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In [3] a short proof is given that some strings have maximal plain Kolmogorov complexity but not maximal prefix-free complexity. The proof uses Levin's symmetry of information, Levin's formula relating plain and prefix complexity and Gacs'…

Kolmogorov Arnold Networks (KANs) are neural architectures inspired by the Kolmogorov Arnold representation theorem that leverage B Spline parameterizations for flexible, locally adaptive function approximation. Although KANs can capture…

What are the effects of authoritarian regimes on scholarly research in economics? And how might economic theory survive ideological pressures? The article addresses these questions by focusing on the mathematization of economics over the…

In the case of ergodicity much of the structure of a one-dimensional time-discrete dynamical system is already determined by its ordinal structure. We generally discuss this phenomenon by considering the distribution of ordinal patterns,…

In math.AG/0207028 we began the study of higher sheaf theory (i.e. stacks theory) on higher categories endowed with a suitable notion of topology: precisely, we defined the notions of S-site and of model site, and the associated categories…

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for…

We discuss some mistakes and curiosities concerned with the celebrated First International Topological Conference in Moscow, 1935.

The paper studies randomness extraction from sources with bounded independence and the issue of independence amplification of sources, using the framework of Kolmogorov complexity. The dependency of strings $x$ and $y$ is ${\rm dep}(x,y) =…

This is the history of translating Cantor's works into Russian from 1892 to 1985 in Odessa, Moscow, Tomsk, Kazan, S.-Petersburg, Leningrad. Mathematicians and philosophers in Russia took the ideas of the theory of sets enthusiastically.…

The research undertakes a comprehensive comparative analysis of Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptrons (MLP), highlighting their effectiveness in solving essential computational challenges like nonlinear function…

The Multiplier Hopf Group Coalgebra was introduced by Hegazi in 2002 [7] as a generalization of Hope group caolgebra, introduced by Turaev in 2000 [5], in the non-unital case. We prove that the concepts introduced by A.Van Daele in…

Lord Kelvin (William Thomson) made important contributions to the study of atmospheric electricity during a brief but productive period from 1859-1861. By 1859 Kelvin had recognised the need for "incessant recording" of atmospheric…

We survey the diverse approaches to the notion of information content: from Shannon entropy to Kolmogorov complexity. The main applications of Kolmogorov complexity are presented namely, the mathematical notion of randomness (which goes…

Analogues of Kolmogorov comparison theorems and some of their applications were established.

Wextend the results obtained recently by G. D'Ambra and A. Loi towards the proof of a conjecture of M.Gromov on isometric immersions via non-free maps.

We show that objective Martin-Lof randomness and Kolmogorov complexity of instantaneous detailed data lists for $N$ helium gas atoms on $M$ possible energies is necessary and sufficient to directly write down its Helmholtz free energy and…

Let $f \colon X \dashrightarrow X$ be a dominant rational self-map of a smooth projective variety defined over $\overline{\mathbb Q}$. For each point $P\in X(\overline{\mathbb Q})$ whose forward $f$-orbit is well-defined, Silverman…

Both the Kelvin wave and the Kolmogorov turbulence interpretations presented in the PRL, [v. 103, 084501 (2009) by J. Yepez, G. Vahala, L.Vahala and M. Soe, arXiv:0905.0159] are misleading, and much more theoretical analysis needs to be…

This paper constructs an exact field redefinition that maps the Akulov-Volkov action to that recently studied by Komargodski and Seiberg in arXiv:0907.2441. It is also shown that the approach advocated in arXiv:1003.4143v2 and…

During the Italian research assessment exercise, the national agency ANVUR performed an experiment to assess agreement between grades attributed to journal articles by informed peer review (IR) and by bibliometrics. A sample of articles was…