Related papers: Understanding Persistence: A 3D Trap Map of an H2R…
Persistent homology is a tool from Topological Data Analysis (TDA) used to summarize the topology underlying data. It can be conveniently represented through persistence diagrams. Observing a noisy signal, common strategies to infer its…
There is a need for numerical models capable of predicting local accumulation of hydrogen near stress concentrators and crack tips to prevent and mitigate hydrogen assisted fracture in steels. The experimental characterisation of trapping…
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…
We obtained a semi-analytical treatment obtaining estimators for the sample variance and variance of sample variance for the RTS noise. Our method suggests a way to experimentally determine the constants of capture and emission in the case…
The stability of electron current sheets embedded within the reconnection exhaust is studied with a 3D fully kinetic particle-in-cell simulation. The electron current layers studied here form self-consistently in a reconnection regime with…
One of the primary goals in spectrum occupancy mapping is to create a system that is robust to assumptions about the number of sensors, occupancy threshold (in dBm), sensor noise, number of emitters and the propagation environment. We show…
Defect induced trap states are essential in determining the performance of semiconductor photodetectors. The de-trap time of carriers from a deep trap could be prolonged by several orders of magnitude as compared to shallow trap, resulting…
One of the main reasons for topological persistence being useful in data analysis is that it is backed up by a stability (isometry) property: persistence diagrams of $1$-parameter persistence modules are stable in the sense that the…
A distribution shift can have fundamental consequences such as signaling a change in the operating environment or significantly reducing the accuracy of downstream models. Thus, understanding distribution shifts is critical for examining…
We analyze a trapping reaction with a single penetrable trap, in a one dimensional lattice, where both species (particles and trap) are mobile and have a drift velocity. We obtain the density as seen from a reference system attached to the…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a…
We introduce a new problem in the domain of mobile robots, which we term dispersion. In this problem, $n$ robots are placed in an $n$ node graph arbitrarily and must coordinate with each other to reach a final configuration such that…
Transient microscopy is of vital importance in understanding the dynamics of optical excited states in optoelectronic materials, as it allows for a direct visualization of the movement of energy carriers in space and time. Important…
Surface ion traps with two-dimensional layouts of trapping regions are natural architectures for storing large numbers of ions and supporting the connectivity needed to implement quantum algorithms. Many of the components and operations…
In topological data analysis, we want to discern topological and geometric structure of data, and to understand whether or not certain features of data are significant as opposed to simply random noise. While progress has been made on…
We find an exact series solution for the steady-state probability distribution of a harmonically trapped active Brownian particle in two dimensions, in the presence of translational diffusion. This series solution allows us to efficiently…
Tracking of plant cells in images obtained by microscope is a challenging problem due to biological phenomena such as large number of cells, non-uniform growth of different layers of the tightly packed plant cells and cell division.…
Electronic trap states are a critical yet unavoidable aspect of semiconductor devices, impacting performance of various electronic devices such as transistors, memory devices, solar cells, and LEDs. The density, energy level, and position…
Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called…