The role of the rigged Hilbert space in quantum mechanics

International Nuclear Information System (INIS)

Madrid, Rafael de la

2005-01-01

There is compelling evidence that, when a continuous spectrum is present, the natural mathematical setting for quantum mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's braket formalism is fully implemented by the rigged Hilbert space rather than just by the Hilbert space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert space plays in quantum mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert space

A constructive presentation of rigged Hilbert spaces

International Nuclear Information System (INIS)

Celeghini, Enrico

2015-01-01

We construct a rigged Hilbert space for the square integrable functions on the line L2(R) adding to the generators of the Weyl-Heisenberg algebra a new discrete operator, related to the degree of the Hermite polynomials. All together, continuous and discrete operators, constitute the generators of the projective algebra io(2). L 2 (R) and the vector space of the line R are shown to be isomorphic representations of such an algebra and, as both these representations are irreducible, all operators defined on the rigged Hilbert spaces L 2 (R) or R are shown to belong to the universal enveloping algebra of io(2). The procedure can be extended to orthogonal and pseudo-orthogonal spaces of arbitrary dimension by tensorialization.Circumventing all formal problems the paper proposes a kind of toy model, well defined from a mathematical point of view, of rigged Hilbert spaces where, in contrast with the Hilbert spaces, operators with different cardinality are allowed. (paper)

On a Hilbert-Type Operator with a Symmetric Homogeneous Kernel of −1-Order and Applications

Directory of Open Access Journals (Sweden)

Bicheng Yang

2007-10-01

Full Text Available Some character of the symmetric homogenous kernel of −1-order in Hilbert-type operator T:lr→lr (r>1 is obtained. Two equivalent inequalities with the symmetric homogenous kernel of −λ-order are given. As applications, some new Hilbert-type inequalities with the best constant factors and the equivalent forms as the particular cases are established.

Transverse entanglement migration in Hilbert space

International Nuclear Information System (INIS)

Chan, K. W.; Torres, J. P.; Eberly, J. H.

2007-01-01

We show that, although the amount of mutual entanglement of photons propagating in free space is fixed, the type of correlations between the photons that determine the entanglement can dramatically change during propagation. We show that this amounts to a migration of entanglement in Hilbert space, rather than real space. For the case of spontaneous parametric down-conversion, the migration of entanglement in transverse coordinates takes place from modulus to phase of the biphoton state and back again. We propose an experiment to observe this migration in Hilbert space and to determine the full entanglement

Efficient Online Subspace Learning With an Indefinite Kernel for Visual Tracking and Recognition

NARCIS (Netherlands)

Liwicki, Stephan; Zafeiriou, Stefanos; Tzimiropoulos, Georgios; Pantic, Maja

2012-01-01

We propose an exact framework for online learning with a family of indefinite (not positive) kernels. As we study the case of nonpositive kernels, we first show how to extend kernel principal component analysis (KPCA) from a reproducing kernel Hilbert space to Krein space. We then formulate an

Rigged Hilbert spaces for chaotic dynamical systems

International Nuclear Information System (INIS)

Suchanecki, Z.; Antoniou, I.; Bandtlow, O.F.

1996-01-01

We consider the problem of rigging for the Koopman operators of the Renyi and the baker maps. We show that the rigged Hilbert space for the Renyi maps has some of the properties of a strict inductive limit and give a detailed description of the rigged Hilbert space for the baker maps. copyright 1996 American Institute of Physics

Open superstring field theory on the restricted Hilbert space

International Nuclear Information System (INIS)

Konopka, Sebastian; Sachs, Ivo

2016-01-01

It appears that the formulation of an action for the Ramond sector of open superstring field theory requires to either restrict the Hilbert space for the Ramond sector or to introduce auxiliary fields with picture −3/2. The purpose of this note is to clarify the relation of the restricted Hilbert space with other approaches and to formulate open superstring field theory entirely in the small Hilbert space.

On Hilbert space of paths

International Nuclear Information System (INIS)

Exner, P.; Kolerov, G.I.

1980-01-01

A Hilbert space of paths, the elements of which are determined by trigonometric series, was proposed and used recently by Truman. This space is shown to consist precisely of all absolutely continuous paths ending in the origin with square-integrable derivatives

The method of moments and nested Hilbert spaces in quantum mechanics

International Nuclear Information System (INIS)

Adeniyi Bangudu, E.

1980-08-01

It is shown how the structures of a nested Hilbert space Hsub(I), associated with a given Hilbert space Hsub(O), may be used to simplify our understanding of the effects of parameters, whose values have to be chosen rather than determined variationally, in the method of moments. The result, as applied to non-relativistic quartic oscillator and helium atom, is to associate the parameters with sequences of Hilbert spaces, while the error of the method of moments relative to the variational method corresponds to a nesting operator of the nested Hilbert space. Difficulties hindering similar interpretations in terms of rigged Hilbert space structures are highlighted. (author)

Frames and bases in tensor products of Hilbert spaces and Hilbert C ...

Indian Academy of Sciences (India)

[14] Heil C E and Walnut D F, Continuous and discrete wavelet transforms, SIAM Review 31. (1989) 628–666. [15] Khosravi A and Asgari M S, Frames and bases in tensor product of Hilbert spaces, Int. J. Math. 4(6) (2003) 527–538. [16] Lance E C, Hilbert C. ∗. -modules – a toolkit for operator algebraists, London Math. Soc.

Convexity Of Inversion For Positive Operators On A Hilbert Space

International Nuclear Information System (INIS)

Sangadji

2001-01-01

This paper discusses and proves three theorems for positive invertible operators on a Hilbert space. The first theorem gives a comparison of the generalized arithmetic mean, generalized geometric mean, and generalized harmonic mean for positive invertible operators on a Hilbert space. For the second and third theorems each gives three inequalities for positive invertible operators on a Hilbert space that are mutually equivalent

A note on tensor fields in Hilbert spaces

Directory of Open Access Journals (Sweden)

LEONARDO BILIOTTI

2002-06-01

Full Text Available We discuss and extend to infinite dimensional Hilbert spaces a well-known tensoriality criterion for linear endomorphisms of the space of smooth vector fields in n.Discutimos e estendemos para espaços de Hilbert um critério de tensorialidade para endomorfismos do espaço dos campos vetoriais em Rpot(n.

Theory of linear operators in Hilbert space

CERN Document Server

Akhiezer, N I

1993-01-01

This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.

Isometric Reflection Vectors and Characterizations of Hilbert Spaces

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Donghai Ji

2014-01-01

Full Text Available A known characterization of Hilbert spaces via isometric reflection vectors is based on the following implication: if the set of isometric reflection vectors in the unit sphere SX of a Banach space X has nonempty interior in SX, then X is a Hilbert space. Applying a recent result based on well-known theorem of Kronecker from number theory, we improve this by substantial reduction of the set of isometric reflection vectors needed in the hypothesis.

ON STRONG AND WEAK CONVERGENCE IN n-HILBERT SPACES

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Agus L. Soenjaya

2014-03-01

Full Text Available We discuss the concepts of strong and weak convergence in n-Hilbert spaces and study their properties. Some examples are given to illustrate the concepts. In particular, we prove an analogue of Banach-Saks-Mazur theorem and Radon-Riesz property in the case of n-Hilbert space.

κ-Minkowski representations on Hilbert spaces

International Nuclear Information System (INIS)

Agostini, Alessandra

2007-01-01

The algebra of functions on κ-Minkowski noncommutative space-time is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction of integration in κ-Minkowski space-time in terms of the usual trace of operators

Kernel-based tests for joint independence

DEFF Research Database (Denmark)

Pfister, Niklas; Bühlmann, Peter; Schölkopf, Bernhard

2018-01-01

if the $d$ variables are jointly independent, as long as the kernel is characteristic. Based on an empirical estimate of dHSIC, we define three different non-parametric hypothesis tests: a permutation test, a bootstrap test and a test based on a Gamma approximation. We prove that the permutation test......We investigate the problem of testing whether $d$ random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two variable Hilbert-Schmidt independence criterion (HSIC) but allows for an arbitrary number of variables. We embed...... the $d$-dimensional joint distribution and the product of the marginals into a reproducing kernel Hilbert space and define the $d$-variable Hilbert-Schmidt independence criterion (dHSIC) as the squared distance between the embeddings. In the population case, the value of dHSIC is zero if and only...

Spectral Theory of Operators on Hilbert Spaces

CERN Document Server

Kubrusly, Carlos S

2012-01-01

This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated. Spectral Theory of Operators on Hilbert Space is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will also be useful to working mathemat

Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods

DEFF Research Database (Denmark)

Arenas-Garcia, J.; Petersen, K.; Camps-Valls, G.

2013-01-01

correlation analysis (CCA), and orthonormalized PLS (OPLS), as well as their nonlinear extensions derived by means of the theory of reproducing kernel Hilbert spaces (RKHSs). We also review their connections to other methods for classification and statistical dependence estimation and introduce some recent...

Generalization Performance of Regularized Ranking With Multiscale Kernels.

Science.gov (United States)

Zhou, Yicong; Chen, Hong; Lan, Rushi; Pan, Zhibin

2016-05-01

The regularized kernel method for the ranking problem has attracted increasing attentions in machine learning. The previous regularized ranking algorithms are usually based on reproducing kernel Hilbert spaces with a single kernel. In this paper, we go beyond this framework by investigating the generalization performance of the regularized ranking with multiscale kernels. A novel ranking algorithm with multiscale kernels is proposed and its representer theorem is proved. We establish the upper bound of the generalization error in terms of the complexity of hypothesis spaces. It shows that the multiscale ranking algorithm can achieve satisfactory learning rates under mild conditions. Experiments demonstrate the effectiveness of the proposed method for drug discovery and recommendation tasks.

Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincaré symmetry

Science.gov (United States)

Moretti, Valter; Oppio, Marco

As earlier conjectured by several authors and much later established by Solèr (relying on partial results by Piron, Maeda-Maeda and other authors), from the lattice theory point of view, Quantum Mechanics may be formulated in real, complex or quaternionic Hilbert spaces only. Stückelberg provided some physical, but not mathematically rigorous, reasons for ruling out the real Hilbert space formulation, assuming that any formulation should encompass a statement of Heisenberg principle. Focusing on this issue from another — in our opinion, deeper — viewpoint, we argue that there is a general fundamental reason why elementary quantum systems are not described in real Hilbert spaces. It is their basic symmetry group. In the first part of the paper, we consider an elementary relativistic system within Wigner’s approach defined as a locally-faithful irreducible strongly-continuous unitary representation of the Poincaré group in a real Hilbert space. We prove that, if the squared-mass operator is non-negative, the system admits a natural, Poincaré invariant and unique up to sign, complex structure which commutes with the whole algebra of observables generated by the representation itself. This complex structure leads to a physically equivalent reformulation of the theory in a complex Hilbert space. Within this complex formulation, differently from what happens in the real one, all selfadjoint operators represent observables in accordance with Solèr’s thesis, and the standard quantum version of Noether theorem may be formulated. In the second part of this work, we focus on the physical hypotheses adopted to define a quantum elementary relativistic system relaxing them on the one hand, and making our model physically more general on the other hand. We use a physically more accurate notion of irreducibility regarding the algebra of observables only, we describe the symmetries in terms of automorphisms of the restricted lattice of elementary propositions of the

On convergence of kernel learning estimators

NARCIS (Netherlands)

Norkin, V.I.; Keyzer, M.A.

2009-01-01

The paper studies convex stochastic optimization problems in a reproducing kernel Hilbert space (RKHS). The objective (risk) functional depends on functions from this RKHS and takes the form of a mathematical expectation (integral) of a nonnegative integrand (loss function) over a probability

Reproducing Kernels and Coherent States on Julia Sets

Energy Technology Data Exchange (ETDEWEB)

Thirulogasanthar, K., E-mail: santhar@cs.concordia.ca; Krzyzak, A. [Concordia University, Department of Computer Science and Software Engineering (Canada)], E-mail: krzyzak@cs.concordia.ca; Honnouvo, G. [Concordia University, Department of Mathematics and Statistics (Canada)], E-mail: g_honnouvo@yahoo.fr

2007-11-15

We construct classes of coherent states on domains arising from dynamical systems. An orthonormal family of vectors associated to the generating transformation of a Julia set is found as a family of square integrable vectors, and, thereby, reproducing kernels and reproducing kernel Hilbert spaces are associated to Julia sets. We also present analogous results on domains arising from iterated function systems.

Reproducing Kernels and Coherent States on Julia Sets

International Nuclear Information System (INIS)

Thirulogasanthar, K.; Krzyzak, A.; Honnouvo, G.

2007-01-01

We construct classes of coherent states on domains arising from dynamical systems. An orthonormal family of vectors associated to the generating transformation of a Julia set is found as a family of square integrable vectors, and, thereby, reproducing kernels and reproducing kernel Hilbert spaces are associated to Julia sets. We also present analogous results on domains arising from iterated function systems

Resonances, scattering theory and rigged Hilbert spaces

International Nuclear Information System (INIS)

Parravicini, G.; Gorini, V.; Sudarshan, E.C.G.

1979-01-01

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free, in, and out eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian; the singularities of the out eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of complete sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the out eigenvectors. The free, in and out eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee-Friedrichs model. 48 references

Elements of Hilbert spaces and operator theory

CERN Document Server

Vasudeva, Harkrishan Lal

2017-01-01

The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compressio...

An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

Science.gov (United States)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

Hilbert space, Poincare dodecahedron and golden mean transfiniteness

International Nuclear Information System (INIS)

El Naschie, M.S.

2007-01-01

A rather direct connection between Hilbert space and E-infinity theory is established via an irrational-transfinite golden mean topological probability. Subsequently the ramifications for Kleinian modular spaces and the cosmological Poincare Dodecahedron proposals are considered

Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations

Directory of Open Access Journals (Sweden)

Reza Mokhtari

2012-01-01

Full Text Available On the basis of reproducing kernel Hilbert spaces theory, an iterative algorithm for solving some nonlinear differential-difference equations (NDDEs is presented. The analytical solution is shown in a series form in a reproducing kernel space, and the approximate solution , is constructed by truncating the series to terms. The convergence of , to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such differential-difference problems.

Hilbert W*-modules and coherent states

International Nuclear Information System (INIS)

Bhattacharyya, T; Roy, S Shyam

2012-01-01

Hilbert C*-module valued coherent states was introduced earlier by Ali, Bhattacharyya and Shyam Roy. We consider the case when the underlying C*-algebra is a W*-algebra. The construction is similar with a substantial gain. The associated reproducing kernel is now algebra valued, rather than taking values in the space of bounded linear operators between two C*-algebras. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

Hilbert space methods in partial differential equations

CERN Document Server

Showalter, Ralph E

1994-01-01

This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.

Invariant Hilbert spaces of holomorphic functions

NARCIS (Netherlands)

Faraut, J; Thomas, EGF

1999-01-01

A Hilbert space of holomorphic functions on a complex manifold Z, which is invariant under a group G of holomorphic automorphisms of Z, can be decomposed into irreducible subspaces by using Choquet theory. We give a geometric condition on Z and G which implies that this decomposition is multiplicity

Hilbert space theory of classical electrodynamics

Indian Academy of Sciences (India)

Hilbert space; Koopman–von Neumann theory; classical electrodynamics. PACS No. 03.50. ... The paper is divided into four sections. Section 2 .... construction of Sudarshan is to be contrasted with that of Koopman and von Neumann. ..... ture from KvN and [16] in this formulation is to define new momentum and coordinate.

Semiclassical propagation: Hilbert space vs. Wigner representation

Science.gov (United States)

Gottwald, Fabian; Ivanov, Sergei D.

2018-03-01

A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert space and their recently developed counterparts in Wigner representation is presented. Based on this viewpoint, the Wigner Herman-Kluk propagator is conceptually the most general one. Nonetheless, the respective semiclassical expressions for expectation values in terms of the density matrix and the Wigner function are mathematically proven here to coincide. The only remaining difference is a mere technical flexibility of the Wigner version in choosing the Gaussians' width for the underlying coherent states beyond minimal uncertainty. This flexibility is investigated numerically on prototypical potentials and it turns out to provide neither qualitative nor quantitative improvements. Given the aforementioned generality, utilizing the Wigner representation for semiclassical propagation thus leads to the same performance as employing the respective most-developed (Hilbert-space) methods for the density matrix.

Theory of reproducing kernels and applications

CERN Document Server

Saitoh, Saburou

2016-01-01

This book provides a large extension of the general theory of reproducing kernels published by N. Aronszajn in 1950, with many concrete applications. In Chapter 1, many concrete reproducing kernels are first introduced with detailed information. Chapter 2 presents a general and global theory of reproducing kernels with basic applications in a self-contained way. Many fundamental operations among reproducing kernel Hilbert spaces are dealt with. Chapter 2 is the heart of this book. Chapter 3 is devoted to the Tikhonov regularization using the theory of reproducing kernels with applications to numerical and practical solutions of bounded linear operator equations. In Chapter 4, the numerical real inversion formulas of the Laplace transform are presented by applying the Tikhonov regularization, where the reproducing kernels play a key role in the results. Chapter 5 deals with ordinary differential equations; Chapter 6 includes many concrete results for various fundamental partial differential equations. In Chapt...

Vertical integration from the large Hilbert space

Science.gov (United States)

Erler, Theodore; Konopka, Sebastian

2017-12-01

We develop an alternative description of the procedure of vertical integration based on the observation that amplitudes can be written in BRST exact form in the large Hilbert space. We relate this approach to the description of vertical integration given by Sen and Witten.

Weaving Hilbert space fusion frames

OpenAIRE

Neyshaburi, Fahimeh Arabyani; Arefijamaal, Ali Akbar

2018-01-01

A new notion in frame theory, so called weaving frames has been recently introduced to deal with some problems in signal processing and wireless sensor networks. Also, fusion frames are an important extension of frames, used in many areas especially for wireless sensor networks. In this paper, we survey the notion of weaving Hilbert space fusion frames. This concept can be had potential applications in wireless sensor networks which require distributed processing using different fusion frames...

Frames in super Hilbert modules

Directory of Open Access Journals (Sweden)

Mehdi Rashidi-Kouchi

2018-01-01

Full Text Available In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are  generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.

Oscillatory integrals on Hilbert spaces and Schroedinger equation with magnetic fields

International Nuclear Information System (INIS)

Albeverio, S.; Brzezniak, Z.

1994-01-01

We extend the theory of oscillatory integrals on Hilbert spaces (the mathematical version of ''Feynman path integrals'') to cover more general integrable functions, preserving the property of the integrals to have converging finite dimensional approximations. We give an application to the representation of solutions of the time dependent Schroedinger equation with a scalar and a magnetic potential by oscillatory integrals on Hilbert spaces. A relation with Ramer's functional in the corresponding probabilistic setting is found. (orig.)

Eigenfunction expansions and scattering theory in rigged Hilbert spaces

Energy Technology Data Exchange (ETDEWEB)

Gomez-Cubillo, F [Dpt. de Analisis Matematico, Universidad de Valladolid. Facultad de Ciencias, 47011 Valladolid (Spain)], E-mail: fgcubill@am.uva.es

2008-08-15

The work reviews some mathematical aspects of spectral properties, eigenfunction expansions and scattering theory in rigged Hilbert spaces, laying emphasis on Lippmann-Schwinger equations and Schroedinger operators.

Spinors in Hilbert Space

Science.gov (United States)

Plymen, Roger; Robinson, Paul

1995-01-01

Infinite-dimensional Clifford algebras and their Fock representations originated in the quantum mechanical study of electrons. In this book, the authors give a definitive account of the various Clifford algebras over a real Hilbert space and of their Fock representations. A careful consideration of the latter's transformation properties under Bogoliubov automorphisms leads to the restricted orthogonal group. From there, a study of inner Bogoliubov automorphisms enables the authors to construct infinite-dimensional spin groups. Apart from assuming a basic background in functional analysis and operator algebras, the presentation is self-contained with complete proofs, many of which offer a fresh perspective on the subject.

Ad Hoc Physical Hilbert Spaces in Quantum Mechanics

Czech Academy of Sciences Publication Activity Database

Fernandez, F. M.; Garcia, J.; Semorádová, Iveta; Znojil, Miloslav

2015-01-01

Roč. 54, č. 12 (2015), s. 4187-4203 ISSN 0020-7748 Institutional support: RVO:61389005 Keywords : quantum mechanics * physical Hilbert spaces * ad hoc inner product * singular potentials regularized * low lying energies Subject RIV: BE - Theoretical Physics Impact factor: 1.041, year: 2015

Structure of Hilbert space operators

CERN Document Server

Jiang, Chunlan

2006-01-01

This book exposes the internal structure of non-self-adjoint operators acting on complex separable infinite dimensional Hilbert space, by analyzing and studying the commutant of operators. A unique presentation of the theorem of Cowen-Douglas operators is given. The authors take the strongly irreducible operator as a basic model, and find complete similarity invariants of Cowen-Douglas operators by using K -theory, complex geometry and operator algebra tools. Sample Chapter(s). Chapter 1: Background (153 KB). Contents: Jordan Standard Theorem and K 0 -Group; Approximate Jordan Theorem of Opera

Alternative structures and bi-Hamiltonian systems on a Hilbert space

International Nuclear Information System (INIS)

Marmo, G; Scolarici, G; Simoni, A; Ventriglia, F

2005-01-01

We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space. We introduce the notion of Hermitian structures in generic relative position. We provide a few necessary and sufficient conditions for two Hermitian structures to be in generic relative position to better illustrate the relevance of this notion. The group of bi-unitary transformations is considered in both the generic and the non-generic case. Finally, we generalize the analysis to real Hilbert spaces and extend to infinite dimensions results already available in the framework of finite-dimensional linear bi-Hamiltonian systems

States in the Hilbert space formulation and in the phase space formulation of quantum mechanics

International Nuclear Information System (INIS)

Tosiek, J.; Brzykcy, P.

2013-01-01

We consider the problem of testing whether a given matrix in the Hilbert space formulation of quantum mechanics or a function considered in the phase space formulation of quantum theory represents a quantum state. We propose several practical criteria for recognising states in these two versions of quantum physics. After minor modifications, they can be applied to check positivity of any operators acting in a Hilbert space or positivity of any functions from an algebra with a ∗-product of Weyl type. -- Highlights: ► Methods of testing whether a given matrix represents a quantum state. ► The Stratonovich–Weyl correspondence on an arbitrary symplectic manifold. ► Criteria for checking whether a function on a symplectic space is a Wigner function

Multi-view Multi-sparsity Kernel Reconstruction for Multi-class Image Classification

KAUST Repository

Zhu, Xiaofeng

2015-05-28

This paper addresses the problem of multi-class image classification by proposing a novel multi-view multi-sparsity kernel reconstruction (MMKR for short) model. Given images (including test images and training images) representing with multiple visual features, the MMKR first maps them into a high-dimensional space, e.g., a reproducing kernel Hilbert space (RKHS), where test images are then linearly reconstructed by some representative training images, rather than all of them. Furthermore a classification rule is proposed to classify test images. Experimental results on real datasets show the effectiveness of the proposed MMKR while comparing to state-of-the-art algorithms.

Quantum mechanics in an evolving Hilbert space

Science.gov (United States)

Artacho, Emilio; O'Regan, David D.

2017-03-01

Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalization, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fiber bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge implied by a smoothly varying basis set readily connects with Berry's formalism for geometric phases. Generalized expressions for the Berry connection and curvature are obtained for a parameter-dependent occupied Hilbert space spanned by nonorthogonal Wannier functions. The formalism is applicable to basis sets made of atomic-like orbitals and also more adaptative moving basis functions (such as in methods using Wannier functions as intermediate or support bases), but should also apply to other situations in which nonorthogonal functions or related projectors should arise. The formalism is applied to the time-dependent quantum evolution of electrons for moving atoms. The geometric insights provided here allow us to propose new finite-difference time integrators, and also better understand those already proposed.

Numerical method in reproducing kernel space for an inverse source problem for the fractional diffusion equation

International Nuclear Information System (INIS)

Wang, Wenyan; Han, Bo; Yamamoto, Masahiro

2013-01-01

We propose a new numerical method for reproducing kernel Hilbert space to solve an inverse source problem for a two-dimensional fractional diffusion equation, where we are required to determine an x-dependent function in a source term by data at the final time. The exact solution is represented in the form of a series and the approximation solution is obtained by truncating the series. Furthermore, a technique is proposed to improve some of the existing methods. We prove that the numerical method is convergent under an a priori assumption of the regularity of solutions. The method is simple to implement. Our numerical result shows that our method is effective and that it is robust against noise in L 2 -space in reconstructing a source function. (paper)

Means of Hilbert space operators

CERN Document Server

Hiai, Fumio

2003-01-01

The monograph is devoted to a systematic study of means of Hilbert space operators by a unified method based on the theory of double integral transformations and Peller's characterization of Schur multipliers. General properties on means of operators such as comparison results, norm estimates and convergence criteria are established. After some general theory, special investigations are focused on three one-parameter families of A-L-G (arithmetic-logarithmic-geometric) interpolation means, Heinz-type means and binomial means. In particular, norm continuity in the parameter is examined for such means. Some necessary technical results are collected as appendices.

Implementing Kernel Methods Incrementally by Incremental Nonlinear Projection Trick.

Science.gov (United States)

Kwak, Nojun

2016-05-20

Recently, the nonlinear projection trick (NPT) was introduced enabling direct computation of coordinates of samples in a reproducing kernel Hilbert space. With NPT, any machine learning algorithm can be extended to a kernel version without relying on the so called kernel trick. However, NPT is inherently difficult to be implemented incrementally because an ever increasing kernel matrix should be treated as additional training samples are introduced. In this paper, an incremental version of the NPT (INPT) is proposed based on the observation that the centerization step in NPT is unnecessary. Because the proposed INPT does not change the coordinates of the old data, the coordinates obtained by INPT can directly be used in any incremental methods to implement a kernel version of the incremental methods. The effectiveness of the INPT is shown by applying it to implement incremental versions of kernel methods such as, kernel singular value decomposition, kernel principal component analysis, and kernel discriminant analysis which are utilized for problems of kernel matrix reconstruction, letter classification, and face image retrieval, respectively.

Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment

International Nuclear Information System (INIS)

El Naschie, M.S.

2006-01-01

On the one hand, a rigorous mathematical formulation of quantum mechanics requires the introduction of a Hilbert space and as we move to the second quantization, a Fock space. On the other hand, the Cantorian E-infinity approach to quantum physics was developed largely without any direct reference to the afore mentioned mathematical spaces. In the present work we utilize some novel reinterpretations of basic E (∞) Cantorian spacetime relations in terms of the Hilbert space of quantum mechanics. Proceeding in this way, we gain a better understanding of the physico-mathematical structure of quantum spacetime which is at the heart of the paradoxical and non-intuitive outcome of the famous quantum two-slit gedanken experiment

Study of the convergence behavior of the complex kernel least mean square algorithm.

Science.gov (United States)

Paul, Thomas K; Ogunfunmi, Tokunbo

2013-09-01

The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.

An introduction of gauge field by the Lie-isotopic lifting of the Hilbert space

International Nuclear Information System (INIS)

Nishioka, M.

1984-01-01

It is introduced the gauge field by the Lie-isotopic lifting of the Hilbert space. Our method is different from other's in that the commutator between the isotropic element and the generators of the Lie algebra does not vanish in our case, but vanishes in other cases. Our method uses the Lie-isotopic lifting of the Hilbert space, but others do not use it

Introduction to Hilbert space and the theory of spectral multiplicity

CERN Document Server

Halmos, Paul R

2017-01-01

Concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. A background in measure theory is the sole prerequisite. 1957 edition.

Feature Selection and Kernel Learning for Local Learning-Based Clustering.

