Time–frequency analysis | Wavelets | Signal processing
In applied mathematical analysis, shearlets are a multiscale framework which allows efficient encoding of anisotropic features in multivariate problem classes. Originally, shearlets were introduced in 2006 for the analysis and sparse approximation of functions . They are a natural extension of wavelets, to accommodate the fact that multivariate functions are typically governed by anisotropic features such as edges in images, since wavelets, as isotropic objects, are not capable of capturing such phenomena. Shearlets are constructed by parabolic scaling, shearing, and translation applied to a few generating functions. At fine scales, they are essentially supported within skinny and directional ridges following the parabolic scaling law, which reads length² ≈ width. Similar to wavelets, shearlets arise from the affine group and allow a unified treatment of the continuum and digital situation leading to faithful implementations. Although they do not constitute an orthonormal basis for , they still form a frame allowing stable expansions of arbitrary functions . One of the most important properties of shearlets is their ability to provide optimally sparse approximations (in the sense of optimality in ) for cartoon-like functions . In imaging sciences, cartoon-like functions serve as a model for anisotropic features and are compactly supported in while being apart from a closed piecewise singularity curve with bounded curvature. The decay rate of the -error of the -term shearlet approximation obtained by taking the largest coefficients from the shearlet expansion is in fact optimal up to a log-factor: where the constant depends only on the maximum curvature of the singularity curve and the maximum magnitudes of , and . This approximation rate significantly improves the best -term approximation rate of wavelets providing only for such class of functions. Shearlets are to date the only directional representation system that provides sparse approximation of anisotropic features while providing a unified treatment of the continuum and digital realm that allows faithful implementation. Extensions of shearlet systems to are also available. A comprehensive presentation of the theory and applications of shearlets can be found in. (Wikipedia).
Physics - Mechanics: Stress and Strain (9 of 16) Basics: Shear Modulus-S
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the basics of shear modulus.
From playlist PHYSICS 10.5 STRESS AND STRAIN
Shear Stress Example | Statics
https://goo.gl/o7Evid for more FREE video tutorials covering Engineering Mechanics (Statics & Dynamics) The objectives of this video are to discuss about shear stress & to work out on finding shear stress in a rivet joint. First of all, the video clears the concept of shear stresses which
From playlist SpoonFeedMe: Engineering Mechanics (Statics & Dynamics)
Shear Stress and Shear Strain | Mechanical Properties of Solids | Don't Memorise
"In the last video, we looked at one type of Stress & Strain called Normal Stress and Normal Strain. But there is another type of them - shear stress and shear strain In this video, we will learn: 0:00 Shear stress (example 1) 1:02 Difference between normal stress and shear stress 1:26
From playlist Physics
Beam Design Example: Shear Envelope (Part 3) | Reinforced Concrete Design
http://goo.gl/cDYRBl for more FREE video tutorials covering Concrete Structural Design This is the final video of developing a shear envelope where all the previously obtained values of shear forces are plotted all together. Very first, the video draws a horizontal line that represents th
From playlist SpoonFeedMe: Concrete Structures
Philipp Grohs: Wavelets, shearlets and geometric frames - Part 2
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Analysis and its Applications
Understanding Stresses in Beams
In this video we explore bending and shear stresses in beams. A bending moment is the resultant of bending stresses, which are normal stresses acting perpendicular to the beam cross-section. We can easily derive an equation for these bending stresses by observing how a beam deforms for a c
From playlist Mechanics of Materials / Strength of Materials
Physics - Mechanics: Stress and Strain (11 of 16) Ex. 2: Cutting Steel Sheet
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the force needed to cut through a steel sheet.
From playlist PHYSICS 10.5 STRESS AND STRAIN
Deep Learning meets Shearlets: Gitta Kutyniok
Machine Learning for the Working Mathematician: Week Twelve 19 May 2022 Gitta Kutyniok, Deep Learning meets Shearlets: Explainable Hybrid Solvers for Inverse Problems in Imaging Science Abstract: Pure model-based approaches are today often insufficient for solving complex inverse problem
From playlist Machine Learning for the Working Mathematician
An Introduction to Stress and Strain
This video is an introduction to stress and strain, which are fundamental concepts that are used to describe how an object responds to externally applied loads. Stress is a measure of the distribution of internal forces that develop within a body to resist these applied loads. There are
From playlist Mechanics of Materials / Strength of Materials
Philipp Grohs: Somes perspectives of computational harmonic analysis in numerics
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist 30 years of wavelets
Hans Feichtinger: Wavelet theory, coorbit spaces and ramifications
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist 30 years of wavelets
Beam Design Example: Shear Envelope (Part 1) | Reinforced Concrete Design
http://goo.gl/ZBnKMi for more FREE video tutorials covering Concrete Structural Design Everything demonstrated so far in this video series basically works out on design bending moment and reinforcing requirements; now from this video onward it is going to look at the design of shear force
From playlist SpoonFeedMe: Concrete Structures
Mechanical Engineering: Internal Forces on Beams (6 of 27) Shears & Moments Along the Beam
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the shears (V=?) and the moments (M=?) of the 5 different sections of a load on a beam. Next video in this series can be seen at: https://youtu.be/Xj8aZFidm9U
From playlist MECHANICAL ENGINEERING 9 INTERNAL FORCES ON BEAMS
Emily King - PCA is not dead: Vectorized persistent homology and flag medians - IPAM at UCLA
Recorded 26 October 2022. Emily King of Colorado State University presents "PCA is not dead: Vectorized persistent homology and flag medians" at IPAM's Mathematical Advances for Multi-Dimensional Microscopy Workshop. Abstract: In this talk two methods will be presented which both make use
From playlist 2022 Mathematical Advances for Multi-Dimensional Microscopy
Gitta Kutyniok: "Deep Learning and Modeling: Taking the Best out of Both Worlds"
Deep Learning and Medical Applications 2020 "Deep Learning and Modeling: Taking the Best out of Both Worlds" Gitta Kutyniok - Technische Universität Berlin, Program in Applied and Computational Mathematics Abstract: Pure model-based approaches are today often insufficient for solving com
From playlist Deep Learning and Medical Applications 2020
Axial, Shear and Bending Diagrams | Statics
https://goo.gl/a4d0ct for more FREE video tutorials covering Engineering Mechanics (Statics & Dynamics) The objectives of this video are to clear the concept on axial, shear and bending moments followed by a brief introduction to axial, shear and bending diagram. The video starts up by qu
From playlist SpoonFeedMe: Engineering Mechanics (Statics & Dynamics)