相关论文: Estimation and Quantization of Expected Persistenc…

Kappa distributions are widely used in space plasma physics to model velocity distribution functions with heavy tails. Parameter estimation in these distributions is, however, complicated by the fact that the kappa distribution does not…

Topological descriptors, such as the Euler characteristic function and the persistence diagram, have grown increasingly popular for representing complex data. Recent work showed that a carefully chosen set of these descriptors encodes all…

We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…

We present Euler Characteristic Surfaces as a multiscale spatiotemporal topological summary of time series data encapsulating the topology of the system at different time instants and length scales. Euler Characteristic Surfaces with an…

This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…

The Earth movers distance (EMD) is a measure of distance between probability distributions which is at the heart of mass transportation theory. Recent research has shown that the EMD plays a crucial role in studying the potential impact of…

Laplacian eigenvectors capture natural community structures on graphs and are widely used in spectral clustering and manifold learning. The use of Laplacian eigenvectors as embeddings for the purpose of multiscale graph comparison has…

Penetration depth (PD) is essential for robotics due to its extensive applications in dynamic simulation, motion planning, haptic rendering, etc. The Expanding Polytope Algorithm (EPA) is the de facto standard for this problem, which…

This paper studies the numerical approximation of parametric time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Although many papers in the literature consider reduced…

The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives an approximation algorithm with…

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…

Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting these bifurcations…

We study the consistency of stochastic dynamic programs under converging probability distributions and other approximations. Utilizing results on the epi-convergence of expectation functions with varying measures and integrands, and the…

The Estimation of Distribution Algorithm is a new class of population based search methods in that a probabilistic model of individuals is estimated based on the high quality individuals and used to generate the new individuals. In this…

The Straightness is a measure designed to characterize a pair of vertices in a spatial graph. It is defined as the ratio of the Euclidean distance to the graph distance between these vertices. It is often used as an average, for instance to…

Experimental data in Particle and Nuclear physics, Particle Astrophysics and Radiation Protection Dosimetry are obtained from experimental facilities comprising a complex array of sensors, electronics and software. Computer simulation is…

Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow…

Quasi-probability decompositions (QPDs) have proven essential in many quantum algorithms and protocols -- one replaces a ``difficult'' quantum circuit with an ensemble of ``easier'' circuit variants whose weighted outcomes reproduce any…

Computing efficiently a robust measure of similarity or dissimilarity between graphs is a major challenge in Pattern Recognition. The Graph Edit Distance (GED) is a flexible measure of dissimilarity between graphs which arises in…

Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently…