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Particle velocimetry is essential in solid fuel combustion studies, however, the accurate detection and tracking of particles in high Particle Number Density (PND) combustion scenario remain challenging. The current study advances the…
The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly non-trivial statistical behavior, motivating the development of surrogate models…
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…
Statistic modeling and data-driven learning are the two vital fields that attract many attentions. Statistic models intend to capture and interpret the relationships among variables, while data-based learning attempt to extract information…
This paper contains a transcript of my presentation at the Wyant Tribute Symposium on August 2, 2021 at SPIE's Optics & Photonics conference in San Diego, California. The technical part of the paper has no overlap with a previous article of…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…
The presentations, discussions and findings from the inaugural `PhyStat-$\nu$' workshop held at the Kavli Institute for the Physics and Mathematics of the Universe (IPMU) near Tokyo in 2016 are described. PhyStat-$\nu$ was the first…
This text describes a method to simultaneously reconstruct flow states and determine particle properties from Lagrangian particle tracking (LPT) data. LPT is a popular measurement strategy for fluids in which particles in a flow are…
This is a writeup of lectures on "statistics" that have evolved from the initial version for the 2009 Hadron Collider Physics Summer School at CERN to versions for other venues and, most recently, for the African School of Fundamental…
The automatic summarization of surgical videos is essential for enhancing procedural documentation, supporting surgical training, and facilitating post-operative analysis. This paper presents a novel method at the intersection of artificial…
A patient undergoes multiple examinations in each hospital stay, where each provides different facets of the health status. These assessments include temporal data with varying sampling rates, discrete single-point measurements, therapeutic…
This paper reports the activities and outcomes in the Workshop on Grasping and Manipulation Datasets that was organized under the International Conference on Robotics and Automation (ICRA) 2016. The half day workshop was packed with nine…
The new method of multivariate data analysis based on the complements of classical probability distribution to quantum state and Schmidt decomposition is presented. We considered Schmidt formalism application to problems of statistical…
We develop a method that relates the truncated cumulant-function of the fourth order with the L\'evian cumulant-function. This gives us explicit formulas for the L\'evy-parameters, which allow a real-time analysis of the state of a…
This text is the support for the course of Modeling of Solids, of the Master of Mechanics of the University Paris-Saclay - Curriculum MMM: Mathematical Methods for Mechanics, held at Versailles. The course is the continuation of the course…
This is a survey on the subject of the title corresponding to three lectures I gave in June 2001 at the Workshop on Fourier Analysis and Convexity, at the Universita di Milano-Biccoca.
These are lecture notes for lectures at the Park City Math Institute, summer 2007. We cover aspects of the dimer model on planar, periodic bipartite graphs, including local statistics, limit shapes and fluctuations.
MRI is an indispensable clinical tool, offering a rich variety of tissue contrasts to support broad diagnostic and research applications. Clinical exams routinely acquire multiple structural sequences that provide complementary information…
This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…
Dynamic Mode Decomposition (DMD) is a technique to approximate generally non-linear dynamical systems using linear techniques, which are better understood and easier to analyze. Koopman theory extends DMD by transforming the original system…