Related papers: A simplified algorithm for the topological entropy…
This paper offers an algorithmic solution to the problem of obtaining "economical" formulae for some maps in Simplicial Topology, having, in principle, a high computational cost in their evaluation. In particular, maps of this kind are used…
Iterations of odd piecewise continuous maps with two discontinuities, i.e., symmetric discontinuous bimodal maps, are studied. Symbolic dynamics is introduced. The tools of kneading theory are used to study the homology of the discrete…
The monotonicity of entropy is investigated for real quadratic rational maps on the real circle $\mathbb{R}\cup\{\infty\}$ based on the natural partition of the corresponding moduli space $\mathcal{M}_2(\mathbb{R})$ into its monotonic,…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
Stirring a two-dimensional viscous fluid with rods is often an effective way to mix. The topological features of periodic rod motions give a lower bound on the topological entropy of the induced flow map, since material lines must `catch'…
We establish the analogue for maps on trees of the result established in two papers by the first author for interval maps, that a continuous self- map for which all but countably many points have at least m preimages (and none have less…
In this paper, we present a receding-horizon, sampling-based planner capable of reasoning over multimodal policy distributions. By using the cross-entropy method to optimize a multimodal policy under a common cost function, our approach…
We apply a recently developed method, multicanonical algorithm, to the problem of tertiary structure prediction of peptides and proteins. As a simple example to test the effectiveness of the algorithm, Met-enkephalin is studied and the…
In this paper, an estimation of lower bound of topological entropy for coupled-expanding systems associated with transition matrices in compact Hausdorff spaces is given. Estimations of upper and lower bounds of topological entropy for…
This article presents a novel approach to identifying and classifying intersections for semantic and topological mapping. More specifically, the proposed novel approach has the merit of generating a semantically meaningful map containing…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…
This work presents a maximum entropy principle based algorithm for solving minimum multiway $k$-cut problem defined over static and dynamic {\em digraphs}. A multiway $k$-cut problem requires partitioning the set of nodes in a graph into…
In the machine learning field, dimensionality reduction is an important task. It mitigates the undesired properties of high-dimensional spaces to facilitate classification, compression, and visualization of high-dimensional data. During the…
We consider the category of partially observable dynamical systems, to which the entropy theory of dynamical systems extends functorially. This leads us to introduce quotient-topological entropy. We discuss the structure that emerges. We…
Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…
Mapping is an essential task for mobile robots and topological representation often works as a basis for the various applications. In this paper, a novel framework that can build topological maps incrementally is proposed. The algorithm is…
We introduce and study the notion of a directional complexity and entropy for maps of degree 1 on the circle. For piecewise affine Markov maps we use symbolic dynamics to relate this complexity to the symbolic complexity. We apply a…
I propose a new algorithm, a free energy Monte Carlo algorithm, for calculations where conventional Monte Carlo simulations struggle with ergodicity problems. The simplest version of the proposed algorithm allows for the determination of…