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Extraordinary dimension of maps  [PDF]
A. Chigogidze,V. Valov
Mathematics , 2003,
Abstract: We establish a characterization of the extraordinary dimension of perfect maps between metrizable spaces.
On GROUSE and Incremental SVD  [PDF]
Laura Balzano,Stephen J. Wright
Computer Science , 2013,
Abstract: GROUSE (Grassmannian Rank-One Update Subspace Estimation) is an incremental algorithm for identifying a subspace of Rn from a sequence of vectors in this subspace, where only a subset of components of each vector is revealed at each iteration. Recent analysis has shown that GROUSE converges locally at an expected linear rate, under certain assumptions. GROUSE has a similar flavor to the incremental singular value decomposition algorithm, which updates the SVD of a matrix following addition of a single column. In this paper, we modify the incremental SVD approach to handle missing data, and demonstrate that this modified approach is equivalent to GROUSE, for a certain choice of an algorithmic parameter.
Ordinary and Extraordinary Hadrons
Jaffe, R. L.
High Energy Physics - Phenomenology , 2007, DOI: 10.1063/1.2823850
Abstract: Resonances and enhancements in meson-meson scattering can be divided into two classes distinguished by their behavior as the number of colors N_c in QCD becomes large: The first are ordinary mesons that become stable as N_c goes to infinity. This class includes textbook q-bar q mesons as well as glueballs and hybrids. The second class, extraordinary mesons, are enhancements that disappear as N_c goes to infinity; they subside into the hadronic continuum. This class includes indistinct and controversial objects that have been classified as q-bar q-bar q q mesons or meson-meson molecules. Pelaez's study of the N_c dependence of unitarized chiral dynamics illustrates both classes: the p-wave pi-pi and K-pi resonances, the rho(770) and K*(892), behave as ordinary mesons; the s-wave pi-pi and K-pi enhancements, the sigma(600) and kappa(800), behave like extraordinary mesons. Ordinary mesons resemble Feshbach resonances while extraordinary mesons look more like effects due to potentials in meson-meson scattering channels. I build and explore toy models along these lines. Finally I discuss some related dynamical issues affecting the interpretation of extraordinary mesons.
Superconducting plasmonics and extraordinary transmission  [PDF]
A. Tsiatmas,R. Buckingham,V. A. Fedotov,S. Wang,Y. Chen,P. de Groot,N. I. Zheludev
Physics , 2010, DOI: 10.1063/1.3489091
Abstract: Negative dielectric constant and dominant kinetic resistance make superconductors an intriguing plasmonic media. Here we report on the first study of one of the most important and disputed manifestations of plasmonics, the effect of extraordinary transmission through an array of sub-wavelength holes, using a perforated film of high-temperature superconductor.
SVD Approach to Data Unfolding  [PDF]
Andreas Hoecker,Vakhtang Kartvelishvili
Physics , 1995, DOI: 10.1016/0168-9002(95)01478-0
Abstract: Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the Singular Value Decomposition (SVD) of the response matrix. A relatively simple, yet quite efficient unfolding procedure is explained in detail. The concise linear algorithm results in a straightforward implementation with full error propagation, including the complete covariance matrix and its inverse. Several improvements upon widely used procedures are proposed, and recommendations are given how to simplify the task by the proper choice of the matrix. Ways of determining the optimal value of the regularization parameter are suggested and discussed, and several examples illustrating the use of the method are presented.
