Related papers: Multi-scale Mining of Kinematic Distributions with…
High-energy collisions at the Large Hadron Collider (LHC) provide valuable insights into open questions in particle physics. However, detector effects must be corrected before measurements can be compared to certain theoretical predictions…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
In this short paper we discuss how the position - scale half-space of wavelet analysis may be cut into different regions. We discuss conditions under which they are independent in the sense that the T\"oplitz operators associated with their…
Distributions of wave characteristics of ocean waves, such as wave slope, waveheight or wavelength, are an important tool in a variety of oceanographic applications such as safety of ocean structures or in the study of ship stability, as…
We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis…
Capturing high-frequency data concerning the condition of complex systems, e.g. by acoustic monitoring, has become increasingly prevalent. Such high-frequency signals typically contain time dependencies ranging over different time scales…
We introduce Wavelet Phase Harmonics (WPH) statistics: interpretable low-dimensional statistics that describe 2D non-Gaussian fields. These statistics are built from WPH moments, which were recently introduced in the data science and…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
Cloud detection is a specialized application of image recognition and object detection using remotely sensed data. The task presents a number of challenges, including analyzing images obtained in visible, infrared and multi-spectral…
In this paper, we study the problem of learning dynamical properties of ensemble systems from their collective behaviors using statistical approaches in reproducing kernel Hilbert space (RKHS). Specifically, we provide a framework to…
How does one search for a needle in a multi-dimensional haystack without knowing what a needle is and without knowing if there is one in the haystack? This kind of problem requires a paradigm shift - away from hypothesis driven searches of…
The system of Lama's equations is investigated, describing the motion of the elastic media under subsonic, transonic and supersonic velocities of the moving source of distributions, and its decisions in space of generalized…
We introduce a systematic method for extracting multivariable universal scaling functions and critical exponents from data. We exemplify our insights by analyzing simulations of avalanches in an interface using simulations from a driven…
Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly-evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism,…
We introduce the concept of Hypoelliptic Diffusion Maps (HDM), a framework generalizing Diffusion Maps in the context of manifold learning and dimensionality reduction. Standard non-linear dimensionality reduction methods (e.g., LLE,…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
Propagation of monochromatic elastic waves across cracks is investigated in 1D, both theoretically and numerically. Cracks are modeled by nonlinear jump conditions. The mean dilatation of a single crack and the generation of harmonics are…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based…