- Full text PDF available (7)
- This year (1)
- Last 5 years (6)
- Last 10 years (7)
Journals and Conferences
We propose a new approach to detect and quantify the periodic structure of dynamical systems using topological methods. We propose to use delay-coordinate embedding as a tool to detect the presence of harmonic structures by using persistent homology for robust analysis of point clouds of delay-coordinate embeddings. To discover the proper delay, we propose… (More)
The increasing interest in big data applications is ushering in a large effort in seeking new, efficient, and adapted data models to reduce complexity, while preserving maximal intrinsic information. Graph-based models have recently been getting a lot of attention on account of their intuitive and direct connection to the data . The cost of these… (More)
In persistent homology, the persistence barcode encodes pairs of simplices meaning birth and death of homology classes. Persistence barcodes depend on the ordering of the simplices (called a filter) of the given simplicial complex. In this paper, we define the notion of “minimal” barcodes in terms of entropy. Starting from a given filtration of a simplicial… (More)
We prove that if a finitely presented group is one-ended then its asymptotic dimension is bigger than 1. It follows that a finitely presented group of asymptotic dimension 1 is virtually free.
In this paper we describe a model based on persistent homology that describes interactions between mathematicians in terms of collaborations. Some ideas from classical data analysis are used.
In applications where the use of video surveillance is necessary and/or beneficial, it is a common goal to identify the contents of the video automatically. Of particular interest in such applications is the ability to recognize locations in the environment, where events occur, and describe the events common to those locations. This is one of the goals of… (More)
We prove that the property to be limit aperiodic is preserved by the standard construction with groups like extension, HNN extension and free product. We also construct a non-limit aperiodic G-space.
We introduce the idea of Data Readiness Level (DRL) to measure the relative richness of data to answer specific questions often encountered by data scientists. We first approach the problem in its full generality explaining its desired mathematical properties and applications and then we propose and study two DRL metrics. Specifically, we define DRL as a… (More)