Related papers: A randomly determined unpredictable function

We study nonautonomous discrete dynamical systems with randomly perturbed trajectories. We suppose that such a system is generated by a sequence of continuous maps which converges uniformly to a map $f$. We give conditions, under which a…

Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…

The probabilistic reachability problems of nondeterministic systems are studied. Based on the existing studies, the definition of probabilistic reachable sets is generalized by taking into account time-varying target set and obstacle. A…

The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…

In this article we propose a method of performing arithmetic operations on varia-bles with unknown distribution. The approach to the evaluation results of arithme-tic operations can select probability intervals of the algebraic equations…

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…

The field of performative prediction had its beginnings in 2020 with the seminal paper "Performative Prediction" by Perdomo et al., which established a novel machine learning setup where the deployment of a predictive model causes a…

Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued…

There exists an injective, information-preserving function that maps a semantic network (i.e a directed labeled network) to a directed network (i.e. a directed unlabeled network). The edge label in the semantic network is represented as a…

We introduce a new concept called uncertainty spaces which is an extended concept of probability spaces. Then, we express n-layer uncertainty which we call hierarchical uncertainty by a hierarchically constructed sequence of uncertainty…

A particular case of a causal set is considered that is a directed dyadic acyclic graph. This is a model of a discrete pregeometry on a microscopic scale. The dynamics is a stochastic sequential growth of the graph. New vertexes of the…

In this paper, we investigate how to achieve the unpredictability against malicious inferences for linear systems. The key idea is to add stochastic control inputs, named as unpredictable control, to make the outputs irregular. The future…

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

A procedure to obtain the symbolic dynamics for conservative dynamical systems is introduced with reference to the standard map in a strongly chaotic regime. The method extends an approach previously developed for highly dissipative…

We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…

A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…

Probabilistic powerdomain in domain theory plays an important role in modeling the semantics of nondeterministic functional programming languages with probabilistic choice. In this paper, we extend the notion of powerdomain to directed…

Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…

In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…

We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems…