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This study proposed an exhaustive stable/reproducible rule-mining algorithm combined to a classifier to generate both accurate and interpretable models. Our method first extracts rules (i.e., a conjunction of conditions about the values of…
In previous work, the second author introduced a topology, for spaces of irreducible representations, that reduces to the classical Zariski topology over commutative rings but provides a proper refinement in various noncommutative settings.…
It was shown in \cite{sc12} that for a certain class of structures $\I$, $\I$-indexed indiscernible sets have the modeling property just in case the age of $\I$ is a Ramsey class. We expand this known class of structures from ordered…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Prime number multiplet classifications and patterns are extended to negative integers. The extension from prime numbers to single prime powers is also studied. Prime number septets at equal distance are given. It is also shown that each…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
The randomization of a complete first order theory T is the complete continuous theory T^R with two sorts, a sort for random elements of models of T, and a sort for events in an underlying probability space. We give necessary and sufficient…
We present a method for constructing countable models of small theories and apply it to prove theorems on the maximal number of countable non-isomorphic models of linearly ordered theories.
We define an enumerative function F(n,k,P,m) which is a generalization of binomial coefficients. Special cases of this function are also power function, factorials, rising factorials and falling factorials. The first section of the paper is…
We introduce a family of comparative plausibility logics over neighbourhood models, generalising Lewis' comparative plausibility operator over sphere models. We provide axiom systems for the logics, and prove their soundness and…
We consider methods for aggregating preferences that are based on the resolution of discrete optimization problems. The preferences are represented by arbitrary binary relations (possibly weighted) or incomplete paired comparison matrices.…
For a nontrivial measurable set on the real line, there are always exceptional points, where the lower and upper densities of the set are neither zero nor one. We quantify this statement, following work by V. Kolyada, and obtain the…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
This paper provides two extensions of first order logic by `$\omega$-rules'. In each case we characterize the countable structures whose theory in the logic is categorical (has a unique model). In the one-sorted inferential $\omega$-logic,…
We generalize the definition and properties of root systems to complex reflection groups - roots become rank one projective modules over the ring of integers of a number field k. In the irreducible case, we provide a classification of root…
We start by presenting a theory of finite sets using the approach which is essentially that taken by Whitehead and Russell in Principia Mathematica}, and which does not involve the natural numbers (or any other infinite set). This theory is…
Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…
We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…
We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a $p$-adic field, together with relevant arithmetic information about the fields generated by the irreducible…
A parametrization of irreducible unitary representations associated with the regular adjoint orbits of a hyperspecial compact subgroup of a reductive group over a non-dyadic non-archimedean local filed is presented. The parametrization is…