Related papers: The Kinetic Hourglass Data Structure for Computing…
Dynamic Bayesian networks (DBNs) are a widely used framework for modeling systems whose probabilistic structure evolves over time. Standard inference methods focus on local conditional distributions and can miss larger-scale patterns in how…
We propose a hyperbolic set-to-set distance measure for computing dissimilarity between sets in hyperbolic space. While point-to-point distances in hyperbolic space effectively capture hierarchical relationships between data points, many…
Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the…
Several statistical and machine learning methods are proposed to estimate the type and intensity of physical load and accumulated fatigue . They are based on the statistical analysis of accumulated and moving window data subsets with…
Kinetically constrained models (KCMs) are models of glass formers based on the concept of dynamic facilitation. This concept accounts for many of the characteristics of the glass transition. KCMs usually display a combination of simple…
In the last decade, the accelerated advancements in manufacturing techniques and material science enabled the automotive industry to manufacture commercial vehicles at more affordable rates. This, however, brought about roadways having to…
Investigating the network stability or synchronization dynamics of multi-agent systems with time delays is of significant importance in numerous real-world applications. Such investigations often rely on solving the transcendental…
Persistent homology (PH) encodes global information, such as cycles, and is thus increasingly integrated into graph neural networks (GNNs). PH methods in GNNs typically traverse an increasing sequence of subgraphs. In this work, we first…
Distance measures play an important role in shape classification and data analysis problems. Topological distances based on Reeb graphs and persistence diagrams have been employed to obtain effective algorithms in shape matching and scalar…
We introduce a framework to dynamically combine heterogeneous models called \texttt{DYCHEM}, which forecasts a set of time series that are related through an aggregation hierarchy. Different types of forecasting models can be employed as…
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
The natural pseudo-distance of spaces endowed with filtering functions is precious for shape classification and retrieval; its optimal estimate coming from persistence diagrams is the bottleneck distance, which unfortunately suffers from…
Motion planning is a mature area of research in robotics with many well-established methods based on optimization or sampling the state space, suitable for solving kinematic motion planning. However, when dynamic motions under constraints…
Accurate long-horizon prediction of spatiotemporal fields on complex geometries is a fundamental challenge in scientific machine learning, with applications such as additive manufacturing where temperature histories govern defect formation…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
Traffic flow prediction is a typical spatio-temporal prediction problem and has a wide range of applications. The core challenge lies in modeling the underlying complex spatio-temporal dependencies. Various methods have been proposed, and…
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…
The extended persistence diagram is an invariant of piecewise linear functions, which is known to be stable under perturbations of functions with respect to the bottleneck distance as introduced by Cohen-Steiner, Edelsbrunner, and Harer. We…
Let $K$ be a compact, centrally-symmetric, strictly-convex region in ${\mathbb R}^3$, which is a semi-algebraic set of constant complexity, i.e. the unit ball of a corresponding metric, denoted as $\|\cdot\|_K$. Let ${\mathcal{K}}$ be a set…
Enhancing the kinetic stability of glasses often necessitates deepening thermodynamic stability, which typically compromises ductility due to increased structural rigidity. Decoupling these properties remains a critical challenge for…