相关论文: Independence and Product Systems

A recently proposed axiom system for Andr\'e's central translation structures is improved upon. First, one of its axioms turns out to be dependent (derivable from the other axioms). Without this axiom, the axiom system is indeed…

We propose a novel approach to concentration for non-independent random variables. The main idea is to ``pretend'' that the random variables are independent and pay a multiplicative price measuring how far they are from actually being…

Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…

We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…

The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…

We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to…

We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…

It is known that the spatial product of two product systems is intrinsic. Here we extend this result by analyzing subsystems of the tensor product of product systems. A relation with cluster systems is established. In a special case, we…

We establish a bijection between marginal independence models on $n$ random variables and split closed order ideals in the poset of partial set partitions. We also establish that every discrete marginal independence model is toric in cdf…

In this paper, building on previous work, we extend the thermodynamic formalism for random open dynamical systems generated by piecewise monotone interval maps with countably many branches. Under summable and contracting assumptions on the…

We introduce a way of regarding Hilbert von Neumann modules as spaces of operators between Hilbert space, not unlike [Skei], but in an apparently much simpler manner and involving far less machinery. We verify that our definition is…

We characterize the expressive power of extensions of Dependence Logic and Independence Logic by monotone generalized quantifiers in terms of quantifier extensions of existential second-order logic.

We define and study a metric independence notion in a homogeneous metric abstract elementary class with perturbations that is $d^p$-superstable (superstable wrt. the perturbation topology), weakly simple and has complete type spaces and we…

This paper introduces the \textit{weighted partial copula} function for testing conditional independence. The proposed test procedure results from these two ingredients: (i) the test statistic is an explicit Cramer-von Mises transformation…

Self-organisation lies at the core of fundamental but still unresolved scientific questions, and holds the promise of de-centralised paradigms crucial for future technological developments. While self-organising processes have been…

We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…

We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices.…

Multi-agent Markov Decision Processes (MMDPs) arise in a variety of applications including target tracking, control of multi-robot swarms, and multiplayer games. A key challenge in MMDPs occurs when the state and action spaces grow…

This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…

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…