Related papers: Persistence Concepts for 2D Skeleton Evolution Ana…
This is a brief review of recent theoretical efforts to understand persistence in nonequilibrium systems. Some of the recent experimental results are also briefly mentioned. I also discuss recent generalizations of persistence in various…
Dislocations, as topological defects in crystal lattices, are fundamental to understanding plasticity in materials. Similar periodic structures also arise in continuum field theories, such as chiral soliton lattices (CSLs), which appear in…
We study the persistence probability for some discrete-time, time-reversible processes. In particular, we deduce the persistence exponent in a number of examples: first, we deal with random walks in random sceneries (RWRS) in any dimension…
Skeletonization extracts thin representations from images that compactly encode their geometry and topology. These representations have become an important topological prior for preserving connectivity in curvilinear structures, aiding…
The outcome of vertebroplasty is hard to predict due to its dependence on complex factors like bone cement and marrow rheologies. Cement leakage could occur if the procedure is done incorrectly, potentially causing adverse complications. A…
The theory of persistence modules is an emerging field of algebraic topology which originated in topological data analysis. In these notes we provide a concise introduction into this field and give an account on some of its interactions…
We study the shapes of elastic membranes under the simultaneous exertion of tensile and compressive forces when the translational symmetry along the tension direction is broken. We predict a multitude of novel morphological phases in…
Biomaterial systems have allowed for the in vitro production of complex, emergent tissue behaviors that were not possible with conventional 2D culture systems allowing for analysis of the normal development as well as disease processes. We…
Skeleton creation is an important phase in the character animation pipeline. However, handcrafting skeleton takes extensive labor time and domain knowledge. Automatic skeletonization provides a solution. However, most of the current…
We present a multi-stage pipeline for simple gesture recognition. The novelty of our approach is the association of different technologies, resulting in the first real-time system as of now to conjointly extract skeletons and recognise…
An intriguing unanswered question about the evolution of bilateral animals with internal skeletons is how an internal skeleton evolved in the first place. Computational modeling of the development of bilateral symmetric organisms suggests…
Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions. The rank invariant completely determines the multidimensional analogue of persistent homology groups. We prove…
Over the past two decades, there has been a tremendous increase in the growth of representation learning methods for graphs, with numerous applications across various fields, including bioinformatics, chemistry, and the social sciences.…
Dynamical simulations are a fundamental tool for studying the secular evolution of disc galaxies. Even at their maximum resolution, they still follow a limited number of particles and typically resolve scales of the order of a few tens of…
This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an…
The present article introduces a reference framework for discussing resilience of computational systems. Rather than a property that may or may not be exhibited by a system, resilience is interpreted here as the emerging result of a dynamic…
Using the time-dependent superfluid local density approximation, the dynamics of fission is investigated in real time from just beyond the saddle to fully separated fragments. Simulations produced in this fully microscopic framework can…
Phase separation has emerged as an essential concept for the spatial organization inside biological cells. However, despite the clear relevance to virtually all physiological functions, we understand surprisingly little about what phases…
A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…
A general model is formulated for elasto-plastic materials undergoing linear kinematic hardening to describe microstructure evolution associated with phase transformations. Using infinitesimal strain theory, the model is based on…