Related papers: Surgery and Stratified Spaces
In this paper, we mainly build up the theory of sheaf-correspondence filtered spaces and stratified de Rham complexes for studying singular spaces. We prove the finiteness of a stratified de Rham cohomology and obtain its isomorphism to…
Recent advancements in model checking have demonstrated significant potential across diverse applications, particularly in signal and image analysis. Medical imaging stands out as a critical domain where model checking can be effectively…
Surgical robots have had clinical use since the mid 1990s. Robot-assisted surgeries offer many benefits over the conventional approach including lower risk of infection and blood loss, shorter recovery, and an overall safer procedure for…
We report on recent progress in understanding mirror symmetry. Some of more recent generalizations and applications are also presented. --- A contribution to the Proceedings of ``Strings 2001'' at Mumbai, India.
The exposition has been significantly altered, hopefully improved.
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…
This paper is a systematic study about the syndetically proximal relation and the possible existence of syndetically scrambled sets for the dynamics of continuous self-maps of compact metric spaces. Especially we consider various classes of…
A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differential geometry from the study of spaces of constant curvature…
In this paper, we develop the theory of constrained motion spaces of robotic arms. We compute their homology groups in two cases: when the constraint is a horizontal line and when it is a smooth curve whose motion space is a smooth…
This is the first of the two articles where we determine the higher smooth surgery structure sets of complex projective spaces (up to some extension problems) and the forgetful map to their topological versions in low dimensions. In this…
We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.
The author reviews the computer and robotic tools available to urologists to help in diagnosis and technical procedures. The first part concerns the contribution of robotics and presents several systems at various stages of development…
Directed Algebraic Topology studies spaces equipped with a form of direction, to include models of non-reversible processes. In the present extension we also want to cover critical processes, indecomposable and unstoppable. The previous…
This is a survey paper on spaces of automorphisms of manifolds and spaces of manifolds in a fixed homotopy type. It describes the main theorems of traditional surgery theory, but also the main theorems of pseudoisotopy theory, alias…
Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in…
Graphical models are used in many applications such as medical diagnostic, computer security, etc. More and more often, the estimation of such models has to be performed on several predefined strata of the whole population. For instance, in…
Mass partition problems describe the partitions we can induce on a family of measures or finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this survey we describe recent progress in the area in addition…
This paper reviews recent advances in the field of metallic glasses, focusing on the development of novel experimental techniques and in silico models. We discuss progress in experimental characterization, additive manufacturing, multiscale…
In previous work, the first author defined homotopy theories for stratified spaces from a simplicial and a topological perspective. In both frameworks stratified weak-equivalences are detected by suitable generalizations of homotopy links.…
The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…