Recent advances in molecular biology and fluorescence microscopy imaging have made
possible the inference of the dynamics of molecules in living cells. Such inference allows us …

Superresolution tools, such as PALM and STORM, provide nanoscale localization accuracy
by relying on rare photophysical events, limiting these methods to static samples. By …

Persistence diagrams offer a way to summarize topological and geometric properties latent
in datasets. While several methods have been developed that use persistence diagrams in …

In this paper, we consider the problem of signal classification. First, the signal is translated
into a persistence diagram through the use of delay-embedding and persistent homology …

An adaptive meshfree approach is proposed to solve the nonlinear filtering problem based
on forward backward stochastic differential equations. The algorithm relies on the fact that …

A novel distributed particle filter algorithm is presented, called drift homotopy likelihood
bridging particle filter (DHLB-PF). The DHLB-PF is designed to surmount the degeneracy …

Microscopy imaging allows detailed observations of intracellular movements and the
acquisition of large datasets that can be fully analyzed only by automated algorithms. Here …

Investigation of human brain states through electroencephalograph (EEG) signals is a
crucial step in human-machine communications. However, classifying and analyzing EEG …

A new continuous-time Markov chain rate change formula is proven. This theorem is used to
derive existence and uniqueness of novel filtering equations akin to the Duncan–Mortensen …

Actin cytoskeleton networks generate local topological signatures due to the natural
variations in the number, size, and shape of holes of the networks. Persistent homology is a …