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Monads play an important role in both the syntax and semantics of modern functional programming languages. The problem of combining them has been of profound interest at least since the 90s, and different approaches have been employed to…
Each Multiplicative Exponential Linear Logic (MELL) proof-net can be expanded into a differential net, which is its Taylor expansion. We prove that two different MELL proof-nets have two different Taylor expansions. As a corollary, we prove…
The pattern $(k_1, k_2, \dots, k_\ell)$ is defined to have at least $k_1$ consecutive $1$'s followed by at least $k_2$ consecutive $2$'s, $\dots$, followed by at least $k_\ell$ consecutive $\ell$'s. By iteratively applying the method that…
The main result of the paper is the following. Let a non-degenerate distribution have finite moments $\mu_k$ of all orders $k=0,1,2,\ldots$. Then the sequence $\{\mu_k/k!, \; k=0,1,2,\ldots\}$ either contains infinitely many different terms…
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
A basic theory of cowreath or extended distributive laws in the bicategory of unital bimodules, is deciphered. Precisely, we give in terms of tensor product over a scalar base ring, a simplest and equivalent definition for cowreath over…
We determine the asymptotic distribution of Manin's iterated integrals of length at most 2. For all lengths we compute all the asymptotic moments. We show that if the length is at least 3 these moments do in general not determine a unique…
This article provides some characterizations of extended COM-Poisson distribution: conditional distribution given the sum, functional operator characterization (Stein identity). We also give some conditions such that the extended…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
We prove that among the finite dimensional algebras of finite representation type those that are string algebras are precisely the ones that have the property that the middle term of an arbitrary extension of indecomposable modules has at…
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
The scattering formulation of characteristic mode decomposition is utilized to extend modal analysis to lossless scatterers breaking time-reversal symmetry. This enables characteristic modes analysis on devices containing gyrotropic or…
We discuss several extension properties of matroids and polymatroids and their application as necessary conditions for the existence of different matroid representations, namely linear, folded linear, algebraic, and entropic…
We propose a characteristic representation ofone-dimensional and 2-state, 3-neighbor cellular automaton rules, which describes an effective form of each rule after many time steps. Simulated results of the representation show that complex…
The present paper is the continuity of the previous papers "Non-linear field theory" I and II. Here on the basis of the electromagnetic representation of Dirac's electron theory we consider the geometrical distribution of the…
Two field 2-forms on the space-time manifold, in a relationship of duality, are presented and included in the extended phase-space structure used to describe relativistic particles having both electric and magnetic charges. By exterior…
We give a characterisation of central extensions of a Lie group G by the non-zero complex numbers in terms of a differential two-form on G and a differential one-form on GxG. This is applied to the case of the central extension of the loop…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
A proof of the relativistic $H$-theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics…
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…