Related papers: Computing multiparameter persistent homology throu…
This work proposes a unifying probabilistic framework for the design of robustly asymptotically stable moving-horizon estimators (MHE) for discrete-time nonlinear systems, and a mechanism to incorporate differential privacy in…
Using Banchoff's discrete Morse Theory, in tandem with Bloch's result on the strong connection between the former and Forman's Morse Theory, and our own previous algorithm based on the later, we show that there exists a curvature-based,…
Discrete Morse theory has emerged as a powerful tool for a wide range of problems, including the computation of (persistent) homology. In this context, discrete Morse theory is used to reduce the problem of computing a topological invariant…
Datasets often possess an intrinsic multiscale structure with meaningful descriptions at different levels of coarseness. Such datasets are naturally described as multi-resolution clusterings, i.e., not necessarily hierarchical sequences of…
A central problem in topological data analysis is that of computing the homology of a given simplicial complex. Said complexes can have arbitrary large number of simplices, as can happen, for example, if the space is the Rips-Vietoris or…
Tumor segmentation in whole-slide images of histology slides is an important step towards computer-assisted diagnosis. In this work, we propose a tumor segmentation framework based on the novel concept of persistent homology profiles…
The port-Hamiltonian framework is a structure-preserving modeling approach that preserves key physical properties such as energy conservation and dissipation. When subsystems are modeled as port-Hamiltonian systems (pHS) with linearly…
We develop a framework for computing two foundational analyses for concurrent higher-order programs: (control-)flow analysis (CFA) and may-happen-in-parallel analysis (MHP). We pay special attention to the unique challenges posed by the…
Recently, persistent homology has had tremendous success in biomolecular data analysis. It works by examining the topological relationship or connectivity of a group of atoms in a molecule at a variety of scales, then rendering a family of…
We introduce PMODE (Partitioned Mixture Of Density Estimators), a general and modular framework for mixture modeling with both parametric and nonparametric components. PMODE builds mixtures by partitioning the data and fitting separate…
In this paper, we consider the problem of probabilistic stability analysis of a subclass of Stochastic Hybrid Systems, namely, Polyhedral Probabilistic Hybrid Systems (PPHS), where the flow dynamics is given by a polyhedral inclusion, the…
We propose a functorial framework for persistent homology based on finite topological spaces and their associated posets. Starting from a finite metric space, we associate a filtration of finite topologies whose structure maps are…
Phase-type (PH) distributions are a popular tool for the analysis of univariate risks in numerous actuarial applications. Their multivariate counterparts (MPH$^\ast$), however, have not seen such a proliferation, due to lack of explicit…
Art is a deeply personal and expressive medium, where each artist brings their own style, technique, and cultural background into their work. Traditionally, identifying artistic styles has been the job of art historians or critics, relying…
Many applications require comparing multimodal data with different structure and dimensionality that cannot be compared directly. Recently, there has been increasing interest in methods for learning and efficiently representing such…
This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the…
Multiparameter persistent homology is a generalization of classical persistent homology, a central and widely-used methodology from topological data analysis, which takes into account density estimation and is an effective tool for data…
Multi-target tracking is an important problem in civilian and military applications. This paper investigates multi-target tracking in distributed sensor networks. Data association, which arises particularly in multi-object scenarios, can be…
Multivector fields provide an avenue for studying continuous dynamical systems in a combinatorial framework. There are currently two approaches in the literature which use persistent homology to capture changes in combinatorial dynamical…
Persistent homology (PH) is one of the main methods used in Topological Data Analysis. An active area of research in the field is the study of appropriate notions of PH representatives, which allow to interpret the meaning of the…