Optimization and Control · Mathematics 2018-08-14 Boris Mordukhovich , Ebrahim Sarabi

Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…

Computational Engineering, Finance, and Science · Computer Science 2008-11-06 Michel Fliess , Cédric Join , Hebertt Sira-Ramirez

We present and experimentally demonstrate a novel non-classical phenomenon, bi-contextuality, observed in quantum systems prepared by two independent sources. This discovery plays a key role in the developing framework of network…

A datatype defining rewrite system (DDRS) is an algebraic (equational) specification intended to specify a datatype. When interpreting the equations from left-to-right, a DDRS defines a term rewriting system that must be ground-complete.…

Logic in Computer Science · Computer Science 2023-06-22 Jan A. Bergstra , Alban Ponse

Learning the unknown causal parameters of a linear structural causal model is a fundamental task in causal analysis. The task, known as the problem of identification, asks to estimate the parameters of the model from a combination of…

Artificial Intelligence · Computer Science 2024-07-18 Julian Dörfler , Benito van der Zander , Markus Bläser , Maciej Liskiewicz

A recent approach to the Beck-Fiala conjecture, a fundamental problem in combinatorics, has been to understand when random integer matrices have constant discrepancy. We give a complete answer to this question for two natural models:…

Probability · Mathematics 2021-08-17 Dylan J. Altschuler , Jonathan Niles-Weed

Matthes and Uustalu (TCS 327(1-2):155-174, 2004) presented a categorical description of substitution systems capable of capturing syntax involving binding which is independent of whether the syntax is made up from least or greatest fixed…

Logic in Computer Science · Computer Science 2023-08-17 Benedikt Ahrens , Ralph Matthes

Consider the minimal $\beta$-shift containing the shift space generated by given Sturmian word. In this paper we characterize such $\beta$ and investigate its combinatorial, dynamical and topological properties and prove that such $\beta$…

Combinatorics · Mathematics 2007-05-23 Dong Pyo Chi , DoYong Kwon

A new number system, the set of the non-Dedekindian numbers, is introduced and characterized axiomatically. It is then proved that any hypercontinous hyperreal number system is strictly included in the set of the Non-Dedekindian Numbers.…

General Mathematics · Mathematics 2007-05-23 Gavriel Segre

In applications with significant class imbalance or asymmetric costs, metrics such as the $F_\beta$-measure, AM measure, Jaccard similarity coefficient, and weighted accuracy offer more suitable evaluation criteria than standard binary…

Machine Learning · Computer Science 2025-12-30 Anqi Mao , Mehryar Mohri , Yutao Zhong

This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…

Optimization and Control · Mathematics 2007-05-23 L. Dorcak , V. Lesko , I. Kostial

Feng and Wang showed that two homogeneous iterated function systems in $\mathbb{R}$ with multiplicatively independent contraction ratios necessarily have different attractors. In this paper, we extend this result to graph directed iterated…

Dynamical Systems · Mathematics 2013-11-26 Emilie Charlier , Julien Leroy , Michel Rigo

The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…

Methodology · Statistics 2019-11-15 Jon Cockayne , Chris Oates , Tim Sullivan , Mark Girolami

Pretrained transformers achieve the state of the art across tasks in natural language processing, motivating researchers to investigate their inner mechanisms. One common direction is to understand what features are important for…

Computation and Language · Computer Science 2021-08-06 Zhiying Jiang , Raphael Tang , Ji Xin , Jimmy Lin

An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through…

Methodology · Statistics 2016-09-19 Gero Walter , Louis J. M. Aslett , Frank P. A. Coolen