Related papers: Irreversibility and maximum generation in $\kappa$…

Empirical evidence shows stock returns are often heavy-tailed rather than normally distributed. The $\kappa$-generalised distribution, originated in the context of statistical physics by Kaniadakis, is characterised by the…

The estimation of categorical distributions under marginal constraints summarizing some sample from a population in the most-generalizable way is key for many machine-learning and data-driven approaches. We provide a parameter-agnostic…

A model with a sequence of indiscernibles depending on a particular precovering set is constructed.The initial assumption is as follows: for every n<omega the set {alpha | o(alpha)=alpha^+n } is unbounded in kappa.

Generalizing Krieger's finite generation theorem, we give conditions for an ergodic system to be generated by a pair of partitions, each required to be measurable with respect to a given sub-algebra, and also required to have a fixed size.

We give an example of a long range Bernoulli percolation process on a group non-quasi-isometric with $\mathbb{Z}$, in which clusters are almost surely finite for all values of the parameter. This random graph admits diverse equivalent…

We prove, for various important classes of Mealy automata, that almost all generated groups have an element of infinite order. In certain cases, it also implies other results such as exponential growth.

We consider, for infinite cardinals kappa and alpha <= kappa^+, the group Pi(kappa,< alpha) of sequences of integers, of length kappa, with non-zero entries in fewer than alpha positions. Our main result tells when Pi(kappa,< alpha) can be…

The statistically unbounded $p$-convergence is an abstraction of the statistical order, unbounded order, and $p$-convergences. We investigate the concept of the statistically unbounded convergence on lattice-normed Riesz spaces with respect…

We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.

Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d.\ test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such…

We show that generalized eventually narrow sequences on a strongly inaccessible cardinal $\kappa$ are preserved under the Cummings-Shaleh non-linear iterations of the higher Hechler forcing on $\kappa$. Moreover assuming GCH,…

We survey several methods of generating large random lambda-terms, focusing on their closed and simply-typed variants. We discuss methods of exact- and approximate-size generation, as well as methods of achieving size-uniform and…

We present results obtained by using nonlinear irreversible models for heat devices. In particular, we focus on the global performance characteristics, the maximum efficiency and the efficiency at maximum power regimes for heat engines, and…

A finite group $G$ is coprimely-invariably generated if there exists a set of generators $\{g_1, \ldots, g_d\}$ of $G$ with the property that the orders $|g_1|, \ldots, |g_d|$ are pairwise coprime and that for all $x_1, \ldots, x_d \in G$…

An equation describing the irreversible evolution of the local density of a continuous medium without involving any statistical hypotheses and assumptions is derived. The derivation is based on the smoothing of the microscopic dynamic…

We review the recent result of Sato, Sekimoto, Hondou, and Takagi (cond-mat/0008393) on the irreversibility inevitably observed in systems consisting of many non-interacting ``small'' pieces. We focus on quantum models, and supply an…

This paper introduces the concept of a generating set for stochastic matrices -- a subset of matrices whose repeated composition generates the entire set. Understanding such generating sets requires specifying the "indivisible elements" and…

A general achievable upper bound of extractable work under feedback control is given, where nonequilibrium equalities are generalized so as to be applicable to error-free measurements. The upper bound involves a term which arises from the…

This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…

For every uncountable regular $\kappa$, we give two examples of proper posets which turn improper in some $\kappa$-closed forcing extension.