Abstract It has long been suggested that the mid-latitude atmospheric circulation possesses what come to be known as ‘weather regimes’, loosely categorised regions of phase space with above-average density and/or extended persistence. Their existence and behaviour extensively studied in meteorology climate science, due their potential for drastically simplifying complex chaotic dynamics. Severa...

conclusions based on the location of detected rccs in the structure of hbv proteins, it was found that these rccs may have a critical role in correct folding of hbv proteins and can be considered as drug targets. the results of this study provide new and deep perspectives about structure of hbv proteins for further researches and designing new drugs for treatment of hbv. results the pfam search...

Understanding and comparing images for the purposes of data analysis is currently a very computationally demanding task. A group at Australian National University (ANU) recently developed open-source code that can detect fundamental topological features of a grayscale image in a computationally feasible manner. This is made possible by the fact that computers store grayscale images as cubical c...

This paper discusses the connection between the texture operator LBP (local binary pattern) and an application of LBPs to persistent homology. A shape representation the LBP scale space is defined as a filtration based on the variation of an LBP parameter. A relation between the LBP scale space and a variation of thresholds used in the segmentation of a graylevel image is discussed. Using the L...

In topological data analysis, a point cloud data P extracted from a metric space is often analyzed by computing the persistence diagram or barcodes of a sequence of Rips complexes built on P indexed by a scale parameter. Unfortunately, even for input of moderate size, the size of the Rips complex may become prohibitively large as the scale parameter increases. Starting with the Sparse Rips filt...

Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically – as long as the algorithm does not exhaust the available memory. Following up on a recently presented parallel method for persistence computation on shared memory systems, we demonstrate that a simp...

In Persistent Homology and Topology, filtrations are usually given by introducing an ordered collection of sets or a continuous function from a topological space to R. A natural question arises, whether these approaches are equivalent or not. In this paper we study this problem and prove that, while the answer to the previous question is negative in the general case, the approach by continuous ...

Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persistent homology with respect to function perturbations to results concerning the stability with respect to domain perturbations. Domain perturbations can be measured in a number of different ways. An important method to ...

Persistent homology is a vital tool for topological data analysis. Previous work has developed some statistical estimators for characteristics of collections of persistence diagrams. However, tools that provide statistical inference for observations that are persistence diagrams are limited. Specifically, there is a need for tests that can assess the strength of evidence against a claim that tw...