Related papers: Independence of Sets Without Stability

To most applied statisticians, a fitting procedure's degrees of freedom is synonymous with its model complexity, or its capacity for overfitting to data. In particular, it is often used to parameterize the bias-variance tradeoff in model…

We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…

We study the model theory of vector spaces with a bilinear form over a fixed field. For finite fields this can be, and has been, done in the classical framework of full first-order logic. For infinite fields we need different logical…

This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…

This is an introduction to the set-theoretic method of forcing, including its application in proving the independence of the Continuum Hypothesis from the Zermelo-Fraenkel axioms of set theory. I presuppose no particular mathematical…

The erosion of a set in Euclidean space by a radius r>0 is the subset of X consisting of points at distance >/-r from the complement of X. A set is resilient to erosion if it is similar to its erosion by some positive radius. We give a…

In this paper we show that an instance of dividing in pseudofinite structures can be witnessed by a drop of the pseudofinite dimension. As an application of this result we give new proofs of known results for asymptotic classes of finite…

The larger the distance to instability from a matrix is, the more robustly stable the associated autonomous dynamical system is in the presence of uncertainties and typically the less severe transient behavior its solution exhibits.…

The paper gives estimations for the sizes of the the following sets: (1) the set of strings that have a given dependency with a fixed string, (2) the set of strings that are pairwise \alpha independent, (3) the set of strings that are…

We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the…

Independence of premise principles play an important role in characterizing the modified realizability and the Dialectica interpretations. In this paper we show that a great many intuitionistic set theories are closed under the…

For a family F (a collection of subsets of Z_+), the notion of F-independence is defined both for topological dynamics (t.d.s.) and measurable dynamics (m.d.s.). It is shown that there is no non-trivial {syndetic}-independent m.d.s.; a…

Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…

This paper is concerned with the axiomatic basis of structures within Hypercompositional Algebra. It is proven that the axioms employed in the definition of numerous hypercompositional structures lack independence. Accordingly, novel…

Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…

We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…

Uniqueness and independence are two fundamental properties of data. Their enforcement in database systems can lead to higher quality data, faster data service response time, better data-driven decision making and knowledge discovery from…

We investigate different aspects of independence here, in the context of theory revision, generalizing slightly work by Chopra, Parikh, and Rodrigues, and in the context of preferential reasoning.

It is known that, in finite dimensions, the support function of a compact convex set with non empty interior is differentiable excepting the origin if and only if the set is strictly convex. In this paper we realize a thorough study of the…

We provide a treatment of isomorphism within a set-theoretic formulation of dependent type theory. Type expressions are assigned their natural set-theoretic compositional meaning. Types are divided into small and large types --- sets and…