Science.gov (United States)

Zeng, Hong; Cheung, Yiu-ming

2011-08-01

The performance of the most clustering algorithms highly relies on the representation of data in the input space or the Hilbert space of kernel methods. This paper is to obtain an appropriate data representation through feature selection or kernel learning within the framework of the Local Learning-Based Clustering (LLC) (Wu and Schölkopf 2006) method, which can outperform the global learning-based ones when dealing with the high-dimensional data lying on manifold. Specifically, we associate a weight to each feature or kernel and incorporate it into the built-in regularization of the LLC algorithm to take into account the relevance of each feature or kernel for the clustering. Accordingly, the weights are estimated iteratively in the clustering process. We show that the resulting weighted regularization with an additional constraint on the weights is equivalent to a known sparse-promoting penalty. Hence, the weights of those irrelevant features or kernels can be shrunk toward zero. Extensive experiments show the efficacy of the proposed methods on the benchmark data sets.

Open Problem: Kernel methods on manifolds and metric spaces

DEFF Research Database (Denmark)

Feragen, Aasa; Hauberg, Søren

2016-01-01

Radial kernels are well-suited for machine learning over general geodesic metric spaces, where pairwise distances are often the only computable quantity available. We have recently shown that geodesic exponential kernels are only positive definite for all bandwidths when the input space has strong...... linear properties. This negative result hints that radial kernel are perhaps not suitable over geodesic metric spaces after all. Here, however, we present evidence that large intervals of bandwidths exist where geodesic exponential kernels have high probability of being positive definite over finite...... datasets, while still having significant predictive power. From this we formulate conjectures on the probability of a positive definite kernel matrix for a finite random sample, depending on the geometry of the data space and the spread of the sample....

On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space

Directory of Open Access Journals (Sweden)

Hamdy M. Ahmed

2009-01-01

Full Text Available We study a class of fractional stochastic integrodifferential equations considered in a real Hilbert space. The existence and uniqueness of the Mild solutions of the considered problem is also studied. We also give an application for stochastic integropartial differential equations of fractional order.

The Hilbert Series of the One Instanton Moduli Space

CERN Document Server

Benvenuti, Sergio; Mekareeya, Noppadol; 10.1007

2010-01-01

The moduli space of k G-instantons on R^4 for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1) dimensional gauge theories have N = 2 supersymmetry and can be represented by quiver diagrams. The F and D term equations coincide with the ADHM construction. The Hilbert series of the moduli spaces of one instanton for classical gauge groups is easy to compute and turns out to take a particularly simple form which is previously unknown. This allows for a G invariant character expansion and hence easily generalisable for exceptional gauge groups, where an ADHM construction is not known. The conjectures for exceptional groups are further checked using some new techniques like sewing relations in Hilbert Series. This is applied to Argyres-Seiberg dualities.

Quantum holonomy theory and Hilbert space representations

Energy Technology Data Exchange (ETDEWEB)

Aastrup, Johannes [Mathematisches Institut, Universitaet Hannover (Germany); Moeller Grimstrup, Jesper [QHT Gruppen, Copenhagen Area (Denmark)

2016-11-15

We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state that generates the representation exist is left for later publications. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Space Inside a Liquid Sphere Transforms into De Sitter Space by Hilbert Radius

Science.gov (United States)

Rabounski, Dmitri; Borissova, Larissa

2010-04-01

Consider space inside a sphere of incompressible liquid, and space surrounding a mass-point. Metrics of the spaces were deduced in 1916 by Karl Schwarzschild. 1) Our calculation shows that a liquid sphere can be in the state of gravitational collapse (g00 = 0) only if its mass and radius are close to those of the Universe (M = 8.7x10^55 g, a = 1.3x10^28 cm). However if the same mass is presented as a mass-point, the radius of collapse rg (Hilbert radius) is many orders lesser: g00 = 0 realizes in a mass-point's space by other conditions. 2) We considered a liquid sphere whose radius meets, formally, the Hilbert radius of a mass-point bearing the same mass: a = rg, however the liquid sphere is not a collapser (see above). We show that in this case the metric of the liquid sphere's internal space can be represented as de Sitter's space metric, wherein λ = 3/a^2 > 0: physical vacuum (due to the λ-term) is the same as the field of an ideal liquid where ρ0 0 (the mirror world liquid). The gravitational redshift inside the sphere is produced by the non-Newtonian force of repulsion (which is due to the λ-term, λ = 3/a^2 > 0); it is also calculated.

On the minimizers of calculus of variations problems in Hilbert spaces

KAUST Repository

Gomes, Diogo A.

2014-01-19

The objective of this paper is to discuss existence, uniqueness and regularity issues of minimizers of one dimensional calculus of variations problem in Hilbert spaces. © 2014 Springer-Verlag Berlin Heidelberg.

On the minimizers of calculus of variations problems in Hilbert spaces

KAUST Repository

Gomes, Diogo A.; Nurbekyan, Levon

2014-01-01

The objective of this paper is to discuss existence, uniqueness and regularity issues of minimizers of one dimensional calculus of variations problem in Hilbert spaces. © 2014 Springer-Verlag Berlin Heidelberg.

Coherent states in the fermionic Fock space

International Nuclear Information System (INIS)

Oeckl, Robert

2015-01-01

We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing kernel Hilbert space of continuous holomorphic functions. (paper)

Ordering of ''ladder'' operators, the Wigner function for number and phase, and the enlarged Hilbert space

International Nuclear Information System (INIS)

Luks, A.; Perinova, V.

1993-01-01

A suitable ordering of phase exponential operators has been compared with the antinormal ordering of the annihilation and creation operators of a single mode optical field. The extended Wigner function for number and phase in the enlarged Hilbert space has been used for the derivation of the Wigner function for number and phase in the original Hilbert space. (orig.)

Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations

Directory of Open Access Journals (Sweden)

Omar Abu Arqub

2012-01-01

Full Text Available This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution ( is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution ( is obtained and it is proved to converge to the exact solution (. Furthermore, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solution and its derivative will be applicable. Numerical examples are included to demonstrate the accuracy and applicability of the presented technique. The results reveal that the method is very effective and simple.

On the representation of contextual probabilistic dynamics in the complex Hilbert space: Linear and nonlinear evolutions, Schrodinger dynamics

International Nuclear Information System (INIS)

Khrennikov, A.

2005-01-01

We constructed the representation of contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function can be considered as Hilbert space projection of realistic dynamics in a pre space. The basic condition for representing the pre space-dynamics is the law of statistical conservation of energy-conservation of probabilities. The construction of the dynamical representation is an important step in the development of contextual statistical viewpoint of quantum processes. But the contextual statistical model is essentially more general than the quantum one. Therefore in general the Hilbert space projection of the pre space dynamics can be nonlinear and even irreversible (but it is always unitary). There were found conditions of linearity and reversibility of the Hilbert space dynamical projection. We also found conditions for the conventional Schrodinger dynamics (including time-dependent Hamiltonians). We remark that in general even the Schrodinger dynamics is based just on the statistical conservation of energy; for individual systems the law of conservation of energy can be violated (at least in our theoretical model)

Spaces of positive and negative frequency solutions of field equations in curved space--times. I. The Klein--Gordon equation in stationary space--times

International Nuclear Information System (INIS)

Moreno, C.

1977-01-01

In stationary space--times V/sub n/ x R with compact space-section manifold without boundary V/sub n/, the Klein--Gordon equation is solved by the one-parameter group of unitary operators generated by the energy operator i -1 T -1 in the Sobolev spaces H/sup l/(V/sub n/) x H/sup l/(V/sub n/). The canonical symplectic and complex structures of the associated dynamical system are calculated. The existence and the uniqueness of the Lichnerowicz kernel are established. The Hilbert spaces of positive and negative frequency-part solutions defined by means of this kernel are constructed

Epileptic Seizure Detection with Log-Euclidean Gaussian Kernel-Based Sparse Representation.

Science.gov (United States)

Yuan, Shasha; Zhou, Weidong; Wu, Qi; Zhang, Yanli

2016-05-01

Epileptic seizure detection plays an important role in the diagnosis of epilepsy and reducing the massive workload of reviewing electroencephalography (EEG) recordings. In this work, a novel algorithm is developed to detect seizures employing log-Euclidean Gaussian kernel-based sparse representation (SR) in long-term EEG recordings. Unlike the traditional SR for vector data in Euclidean space, the log-Euclidean Gaussian kernel-based SR framework is proposed for seizure detection in the space of the symmetric positive definite (SPD) matrices, which form a Riemannian manifold. Since the Riemannian manifold is nonlinear, the log-Euclidean Gaussian kernel function is applied to embed it into a reproducing kernel Hilbert space (RKHS) for performing SR. The EEG signals of all channels are divided into epochs and the SPD matrices representing EEG epochs are generated by covariance descriptors. Then, the testing samples are sparsely coded over the dictionary composed by training samples utilizing log-Euclidean Gaussian kernel-based SR. The classification of testing samples is achieved by computing the minimal reconstructed residuals. The proposed method is evaluated on the Freiburg EEG dataset of 21 patients and shows its notable performance on both epoch-based and event-based assessments. Moreover, this method handles multiple channels of EEG recordings synchronously which is more speedy and efficient than traditional seizure detection methods.

Quantum tomography, phase-space observables and generalized Markov kernels

International Nuclear Information System (INIS)

Pellonpaeae, Juha-Pekka

2009-01-01

We construct a generalized Markov kernel which transforms the observable associated with the homodyne tomography into a covariant phase-space observable with a regular kernel state. Illustrative examples are given in the cases of a 'Schroedinger cat' kernel state and the Cahill-Glauber s-parametrized distributions. Also we consider an example of a kernel state when the generalized Markov kernel cannot be constructed.

Multipliers for continuous frames in Hilbert spaces

International Nuclear Information System (INIS)

Balazs, P; Bayer, D; Rahimi, A

2012-01-01

In this paper, we examine the general theory of continuous frame multipliers in Hilbert space. These operators are a generalization of the widely used notion of (discrete) frame multipliers. Well-known examples include anti-Wick operators, STFT multipliers or Calderón–Toeplitz operators. Due to the possible peculiarities of the underlying measure spaces, continuous frames do not behave quite as their discrete counterparts. Nonetheless, many results similar to the discrete case are proven for continuous frame multipliers as well, for instance compactness and Schatten-class properties. Furthermore, the concepts of controlled and weighted frames are transferred to the continuous setting. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

Reproducing kernel method with Taylor expansion for linear Volterra integro-differential equations

Directory of Open Access Journals (Sweden)

Azizallah Alvandi

2017-06-01

Full Text Available This research aims of the present a new and single algorithm for linear integro-differential equations (LIDE. To apply the reproducing Hilbert kernel method, there is made an equivalent transformation by using Taylor series for solving LIDEs. Shown in series form is the analytical solution in the reproducing kernel space and the approximate solution $ u_{N} $ is constructed by truncating the series to $ N $ terms. It is easy to prove the convergence of $ u_{N} $ to the analytical solution. The numerical solutions from the proposed method indicate that this approach can be implemented easily which shows attractive features.

Hilbert space representation of the SOq(N)-covariant Heisenberg algebra

International Nuclear Information System (INIS)

Hebecker, A.; Weich, W.

1993-01-01

The differential calculus on SO q (N)-covariant quantum planes is rewritten in polar co-ordinates. Thus a Hilbert space formulation of q-deformed quantum mechanics can be developed particularly suitable for spherically symmetric potentials. The simplest case of a free particle is solved showing a discrete energy spectrum. (orig.)

Frame transforms, star products and quantum mechanics on phase space

International Nuclear Information System (INIS)

Aniello, P; Marmo, G; Man'ko, V I

2008-01-01

Using the notions of frame transform and of square integrable projective representation of a locally compact group G, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert space of the representation into the space of square integrable functions on the direct product group G x G. These transforms have remarkable properties. In particular, their ranges are reproducing kernel Hilbert spaces endowed with a suitable 'star product' which mimics, at the level of functions, the original product of operators. A 'phase space formulation' of quantum mechanics relying on the frame transforms introduced in the present paper, and the link of these maps with both the Wigner transform and the wavelet transform are discussed

Wiener-Hopf operators on spaces of functions on R+ with values in a Hilbert space

OpenAIRE

Petkova, Violeta

2006-01-01

A Wiener-Hopf operator on a Banach space of functions on R+ is a bounded operator T such that P^+S_{-a}TS_a=T, for every positive a, where S_a is the operator of translation by a. We obtain a representation theorem for the Wiener-Hopf operators on a large class of functions on R+ with values in a separable Hilbert space.

Generalized Polar Decompositions for Closed Operators in Hilbert Spaces and Some Applications

OpenAIRE

Gesztesy, Fritz; Malamud, Mark; Mitrea, Marius; Naboko, Serguei

2008-01-01

We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and m-sectorial operators.

a Comparison Study of Different Kernel Functions for Svm-Based Classification of Multi-Temporal Polarimetry SAR Data

Science.gov (United States)

Yekkehkhany, B.; Safari, A.; Homayouni, S.; Hasanlou, M.

2014-10-01

In this paper, a framework is developed based on Support Vector Machines (SVM) for crop classification using polarimetric features extracted from multi-temporal Synthetic Aperture Radar (SAR) imageries. The multi-temporal integration of data not only improves the overall retrieval accuracy but also provides more reliable estimates with respect to single-date data. Several kernel functions are employed and compared in this study for mapping the input space to higher Hilbert dimension space. These kernel functions include linear, polynomials and Radial Based Function (RBF). The method is applied to several UAVSAR L-band SAR images acquired over an agricultural area near Winnipeg, Manitoba, Canada. In this research, the temporal alpha features of H/A/α decomposition method are used in classification. The experimental tests show an SVM classifier with RBF kernel for three dates of data increases the Overall Accuracy (OA) to up to 3% in comparison to using linear kernel function, and up to 1% in comparison to a 3rd degree polynomial kernel function.

Diagonalization of Bounded Linear Operators on Separable Quaternionic Hilbert Space

International Nuclear Information System (INIS)

Feng Youling; Cao, Yang; Wang Haijun

2012-01-01

By using the representation of its complex-conjugate pairs, we have investigated the diagonalization of a bounded linear operator on separable infinite-dimensional right quaternionic Hilbert space. The sufficient condition for diagonalizability of quaternionic operators is derived. The result is applied to anti-Hermitian operators, which is essential for solving Schroedinger equation in quaternionic quantum mechanics.

Tensor algebra over Hilbert space: Field theory in classical phase space

International Nuclear Information System (INIS)

Matos Neto, A.; Vianna, J.D.M.

1984-01-01

It is shown using tensor algebras, namely Symmetric and Grassmann algebras over Hilbert Space that it is possible to introduce field operators, associated to the Liouville equation of classical statistical mechanics, which are characterized by commutation (for Symmetric) and anticommutation (for Grassmann) rules. The procedure here presented shows by construction that many-particle classical systems admit an algebraic structure similar to that of quantum field theory. It is considered explicitly the case of n-particle systems interacting with an external potential. A new derivation of Schoenberg's result about the equivalence between his field theory in classical phase space and the usual classical statistical mechanics is obtained as a consequence of the algebraic structure of the theory as introduced by our method. (Author) [pt

Unstable quantum states and rigged Hilbert spaces

International Nuclear Information System (INIS)

Gorini, V.; Parravicini, G.

1978-10-01

Rigged Hilbert space techniques are applied to the quantum mechanical treatment of unstable states in nonrelativistic scattering theory. A method is discussed which is based on representations of decay amplitudes in terms of expansions over complete sets of generalized eigenvectors of the interacting Hamiltonian, corresponding to complex eigenvalues. These expansions contain both a discrete and a continuum contribution. The former corresponds to eigenvalues located at the second sheet poles of the S matrix, and yields the exponential terms in the survival amplitude. The latter arises from generalized eigenvectors associated to complex eigenvalues on background contours in the complex plane, and gives the corrections to the exponential law. 27 references

A One-Sample Test for Normality with Kernel Methods

OpenAIRE

Kellner , Jérémie; Celisse , Alain

2015-01-01

We propose a new one-sample test for normality in a Reproducing Kernel Hilbert Space (RKHS). Namely, we test the null-hypothesis of belonging to a given family of Gaussian distributions. Hence our procedure may be applied either to test data for normality or to test parameters (mean and covariance) if data are assumed Gaussian. Our test is based on the same principle as the MMD (Maximum Mean Discrepancy) which is usually used for two-sample tests such as homogeneity or independence testing. O...

Rosette of rosettes of Hilbert spaces in the indefinite metric state space of the quantized Maxwell field

International Nuclear Information System (INIS)

Gessner, W.; Ernst, V.

1980-01-01

The indefinite metric space O/sub M/ of the covariant form of the quantized Maxwell field M is analyzed in some detail. S/sub M/ contains not only the pre-Hilbert space X 0 of states of transverse photons which occurs in the Gupta--Bleuler formalism of the free M, but a whole rosette of continuously many, isomorphic, complete, pre-Hilbert spaces L/sup q/ disjunct up to the zero element o of S/sub M/. The L/sup q/ are the maximal subspaces of S/sub M/ which allow the usual statistical interpretation. Each L/sup q/ corresponds uniquely to one square integrable, spatial distribution j/sup o/(x) of the total charge Q=0. If M is in any state from L/sup q/, the bare charge j 0 (x) appears to be inseparably dressed by the quantum equivalent of its proper, classical Coulomb field E(x). The vacuum occurs only in the state space L 0 of the free Maxwell field. Each L/sup q/ contains a secondary rosette of continuously many, up to o disjunct, isomorphic Hilbert spaces H/sub g//sup q/ related to different electromagnetic gauges. The space H/sub o//sup q/, which corresponds to the Coulomb gauge within the Lorentz gauge, plays a physically distinguished role in that only it leads to the usual concept of energy. If M is in any state from H/sub g//sup q/, the bare 4-current j 0 (x), j(x), where j(x) is any square integrable, transverse current density in space, is endowed with its proper 4-potential which depends on the chosen gauge, and with its proper, gauge independent, Coulomb--Oersted field E(x), B(x). However, these fields exist only in the sense of quantum mechanical expectation values equipped with the corresponding field fluctuations. So they are basically different from classical electromagnetic fields

Real analysis measure theory, integration, and Hilbert spaces

CERN Document Server

Stein, Elias M

2005-01-01

Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After

The kinematical Hilbert space of loop quantum gravity from BF theories

International Nuclear Information System (INIS)

Cianfrani, Francesco

2011-01-01

In this work, it is demonstrated how the kinematical Hilbert space of loop quantum gravity (LQG) can be inferred from the configuration space of BF theories via the imposition of the Hamiltonian constraints. In particular, it is outlined how the projection to the representations associated with Ashtekar-Barbero connections provides the correct procedure to implement second-class constraints and the corresponding nontrivial induced symplectic structure. Then, the reduction to SU(2) invariant intertwiners is analyzed and the properties of LQG states under Lorentz transformations are discussed.

CLAss-Specific Subspace Kernel Representations and Adaptive Margin Slack Minimization for Large Scale Classification.

Science.gov (United States)

Yu, Yinan; Diamantaras, Konstantinos I; McKelvey, Tomas; Kung, Sun-Yuan

2018-02-01

In kernel-based classification models, given limited computational power and storage capacity, operations over the full kernel matrix becomes prohibitive. In this paper, we propose a new supervised learning framework using kernel models for sequential data processing. The framework is based on two components that both aim at enhancing the classification capability with a subset selection scheme. The first part is a subspace projection technique in the reproducing kernel Hilbert space using a CLAss-specific Subspace Kernel representation for kernel approximation. In the second part, we propose a novel structural risk minimization algorithm called the adaptive margin slack minimization to iteratively improve the classification accuracy by an adaptive data selection. We motivate each part separately, and then integrate them into learning frameworks for large scale data. We propose two such frameworks: the memory efficient sequential processing for sequential data processing and the parallelized sequential processing for distributed computing with sequential data acquisition. We test our methods on several benchmark data sets and compared with the state-of-the-art techniques to verify the validity of the proposed techniques.

Controlled G-Frames and Their G-Multipliers in Hilbert spaces

OpenAIRE

Rahimi, Asghar; Fereydooni, Abolhassan

2012-01-01

Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are operators that combine (frame-like) analysis, a multiplication with a fixed sequence (called the symbol) and synthesis. Weighted and controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator Also g-frames are the most popular generalization of frames that include almost all of the frame extens...

Multiple kernel learning using single stage function approximation for binary classification problems

Science.gov (United States)

Shiju, S.; Sumitra, S.

2017-12-01

In this paper, the multiple kernel learning (MKL) is formulated as a supervised classification problem. We dealt with binary classification data and hence the data modelling problem involves the computation of two decision boundaries of which one related with that of kernel learning and the other with that of input data. In our approach, they are found with the aid of a single cost function by constructing a global reproducing kernel Hilbert space (RKHS) as the direct sum of the RKHSs corresponding to the decision boundaries of kernel learning and input data and searching that function from the global RKHS, which can be represented as the direct sum of the decision boundaries under consideration. In our experimental analysis, the proposed model had shown superior performance in comparison with that of existing two stage function approximation formulation of MKL, where the decision functions of kernel learning and input data are found separately using two different cost functions. This is due to the fact that single stage representation helps the knowledge transfer between the computation procedures for finding the decision boundaries of kernel learning and input data, which inturn boosts the generalisation capacity of the model.

Compact Hilbert Curve Index Algorithm Based on Gray Code

Directory of Open Access Journals (Sweden)

CAO Xuefeng

2016-12-01

Full Text Available Hilbert curve has best clustering in various kinds of space filling curves, and has been used as an important tools in discrete global grid spatial index design field. But there are lots of redundancies in the standard Hilbert curve index when the data set has large differences between dimensions. In this paper, the construction features of Hilbert curve is analyzed based on Gray code, and then the compact Hilbert curve index algorithm is put forward, in which the redundancy problem has been avoided while Hilbert curve clustering preserved. Finally, experiment results shows that the compact Hilbert curve index outperforms the standard Hilbert index, their 1 computational complexity is nearly equivalent, but the real data set test shows the coding time and storage space decrease 40%, the speedup ratio of sorting speed is nearly 4.3.

Asymptotic behaviour of unbounded trajectories for some non-autonomous systems in a Hilbert space

International Nuclear Information System (INIS)

Djafari Rouhani, B.

1990-07-01

The asymptotic behaviour of unbounded trajectories for non expansive mappings in a real Hilbert space and the extension to more general Banach spaces and to nonlinear contraction semi-group have been studied by many authors. In this paper we study the asymptotic behaviour of unbounded trajectories for a quasi non-autonomous dissipative systems. 26 refs

Quantum computation via local control theory: Direct sum vs. direct product Hilbert spaces

International Nuclear Information System (INIS)

Sklarz, Shlomo E.; Tannor, David J.

2006-01-01

The central objective in any quantum computation is the creation of a desired unitary transformation; the mapping that this unitary transformation produces between the input and output states is identified with the computation. In [S.E. Sklarz, D.J. Tannor, arXiv:quant-ph/0404081 (submitted to PRA) (2004)] it was shown that local control theory can be used to calculate fields that will produce such a desired unitary transformation. In contrast with previous strategies for quantum computing based on optimal control theory, the local control scheme maintains the system within the computational subspace at intermediate times, thereby avoiding unwanted decay processes. In [S.E. Sklarz et al.], the structure of the Hilbert space had a direct sum structure with respect to the computational register and the mediating states. In this paper, we extend the formalism to the important case of a direct product Hilbert space. The final equations for the control algorithm for the two cases are remarkably similar in structure, despite the fact that the derivations are completely different and that in one case the dynamics is in a Hilbert space and in the other case the dynamics is in a Liouville space. As shown in [S.E. Sklarz et al.], the direct sum implementation leads to a computational mechanism based on virtual transitions, and can be viewed as an extension of the principles of Stimulated Raman Adiabatic Passage from state manipulation to evolution operator manipulation. The direct product implementation developed here leads to the intriguing concept of virtual entanglement - computation that exploits second-order transitions that pass through entangled states but that leaves the subsystems nearly separable at all intermediate times. Finally, we speculate on a connection between the algorithm developed here and the concept of decoherence free subspaces

Positive-definite functions and unitary representations of locally compact groups in a Hilbert space

International Nuclear Information System (INIS)

Gali, I.M.; Okb el-Bab, A.S.; Hassan, H.M.

1977-08-01

It is proved that the necessary and sufficient condition for the existence of an integral representation of a group of unitary operators in a Hilbert space is that it is positive-definite and continuous in some topology

Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space

Science.gov (United States)

Cao, ChunJun; Carroll, Sean M.

2018-04-01

We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.

The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems

Directory of Open Access Journals (Sweden)

George Isac

2004-01-01

Full Text Available In the first part of this paper we present a representation theorem for the directional derivative of the metric projection operator in an arbitrary Hilbert space. As a consequence of the representation theorem, we present in the second part the development of the theory of projected dynamical systems in infinite dimensional Hilbert space. We show that this development is possible if we use the viable solutions of differential inclusions. We use also pseudomonotone operators.

Least square regularized regression in sum space.

Science.gov (United States)

Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu

2013-04-01

This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.

Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space.

Science.gov (United States)

Stępień, Grzegorz

2018-03-17

The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative oblique orthogonal coordinate systems-interior and exterior orientation of sensors-to a common, known in both systems, point. Each of the systems is translated along its axis (the systems have common origins) and at the same time the angular relative orientation of both coordinate systems is constant. The translation of both coordinate systems is defined by the spatial norm determining the length of vectors in the new Hilbert type space. As such, the displacement of two relative oblique orthogonal systems is reduced to zero. This makes it possible to directly calculate the rotation matrix of the sensor. The next and final step is the return translation of the system along an already known track. The method can be used for big rotation angles. The method was verified in laboratory conditions for the test data set and measurement data (field data). The accuracy of the results in the laboratory test is on the level of 10 -6 of the input data. This confirmed the correctness of the assumed calculation method. The method is a further development of the author's 2017 Total Free Station (TFS) transformation to several centroids in Hilbert type space. This is the reason why the method is called Multi-Centroid Isometric Transformation-MCIT. MCIT is very fast and enables, by reducing to zero the translation of two relative oblique orthogonal coordinate systems, direct calculation of the exterior orientation of the sensors.

Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space

Directory of Open Access Journals (Sweden)

Grzegorz Stępień

2018-03-01

Full Text Available The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative oblique orthogonal coordinate systems—interior and exterior orientation of sensors—to a common, known in both systems, point. Each of the systems is translated along its axis (the systems have common origins and at the same time the angular relative orientation of both coordinate systems is constant. The translation of both coordinate systems is defined by the spatial norm determining the length of vectors in the new Hilbert type space. As such, the displacement of two relative oblique orthogonal systems is reduced to zero. This makes it possible to directly calculate the rotation matrix of the sensor. The next and final step is the return translation of the system along an already known track. The method can be used for big rotation angles. The method was verified in laboratory conditions for the test data set and measurement data (field data. The accuracy of the results in the laboratory test is on the level of 10−6 of the input data. This confirmed the correctness of the assumed calculation method. The method is a further development of the author’s 2017 Total Free Station (TFS transformation to several centroids in Hilbert type space. This is the reason why the method is called Multi-Centroid Isometric Transformation—MCIT. MCIT is very fast and enables, by reducing to zero the translation of two relative oblique orthogonal coordinate systems, direct calculation of the exterior orientation of the sensors.

Geometry of quantum dynamics in infinite-dimensional Hilbert space

Science.gov (United States)

Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana

2018-04-01

We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.

Perturbation for Frames for a Subspace of a Hilbert Space

DEFF Research Database (Denmark)

Christensen, Ole; deFlicht, C.; Lennard, C.

