Related papers: Induced and higher-dimensional stable independence

We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and…

We consider the general higher derivative field theories of derived type. At free level, the wave operator of derived-type theory is a polynomial of the order $n\geq 2$ of another operator $W$ which is of the lower order. Every symmetry of…

We introduce the new concept of cartesian module over a pseudofunctor $R$ from a small category to the category of small preadditive categories. Already the case when $R$ is a (strict) functor taking values in the category of commutative…

Decidability and synthesis of inductive invariants ranging in a given domain play an important role in many software and hardware verification systems. We consider here inductive invariants belonging to an abstract domain $A$ as defined in…

First, we prove that a random metric space can be isometrically embedded into a complete random normed module, as an application of which, it is easy to see that the notion of $d$-$\sigma$-stability introduced for a nonempty subset of a…

By a theorem due to the first author, the bounded derived category of a finite-dimensional algebra over a field embeds fully faithfully into the stable category over its repetitive algebra. This embedding is an equivalence iff the algebra…

We extend the framework of combinatorial model categories, so that the category of small presheaves over large indexing categories and ind-categories would be embraced by the new machinery called class-combinatorial model categories. The…

In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…

This paper is a continuation of our 2005 paper on complex topology and its implication on invertibility (or non-invertibility). In this paper, we will try to classify the complexity of inversion into 3 different classes. We will use…

A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…

Finsler's lemma is a classic mathematical result with applications in control and optimization. When the lemma is applied to parameter-dependent LMIs, as such those that arise from problems of robust stability, the extra variables…

We show that given a separable cocontinuous monad on a stable derivator, the levelwise Eilenberg-Moore categories of modules glue together to a stable derivator. As an application, we give examples of derivators that satisfy all the axioms…

We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…

We axiomatically define (pre-)Hilbert categories. The axioms resemble those for monoidal Abelian categories with the addition of an involutive functor. We then prove embedding theorems: any locally small pre-Hilbert category whose monoidal…

High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov…

We translate notions and results of decomposition and dimension theories for module categories, into the lattice environment. In particular we translate dimension theory in module categories to complete modular upper-continuous lattices.

We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…

This paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems, and establishes the relationship between the eigenvalue distribution and delay-independent stability of neutral…

Variable independence and decomposability are algorithmic techniques for simplifying logical formulas by tearing apart connections between free variables. These techniques were originally proposed to speed up query evaluation in constraint…

The R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom is reviewed. Its application to Poisson, noncommutative and loop algebras as well as central extension procedure are presented. The…