Results 21 to 30 of about 3,040,184 (131)
Local Marchenko-Pastur law at the hard edge of sample covariance matrices [PDF]
, 2012 Let XN be a N × N matrix whose entries are independent identically distributed complex random variables with mean zero and variance 1N. We study the asymptotic spectral distribution of the eigenvalues of the covariance matrix XN*XN for N → ∞.
C. Cacciapuoti, A. Maltsev, B. Schlein
semanticscholar +1 more source
Using Marchenko–Pastur SVD and Linear MMSE Estimation for Reducing Image Noise
International Journal of Next-Generation Computing, 2022 The degradation in visual quality of images is often seen due to a variety of noise added inevitably at the time of image acquisition. Its restoration has thus become a fundamental and significant problem in image processing.
Swati Rane +3 more
semanticscholar +1 more source
Freezing limits for Calogero–Moser–Sutherland particle models
Studies in Applied Mathematics, Volume 151, Issue 4, Page 1230-1281, November 2023., 2023 Abstract One‐dimensional interacting particle models of Calogero–Moser–Sutherland type with N particles can be regarded as diffusion processes on suitable subsets of RN$\mathbb {R}^N$ like Weyl chambers and alcoves with second‐order differential operators as generators of the transition semigroups, where these operators are singular on the boundaries ...
Michael Voit
wiley +1 more source
Pore size estimation in axon-mimicking microfibers with diffusion-relaxation MRI. [PDF]
Magn Reson MedAbstract Purpose This study aims to evaluate two distinct approaches for fiber radius estimation using diffusion‐relaxation MRI data acquired in biomimetic microfiber phantoms that mimic hollow axons. The methods considered are the spherical mean power‐law approach and a T2‐based pore size estimation technique.
Canales-Rodríguez EJ +7 more
europepmc +2 more sources
A note on the Marchenko-Pastur law for a class of random matrices with dependent entries [PDF]
, 2012 We consider a class of real random matrices with dependent entries and show that the limiting empirical spectral distribution is given by the Marchenko-Pastur law.
Sean O’Rourke
semanticscholar +1 more source
On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions [PDF]
, 2008 n this paper, we prove a result linking the square and the rectangular R-transforms, the consequence of which is a surprising relation between the square and rectangular versions the free additive convolutions, involving the Marchenko-Pastur law ...
Florent Benaych-Georges
semanticscholar +1 more source
Magnetic Resonance in Medicine, Volume 88, Issue 1, Page 365-379, July 2022., 2022 Purpose Relationships between diffusion‐weighted MRI signals and hepatocyte microstructure were investigated to inform liver diffusion MRI modeling, focusing on the following question: Can cell size and diffusivity be estimated at fixed diffusion time, realistic SNR, and negligible contribution from extracellular/extravascular water and exchange ...
Francesco Grussu +7 more
wiley +1 more source
Development Model of College English Education Service Talents Based on Nonlinear Random Matrix
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 The development of artificial intelligence makes people’s life and work easier and more effective, and computer‐based online exams and marking not only improve students’ learning efficiency but also reduce the pressure of teachers’ marking work. For objective questions, marking has gone from manual marking to cursor reader marking to computerized ...
Xiaoyan Gao, Ning Cao
wiley +1 more source
In Vivo Characterization of Magnetic Inclusions in the Subcortex From Nonexponential Transverse Relaxation Decay. [PDF]
NMR BiomedNonexponential transverse relaxation decay allows to characterize the spatial distribution of magnetic material within subcortical grey matter tissue. ABSTRACT According to theoretical studies, MRI signal decay due to transverse relaxation in brain tissue with magnetic inclusions (e.g., blood vessels and iron‐rich cells) is expected to follow a ...
Oliveira R +5 more
europepmc +2 more sources
On the Marchenko–Pastur law in analog bipartite spin-glasses
Journal of Physics A: Mathematical and Theoretical, 2019 In recent decades, statistical mechanics of disordered systems (mainly spin-glasses) has become one of the main tools to investigate complex systems, probably due to the celebrated Replica Symmetry Breaking scheme of Parisi Theory and its deep ...
E. Agliari +3 more
semanticscholar +1 more source