Related papers: Induced and higher-dimensional stable independence
In the study of extremes, the presence of asymptotic independence signifies that extreme events across multiple variables are probably less likely to occur together. Although well-understood in a bivariate context, the concept remains…
We show a transfer principle for the property that all types realised in a given elementary extension are definable. It can be written as follows: a Henselian valued fields is stably embedded in an elementary extension if and only if its…
We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…
Microlocal sheaf theory of \cite{KS90} makes an essential use of an extension lemma for sheaves due to Kashiwara, and this lemma is based on a criterion of the same author giving conditions in order that a functor defined in $\mathbb{R}$…
Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension. Here we discuss several new aspects, present a concise…
Power injection uncertainties in distribution power grids, which are mostly induced by aggressive introduction of intermittent renewable sources, may drive the system away from normal operating regimes and potentially lead to the loss of…
A common technique for verifying the safety of complex systems is the inductive invariant method. Inductive invariants are inductive formulas that overapproximate the reachable states of a system and imply a desired safety property.…
We define and study the independent natural extension of two local uncertainty models for the general case of infinite spaces, using the frameworks of sets of desirable gambles and conditional lower previsions. In contrast to Miranda and…
We show that certain tilting results for quivers are formal consequences of stability, and as such are part of a formal calculus available in any abstract stable homotopy theory. Thus these results are for example valid over arbitrary…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
We introduce basic notions in category theory to type theorists, including comprehension categories, categories with attributes, contextual categories, type categories, and categories with families along with additional discussions that are…
We propose a semantic foundation for logics for reasoning in settings that possess a distinction between equality of variables, a coarser equivalence of variables, and a notion of conditional independence between variables. We show that…
Hadar and Russell (1974) and Levy and Paroush (1974) presented sufficient conditions for multivariate stochastic dominance when the distributions involved are continuous with compact support. Further generalizations involved either…
Input-to-state stability (ISS) unifies the stability and robustness in one notion, and serves as a basis for broad areas of nonlinear control theory. In this contribution, we covered the most fundamental facts in the infinite-dimensional…
Multivariate time series exhibit two types of dependence: across variables and across time points. Vine copulas are graphical models for the dependence and can conveniently capture both types of dependence in the same model. We derive the…
Here we introduce some new classes of discrete stable random variables, which are useful for understanding of a new general notion of stability of random variables called us as casual stability. There are given some examples of casual and…
We show how the superintegrability of certain systems can be deduced from the presence of multiple parameters in the rational Lax matrix representation. This is also related to the fact that such systems admit a separation of variables in…
Adapting a proof of Bouscaren and Delon, we show that every type-definable connected group in a given stable theory of fields embeds into an algebraic group, under a condition on the definable closure. We also present general hypotheses…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…