155 citations · 446 across the 15 of their papers we have counts for
18 papers
Characterizing High-dimensional Dynamics by Combinatorial-Topological Methods on a Latent Space
Patrick Bailon, Marcio Gameiro, Brittany Gelb +5
Combinatorial-topological methods for characterizing dynamics are rigorous, generalizable, computable, and they only require approximations, but the dimension of the phase space is…
Data-driven Identification of Attractors Using Machine Learning
Marcio Gameiro, Brittany Gelb, William Kalies +3
In this paper we explore challenges in developing a topological framework in which machine learning can be used to robustly characterize global dynamics. Specifically, we focus on…
Stochastic methods for slip prediction in a sheared granular system
Philip Bretz, Lou Kondic, Miro Kramar
We consider a sheared granular system experiencing intermittent dynamics of stick-slip type via discrete element simulations. The considered setup consists of a two-dimensional sys…
On intermittency in sheared granular systems
Miroslav Kramar, Chao Cheng, Rituparna Basak +1
We consider a system of granular particles, modeled by two dimensional frictional elastic disks, that is exposed to externally applied time-dependent shear stress in a planar Couet…
Two approaches to quantification of force networks in particulate systems
Rituparna Basak, C. Manuel Carlevaro, Ryan Kozlowski +6
The interactions between particles in particulate systems are organized in `force networks', mesoscale features that bridge between the particle scale and the scale of the system a…
Machine learning approach to force reconstruction in photoelastic materials
Renat Sergazinov, Miroslav Kramar
Photoelastic techniques have a long tradition in both qualitative and quantitative analysis of the stresses in granular materials. Over the last two decades, computational methods…
Quantitative Measure of Memory Loss in Complex Spatio-Temporal Systems
Miroslav Kramar, Lenka Kovalcinova, Konstantin Mischaikow +1
To make progress in understanding the issue of memory loss and history dependence in evolving complex systems, we consider the mixing rate that specifies how fast the future states…
Dynamics of silo deformation under granular discharge
Claudia Colonnello, Miroslav Kramar
We use Topological Data Analysis to study the post buckling behavior of laboratory scale cylindrical silos under gravity driven granular discharges. Thin walled silos buckle during…
A Comparison Framework for Interleaved Persistence Modules
Shaun Harker, Miroslav Kramar, Rachel Levanger +1
We present a generalization of the induced matching theorem and use it to prove a generalization of the algebraic stability theorem for -indexed pointwise finite-dimens…
Characterizing Granular Networks Using Topological Metrics
Joshua A. Dijksman, Lenka Kovalcinova, Jie Ren +4
We carry out a direct comparison of experimental and numerical realizations of the exact same granular system as it undergoes shear jamming. We adjust the numerical methods used to…
Evolution of force networks in dense granular matter close to jamming
Lou Kondic, Miroslav Kramar, Lenka Kovalcinova +1
When dense granular systems are exposed to external forcing, they evolve on the time scale that is typically related to the externally imposed one (shear or compression rate, for e…
Structure of force networks in tapped particulate systems of disks and pentagons (Part 2): Persistence analysis
L. Kondic, M. Kramar, L. A. Pangolin +2
In the companion paper~\cite{paper1}, we use classical measures based on force probability density functions (PDFs), as well as Betti numbers (quantifying the number of components,…
Structure of force networks in tapped particulate systems of disks and pentagons (Part 1): Clusters and Loops
L. A. Pugnaloni, C. M. Carlevaro, M. Kramar +2
The force network of a granular assembly, defined by the contact network and the corresponding contact forces, carries valuable information about the state of the packing. Simple a…
Analysis of Kolmogorov Flow and Rayleigh-Bénard Convection using Persistent Homology
Miroslav Kramar, Rachel Levanger, Jeffrey Tithof +5
We use persistent homology to build a quantitative understanding of large complex systems that are driven far-from-equilibrium; in particular, we analyze image time series of flow…
On Approximations of Persistence Diagrams
Jonathan Jaquette, Miroslav Kramár
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framew…
Topological data analysis of contagion maps for examining spreading processes on networks
Dane Taylor, Florian Klimm, Heather A. Harrington +4
Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however,…
Evolution of Force Networks in Dense Particulate Media
Miroslav Kramar, Arnaud Goullet, Lou Kondic +1
We introduce novel sets of measures with the goal of describing dynamical properties of force networks in dense particulate systems. The presented approach is based on persistent h…
Quantifying force networks in particulate systems
M. Kramar, A. Goullet, L. Kondic +1
We present mathematical models based on persistent homology for analyzing force distributions in particulate systems. We define three distinct chain complexes: digital, position, a…