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The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this geometrical description is less trivial, it can be…
We examine some properties of pseudo-multiplications, which are a special kind of associative binary relations defined on $\bar{\mathbb{R}}_+ \times \bar{\mathbb{R}}_+$.
We show algorithmic randomness versions of the two classical theorems on subsequences of normal numbers. One is Kamae-Weiss theorem (Kamae 1973) on normal numbers, which characterize the selection function that preserves normal numbers.…
A function from sequences to their subsequences is called selection function. A selection function is called admissible (with respect to normal numbers) if for all normal numbers, their subsequences obtained by the selection function are…
In this study, explicit differential equations representing commutative pairs of some well-known second-order linear time-varying systems have been derived. The commutativity of these systems are investigated by considering 30 second-order…
Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncertain domain models. Even though the correct working of these…
We can, and should, do statistical inference on simulation models by adjusting the parameters in the simulation so that the values of {\em randomly chosen} functions of the simulation output match the values of those same functions…
Wall published a paper in 1960 on the Fibonacci sequence where he derived many results concerning the period and prime power divisibility modulo m. His periodicity results have been generalized to second order linear recurrences. Here we…
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is…
We show that many theorems which assert that two kinds of partitions of the same integer $n$ are equinumerous are actually special cases of a much stronger form of equality. We show that in fact there correspond partition statistics $X$ and…
Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…
Stern's diatomic sequence with its intrinsic repetition and refinement structure between consecutive powers of $2$ gives rise to a rather natural probability measure on the unit interval. We construct this measure and show that it is purely…
Periodic and semi periodic patterns are very common in nature. In this paper we introduce a topological toolbox aiming in detecting and quantifying periodicity. The presented technique is of a general nature and may be employed wherever…
We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis,…
The $t$-e.c. and pseudo-random property are typical properties of random graphs. In this note, we study the gap between them which has not been studied well. As a main result, we give the first explicit construction of infinite families of…
We investigate the second-order correlation function of the characteristic polynomial of a sample covariance matrix. Starting from an explicit formula for the generating function, we re-obtain several well-known kernels from random matrix…
We study a large class of stochastic $p$-Laplace Allen-Cahn equations with singular potential. Under suitable assumptions on the (multiplicative-type) noise we first prove existence, uniqueness, and regularity of variational solutions.…
The aim of sequential change-point detection is to issue an alarm when it is thought that certain probabilistic properties of the monitored observations have changed. This work is concerned with nonparametric, closed-end testing procedures…
In the theory of algebraic function fields and their applications to the information theory, the Riemann-Roch theorem plays a fundamental role. But its use, delicate in general, is efficient and practical for applications especially in the…
Causal functions of sequences occur throughout computer science, from theory to hardware to machine learning. Mealy machines, synchronous digital circuits, signal flow graphs, and recurrent neural networks all have behaviour that can be…