Related papers: Abstract Action Spaces and their topological and d…

We introduce a framework for engineering active quantum matter that involves mimicking the role of self-propulsion through an external trapping potential that is moving along imposed trajectories traced by classical active dynamics. This…

We want to investigate 'spaces' where paths have a 'weight', or 'cost', expressing length, duration, price, energy, etc. The weight function is not assumed to be invariant up to path-reversion. Thus, 'weighted algebraic topology' can be…

Mean dimension is a topological invariant of dynamical systems, which originates with Mikhail Gromov in 1999 and which was studied with deep applications around 2000 by Elon Lindenstrauss and Benjamin Weiss within the framework of amenable…

This article is an investigation of a method of deriving a topology from a space and an elementary submodel containing it. We first define and give the basic properties of this construction, known as $X/M$. In the next section, we construct…

If $X$ is a (topological) space, the $n$th finite subset space of $X$, denoted by $X(n)$, consists of $n$-point subsets of $X$ (i.e., nonempty subsets of cardinality at most $n$) with the quotient topology induced by the unordering map…

We look at group actions on metric spaces, particularly at group actions on geodesic hyperbolic spaces. We classify the types of automorphisms on these spaces and prove several results about the density of the hyperbolic limit set of the…

This paper introduces a probabilistic graphical model for continuous action recognition with two novel components: substructure transition model and discriminative boundary model. The first component encodes the sparse and global temporal…

We study the topological structure of the space $\mathcal{X}$ of isomorphism classes of metric measure spaces equipped with the box or concentration topologies. We consider the scale-change action of the multiplicative group $\mathbb{R}_+$…

A general set of fluid equations that allow for energy-conserving momentum transport by gyroscopic motion of fluid elements is obtained. The equations are produced by a class of action principles that yield a large subset of the known fluid…

We present the set of axioms for topological space with the operation of boundary as primitive notion.

Topological groupoids admit various types of morphisms. We push these notions to the level of continuous groupoid actions to obtain various types of groupoid action morphisms. Some dynamical properties and their relation to these morphisms…

Pointwise tangential dimensions are introduced for metric spaces. Under regularity conditions, the upper, resp. lower, tangential dimensions of X at x can be defined as the supremum, resp. infimum, of box dimensions of the tangent sets, a…

We give a geometrical interpretation for the principle of stationary action in classical Lagrangian particle mechanics. In a nutshell, the difference of the action along a path and its variation effectively ``counts'' the possible…

Given an action of a group G on a topological space X, we establish a necessary and sufficient condition for the existence of a free subgroup F of rank 2 of G acting properly discontinuously on at least one nonempty, open, F-invariant…

Human-centred systems require an understanding of human actions in the physical world. Temporally extended sequences of actions are intentional and structured, yet existing methods for recognising what actions are performed often do not…

For equilibrium hard spheres the stochastic geometry of the insertion space, the room to accommodate another sphere, relates exactly to the equation of state. We begin to extend this idea to active matter, analyzing insertion space for…

We define an admissibility condition for abstractions expressed using angelic semantics and show that these conditions allow us to accelerate planning while preserving the ability to find the optimal motion plan. We then derive admissible…

Given an action of a finite group $G$, we can define its index. The $G$-index roughly measures a size of the given $G$-space. We explore connections between the $G$-index theory and topological dynamics. For a fixed-point free dynamical…

The purpose of this note is to characterize the asymptotic dimension $asdim(X)$ of metric spaces $X$ in terms similar to Property A of Yu: If $(X,d)$ is a metric space and $n\ge 0$, then the following conditions are equivalent: [a.]…

Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…