1997-01-01

We extend a classical result stating that a sufficiently small perturbation$\\{ g_i \\}$ of a Riesz sequence $\\{ f_i \\}$ in a Hilbert space $H$ is again a Riesz sequence. It turns out that the analog result for a frame does not holdunless the frame is complete. However, we are able to prove a very...... similarresult for frames in the case where the gap between the subspaces$\\overline{span} \\{f_i \\}$ and $\\overline{span} \\{ g_i \\}$ is small enough. We give a geometric interpretation of the result....

Nonrelativistic multichannel quantum scattering theory in a two Hilbert space formulation

International Nuclear Information System (INIS)

Chandler, C.

1977-08-01

A two-Hilbert-space form of an abstract scattering theory specifically applicable to multichannel quantum scattering problems is outlined. General physical foundations of the theory are reviewed. Further topics discussed include the invariance principle, asymptotic completeness of the wave operators, representations of the scattering operator in terms of transition operators and fundamental equations that these transition operators satisfy. Outstanding problems, including the difficulties of including Coulomb interactions in the theory, are pointed out. (D.P.)

Approximately dual frames in Hilbert spaces and applications to Gabor frames

OpenAIRE

Christensen, Ole; Laugesen, Richard S.

2011-01-01

Approximately dual frames are studied in the Hilbert space setting. Approximate duals are easier to construct than classical dual frames, and can be tailored to yield almost perfect reconstruction. Bounds on the deviation from perfect reconstruction are obtained for approximately dual frames constructed via perturbation theory. An alternative bound is derived for the rich class of Gabor frames, by using the Walnut representation of the frame operator to estimate the deviation from equality in...

Parametric output-only identification of time-varying structures using a kernel recursive extended least squares TARMA approach

Science.gov (United States)

Ma, Zhi-Sai; Liu, Li; Zhou, Si-Da; Yu, Lei; Naets, Frank; Heylen, Ward; Desmet, Wim

2018-01-01

The problem of parametric output-only identification of time-varying structures in a recursive manner is considered. A kernelized time-dependent autoregressive moving average (TARMA) model is proposed by expanding the time-varying model parameters onto the basis set of kernel functions in a reproducing kernel Hilbert space. An exponentially weighted kernel recursive extended least squares TARMA identification scheme is proposed, and a sliding-window technique is subsequently applied to fix the computational complexity for each consecutive update, allowing the method to operate online in time-varying environments. The proposed sliding-window exponentially weighted kernel recursive extended least squares TARMA method is employed for the identification of a laboratory time-varying structure consisting of a simply supported beam and a moving mass sliding on it. The proposed method is comparatively assessed against an existing recursive pseudo-linear regression TARMA method via Monte Carlo experiments and shown to be capable of accurately tracking the time-varying dynamics. Furthermore, the comparisons demonstrate the superior achievable accuracy, lower computational complexity and enhanced online identification capability of the proposed kernel recursive extended least squares TARMA approach.

Lectures on Hilbert modular varieties and modular forms

CERN Document Server

Goren, Eyal Z

2001-01-01

This book is devoted to certain aspects of the theory of p-adic Hilbert modular forms and moduli spaces of abelian varieties with real multiplication. The theory of p-adic modular forms is presented first in the elliptic case, introducing the reader to key ideas of N. M. Katz and J.-P. Serre. It is re-interpreted from a geometric point of view, which is developed to present the rudiments of a similar theory for Hilbert modular forms. The theory of moduli spaces of abelian varieties with real multiplication is presented first very explicitly over the complex numbers. Aspects of the general theory are then exposed, in particular, local deformation theory of abelian varieties in positive characteristic. The arithmetic of p-adic Hilbert modular forms and the geometry of moduli spaces of abelian varieties are related. This relation is used to study q-expansions of Hilbert modular forms, on the one hand, and stratifications of moduli spaces on the other hand. The book is addressed to graduate students and non-exper...

Local coding based matching kernel method for image classification.

Directory of Open Access Journals (Sweden)

Yan Song

Full Text Available This paper mainly focuses on how to effectively and efficiently measure visual similarity for local feature based representation. Among existing methods, metrics based on Bag of Visual Word (BoV techniques are efficient and conceptually simple, at the expense of effectiveness. By contrast, kernel based metrics are more effective, but at the cost of greater computational complexity and increased storage requirements. We show that a unified visual matching framework can be developed to encompass both BoV and kernel based metrics, in which local kernel plays an important role between feature pairs or between features and their reconstruction. Generally, local kernels are defined using Euclidean distance or its derivatives, based either explicitly or implicitly on an assumption of Gaussian noise. However, local features such as SIFT and HoG often follow a heavy-tailed distribution which tends to undermine the motivation behind Euclidean metrics. Motivated by recent advances in feature coding techniques, a novel efficient local coding based matching kernel (LCMK method is proposed. This exploits the manifold structures in Hilbert space derived from local kernels. The proposed method combines advantages of both BoV and kernel based metrics, and achieves a linear computational complexity. This enables efficient and scalable visual matching to be performed on large scale image sets. To evaluate the effectiveness of the proposed LCMK method, we conduct extensive experiments with widely used benchmark datasets, including 15-Scenes, Caltech101/256, PASCAL VOC 2007 and 2011 datasets. Experimental results confirm the effectiveness of the relatively efficient LCMK method.

Friedrichs systems in a Hilbert space framework: Solvability and multiplicity

Science.gov (United States)

Antonić, N.; Erceg, M.; Michelangeli, A.

2017-12-01

The Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antonić and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide sufficient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.

Quantum limits to information about states for finite dimensional Hilbert space

International Nuclear Information System (INIS)

Jones, K.R.W.

1990-01-01

A refined bound for the correlation information of an N-trial apparatus is developed via an heuristic argument for Hilbert spaces of arbitrary finite dimensionality. Conditional upon the proof of an easily motivated inequality it was possible to find the optimal apparatus for large ensemble quantum Inference, thereby solving the asymptotic optimal state determination problem. In this way an alternative inferential uncertainty principle, is defined which is then contrasted with the usual Heisenberg uncertainty principle. 6 refs

Weighted Traffic Equilibrium Problem in Non Pivot Hilbert Spaces with Long Term Memory

International Nuclear Information System (INIS)

Giuffre, Sofia; Pia, Stephane

2010-01-01

In the paper we consider a weighted traffic equilibrium problem in a non-pivot Hilbert space and prove the equivalence between a weighted Wardrop condition and a variational inequality with long term memory. As an application we show, using recent results of the Senseable Laboratory at MIT, how wireless devices can be used to optimize the traffic equilibrium problem.

Recipes for stable linear embeddings from Hilbert spaces to R^m

OpenAIRE

Puy, Gilles; Davies, Michael; Gribonval, Remi

2017-01-01

We consider the problem of constructing a linear map from a Hilbert space H (possibly infinite dimensional) to Rm that satisfies a restricted isometry property (RIP) on an arbitrary signal model, i.e., a subset of H. We present a generic framework that handles a large class of low-dimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove that a random linear map satisfies a general RIP with high probability. We also describe a generic technique ...

Recipes for stable linear embeddings from Hilbert spaces to R^m

OpenAIRE

Puy, Gilles; Davies, Mike; Gribonval, Rémi

2015-01-01

We consider the problem of constructing a linear map from a Hilbert space $\\mathcal{H}$ (possibly infinite dimensional) to $\\mathbb{R}^m$ that satisfies a restricted isometry property (RIP) on an arbitrary signal model $\\mathcal{S} \\subset \\mathcal{H}$. We present a generic framework that handles a large class of low-dimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove that a random linear map satisfies a general RIP on $\\mathcal{S}$ with h...

Methods for detection and characterization of signals in noisy data with the Hilbert-Huang transform

International Nuclear Information System (INIS)

Stroeer, Alexander; Cannizzo, John K.; Camp, Jordan B.; Gagarin, Nicolas

2009-01-01

The Hilbert-Huang transform is a novel, adaptive approach to time series analysis that does not make assumptions about the data form. Its adaptive, local character allows the decomposition of nonstationary signals with high time-frequency resolution but also renders it susceptible to degradation from noise. We show that complementing the Hilbert-Huang transform with techniques such as zero-phase filtering, kernel density estimation and Fourier analysis allows it to be used effectively to detect and characterize signals with low signal-to-noise ratios.

Riemann-Hilbert approach to the time-dependent generalized sine kernel

Energy Technology Data Exchange (ETDEWEB)

Kozlowski, K.K.

2010-12-15

We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models described by a six-vertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann-Hilbert based analysis. (orig.)

Convex analysis and monotone operator theory in Hilbert spaces

CERN Document Server

Bauschke, Heinz H

2017-01-01

This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, ma...

Estimates of solutions of certain classes of second-order differential equations in a Hilbert space

International Nuclear Information System (INIS)

Artamonov, N V

2003-01-01

Linear second-order differential equations of the form u''(t)+(B+iD)u'(t)+(T+iS)u(t)=0 in a Hilbert space are studied. Under certain conditions on the (generally speaking, unbounded) operators T, S, B and D the correct solubility of the equation in the 'energy' space is proved and best possible (in the general case) estimates of the solutions on the half-axis are obtained

Two New Iterative Methods for a Countable Family of Nonexpansive Mappings in Hilbert Spaces

Directory of Open Access Journals (Sweden)

Hu Changsong

2010-01-01

Full Text Available We consider two new iterative methods for a countable family of nonexpansive mappings in Hilbert spaces. We proved that the proposed algorithms strongly converge to a common fixed point of a countable family of nonexpansive mappings which solves the corresponding variational inequality. Our results improve and extend the corresponding ones announced by many others.

A more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function.

Science.gov (United States)

Wang, Aizhen; Yang, Bicheng

2017-01-01

By means of the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.

Construction of rigged Hilbert spaces to describe resonances and virtual states

International Nuclear Information System (INIS)

Gadella, M.

1983-01-01

In the present communication we present a mathematical formalism for the description of resonances and virtual states. We start by constructing rigged Hilbert spaces of Hardy class functions restricted to the positive half of the real line. Then resonances and virtual states can be written as generalized eigenvectors of the total Hamiltonian. We also define time evolution on functionals. We see that the time evolution group U(t) splits into two semigroups, one for t > 0 and the other for t < 0, hence showing the irreversibility of the decaying process

Construction of rigged Hilbert spaces to describe resonances and virtual states

International Nuclear Information System (INIS)

Gadella, M.

1984-01-01

In the present communication we present a mathematical formalism for the description of resonances and virtual states. We start by constructing rigged Hilbert spaces of Hardy class functions restricted to the positive half of the real line. Then resonances and virtual states can be written as generalized eigenvectors of the total Hamiltonian. We also define time evolution on functionals. We see that the time evolution group U(t) splits into two semigroups, one for t>0 and the other for t<0, hence showing the irreversibility of the decaying process. (orig.)

Classical and quantum contents of solvable game theory on Hilbert space

International Nuclear Information System (INIS)

Cheon, Taksu; Tsutsui, Izumi

2006-01-01

A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be equivalent to a family of classical games supplemented by quantum interference. Our formulation gives a clear perspective to understand why and how quantum strategies outmaneuver classical strategies. It also reveals novel aspects of quantum games such as the stone-scissor-paper phase sub-game and the fluctuation-induced moderation

Kernel and wavelet density estimators on manifolds and more general metric spaces

DEFF Research Database (Denmark)

Cleanthous, G.; Georgiadis, Athanasios; Kerkyacharian, G.

We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the development of smooth functional calculus with well localized...... spectral kernels, Besov regularity spaces, and wavelet type systems. Kernel and both linear and nonlinear wavelet density estimators are introduced and studied. Convergence rates for these estimators are established, which are analogous to the existing results in the classical setting of real...

Hamiltonian and physical Hilbert space in polymer quantum mechanics

International Nuclear Information System (INIS)

Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A

2007-01-01

In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested Schroedinger quantum mechanics. The kinematical cornerstone of our framework is the so-called polymer representation of the Heisenberg-Weyl (HW) algebra, which is the starting point of the construction. The dynamics is constructed as a continuum limit of effective theories characterized by a scale, and requires a renormalization of the inner product. The result is a physical Hilbert space in which the continuum Hamiltonian can be represented and that is unitarily equivalent to the Schroedinger representation of quantum mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed

On convergence of nuclear and correlation operators in Hilbert space

International Nuclear Information System (INIS)

Kubrusly, C.S.

1985-01-01

The convergence of sequences of nuclear operators on a separable Hilbert space is studied. Emphasis is given to trace-norm convergence, which is a basic property in stochastic systems theory. Obviously trace-norm convergence implies uniform convergence. The central theme of the paper focus the opposite way, by investigating when convergence in a weaker topology turns out to imply convergence in a stronger topology. The analysis carried out here is exhaustive in the following sense. All possible implications within a selected set of asymptotic properties for sequences of nuclear operators are established. The special case of correlation operators is also considered in detail. (Author) [pt

Lectures on Hilbert schemes of points on surfaces

CERN Document Server

Nakajima, Hiraku

1999-01-01

This beautifully written book deals with one shining example: the Hilbert schemes of points on algebraic surfaces ... The topics are carefully and tastefully chosen ... The young person will profit from reading this book. --Mathematical Reviews The Hilbert scheme of a surface X describes collections of n (not necessarily distinct) points on X. More precisely, it is the moduli space for 0-dimensional subschemes of X of length n. Recently it was realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory--even theoretical physics. The discussion in the book reflects this feature of Hilbert schemes. One example of the modern, broader interest in the subject is a construction of the representation of the infinite-dimensional Heisenberg algebra, i.e., Fock space. This representation has been studied extensively in the literature in connection with affine Lie algebras, conformal field...

A simple proof to an extension of a theorem of A. Pazy in Hilbert space

International Nuclear Information System (INIS)

Djafari Rouhani, B.

1990-08-01

We prove that if (x n ) n≥0 is a non expansive sequence in a Hilbert space H, the sequence ( n x n ) n≥1 converges strongly in H to the element of minimum norm in the closed convex hull of the sequence (x n+1 -x n ) n≥0 . This result was previously proved; the proof we give here is even much simpler and can be extended to a Banach space. 29 refs

Hilbert-Schmidt and Sobol sensitivity indices for static and time series Wnt signaling measurements in colorectal cancer - part A.

