Related papers: Lifting independence along functors
We construct pairs of algebras with mixed independence relations by using truncations of reduced free products of algebras. For example, we construct free-Boolean pairs of algebras and free-monotone pairs of algebras. We also introduce…
The general {\bf surface group conjecture} asks whether a one-relator group where every subgroup of finite index is again one-relator and every subgroup of infinite index is free (property IF) is a surface group. We resolve several related…
There has been a recent coming together of the Converse Theorem for $\gln$ and the Langlands-Shahidi method of controlling the analytic properties of automorphic $L$-functions which has allowed us to establish a number of new cases of…
Given a suitable collection of partitions of sets, there exists a connection to easy quantum groups via intertwiner maps. A sufficient condition for this correspondence to be one-to-one are particular linear independences on the level of…
In this paper, we develop the theory of bi-freeness in an amalgamated setting. We construct the operator-valued bi-free cumulant functions, and show that the vanishing of mixed cumulants is necessary and sufficient for bi-free independence.…
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,…
In differential algebra, a proper scheme $X$ defined over an algebraically closed field $K$ with a derivation $\partial$ on it descends to the field of constants $K^\partial$ if $X$ itself lifts the derivation $\partial$. This is a result…
Recently, the first author [1] showed that the admissible vector-valued automorphic forms lift to the admissible ones. In this article, we study the lifts for the logarithmic vector-valued automorphic forms and explicitly compute the…
In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain…
Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
Let X be a smooth hypersurface of degree d in P^n over an algebraically closed field of characteristic p. We show that X must be separably rationally connected and must contain a free line if either p is at least d or if p is at least d-1…
Let $K$ be a finite extension of $\mathbb{Q}_p$ that is totally ramified over $\mathbb{Q}_p$. The set $\mathcal{M}\mathcal{F}(K)$ consists of power series in $1+zK[[z]]$ that are solutions of differential operators in $K(z)[d/dz]$ equipped…
In this paper, we develop the notion of free-Boolean independence in an amalgamation setting. We construct free-Boolean cumulants and show that the vanishing of mixed free-Boolean cumulants is equivalent to our free-Boolean independence…
We indicate a way of distinguishing between structures, for which, two structures are said to be separable.Being separable implies being non-isomorphic. We show that for any first order theory $T$ in a countable language, if it has an…
In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major…
Let M be a complete metric space. It is proved that if the space or scalar-valued bounded continuous functions on M admits an isometric shift, then M is separable.
It has been postulated that a good representation is one that disentangles the underlying explanatory factors of variation. However, it remains an open question what kind of training framework could potentially achieve that. Whereas most…
We establish the independence of multipliers for polynomial endomorphisms of $\mathbb C^n$ and endomorphisms of $\mathbb P^n.$ This allows us to extend results about the bifurcation measure and the critical height obtained in…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…