Related papers: Pebbles, graphs and equilibria: higher order shape…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…
After a somewhat rocky start, geometry and topology have established a foothold in machine learning. Message passing, either on graphs or higher-order complexes, is one of the main drivers of geometric deep learning, and paradigms that were…
In this work, we present a novel global descriptor termed stable triangle descriptor (STD) for 3D place recognition. For a triangle, its shape is uniquely determined by the length of the sides or included angles. Moreover, the shape of…
Spectral shape descriptors have been used extensively in a broad spectrum of geometry processing applications ranging from shape retrieval and segmentation to classification. In this pa- per, we propose a spectral graph wavelet approach for…
Identifying the regions responsible for plastic flow in amorphous solids remains an open problem, since structural disorder seems to prevent the direct application of concepts such as dislocations, topological defects that successfully…
Material understanding is critical for design, geometric modeling, and analysis of functional objects. We enable material-aware 3D shape analysis by employing a projective convolutional neural network architecture to learn material- aware…
Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…
Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…
This dissertation presents a method for simulation of motion of the pebbles in a PBR. A new mechanical motion simulator, PEBBLES, efficiently simulates the key elements of motion of the pebbles in a PBR. This model simulates gravitational…
Hydraulic structures such as dams have a direct or indirect influence on the hydro-sedimentary functioning of rivers. They can impact the sediment continuity of the river and can create a sediment imbalance with zones of sediment…
Rocking stones, balanced in counter-intuitive positions have always intrigued geologists. In our paper we explain this phenomenon based on high-precision scans of pebbles which exhibit similar behavior. We construct their convex hull and…
Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
Starting with a first order in derivatives self-dual model which describes a massive spin-4 mode in $D=2+1$ dimensions, we have obtained a sequence of three more new descriptions, which then give us an interconnected self-dual chain $SD(i)$…
Plastic-scintillator detectors are devices used for the detection of elementary particles. They provide good particle identification with excellent time resolution, whilst being inexpensive due to the affordability of plastic materials.…
First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, however, have yet to realize the same utility. In this paper I…
Feature extraction is an essential task in graph analytics. These feature vectors, called graph descriptors, are used in downstream vector-space-based graph analysis models. This idea has proved fruitful in the past, with spectral-based…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…