Science.gov (United States)

Sinha, Shriprakash

2017-12-04

Ever since the accidental discovery of Wingless [Sharma R.P., Drosophila information service, 1973, 50, p 134], research in the field of Wnt signaling pathway has taken significant strides in wet lab experiments and various cancer clinical trials, augmented by recent developments in advanced computational modeling of the pathway. Information rich gene expression profiles reveal various aspects of the signaling pathway and help in studying different issues simultaneously. Hitherto, not many computational studies exist which incorporate the simultaneous study of these issues. This manuscript ∙ explores the strength of contributing factors in the signaling pathway, ∙ analyzes the existing causal relations among the inter/extracellular factors effecting the pathway based on prior biological knowledge and ∙ investigates the deviations in fold changes in the recently found prevalence of psychophysical laws working in the pathway. To achieve this goal, local and global sensitivity analysis is conducted on the (non)linear responses between the factors obtained from static and time series expression profiles using the density (Hilbert-Schmidt Information Criterion) and variance (Sobol) based sensitivity indices. The results show the advantage of using density based indices over variance based indices mainly due to the former's employment of distance measures & the kernel trick via Reproducing kernel Hilbert space (RKHS) that capture nonlinear relations among various intra/extracellular factors of the pathway in a higher dimensional space. In time series data, using these indices it is now possible to observe where in time, which factors get influenced & contribute to the pathway, as changes in concentration of the other factors are made. This synergy of prior biological knowledge, sensitivity analysis & representations in higher dimensional spaces can facilitate in time based administration of target therapeutic drugs & reveal hidden biological information within

Upport vector machines for nonlinear kernel ARMA system identification.

Science.gov (United States)

Martínez-Ramón, Manel; Rojo-Alvarez, José Luis; Camps-Valls, Gustavo; Muñioz-Marí, Jordi; Navia-Vázquez, Angel; Soria-Olivas, Emilio; Figueiras-Vidal, Aníbal R

2006-11-01

Nonlinear system identification based on support vector machines (SVM) has been usually addressed by means of the standard SVM regression (SVR), which can be seen as an implicit nonlinear autoregressive and moving average (ARMA) model in some reproducing kernel Hilbert space (RKHS). The proposal of this letter is twofold. First, the explicit consideration of an ARMA model in an RKHS (SVM-ARMA2K) is proposed. We show that stating the ARMA equations in an RKHS leads to solving the regularized normal equations in that RKHS, in terms of the autocorrelation and cross correlation of the (nonlinearly) transformed input and output discrete time processes. Second, a general class of SVM-based system identification nonlinear models is presented, based on the use of composite Mercer's kernels. This general class can improve model flexibility by emphasizing the input-output cross information (SVM-ARMA4K), which leads to straightforward and natural combinations of implicit and explicit ARMA models (SVR-ARMA2K and SVR-ARMA4K). Capabilities of these different SVM-based system identification schemes are illustrated with two benchmark problems.

Limit distribution function of inhomogeneities in regions with random boundary in the Hilbert space

International Nuclear Information System (INIS)

Rasulova, M.Yu.; Tashpulatov, S.M.

2004-10-01

The interaction of charged particle systems with a membrane consisting of nonhomogeneities which are randomly distributed by the same law in the vicinity of appropriate sites of a planax crystal lattice is studied. A system of equations for the self-consistent potential U 1 (x,ξ 0 ,..., ξ N ,...) and the density of induced charges σ(x,ξ 0 ,...,ξ N ,...) is solved on Hilbert space. (author)

A more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function

Directory of Open Access Journals (Sweden)

Aizhen Wang

2017-06-01

Full Text Available Abstract By means of the weight functions, the technique of real analysis and Hermite-Hadamard’s inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.

New approximation of a scale space kernel on SE(3) and applications in neuroimaging

NARCIS (Netherlands)

Portegies, J.M.; Sanguinetti, G.R.; Meesters, S.P.L.; Duits, R.

2015-01-01

We provide a new, analytic kernel for scale space filtering of dMRI data. The kernel is an approximation for the Green's function of a hypo-elliptic diffusion on the 3D rigid body motion group SE(3), for fiber enhancement in dMRI. The enhancements are described by linear scale space PDEs in the

Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces

Directory of Open Access Journals (Sweden)

Juguo Su

2012-01-01

Full Text Available The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.

A New General Iterative Method for a Finite Family of Nonexpansive Mappings in Hilbert Spaces

Directory of Open Access Journals (Sweden)

Singthong Urailuk

2010-01-01

Full Text Available We introduce a new general iterative method by using the -mapping for finding a common fixed point of a finite family of nonexpansive mappings in the framework of Hilbert spaces. A strong convergence theorem of the purposed iterative method is established under some certain control conditions. Our results improve and extend the results announced by many others.

On quantization of free fields in stationary space-times

International Nuclear Information System (INIS)

Moreno, C.

1977-01-01

In Section 1 the structure of the infinite-dimensional Hamiltonian system described by the Klein-Gordon equation (free real scalar field) in stationary space-times with closed space sections, is analysed, an existence and uniqueness theorem is given for the Lichnerowicz distribution kernel G 1 together with its proper Fourier expansion, and the Hilbert spaces of frequency-part solutions defined by means of G 1 are constructed. In Section 2 an analysis, a theorem and a construction similar to the above are formulated for the free real field spin 1, mass m>0, in one kind of static space-times. (Auth.)

An Hilbert space approach for a class of arbitrage free implied volatilities models

OpenAIRE

Brace, A.; Fabbri, G.; Goldys, B.

2007-01-01

We present an Hilbert space formulation for a set of implied volatility models introduced in \\cite{BraceGoldys01} in which the authors studied conditions for a family of European call options, varying the maturing time and the strike price $T$ an $K$, to be arbitrage free. The arbitrage free conditions give a system of stochastic PDEs for the evolution of the implied volatility surface ${\\hat\\sigma}_t(T,K)$. We will focus on the family obtained fixing a strike $K$ and varying $T$. In order to...

Hilbert schemes of points on some classes surface singularities

OpenAIRE

Gyenge, Ádám

2016-01-01

We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C^2/G], respectively the singular quotient surface C^2/G, where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition of the (equivariant) Hilbert scheme of the orbifold into affine space strata indexed by a certain combinatorial set, the set of Young walls. The generating series of Euler characteristics of Hilbert schemes of points of the singular surface of type A or D is computed in...

Analysis of unbounded operators and random motion

International Nuclear Information System (INIS)

Jorgensen, Palle E. T.

2009-01-01

We study infinite weighted graphs with view to 'limits at infinity' or boundaries at infinity. Examples of such weighted graphs arise in infinite (in practice, that means 'very' large) networks of resistors or in statistical mechanics models for classical or quantum systems. However, more generally, our analysis includes reproducing kernel Hilbert spaces and associated operators on them. If X is some infinite set of vertices or nodes, in applications the essential ingredient going into the definition is a reproducing kernel Hilbert space; it measures the differences of functions on X evaluated on pairs of points in X. Moreover, the Hilbert norm-squared in H(X) will represent a suitable measure of energy. Associated unbounded operators will define a notion or dissipation, it can be a graph Laplacian or a more abstract unbounded Hermitian operator defined from the reproducing kernel Hilbert space under study. We prove that there are two closed subspaces in reproducing kernel Hilbert space H(X) that measure quantitative notions of limits at infinity in X: one generalizes finite-energy harmonic functions in H(X) and the other a deficiency index of a natural operator in H(X) associated directly with the diffusion. We establish these results in the abstract, and we offer examples and applications. Our results are related to, but different from, potential theoretic notions of 'boundaries' in more standard random walk models. Comparisons are made.

Quantum Hilbert Hotel.

Science.gov (United States)

Potoček, Václav; Miatto, Filippo M; Mirhosseini, Mohammad; Magaña-Loaiza, Omar S; Liapis, Andreas C; Oi, Daniel K L; Boyd, Robert W; Jeffers, John

2015-10-16

In 1924 David Hilbert conceived a paradoxical tale involving a hotel with an infinite number of rooms to illustrate some aspects of the mathematical notion of "infinity." In continuous-variable quantum mechanics we routinely make use of infinite state spaces: here we show that such a theoretical apparatus can accommodate an analog of Hilbert's hotel paradox. We devise a protocol that, mimicking what happens to the guests of the hotel, maps the amplitudes of an infinite eigenbasis to twice their original quantum number in a coherent and deterministic manner, producing infinitely many unoccupied levels in the process. We demonstrate the feasibility of the protocol by experimentally realizing it on the orbital angular momentum of a paraxial field. This new non-Gaussian operation may be exploited, for example, for enhancing the sensitivity of NOON states, for increasing the capacity of a channel, or for multiplexing multiple channels into a single one.

Continuous Slice Functional Calculus in Quaternionic Hilbert Spaces

Science.gov (United States)

Ghiloni, Riccardo; Moretti, Valter; Perotti, Alessandro

2013-04-01

The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic C*-algebras and to define, on each of these C*-algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.

Verification of Equivalence of the Axial Gauge to the Coulomb Gauge in QED by Embedding in the Indefinite Metric Hilbert Space : Particles and Fields

OpenAIRE

Yuji, NAKAWAKI; Azuma, TANAKA; Kazuhiko, OZAKI; Division of Physics and Mathematics, Faculty of Engineering Setsunan University; Junior College of Osaka Institute of Technology; Faculty of General Education, Osaka Institute of Technology

1994-01-01

Gauge Equivalence of the A_3=0 (axial) gauge to the Coulomb gauge is directly verified in QED. For that purpose a pair of conjugate zero-norm fields are introduced. This enables us to construct a canonical formulation in the axial gauge embedded in the indefinite metric Hilbert space in such a way that the Feynman rules are not altered. In the indefinite metric Hilbert space we can implement a gauge transformation, which otherwise has to be carried out only by hand, as main parts of a canonic...

Locally linear approximation for Kernel methods : the Railway Kernel

OpenAIRE

Muñoz, Alberto; González, Javier

2008-01-01

In this paper we present a new kernel, the Railway Kernel, that works properly for general (nonlinear) classification problems, with the interesting property that acts locally as a linear kernel. In this way, we avoid potential problems due to the use of a general purpose kernel, like the RBF kernel, as the high dimension of the induced feature space. As a consequence, following our methodology the number of support vectors is much lower and, therefore, the generalization capab...

Quantum physics of an elementary system in de Sitter space

International Nuclear Information System (INIS)

Rabeie, A.

2012-01-01

We present the coherent states of a scalar massive particle on 1+3-de Sitter space. These states are vectors in Hilbert space, and they are labeled by points in the associated phase space. To do this, we use the fact that the phase space of a scalar massive particle on 1+3-de Sitter space is a cotangent bundle T * (S 3 ) which is isomorphic with the complex sphere S C 3 . Then by using the heat kernel on '' S C 3 '' that was presented by Hall-Mitchell, we construct our coherent states. At the end, by these states we quantize the classical kinetic energy on de Sitter space. (orig.)

Reflection Negative Kernels and Fractional Brownian Motion

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Palle E. T. Jorgensen

2018-06-01

Full Text Available In this article we study the connection of fractional Brownian motion, representation theory and reflection positivity in quantum physics. We introduce and study reflection positivity for affine isometric actions of a Lie group on a Hilbert space E and show in particular that fractional Brownian motion for Hurst index 0 < H ≤ 1 / 2 is reflection positive and leads via reflection positivity to an infinite dimensional Hilbert space if 0 < H < 1 / 2 . We also study projective invariance of fractional Brownian motion and relate this to the complementary series representations of GL 2 ( R . We relate this to a measure preserving action on a Gaussian L 2 -Hilbert space L 2 ( E .

Response to the Comment by G. Emch on projective group representations in quaternionic Hilbert space

International Nuclear Information System (INIS)

Adler, S.L.

1996-01-01

We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embeddings, and leads to a detailed theory of quaternionic, as well as complex, projective group representations. copyright 1996 American Institute of Physics

Regularization in Hilbert space under unbounded operators and general source conditions

International Nuclear Information System (INIS)

Hofmann, Bernd; Mathé, Peter; Von Weizsäcker, Heinrich

2009-01-01

The authors study ill-posed equations with unbounded operators in Hilbert space. This setup has important applications, but only a few theoretical studies are available. First, the question is addressed and answered whether every element satisfies some general source condition with respect to a given self-adjoint unbounded operator. This generalizes a previous result from Mathé and Hofmann (2008 Inverse Problems 24 015009). The analysis then proceeds to error bounds for regularization, emphasizing some specific points for regularization under unbounded operators. The study finally reviews two examples within the light of the present study, as these are fractional differentiation and some Cauchy problems for the Helmholtz equation, both studied previously and in more detail by U Tautenhahn and co-authors

Viscosity kernel of molecular fluids

DEFF Research Database (Denmark)

Puscasu, Ruslan; Todd, Billy; Daivis, Peter

2010-01-01

, temperature, and chain length dependencies of the reciprocal and real-space viscosity kernels are presented. We find that the density has a major effect on the shape of the kernel. The temperature range and chain lengths considered here have by contrast less impact on the overall normalized shape. Functional...... forms that fit the wave-vector-dependent kernel data over a large density and wave-vector range have also been tested. Finally, a structural normalization of the kernels in physical space is considered. Overall, the real-space viscosity kernel has a width of roughly 3–6 atomic diameters, which means...

Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces

Directory of Open Access Journals (Sweden)

Mourad Kerboua

2014-12-01

Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.

