Related papers: A New Weak Choice Principle

This paper exposes a contradiction in the Zermelo-Fraenkel set theory with the axiom of choice (ZFC). While Godel's incompleteness theorems state that a consistent system cannot prove its consistency, they do not eliminate proofs using a…

A new notion of thickness for subsets of $B[0,1]\subset \mathbb{R}^n$ called affine thickness is defined; this notion of thickness is a generalisation of Falconer-Yavicoli thickness and is adapted to be used in the study of certain sets…

There is a long history of studying Ramsey theory using the algebraic structure of the Stone-\v{C}ech compactification of discrete semigroup. It has been shown that various Ramsey theoretic structures are contained in different algebraic…

The selection problem, where one wishes to locate the $k^{th}$ smallest element in an unsorted array of size $n$, is one of the basic problems studied in computer science. The main focus of this work is designing algorithms for solving the…

We consider the fragment F of first order arithmetic in which quantification is restricted to ''for all but finitely many.'' We show that the integers form an F-elementary substructure of the real numbers. Consequently, the F-theory of…

In a view for a simple model where natural selection at the individual level is confronted to selection effects at the group level, we consider some individual-based models of some large population subdivided into a large number of groups.…

The problem of all-relevant feature selection is concerned with finding a relevant feature set with preserved redundancies. There exist several approximations to solve this problem but only one could give a distinction between strong and…

We show that Dependent Choice is a sufficient choice principle for developing the basic theory of proper forcing, and for deriving generic absoluteness for the Chang model in the presence of large cardinals, even with respect to…

Let $\CaC\subset \Q^p$ be a rational cone. An affine semigroup $S\subset \CaC$ is a $\CaC$-semigroup whenever $(\CaC\setminus S)\cap \N^p$ has only a finite number of elements. In this work, we study the tree of $\CaC$-semigroups, give a…

Let $R$ be a commutative Noetherian ring and $M$ be an $R$-module such that the set of associated prime ideals of the quotient module $M/L$ is finite for all submodules $L$ of $M$. In this paper, it is shown that there is a finitely…

A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper…

We introduce a new principle for model selection in regression and classification. Many regression models are controlled by some smoothness or flexibility or complexity parameter c, e.g. the number of neighbors to be averaged over in k…

The potential of neural networks (NN) in engineering is rooted in their capacity to understand intricate patterns and complex systems, leveraging their universal nonlinear approximation capabilities and high expressivity. Meanwhile,…

In this paper we present a new class of complexity measures, induced by a new data structure for representing $k$-valued functions (operations), called minor decision diagram. The results are presented in terms of Multi-Valued Logic…

Identifying anomalies has become one of the primary strategies towards security and protection procedures in computer networks. In this context, machine learning-based methods emerge as an elegant solution to identify such scenarios and…

This paper mainly studies nonnegativity decision of forms based on variable substitutions. Unlike existing research, the paper regards simplex subdivisions as new perspectives to study variable substitutions, gives some subdivisions of the…

Assume $X$ is a variety over $\mathbb{C}$, $A \subseteq \mathbb{C}$ is a finitely generated $\mathbb{Z}$-algebra and $X_A$ a model of $X$ (i.e. $X_A \times_A \mathbb{C} \cong X$). Assuming the weak ordinarity conjecture we show that there…

A reasonable node selection criterion (NSC) is crucial for the network reduction in power systems. In contrast to the previous works that only consider structure property, this paper proposes a comprehensive and quantitative NSC considering…

We write $S_{\leq n}(A)$ and $\Part_{\fin}(A)$ for the set of permutations with at most $n$ non-fixed points, where $n$ is a natural number, and the set of partitions whose members are finite, respectively, of a set $A$. Among our results,…

We study subset selection for matrices defined as follows: given a matrix $\matX \in \R^{n \times m}$ ($m > n$) and an oversampling parameter $k$ ($n \le k \le m$), select a subset of $k$ columns from $\matX$ such that the pseudo-inverse of…