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Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading…
We introduce the persistence heatmap, a parametrized summary based on representative cycles in persistence diagrams, designed to enhance stability and explainability in topological data analysis. Algorithms to compute persistence diagrams…
The supercell method is used to study the variation of the photonic bandgaps in one-dimensional photonic crystals under random perturbations to thicknesses of the layers. The results of both plane wave and analytical band structure and…
Persistence diagrams offer a way to summarize topological and geometric properties latent in datasets. While several methods have been developed that utilize persistence diagrams in statistical inference, a full Bayesian treatment remains…
A recently suggested reciprocity relation states that the current transport efficiency from the junction to the cell terminal can be determined by differentiating luminescence images with respect to the terminal voltage. The validity of…
Visualization in the emerging field of topological data analysis has progressed from persistence barcodes and persistence diagrams to display of two-parameter persistent homology. Although persistence barcodes and diagrams have permitted…
Frustrated total internal reflection is analyzed from an unusual point of view Unlike most similar works, incident angles are used here as the scanning variable, instead of the tunneled film thickness. The theoretical framework is presented…
In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this setting, and propose the use of bipath persistent homology,…
The objective of this paper is to examine the asymptotic behavior of persistence diagrams associated with \v{C}ech filtration. A persistence diagram is a graphical descriptor of a topological and algebraic structure of geometric objects. We…
In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…
Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems' persistence involves different…
The problem of a diffusing particle moving among diffusing traps is analyzed in general space dimension d. We consider the case where the traps are initially randomly distributed in space, with uniform density rho, and derive upper and…
Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances}, most of the recent attempts at using persistence diagrams…
Two mechanisms of decoherence in ion traps are studied, specially related to the experiment [Kielpinski et al., Science 291 (2001) 1013]. Statistical hypothesis are made about the unknown variables and the expected behaviour of the…
Time-resolved image sensors that capture light at pico-to-nanosecond timescales were once limited to niche applications but are now rapidly becoming mainstream in consumer devices. We propose low-cost and low-power imaging modalities that…
In this paper we study the persistent homology associated with topological crackle generated by distributions with an unbounded support. Persistent homology is a topological and algebraic structure that tracks the creation and destruction…
In this work, we tackle the problem of estimating a camera capability to preserve fine texture details at a given lighting condition. Importantly, our texture preservation measurement should coincide with human perception. Consequently, we…
It is shown that recent experiments indicating a metal-insulator transition in 2D electron systems can be interpreted in terms of a simple model, in which the resistivity is controlled by scattering at charged hole traps located in the…
The theory of zigzag persistence is a substantial extension of persistent homology, and its development has enabled the investigation of several unexplored avenues in the area of topological data analysis. In this paper, we discuss three…
Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…