Characterizing sequential isomorphisms on Hilbert-space effect algebras

International Nuclear Information System (INIS)

Hou Jinchuan; He Kan; Qi Xiaofei

2010-01-01

Let * be any sequential product on the Hilbert-space effect algebra E(H) with dim H≥2, and Φ:E(H)→E(H) be a bijective map. We show that if Φ satisfies Φ(A*B) = Φ(A)*Φ(B) for A,B element of E(H), then there is either a unitary or an anti-unitary operator U such that Φ(A) = UAU† for every A element of E(H). Let g:[0,1]→{λ|λ element of C, |λ|=0 or 1} be a Borel function satisfying g(0) = 0, g(1) = 1 and let us define a binary operation lozenge g on E(H) by A lozenge g B = A 1/2 g(A)Bg(A)†A 1/2 , where T† denotes the conjugate of the operator T. We also show that a bijective map Φ:E(H)→E(H) satisfies Φ(A lozenge g B) = Φ(A) lozenge g Φ(B) for A,B element of E(H) if and only if there is either a unitary or an anti-unitary operator U such that Φ(A) = UAU† for every A element of E(H).

A Unified and Comprehensible View of Parametric and Kernel Methods for Genomic Prediction with Application to Rice.

Science.gov (United States)

Jacquin, Laval; Cao, Tuong-Vi; Ahmadi, Nourollah

2016-01-01

One objective of this study was to provide readers with a clear and unified understanding of parametric statistical and kernel methods, used for genomic prediction, and to compare some of these in the context of rice breeding for quantitative traits. Furthermore, another objective was to provide a simple and user-friendly R package, named KRMM, which allows users to perform RKHS regression with several kernels. After introducing the concept of regularized empirical risk minimization, the connections between well-known parametric and kernel methods such as Ridge regression [i.e., genomic best linear unbiased predictor (GBLUP)] and reproducing kernel Hilbert space (RKHS) regression were reviewed. Ridge regression was then reformulated so as to show and emphasize the advantage of the kernel "trick" concept, exploited by kernel methods in the context of epistatic genetic architectures, over parametric frameworks used by conventional methods. Some parametric and kernel methods; least absolute shrinkage and selection operator (LASSO), GBLUP, support vector machine regression (SVR) and RKHS regression were thereupon compared for their genomic predictive ability in the context of rice breeding using three real data sets. Among the compared methods, RKHS regression and SVR were often the most accurate methods for prediction followed by GBLUP and LASSO. An R function which allows users to perform RR-BLUP of marker effects, GBLUP and RKHS regression, with a Gaussian, Laplacian, polynomial or ANOVA kernel, in a reasonable computation time has been developed. Moreover, a modified version of this function, which allows users to tune kernels for RKHS regression, has also been developed and parallelized for HPC Linux clusters. The corresponding KRMM package and all scripts have been made publicly available.

Galerkin approximations of nonlinear optimal control problems in Hilbert spaces

Directory of Open Access Journals (Sweden)

Mickael D. Chekroun

2017-07-01

Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.

The Schrödinger–Robinson inequality from stochastic analysis on a complex Hilbert space

International Nuclear Information System (INIS)

Khrennikov, Andrei

2013-01-01

We explored the stochastic analysis on a complex Hilbert space to show that one of the cornerstones of quantum mechanics (QM), namely Heisenberg's uncertainty relation, can be derived in the classical probabilistic framework. We created a new mathematical representation of quantum averages: as averages with respect to classical random fields. The existence of a classical stochastic model matching with Heisenberg's uncertainty relation makes the connection between classical and quantum probabilistic models essentially closer. In real physical situations, random fields are valued in the L 2 -space. Hence, although we model QM and not QFT, the classical systems under consideration have an infinite number of degrees of freedom. And in our modeling, infinite-dimensional stochastic analysis is the basic mathematical tool. (comment)

Four-dimensional hilbert curves for R-trees

DEFF Research Database (Denmark)

Haverkort, Herman; Walderveen, Freek van

2011-01-01

Two-dimensional R-trees are a class of spatial index structures in which objects are arranged to enable fast window queries: report all objects that intersect a given query window. One of the most successful methods of arranging the objects in the index structure is based on sorting the objects...... according to the positions of their centers along a two-dimensional Hilbert space-filling curve. Alternatively, one may use the coordinates of the objects' bounding boxes to represent each object by a four-dimensional point, and sort these points along a four-dimensional Hilbert-type curve. In experiments...

Unexplored regions in QFT: an alternative resolution of the gauge-theoretic clash between localization and the Hilbert space of quantum theory

International Nuclear Information System (INIS)

Schroer, Bert; FU-Berlin

2012-02-01

Massive quantum matter of prescribed spin permits infinitely many possibilities of covariantization in terms of spinorial (undotted/dotted) pointlike fields, whereas massless nite helicity representations lead to large gap in this spinorial spectrum which for s=1 excludes vector potentials. Since the nonexistence of such pointlike generators is the result of a deep structural clash between modular localization and the Hilbert space setting of QT, there are two ways out: gauge theory which sacrifices the Hilbert space and keeps the pointlike formalism and the use of string like potentials which allows to preserve the Hilbert space. The latter setting contains also string-localized charge-carrying operators whereas the gauge theoretic formulation is limited to point-like generated observables. This description also gives a much better insight into the Higgs mechanism which leads to a revival of the more physical 'Schwinger-Higgs' screening idea. The new formalism is not limited to m=0, s=1, it leads to renormalizable inter- actions in the sense of power-counting for all s in massless representations. The existence of string like vector potentials is preempted by the Aharonov-Bohm effect in QFT; it is well-known that the use of pointlike vector potentials in Stokes theorem would with lead to wrong results. Their use in Maxwell's equations is known to lead to zero Maxwell charge. The role of string-localization in the problem behind the observed invisibility and confinement of gluons and quarks leads to new questions and problems. (author)

Image decomposition model Shearlet-Hilbert-L2 with better performance for denoising in ESPI fringe patterns.

Science.gov (United States)

Xu, Wenjun; Tang, Chen; Su, Yonggang; Li, Biyuan; Lei, Zhenkun

2018-02-01

In this paper, we propose an image decomposition model Shearlet-Hilbert-L 2 with better performance for denoising in electronic speckle pattern interferometry (ESPI) fringe patterns. In our model, the low-density fringes, high-density fringes, and noise are, respectively, described by shearlet smoothness spaces, adaptive Hilbert space, and L 2 space and processed individually. Because the shearlet transform has superior directional sensitivity, our proposed Shearlet-Hilbert-L 2 model achieves commendable filtering results for various types of ESPI fringe patterns, including uniform density fringe patterns, moderately variable density fringe patterns, and greatly variable density fringe patterns. We evaluate the performance of our proposed Shearlet-Hilbert-L 2 model via application to two computer-simulated and nine experimentally obtained ESPI fringe patterns with various densities and poor quality. Furthermore, we compare our proposed model with windowed Fourier filtering and coherence-enhancing diffusion, both of which are the state-of-the-art methods for ESPI fringe patterns denoising in transform domain and spatial domain, respectively. We also compare our proposed model with the previous image decomposition model BL-Hilbert-L 2 .

On knottings in the physical Hilbert space of LQG as given by the EPRL model

International Nuclear Information System (INIS)

Bahr, Benjamin

2011-01-01

We consider the EPRL spin foam amplitude for arbitrary embedded two-complexes. Choosing a definition of the face- and edge amplitudes which lead to spin foam amplitudes invariant under trivial subdivisions, we investigate invariance properties of the amplitude under consistent deformations, which are deformations of the embedded two-complex where faces are allowed to pass through each other in a controlled way. Using this surprising invariance, we are able to show that the physical Hilbert space, as defined by the sum over all spin foams, contains no information about knotting classes of graphs anymore.

A unified and comprehensible view of parametric and kernel methods for genomic prediction with application to rice

Directory of Open Access Journals (Sweden)

Laval Jacquin

2016-08-01

Full Text Available One objective of this study was to provide readers with a clear and unified understanding ofparametric statistical and kernel methods, used for genomic prediction, and to compare some ofthese in the context of rice breeding for quantitative traits. Furthermore, another objective wasto provide a simple and user-friendly R package, named KRMM, which allows users to performRKHS regression with several kernels. After introducing the concept of regularized empiricalrisk minimization, the connections between well-known parametric and kernel methods suchas Ridge regression (i.e. genomic best linear unbiased predictor (GBLUP and reproducingkernel Hilbert space (RKHS regression were reviewed. Ridge regression was then reformulatedso as to show and emphasize the advantage of the kernel trick concept, exploited by kernelmethods in the context of epistatic genetic architectures, over parametric frameworks used byconventional methods. Some parametric and kernel methods; least absolute shrinkage andselection operator (LASSO, GBLUP, support vector machine regression (SVR and RKHSregression were thereupon compared for their genomic predictive ability in the context of ricebreeding using three real data sets. Among the compared methods, RKHS regression and SVRwere often the most accurate methods for prediction followed by GBLUP and LASSO. An Rfunction which allows users to perform RR-BLUP of marker effects, GBLUP and RKHS regression,with a Gaussian, Laplacian, polynomial or ANOVA kernel, in a reasonable computation time hasbeen developed. Moreover, a modified version of this function, which allows users to tune kernelsfor RKHS regression, has also been developed and parallelized for HPC Linux clusters. The corresponding KRMM package and all scripts have been made publicly available.

Multitask Classification Hypothesis Space With Improved Generalization Bounds.

Science.gov (United States)

Li, Cong; Georgiopoulos, Michael; Anagnostopoulos, Georgios C

2015-07-01

This paper presents a pair of hypothesis spaces (HSs) of vector-valued functions intended to be used in the context of multitask classification. While both are parameterized on the elements of reproducing kernel Hilbert spaces and impose a feature mapping that is common to all tasks, one of them assumes this mapping as fixed, while the more general one learns the mapping via multiple kernel learning. For these new HSs, empirical Rademacher complexity-based generalization bounds are derived, and are shown to be tighter than the bound of a particular HS, which has appeared recently in the literature, leading to improved performance. As a matter of fact, the latter HS is shown to be a special case of ours. Based on an equivalence to Group-Lasso type HSs, the proposed HSs are utilized toward corresponding support vector machine-based formulations. Finally, experimental results on multitask learning problems underline the quality of the derived bounds and validate this paper's analysis.

Complexified de Sitter space: Analytic causal kernels and Kaellen-Lehmann-type representation

International Nuclear Information System (INIS)

Bros, J.

1991-01-01

Global analyticity properties of functions associated with causal kernels on de Sitter space are considered. These properties extend in a reasonable way those implied by the general framework of quantum field theory in complex Minkowski space. Mathematical results of J. Faraut, G.A. Viano and J. Bros (motivated in particular by complex angular momentum analysis in field theory) find here new applications. (orig.)

Online Distributed Learning Over Networks in RKH Spaces Using Random Fourier Features

Science.gov (United States)

Bouboulis, Pantelis; Chouvardas, Symeon; Theodoridis, Sergios

2018-04-01

We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number of parameters as time iterations evolve. Besides complexity, this leads to an increased need of communication resources, in a distributed setting. In contrast, the proposed method approximates the solution as a fixed-size vector (of larger dimension than the input space) using Random Fourier Features. This paves the way to use standard linear combine-then-adapt techniques. To the best of our knowledge, this is the first time that a complete protocol for distributed online learning in RKHS is presented. Conditions for asymptotic convergence and boundness of the networkwise regret are also provided. The simulated tests illustrate the performance of the proposed scheme.

H-SLAM: Rao-Blackwellized Particle Filter SLAM Using Hilbert Maps

Directory of Open Access Journals (Sweden)

Guillem Vallicrosa

2018-05-01

Full Text Available Occupancy Grid maps provide a probabilistic representation of space which is important for a variety of robotic applications like path planning and autonomous manipulation. In this paper, a SLAM (Simultaneous Localization and Mapping framework capable of obtaining this representation online is presented. The H-SLAM (Hilbert Maps SLAM is based on Hilbert Map representation and uses a Particle Filter to represent the robot state. Hilbert Maps offer a continuous probabilistic representation with a small memory footprint. We present a series of experimental results carried both in simulation and with real AUVs (Autonomous Underwater Vehicles. These results demonstrate that our approach is able to represent the environment more consistently while capable of running online.

Regularization methods for ill-posed problems in multiple Hilbert scales

International Nuclear Information System (INIS)

Mazzieri, Gisela L; Spies, Ruben D

2012-01-01

Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a multiple Hilbert scale on a product space is introduced, and regularization methods on these scales are defined, both for the case of a single observation and for the case of multiple observations. In the latter case, it is shown how vector-valued regularization functions in these multiple Hilbert scales can be used. In all cases, convergence is proved and orders and optimal orders of convergence are shown. Finally, some potential applications and open problems are discussed. (paper)

A kernel version of spatial factor analysis

DEFF Research Database (Denmark)

Nielsen, Allan Aasbjerg

2009-01-01

. Schölkopf et al. introduce kernel PCA. Shawe-Taylor and Cristianini is an excellent reference for kernel methods in general. Bishop and Press et al. describe kernel methods among many other subjects. Nielsen and Canty use kernel PCA to detect change in univariate airborne digital camera images. The kernel...... version of PCA handles nonlinearities by implicitly transforming data into high (even infinite) dimensional feature space via the kernel function and then performing a linear analysis in that space. In this paper we shall apply kernel versions of PCA, maximum autocorrelation factor (MAF) analysis...

Kernel versions of some orthogonal transformations

DEFF Research Database (Denmark)

Nielsen, Allan Aasbjerg

Kernel versions of orthogonal transformations such as principal components are based on a dual formulation also termed Q-mode analysis in which the data enter into the analysis via inner products in the Gram matrix only. In the kernel version the inner products of the original data are replaced...... by inner products between nonlinear mappings into higher dimensional feature space. Via kernel substitution also known as the kernel trick these inner products between the mappings are in turn replaced by a kernel function and all quantities needed in the analysis are expressed in terms of this kernel...... function. This means that we need not know the nonlinear mappings explicitly. Kernel principal component analysis (PCA) and kernel minimum noise fraction (MNF) analyses handle nonlinearities by implicitly transforming data into high (even infinite) dimensional feature space via the kernel function...

Kernel-based adaptive learning improves accuracy of glucose predictive modelling in type 1 diabetes: A proof-of-concept study.

