Related papers: Strong dependence, weight, and measure

As consequence of the VC theorem, any pseudo-finite measure over an NIP ultraproduct is generically stable. We demonstrate a converse of this theorem and prove that any finitely approximable measure over an ultraproduct is itself…

We study model theoretic tree properties ($\text{TP}, \text{TP}_1, \text{TP}_2$) and their associated cardinal invariants ($\kappa_{\text{cdt}}, \kappa_{\text{sct}}, \kappa_{\text{inp}}$, respectively). In particular, we obtain a…

The concept of independence plays a crucial role in probability theory and has been the subject of extensive research in recent years. Numerous approaches have been proposed to test for independence; however, most of them address the…

We introduce a new dependence order, termed the conditional convex order, whose minimal and maximal elements characterize independence and perfect dependence. Moreover, it characterizes conditional independence, satisfies information…

Theory of stable models is the mathematical basis of answer set programming. Several results in that theory refer to the concept of the positive dependency graph of a logic program. We describe a modification of that concept and show that…

If $T$ has dependent dividing, then the burden agrees with the dp-rank witnessed by NIP formulas. We use this observation to prove that if $T$ has dependent dividing, then the burden is sub-additive. We also state a connection between the…

An introduction is given to the logic of sheaves of structures and to set theoretic forcing constructions based on this logic. Using these tools, it is presented an alternative proof of the independence of the Continuum Hypothesis; which…

This paper studies the robustness of large-scale interconnected systems with respect to external disturbances, focussing on their scalability properties. Specifically, a notion of scalability is introduced that asks for these robustness…

Strong laws of large numbers are established for random fields with weak or strong dependence. These limit theorems are applicable to random fields with heavy-tailed distributions including fractional stable random fields. The conditions…

Kim's Lemma is a key ingredient in the theory of forking independence in simple theories. It asserts that if a formula divides, then it divides along every Morley sequence in type of the parameters. Variants of Kim's Lemma have formed the…

I review recent developments in the description of the interactions between light and heavy mesons by an effective chiral lagrangian having the symmetries of the Heavy Quark Effective Theory. In particular the problem of the determination…

We prove that any type in an NIP theory can be decomposed into a stable part (a generically stable partial type) and a distal-like quotient.

Asymptotic properties of a dimension-robust dependence measure are investigated. It is related to those used in independence tests, but is derivable, thus suitable for independent component analysis. An adjustable kernel allows to…

In this paper we introduce the notion of "strong $n$-perfect rings" which is in some way a generalization of the notion of "$n$-perfect rings". We are mainly concerned with those class of rings in the context of pullbacks. Also we exhibit a…

We present a new, scalable alternative to the structured singular value, which we call $\nu$, provide a convex upper bound, study their properties and compare them to $\ell_1$ robust control. The analysis relies on a novel result on the…

We introduce the notion of measurable sensitivity, a measure-theoretic version of the condition of sensitive dependence on initial conditions. It is a consequence of light mixing, implies a transformation has only finitely many eigenvalues,…

We relate the local specification and periodic shadowing properties. We also clarify the relation between local weak specification and local specification if the system is measure expansive. The notion of strong measure expansiveness is…

In this paper we fix our attention, on hadron structure, and show that also the strong interaction strength alpha_S, ordinarily called the "(perturbative) coupling--constant square}", can be evaluated within our theory, and found to…

This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of…

An important dividing line in the class of unstable theories is being NSOP$_1$, which is more general than being simple. In NSOP$_1$ theories forking independence may not be as well-behaved as in stable or simple theories, so it is replaced…