Related papers: Divisibility Theory and Complexity of Algorithms i…

In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.

This is a 1971 dissertation. Only its extended abstract was published at the time. While some results appeared in other publications, a number of details remained unpublished and may still have relevance.

We indicate a natural generalization of the concept of subgroup commutativity degree of a finite group and a list of open problems on these new concepts.

Originally published as a Supplemental Appendix to Adjoint Equations in Stability Analysis, Annu. Rev. Fluid Mech. 46:493-517 (2014)

This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…

This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).

This paper has been divided into three papers. arXiv:0809.3232, arXiv:0808.4134, arXiv:cs/0607105

In this paper, we summarize the work on the characterization of finite simple groups and the study on finite groups with the set of element orders and two orders (the order of group and the set of element orders). Some related topics, and…

The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, \textit{Complexity of finite semigroups}, Annals of Mathematics (2) \textbf{88} (1968), 128--160, motivated by the…

This is the English version of the paper: "Complejidad de los n\'umeros naturales", Gaceta de la Real Sociedad Matem\'atica Espa\~nola 3 (2000) 230--250. In this paper, several conjectures about the complexity of natural numbers are…

This is a review article on modular categories, extending an invited talk given at the workshop "Categorical (co)algebraic methods in quantum informatics and linguistics", Oxford, October 29-31, 2010. To appear in C. Heunen, M. Sadrzadeh,…

English translation of "Bemerkungen zur allgemein-relativistischen Fassung der Quantentheorie", originally published in {\em Sitzber. kgl.-preu{\ss}. Akad. Wiss. Berlin, Sitzung der phys.-math. Klasse} {\bf XXIV} (1932) 346--354.

Correction to Annals of Probability 28 (2000) 277--302 [doi:10.1214/aop/1019160120].

This article appeared in the September 2024 issue (Vol. 31, No. 3) of the Bulletin of the International Society for Bayesian Analysis (ISBA).

Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM

This is a copy of the article published in Math Res. Letters 5, (1998) 497-516.

This is a survey article with a limited list of references (as required by the publisher) which appears in the Encyclopedia of Mathematical Physics, eds. J.-P. Francoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006. vol.4, pp.94--104.

We address two sets of long-standing open questions in probability theory, from a computational complexity perspective: divisibility of stochastic maps, and divisibility and decomposability of probability distributions. We prove that finite…

The paper (as posted originally) contains several errors. It has been subsequently split into two papers, the corrected (and accepted for publication) versions appear in the archive as papers cs.CC/0503082 and cs.DM/0503083.

We introduce a finite version of free probability and show the link between recent results using polynomial convolutions and the traditional theory of free probability. One tool for accomplishing this is a seemingly new transformation that…