Related papers: Espaces vectoriels \'echelonn\'es
We introduce a topology on the space of actions modulo weak equivalence finer than the one previously studied in the literature. We show that the product of actions is a continuous operation with respect to this topology, so that the space…
We introduce the notion of stationary actions in the context of C*-algebras. We develop the basics of the theory, and provide applications to several ergodic theoretical and operator algebraic rigidity problems.
In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.
The purpose of this paper is to survey the structure of closed and transitive transformation groups acting on a closed surface. In particular, we prove a number of relations between groups acting on the sphere that contain the rotation…
We consider actions of a group or a semigroup on a set, which generalize the setup of discrete logarithm based cryptosystems. Such cryptographic group actions have gained increasing attention recently in the context of isogeny-based…
The paper is devoted to vector fields on the spaces R^2 and R^3, their flow and invariants. Attention is plaid on the tensor representations of the group GL(2,R) and on fundamental vector fields. The rotation group on R^3 is generalized to…
This paper focuses on rotational phenomena of rigid body kinematics. It discusses them in a group-theoretic approach as completely as possible, using methods and notations as intuitive as possible. With a review of current literature, this…
We define and study Poissonian actions of Polish groups as a framework to Poisson suspensions, characterize them spectrally, and provide a complete characterization of their ergodicity. We further construct 'spatial' Poissonian actions,…
We study a large family of generalized class groups of imaginary quadratic orders $O$ and prove that they act freely and (essentially) transitively on the set of primitively $O$-oriented elliptic curves over a field $k$ (assuming this set…
Action Detection is a complex task that aims to detect and classify human actions in video clips. Typically, it has been addressed by processing fine-grained features extracted from a video classification backbone. Recently, thanks to the…
In this talk, we'll present some recent results related to group actions in several complex variables. We'll not aim at giving a complete survey about the topic but giving some our own results and related ones. We'll divide the results into…
With the advent of drones, aerial video analysis becomes increasingly important; yet, it has received scant attention in the literature. This paper addresses a new problem of parsing low-resolution aerial videos of large spatial areas, in…
This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…
The strategic behaviour of pedestrians is largely determined by how they perceive and react to neighbouring people. This issue is addressed in this paper by a model which combines, in a time and space-dependent way, discrete and continuous…
In this paper we develop an abstract setup for hamiltonian group actions as follows: Starting with a continuous 2-cochain $\omega$ on a Lie algebra $h$ with values in an $h$-module $V$, we associate subalgebras $sp(h,\omega) \supeq…
Pedestrian crowds often include social groups, i.e. pedestrians that walk together because of social relationships. They show characteristic configurations and influence the dynamics of the entire crowd. In order to investigate the impact…
We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…
Our current research lays emphasis on the extended pedestrian perception and copes with both the dynamic group behavior and the individual evaluation of situations, and hence, rather focuses on the tactical level of movement behavior.…