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Random resolution, defined by Buss, Kolodziejczyk and Thapen (JSL, 2014), is a sound propositional proof system that extends the resolution proof system by the possibility to augment any set of initial clauses by a set of randomly chosen…
This paper is devoted to proving the general {\L}ojasiewicz inequality, in both the definable and subanalytic cases, under the most relaxed assumptions. It means that we drop the usual continuity and compactness assumptions. In the second…
We prove the closedness theorem over Henselian valued fields, which was established over rank one valued fields in one of our recent papers. In the proof, as before, we use the local behaviour of definable functions of one variable and the…
We introduce a generalization of the Temperley--Lieb algebra. This generalization is defined by adding certain relations to the algebra of braids and ties. A specialization of this last algebra corresponds to one small Ramified Partition…
This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…
In part \textit{I} we proposed a structure for a general Hypotheses Space $\mathcal{H}$, the Learning Space $\mathbb{L}(\mathcal{H})$, which can be employed to avoid \textit{overfitting} when estimating in a complex space with relative…
We generalize some results in Hodge theory to generalized normal crossing varieties.
We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion…
Bayesian networks are widely utilised in various fields, offering elegant representations of factorisations and causal relationships. We use surjective functions to reduce the dimensionality of the Bayesian networks by combining states and…
In this paper we propose a framework for combining Disjunctive Logic Programming and Poole's Probabilistic Horn Abduction. We use the concept of hypothesis to specify the probability structure. We consider the case in which probabilistic…
Alternative novel measures of the distance between any two partitions of a n-set are proposed and compared, together with a main existing one, namely 'partition-distance' D(.,.). The comparison achieves by checking their restriction to…
Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent…
We propose a new approach to solve the classical Monty Hall problem in its general form. The solution is based on basic tools of probability theory, by defining three elementary events which decompose the sample space into a partition. The…
The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of $n$ is reviewed. Next, the steps for finding analogous formulas for certain restricted classes of partitions or overpartiitons is examined, bearing in…
We describe reduced representatives for positive Rouquier complexes. These are obtained via Morse theoretical Gaussian elimination from the corresponding standard representatives. The underlying graded object is still a direct sum of…
We resolve a conjecture of Cooper-Fenner-Purewal that a certain sequence of combinatorial matrices which can be used to bound small product-Ramsey numbers is positive semidefinite. Because the connection to Ramsey Theory involves solving…
We conduct a computability-theoretic study of Ramsey-like theorems of the form "Every coloring of the edges of an infinite clique admits an infinite sub-clique avoiding some pattern", with a particular focus on transitive patterns. As it…
We develop a technique for normalization for $\infty$-type theories. The normalization property helps us to prove a coherence theorem: the initial model of a given $\infty$-type theory is $0$-truncated. The coherence theorem justifies…
A general Bayesian framework for model selection on random network models regarding their features is considered. The goal is to develop a principle Bayesian model selection approach to compare different fittable, not necessarily nested,…
It has become obvious in the recent development that the structural Ramsey property is a categorical property: it depends not only on the choice of objects, but also on the choice of morphisms involved. In this paper we explicitely put the…