Related papers: Adversarial ergodic optimization
In recent years there has been significant interest in the effect of different types of adversarial perturbations in data classification problems. Many of these models incorporate the adversarial power, which is an important parameter with…
A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations. A group is sofic if it admits a sofic approximation. Sofic…
We investigate the existence and uniqueness of (locally) absolutely continuous trajectories of a penalty term-based dynamical system associated to a constrained variational inequality expressed as a monotone inclusion problem. Relying on…
In the present work, a new computational framework for structural topology optimization based on the concept of moving deformable components is proposed. Compared with the traditional pixel or node point-based solution framework, the…
Topology Optimization seeks to find the best design that satisfies a set of constraints while maximizing system performance. Traditional iterative optimization methods like SIMP can be computationally expensive and get stuck in local…
Recently, Sidford, Wang, Wu and Ye (2018) developed an algorithm combining variance reduction techniques with value iteration to solve discounted Markov decision processes. This algorithm has a sublinear complexity when the discount factor…
In this essay, a general case of information systems contains quantum information systems is considered. By presenting an algorithmic method a new kind of information topology is defined and considered. Continuous maps between two…
Deviation of ergodic sums is studied for substitution dynamical systems with a matrix that admits eigenvalues of modulus 1. We consider the corresponding eigenfunctions, and in Theorem 1.1 we prove that the limit inferior of the ergodic…
We begin development of a method for studying dynamical systems using concepts from computational complexity theory. We associate families of decision problems, called telic problems, to dynamical systems of a certain class. These decision…
In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this…
This paper proposes two novel distributed continuous-time algorithms inspired by PID control to solve distributed optimization problems. The algorithms are referred to as first-order and second-order, respectively, depend on the intrinsic…
We consider two basic problems of algebraic topology, the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational complexity. The extension problem is the following: Given…
When deploying artificial agents in real-world environments where they interact with humans, it is crucial that their behavior is aligned with the values, social norms or other requirements of that environment. However, many environments…
In ergodic optimization theory, the existence of sub-actions is an important tool in the study of the so-called optimizing measures. For transformations with regularly varying property, we highlight a class of moduli of continuity which is…
A method of {\it topological grammars} is proposed for multidimensional data approximation. For data with complex topology we define a {\it principal cubic complex} of low dimension and given complexity that gives the best approximation for…
Given a finite-to-one factor code $\pi: X \to Y$ between irreducible sofic shifts and an ergodic $\nu$ on $Y$ with full support, it is known that the fiber $\pi^{-1}_*(\nu)$ has at most $d_\pi$ ergodic measures in it where $d_\pi$ is the…
Given a compact topological dynamical system (X, f) with positive entropy and upper semi-continuous entropy map, and any closed invariant subset $Y \subset X$ with positive entropy, we show that there exists a continuous roof function such…
In this paper, we introduce dynamics factor graphs as a graphical framework to solve dynamics problems and kinodynamic motion planning problems with full consideration of whole-body dynamics and contacts. A factor graph representation of…
We introduce an effective algorithmic method for the computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach employs interval arithmetic and thus provides a rigorous numerical result (computer-assisted…
Let $f : X\to X$ be a dominating meromorphic map on a compact K\"ahler manifold $X$ of dimension $k$. We extend the notion of topological entropy $h^l_{\mathrm{top}}(f)$ for the action of $f$ on (local) analytic sets of dimension $0\leq l…