Related papers: Algebraic Independence Relations in Randomizations

We give necessary and sufficient geometric conditions for a theory definable in an o-minimal structure to interpret a real closed field. The proof goes through an analysis of thorn-minimal types in super-rosy dependent theories of finite…

A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full…

In this paper, we study local systems of locally finite associative algebras over fields of characteristic p\ge0. We describe the perfect local systems and study the relation between them and their corresponding locally finite associative…

Since its introduction by Symons, the semigroup of maps with restricted range has been studied in the context of transformations on a set, or of linear maps on a vector space. Sets and vector spaces being particular examples of independence…

Let T be an algebraically bounded theory. We consider the $L(\bar\delta)$-expansions of T by a tuple $\bar \delta$ of derivations (which may be commuting or not). We investigate the model completion of either of the above theories, whose…

For years, independence has been considered as an important concept in many disciplines. Nevertheless, we present the first research that investigates the discovery problem of independence in data. In its arguably simplest form,…

One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…

Let $T$ be a complete theory of fields, possibly with extra structure. Suppose that model-theoretic algebraic closure agrees with field-theoretic algebraic closure, or more generally that model-theoretic algebraic closure has the exchange…

This chapter of the forthcoming Handbook of Graphical Models contains an overview of basic theorems and techniques from algebraic geometry and how they can be applied to the study of conditional independence and graphical models. It also…

Let $G=\{e^{tA}:t\in\mathbb{R}\}$ be a closed one-parameter subgroup of the general linear group of matrices of order $n$ acting on $\mathbb{R}^{n}$ by matrix-vector multiplications. We assume that all eigenvalues of $A$ are rationally…

The survey is devoted to the combinatorial and metric theory of filtrations, i.\,e., decreasing sequences of $\sigma$-algebras in measure spaces or decreasing sequences of subalgebras of certain algebras. One of the key notions, that of…

In this memoir, we seek to construct a dynamical theory as complete as possible to describe the algebraic properties of the field of real numbers in constructive mathematics without axiom of dependent choice. We propose a theory which turns…

In this paper we discuss the continuity properties of the integrated density of states for random models based on that of the single site distribution. Our results are valid for models with independent randomness with arbitrary free parts.…

We establish several results regarding dividing and forking in NTP2 theories. We show that dividing is the same as array-dividing. Combining it with existence of strictly invariant sequences we deduce that forking satisfies the chain…

We generalize Gel'fond's criterion of algebraic independence to the context of a sequence of polynomials whose first derivatives take small values on large subsets of a fixed subgroup of the additive group of complex numbers, instead of…

Consider a graph on the non-singular matrices over a finite field, in which two distinct non-singular matrices are joined by an edge whenever their sum is singular. We prove an upper bound for the independence number of this graph. As a…

We observe algebraic derivations on an affine domain B defined over an algebraically closed field of characteristic 0, which are called locally finite derivations in commutative and non-commutative contexts in other references. We observe…

We generalize P. M. Neumann's Lemma to the setting of isometric actions on metric spaces and use it to prove several results in continuous logic related to algebraic independence. In particular, we show that algebraic independence satisfies…

Given any two rational numbers $r_1$ and $r_2$, a necessary and sufficient condition is established for the three numbers $1$, $\cos (\pi r_1)$, and $\cos (\pi r_2)$ to be rationally independent. Extending a classical fact sometimes…

We show that the family of nest algebras with $r$ non-zero nest projections is stable, in the sense that an approximate containment of one such algebra within another is close to an exact containment. We use this result to give a local…