New Ideas: Ordinary is Extraordinary
Michael Dodson, Melinda Fernyhough, Jose Antonio, Luke Bucci
Journal of the International Society of Sports Nutrition , 2004, DOI: 10.1186/1550-2783-1-1-67
Abstract: After reading the first issue of Sports Nutrition Review Journal we immediately thought that one area was missing from the introductory articles. The formation of a team approach to nutritional/performance problem solving is needed, with at least one member of the supporting team being extraordinary. What we propose by this is that at least one member of the sports nutrition "team" needs to be capable of thinking in an almost eccentric manner....with extraordinary ideas being an ordinary occurrence. By having one member performing in this capacity, progress will be made (we believe) at an amazing rate. For this idea, we offer one example: Many of us have been taught that muscles grow in specific ways, with little capacity for postnatal hyperplasia and only minute ability to fully regenerate itself when damaged. Furthermore, we have commonly been told that only a small number of factors (ex. growth hormone, steroids) may directly regulate muscle fiber hypertrophy. Additionally, it has been "beat into us" that as we age, muscle mass will automatically decrease (a process commonly called sarcopenia) – and that little can be done for senile muscular atrophy, except exercise.With the huge number of research papers appearing each day in the scientific literature, there seems to be mounting evidence that some of these "ordinary" and commonly accepted ideas may not be as true as once thought. What if postnatal skeletal muscle could increase numbers of cells (through some as yet undetermined mechanism)? What if nutrients (themselves) could regulate muscle growth dynamics – with the correct exercise regimen? What if we could actually retain our muscle mass as we get older?Who will discover these types of potentially important physiological mechanisms unless someone thinks in an extraordinary manner? Further, what will it take to form research, clinical, and performance "teams" unless someone can see through the present myths regarding muscle growth, nutritional dogma, and per
Enhanced SVD Based Face Recognition  [PDF]
Muhammad SHARIF,Saad ANIS,Mudassar RAZA,Sajjad MOHSIN
Journal of Applied Computer Science & Mathematics , 2012,
Abstract: One of the demanding tasks in face recognition is to handle illumination and expression variations. A lot of research is in progress to overcome such problems. This paper addresses the preprocessing method that is composed of grouping SVD perturbation and DWT. The proposed technique also performs well under one picture per person scenarios. The resulting image of this method is fed in to the simple SVD algorithm for face recognition. This paper performs its accuracy test on ORL, Yale, PIE and AR databases and focuses on the illumination problems
Extraordinary Magnetooptics in Plasmonic Crystals  [PDF]
V. I. Belotelov,I. A. Akimov,M. Poh,V. A. Kotov,S. Kasture,A. S. Vengurlekar,A. V. Gopal,D. Yakovlev,A. K. Zvezdin,M. Bayer
Physics , 2010,
Abstract: Plasmonics has been attracting considerable interest as it allows localization of light at nanoscale dimensions. A breakthrough in integrated nanophotonics can be obtained by fabricating plasmonic functional materials. Such systems may show a rich variety of novel phenomena and also have huge application potential. In particular magnetooptical materials are appealing as they may provide ultrafast control of laser light and surface plasmons via an external magnetic field. Here we demonstrate a new magnetooptical material: a one-dimensional plasmonic crystal formed by a periodically perforated noble metal film on top of a ferromagnetic dielectric film. It provides giant Faraday and Kerr effects as proved by the observation of enhancement of the transverse Kerr effect near Ebbesen's extraordinary transmission peaks by three orders of magnitude. Surface plasmon polaritons play a decisive role in this enhancement, as the Kerr effect depends sensitively on their properties. The plasmonic crystal can be operated in transmission, so that it may be implemented in devices for telecommunication, plasmonic circuitry, magnetic field sensing and all-optical magnetic data storage.
Direction dependency of extraordinary refraction index  [PDF]
Mojca Cepic
Physics , 2001,
Abstract: A simple experiment is presented that enables qualitative and quantitative measurement of the extraordinary refractive index direction dependency in an uniaxial nematic liquid crystal. Three liquid crystaline cells were designed in which elongated molecules of nematic liquid crystal align in directions which enable to observe the variation of extraordinary refractive index as a function of the direction of light.
Compressive spectral embedding: sidestepping the SVD  [PDF]
Dinesh Ramasamy,Upamanyu Madhow
Computer Science , 2015,
Abstract: Spectral embedding based on the Singular Value Decomposition (SVD) is a widely used "preprocessing" step in many learning tasks, typically leading to dimensionality reduction by projecting onto a number of dominant singular vectors and rescaling the coordinate axes (by a predefined function of the singular value). However, the number of such vectors required to capture problem structure grows with problem size, and even partial SVD computation becomes a bottleneck. In this paper, we propose a low-complexity it compressive spectral embedding algorithm, which employs random projections and finite order polynomial expansions to compute approximations to SVD-based embedding. For an m times n matrix with T non-zeros, its time complexity is O((T+m+n)log(m+n)), and the embedding dimension is O(log(m+n)), both of which are independent of the number of singular vectors whose effect we wish to capture. To the best of our knowledge, this is the first work to circumvent this dependence on the number of singular vectors for general SVD-based embeddings. The key to sidestepping the SVD is the observation that, for downstream inference tasks such as clustering and classification, we are only interested in using the resulting embedding to evaluate pairwise similarity metrics derived from the euclidean norm, rather than capturing the effect of the underlying matrix on arbitrary vectors as a partial SVD tries to do. Our numerical results on network datasets demonstrate the efficacy of the proposed method, and motivate further exploration of its application to large-scale inference tasks.
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