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We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.

Number Theory · Mathematics 2022-12-06 Mahmoud Affouf

A multiparameter class of integrable systems is introduced.

Mathematical Physics · Physics 2007-05-23 Jens Hoppe

Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…

Number Theory · Mathematics 2022-03-01 Joseph Burnett , Alex Taylor

Continual learning is crucial for applying machine learning in challenging, dynamic, and often resource-constrained environments. However, catastrophic forgetting - overwriting previously learned knowledge when new information is acquired -…

Machine Learning · Computer Science 2025-05-30 Filip Szatkowski , Yaoyue Zheng , Fei Yang , Bartłomiej Twardowski , Tomasz Trzciński , Joost van de Weijer

When probabilistic classifiers are trained and calibrated, the so-called grouping loss component of the calibration loss can easily be overlooked. Grouping loss refers to the gap between observable information and information actually…

Machine Learning · Statistics 2022-04-26 Dirk Tasche

A concise presentation of Schrodinger's ancilla theorem (1936 Proc. Camb. Phil. Soc. 32, 446) and its several recent rediscoveries.

Quantum Physics · Physics 2007-05-23 K. A. Kirkpatrick

In statistics, researchers use Regression models for data analysis and prediction in many productive sectors (industry, business, academy, etc.). Regression models are mathematical functions representing an approximation of dependent…

Applications · Statistics 2020-09-29 Eduardo M. Vasconcelos , Adriano Gouveia de Souza

Transfer Learning (TL) aims to transfer knowledge acquired in one problem, the source problem, onto another problem, the target problem, dispensing with the bottom-up construction of the target model. Due to its relevance, TL has gained…

Machine Learning · Computer Science 2017-12-07 Ricardo Gamelas Sousa , Luís A. Alexandre , Jorge M. Santos , Luís M. Silva , Joaquim Marques de Sá

Rejoinder of "A significance test for the lasso" by Richard Lockhart, Jonathan Taylor, Ryan J. Tibshirani, Robert Tibshirani [arXiv:1301.7161].

Statistics Theory · Mathematics 2014-10-22 Richard Lockhart , Jonathan Taylor , Ryan J. Tibshirani , Robert Tibshirani

This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the…

Numerical Analysis · Mathematics 2025-10-20 U. D. Jentschura , S. V. Aksenov , P. J. Mohr , M. A. Savageau , G. Soff

This study explores the impact of class outliers on the effectiveness of example-based explainability methods for black-box machine learning models. We reformulate existing explainability evaluation metrics, such as correctness and…

Machine Learning · Computer Science 2024-08-02 Ikhtiyor Nematov , Dimitris Sacharidis , Tomer Sagi , Katja Hose

This mini-course gives an introduction to the techniques used in experimental particle physics with an emphasis on the impact of technological advances. The basic detector types and particle accelerator facilities will be briefly covered…

Instrumentation and Detectors · Physics 2007-05-23 Harry W. K. Cheung

In this paper, some points to the convergence analysis performed in the paper [A new computing approach for power signal modeling using fractional adaptive algorithms, ISA Transactions 68 (2017) 189-202] are presented. It is highlighted…

Optimization and Control · Mathematics 2020-03-24 Abdul Wahab , Shujaat Khan , Farrukh Zeeshan Khan

This article presents a summary graph to show the relationships between Information Retrieval (IR) and other related disciplines. The figure tells the key differences between them and the conditions under which one would transition into…

Information Retrieval · Computer Science 2019-12-06 Grace Hui Yang

An technically interesting proof of a known theorem.

Analysis of PDEs · Mathematics 2007-05-23 Andreas Wannebo

Quantifier-elimination or model-completeness of the affine part of some classical first order theories are proved.

Logic · Mathematics 2025-09-10 Seyed-Mohammad Bagheri

This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack…

Statistics Theory · Mathematics 2012-12-20 Derek S. Young

This text is an appendix to our work "On the growth of Kronecker coefficients", arXiv:1607.02887. Here, we provide some complementary theorems, remarks, and calculations that for the sake of space are not going to appear into the final…

Representation Theory · Mathematics 2016-11-23 Emmanuel Briand , Amarpreet Rattan , Mercedes Rosas

This dissertation collects together results on Patience Sorting and its generalizations. It incorporates the results of math.CO/0506358, math.CO/0507031, and math.CO/0512122, as well as previously unpublished results.

Combinatorics · Mathematics 2007-06-01 Isaiah Lankham

We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations…

Logic in Computer Science · Computer Science 2023-03-22 Tom Hirschowitz , Ambroise Lafont