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We define the pattern fragment for higher-order unification problems in linear and affine type theory and give a deterministic unification algorithm that computes most general unifiers.
We present various constructions of sequences of polynomials satisfying the Binomial Theorem in finite characteristic based on the theory of additive polynomials. Various actions on these constructions are also presented. It is an open…
Finite mixture models have been a very important tool for exploring complex data structures in many scientific areas, for example, economics, epidemiology, finance. In the past decade, semiparametric techniques have been popularly…
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in…
The problem of identifiability of finite mixtures of finite product measures is studied. A mixture model with $K$ mixture components and $L$ observed variables is considered, where each variable takes its value in a finite set with…
The use of patterns in predictive models is a topic that has received a lot of attention in recent years. Pattern mining can help to obtain models for structured domains, such as graphs and sequences, and has been proposed as a means to…
Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression…
In this paper we use finite vector spaces (finite dimension, over finite fields) as a non-standard computational model of linear logic. We first define a simple, finite PCF-like lambda-calculus with booleans, and then we discuss two finite…
Principles of analogical reasoning have recently been applied in the context of machine learning, for example to develop new methods for classification and preference learning. In this paper, we argue that, while analogical reasoning is…
Combinatorial formulas expressing cyclic rook polynomials and cyclic permanents of rectangular matrices in terms of expansions along rows are presented
In this paper, we consider a model of classical linear logic based on coherence spaces endowed with a notion of totality. If we restrict ourselves to total objects, each coherence space can be regarded as a uniform space and each linear map…
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences, and we find the number of distinct solutions. Many examples of solving congruences are given.
We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive…
The conditions of cylindricality and autonomy of first integrals, last multipliers and integral manifolds for linear homogeneous systems of partial differential equations and total differential systems are established.
We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of…
Context: The importance of the feature modeling for the software product lines considering the modeling and management of the variability. Objective: Define a protocol to conduct a systematic mapping study to summarize and synthesize the…