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In the past decades, great progress has been made in the field of optical and particle-based measurement techniques for experimental analysis of fluid flows. Particle Image Velocimetry (PIV) technique is widely used to identify flow…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…
We develop a framework for efficient streaming reconstructions of turbulent velocity fluctuations from limited sensor measurements with the goal of enabling real-time applications. The reconstruction process is simplified by computing…
We develop the pruned continuous Haar transform and the fast continuous Fourier series, two fast and efficient algorithms for rectilinear polygons. Rectilinear polygons are used in VLSI processes to describe design and mask layouts of…
In the analysis of High-Energy Physics data, it is frequently desired to separate resonant signals from a smooth, non-resonant background. This paper introduces a new technique - functional decomposition (FD) - to accomplish this task. It…
Spatio-temporal forecasting is fundamental to intelligent systems in transportation, climate science, and urban planning. However, training deep learning models on the massive, often redundant, datasets from these domains presents a…
Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous…
Particle tracking velocimetry in 3D is becoming an increasingly important imaging tool in the study of fluid dynamics, combustion as well as plasmas. We introduce a dynamic discrete tomography algorithm for reconstructing particle…
The traditional theoretical statistics course which develops the theoretical underpinnings of the discipline (usually following a probability course) is undergoing near-continuous revision in the statistics community. In particular, recent…
Dynamic Mode Decomposition (DMD) is a data-driven decomposition technique extracting spatio-temporal patterns of time-dependent phenomena. In this paper, we perform a comprehensive theoretical analysis of various variants of DMD. We provide…
This article provides a brief overview of statistical network analysis, a rapidly evolving field of statistics, which encompasses statistical models, algorithms, and inferential methods for analyzing data in the form of networks. Particular…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
This document was prepared as part of the MT-LAB research centre. The research centre studies the Modelling of Information Technology and is a VKR Centre of Excellence funded for five years by the VILLUM Foundation. You can read more about…
Particle flows of high particle concentration are important in many fields, including chemical processing, pharmaceutical processing, energy conversion and powder transport. However, despite decades of research and industrial application,…
Near-term prediction of the structured spatio-temporal processes driving our climate is of profound importance to the safety and well-being of millions, but the prounced nonlinear convection of these processes make a complete mechanistic…
Purpose: To develop a data-efficient strategy for accelerated MRI reconstruction with Diffusion Probabilistic Generative Models (DPMs) that enables faster scan times in clinical stroke MRI when only limited fully-sampled data samples are…
We report the complete statistical treatment of a system of particles interacting via Newtonian forces in continuous boundary-driven flow, far from equilibrium. By numerically time-stepping the force-balance equations of a model fluid we…
Koopman spectral analysis has attracted attention for understanding nonlinear dynamical systems by which we can analyze nonlinear dynamics with a linear regime by lifting observations using a nonlinear function. For analysis, we need to…
Imaging sites around the world generate growing amounts of medical scan data with ever more versatile and affordable technology. Large-scale studies acquire MRI for tens of thousands of participants, together with metadata ranging from…
These are the lecture notes for quantum and statistical mechanics courses that are given by DC at Ben-Gurion University. They are complementary to "Lecture Notes in Quantum Mechanics" [arXiv: quant-ph/0605180]. Some additional topics are…