相关论文: On adding a list of numbers (and other one-depende…

In decision theory an act is a function from a set of conditions to the set of real numbers. The set of conditions is a partition in some algebra of events. The expected value of an act can be calculated when a probability measure is given.…

We define a random walk problem which admits analytic results, on a class of infinite periodic lattices which are directed and colored. Our approach is motivated from the fact that such lattices arise in string theoretic constructs of…

We introduce a flow condition on open graph states (graph states with inputs and outputs) which guarantees globally deterministic behavior of a class of measurement patterns defined over them. Dependent Pauli corrections are derived for all…

We give general sufficient conditions to prove the convergence of marked point processes that keep record of the occurrence of rare events and of their impact for non-autonomous dynamical systems. We apply the results to sequential…

Referring to a standard context of voting theory, and to the classic notion of voting situation, here we show that it is possible to observe any arbitrary set of elections' outcomes, no matter how paradoxical it may appear. On this purpose…

In this note, we study a class of random subsets of positive integers induced by Bernoulli random variables. We obtain sufficient conditions such that the random set is almost surely lacunary, does not have bounded gaps and contains…

Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…

We survey recent results on determinantal processes, random growth, random tilings and their relation to random matrix theory.

Two closely related discrete probability distributions are introduced. In each case the support is a set of vectors in $\mathbb{R}^n$ obtained from the partitions of the fixed positive integer $n$. These distributions arise naturally when…

The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…

We introduce tree representations for $ \alpha$-determinantal point processes. The $ \alpha$-determinantal point processes is introduced as a one parameter extension of the determinantal point process. In the previous paper with H.Osada,…

An existing dialogue between number theory and dynamical systems is advanced. A combinatorial device gives necessary and sufficient conditions for a sequence of non-negative integers to count the periodic points in a dynamical system. This…

Probability trees are one of the simplest models of causal generative processes. They possess clean semantics and -- unlike causal Bayesian networks -- they can represent context-specific causal dependencies, which are necessary for e.g.…

We extend the classical preferential attachment random graph model to random simplicial complexes. At each stage of the model, we choose one of the existing $k$-simplices with probability proportional to its $k$-degree. The chosen…

Causal Models are like Dependency Graphs and Belief Nets in that they provide a structure and a set of assumptions from which a joint distribution can, in principle, be computed. Unlike Dependency Graphs, Causal Models are models of…

Simple methods permit to generalize the concepts of iteration and of recursive processes. We shall see briefly on several examples what these methods generate. In additive sequences, we shall encounter not only the golden or the silver…

Determinantal point processes (DPPs), which arise in random matrix theory and quantum physics, are natural models for subset selection problems where diversity is preferred. Among many remarkable properties, DPPs offer tractable algorithms…

Consider a symmetrical conflict relationship between the points of a point process. The Mat\'ern type constructions provide a generic way of selecting a subset of this point process which is conflict-free. The simplest one consists in…

It is known that determinantal point processes have an intimate relation to operator algebras. In the paper, we extend this relationship to encompass dynamical aspects. Especially, we delve into two types of determinantal point processes.…

We consider a pair of causally independent processes, modelled as the tensor product of two channels, acting on a possibly correlated input to produce random outputs X and Y. We show that, assuming the processes produce a sufficient amount…