Science.gov (United States)

Georga, Eleni I; Principe, Jose C; Rizos, Evangelos C; Fotiadis, Dimitrios I

2017-07-01

This study aims at demonstrating the need for nonlinear recursive models to the identification and prediction of the dynamic glucose system in type 1 diabetes. Nonlinear regression is performed in a reproducing kernel Hilbert space, by the Approximate Linear Dependency Kernel Recursive Least Squares (KRLS-ALD) algorithm, such that a sparse model structure is accomplished. The method is evaluated on seven people with type 1 diabetes in free-living conditions, where a change in glycaemic dynamics is forced by increasing the level of physical activity in the middle of the observational period. The univariate input allows for short-term (≤30 min) predictions with KRLS-ALD reaching an average root mean square error of 15.22±5.95 mgdL -1 and an average time lag of 17.14±2.67 min for an horizon of 30 min. Its performance is considerably better than that of time-invariant (regularized) linear regression models.

The physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory

International Nuclear Information System (INIS)

Ding You; Rovelli, Carlo

2010-01-01

A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit). We also generalize the definition of the volume operator in the spin-foam model to the Lorentzian signature and show that it matches the one of loop quantum gravity, as in the Euclidean case.

Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces

International Nuclear Information System (INIS)

Höhn, Philipp A.

2014-01-01

A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in the quantum theory, an according formalism for constrained variational discrete systems is constructed. While this paper focuses on global evolution moves and, for simplicity, restricts to flat configuration spaces R N , a Paper II [P. A. Höhn, “Quantization of systems with temporally varying discretization. II. Local evolution moves,” J. Math. Phys., e-print http://arxiv.org/abs/arXiv:1401.7731 [gr-qc].] discusses local evolution moves. In order to link the covariant and canonical picture, the dynamics of the quantum states is generated by propagators which satisfy the canonical constraints and are constructed using the action and group averaging projectors. This projector formalism offers a systematic method for tracing and regularizing divergences in the resulting state sums. Non-trivial coarse graining evolution moves lead to non-unitary, and thus irreversible, projections of physical Hilbert spaces and Dirac observables such that these concepts become evolution move dependent on temporally varying discretizations. The formalism is illustrated in a toy model mimicking a “creation from nothing.” Subtleties arising when applying such a formalism to quantum gravity models are discussed

Difference between standard and quasi-conformal BFKL kernels

International Nuclear Information System (INIS)

Fadin, V.S.; Fiore, R.; Papa, A.

2012-01-01

As it was recently shown, the colour singlet BFKL kernel, taken in Möbius representation in the space of impact parameters, can be written in quasi-conformal shape, which is unbelievably simple compared with the conventional form of the BFKL kernel in momentum space. It was also proved that the total kernel is completely defined by its Möbius representation. In this paper we calculated the difference between standard and quasi-conformal BFKL kernels in momentum space and discovered that it is rather simple. Therefore we come to the conclusion that the simplicity of the quasi-conformal kernel is caused mainly by using the impact parameter space.

Kernel parameter dependence in spatial factor analysis

DEFF Research Database (Denmark)

Nielsen, Allan Aasbjerg

2010-01-01

kernel PCA. Shawe-Taylor and Cristianini [4] is an excellent reference for kernel methods in general. Bishop [5] and Press et al. [6] describe kernel methods among many other subjects. The kernel version of PCA handles nonlinearities by implicitly transforming data into high (even infinite) dimensional...... feature space via the kernel function and then performing a linear analysis in that space. In this paper we shall apply a kernel version of maximum autocorrelation factor (MAF) [7, 8] analysis to irregularly sampled stream sediment geochemistry data from South Greenland and illustrate the dependence...... of the kernel width. The 2,097 samples each covering on average 5 km2 are analyzed chemically for the content of 41 elements....

nth roots with Hilbert-Schmidt defect operator of normal contractions

International Nuclear Information System (INIS)

Duggal, B.P.

1992-08-01

Let T be a normal contraction (on a complex separable Hilbert space H into itself) with an nth root A such that the defect operator D A =(1-A*A) 1/2 is of the Hilbert-Schmidt class C 2 . Then either A is normal or A is similar to a normal contraction. In the case in which T is hyponormal, A n =T and D A is an element of C 2 , A is a ''coupling'' of a contraction similar to a normal contraction and a contraction which is the quasi-affine transform of a unilateral shift. These results are applied to prove a (Putnam-Fuglede type) commutatively theorem for operator valued roots of commutative analytic functions and hyponormal contractions T which have an nth root with Hilbert-Schmidt defect operator. 23 refs

Reduced multiple empirical kernel learning machine.

Science.gov (United States)

Wang, Zhe; Lu, MingZhe; Gao, Daqi

2015-02-01

Multiple kernel learning (MKL) is demonstrated to be flexible and effective in depicting heterogeneous data sources since MKL can introduce multiple kernels rather than a single fixed kernel into applications. However, MKL would get a high time and space complexity in contrast to single kernel learning, which is not expected in real-world applications. Meanwhile, it is known that the kernel mapping ways of MKL generally have two forms including implicit kernel mapping and empirical kernel mapping (EKM), where the latter is less attracted. In this paper, we focus on the MKL with the EKM, and propose a reduced multiple empirical kernel learning machine named RMEKLM for short. To the best of our knowledge, it is the first to reduce both time and space complexity of the MKL with EKM. Different from the existing MKL, the proposed RMEKLM adopts the Gauss Elimination technique to extract a set of feature vectors, which is validated that doing so does not lose much information of the original feature space. Then RMEKLM adopts the extracted feature vectors to span a reduced orthonormal subspace of the feature space, which is visualized in terms of the geometry structure. It can be demonstrated that the spanned subspace is isomorphic to the original feature space, which means that the dot product of two vectors in the original feature space is equal to that of the two corresponding vectors in the generated orthonormal subspace. More importantly, the proposed RMEKLM brings a simpler computation and meanwhile needs a less storage space, especially in the processing of testing. Finally, the experimental results show that RMEKLM owns a much efficient and effective performance in terms of both complexity and classification. The contributions of this paper can be given as follows: (1) by mapping the input space into an orthonormal subspace, the geometry of the generated subspace is visualized; (2) this paper first reduces both the time and space complexity of the EKM-based MKL; (3

Twenty-first century quantum mechanics Hilbert space to quantum computers mathematical methods and conceptual foundations

CERN Document Server

Fano, Guido

2017-01-01

This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result...

Aspects of a representation of quantum theory in terms of classical probability theory by means of integration in Hilbert space

International Nuclear Information System (INIS)

Bach, A.

1981-01-01

A representation of quantum mechanics in terms of classical probability theory by means of integration in Hilbert space is discussed. This formal hidden-variables representation is analysed in the context of impossibility proofs concerning hidden-variables theories. The structural analogy of this formulation of quantum theory with classical statistical mechanics is used to elucidate the difference between classical mechanics and quantum mechanics. (author)

Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces

Directory of Open Access Journals (Sweden)

Cho Yeol

2011-01-01

Full Text Available Abstract In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed variational inequalities problems, it is clear that it cannot be directly applied to the problems that we have considered in this paper because of φ and g. 2000 AMS Subject Classification: 47H05; 47H09; 47J25; 65J15.

Monopole operators and Hilbert series of Coulomb branches of 3 d = 4 gauge theories

Science.gov (United States)

Cremonesi, Stefano; Hanany, Amihay; Zaffaroni, Alberto

2014-01-01

This paper addresses a long standing problem - to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of an = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a computation of the metric on the moduli space and/or mirror symmetry. These methods are limited to sufficiently small moduli spaces, with enough symmetry, or to Higgs branches of sufficiently small gauge theories. We introduce a simple formula for the Hilbert series of the Coulomb branch, which applies to any good or ugly three-dimensional = 4 gauge theory. The formula counts monopole operators which are dressed by classical operators, the Casimir invariants of the residual gauge group that is left unbroken by the magnetic flux. We apply our formula to several classes of gauge theories. Along the way we make various tests of mirror symmetry, successfully comparing the Hilbert series of the Coulomb branch with the Hilbert series of the Higgs branch of the mirror theory.

Limitations of shallow nets approximation.

Science.gov (United States)

Lin, Shao-Bo

2017-10-01

In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.

Hilbert's programs and beyond

CERN Document Server

2013-01-01

David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations. Ten essays are devoted to the analysis of classical as well as modern proof theory; three papers on the mathematical roots of Hilbert's work precede the analytical core, and three final essays exploit an open philosophical horizon for reflection on the nature of mathematics in the 21st century.

Polygonal-path approximations on the path spaces of quantum-mechanical systems: properties of the polygonal paths

International Nuclear Information System (INIS)

Exner, P.; Kolerov, G.I.

1981-01-01

Properties of the subset of polygonal paths in the Hilbert space H of paths referring to a d-dimensional quantum-mechanical system are examined. Using the reproduction kernel technique we prove that each element of H is approximated by polygonal paths uniformly with respect to the ''norm'' of time-interval partitions. This result will be applied in the second part of the present paper to prove consistency of the uniform polygonal-path extension of the Feynman maps [ru

Context-invariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space

International Nuclear Information System (INIS)

Loubenets, Elena R.

2015-01-01

We prove the existence for each Hilbert space of the two new quasi hidden variable (qHV) models, statistically noncontextual and context-invariant, reproducing all the von Neumann joint probabilities via non-negative values of real-valued measures and all the quantum product expectations—via the qHV (classical-like) average of the product of the corresponding random variables. In a context-invariant model, a quantum observable X can be represented by a variety of random variables satisfying the functional condition required in quantum foundations but each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. The proved existence of this model negates the general opinion that, in terms of random variables, the Hilbert space description of all the joint von Neumann measurements for dimH≥3 can be reproduced only contextually. The existence of a statistically noncontextual qHV model, in particular, implies that every N-partite quantum state admits a local quasi hidden variable model introduced in Loubenets [J. Math. Phys. 53, 022201 (2012)]. The new results of the present paper point also to the generality of the quasi-classical probability model proposed in Loubenets [J. Phys. A: Math. Theor. 45, 185306 (2012)

Wigner functions defined with Laplace transform kernels.

Science.gov (United States)

Oh, Se Baek; Petruccelli, Jonathan C; Tian, Lei; Barbastathis, George

2011-10-24

We propose a new Wigner-type phase-space function using Laplace transform kernels--Laplace kernel Wigner function. Whereas momentum variables are real in the traditional Wigner function, the Laplace kernel Wigner function may have complex momentum variables. Due to the property of the Laplace transform, a broader range of signals can be represented in complex phase-space. We show that the Laplace kernel Wigner function exhibits similar properties in the marginals as the traditional Wigner function. As an example, we use the Laplace kernel Wigner function to analyze evanescent waves supported by surface plasmon polariton. © 2011 Optical Society of America

Some means inequalities for positive operators in Hilbert spaces

Directory of Open Access Journals (Sweden)

Jin Liang

2017-01-01

Full Text Available Abstract In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequalities. Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm. Finally, we introduce a weighted multivariate geometric mean and show that the weighted multivariate operator geometric mean possess several attractive properties and means inequalities.

Heat kernel analysis for Bessel operators on symmetric cones

DEFF Research Database (Denmark)

Möllers, Jan

2014-01-01

. The heat kernel is explicitly given in terms of a multivariable $I$-Bessel function on $Ω$. Its corresponding heat kernel transform defines a continuous linear operator between $L^p$-spaces. The unitary image of the $L^2$-space under the heat kernel transform is characterized as a weighted Bergmann space...

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

Energy Technology Data Exchange (ETDEWEB)

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)

2017-06-15

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.

The Visualization and Analysis of POI Features under Network Space Supported by Kernel Density Estimation

Directory of Open Access Journals (Sweden)

YU Wenhao

2015-01-01

Full Text Available The distribution pattern and the distribution density of urban facility POIs are of great significance in the fields of infrastructure planning and urban spatial analysis. The kernel density estimation, which has been usually utilized for expressing these spatial characteristics, is superior to other density estimation methods (such as Quadrat analysis, Voronoi-based method, for that the Kernel density estimation considers the regional impact based on the first law of geography. However, the traditional kernel density estimation is mainly based on the Euclidean space, ignoring the fact that the service function and interrelation of urban feasibilities is carried out on the network path distance, neither than conventional Euclidean distance. Hence, this research proposed a computational model of network kernel density estimation, and the extension type of model in the case of adding constraints. This work also discussed the impacts of distance attenuation threshold and height extreme to the representation of kernel density. The large-scale actual data experiment for analyzing the different POIs' distribution patterns (random type, sparse type, regional-intensive type, linear-intensive type discusses the POI infrastructure in the city on the spatial distribution of characteristics, influence factors, and service functions.

The q-difference operator, the quantum hyperplane, Hilbert spaces of analytic functions and q-oscillators

International Nuclear Information System (INIS)

Arik, M.

1991-01-01

It is shown that the differential calculus of Wess and Zumino for the quantum hyperplane is intimately related to the q-difference operator acting on the n-dimensional complex space C n . An explicit transformation relates the variables and the q-difference operators on C n to the variables and the quantum derivatives on the quantum hyperplane. For real values of the quantum parameter q, the consideration of the variables and the derivatives as hermitean conjugates yields a quantum deformation of the Bargmann-Segal Hilbert space of analytic functions on C n . Physically such a system can be interpreted as the quantum deformation of the n dimensional harmonic oscillator invariant under the unitary quantum group U q (n) with energy eigenvalues proportional to the basic integers. Finally, a construction of the variables and quantum derivatives on the quantum hyperplane in terms of variables and ordinary derivatives on C n is presented. (orig.)

Anisotropic hydrodynamics with a scalar collisional kernel

Science.gov (United States)

Almaalol, Dekrayat; Strickland, Michael

2018-04-01

Prior studies of nonequilibrium dynamics using anisotropic hydrodynamics have used the relativistic Anderson-Witting scattering kernel or some variant thereof. In this paper, we make the first study of the impact of using a more realistic scattering kernel. For this purpose, we consider a conformal system undergoing transversally homogenous and boost-invariant Bjorken expansion and take the collisional kernel to be given by the leading order 2 ↔2 scattering kernel in scalar λ ϕ4 . We consider both classical and quantum statistics to assess the impact of Bose enhancement on the dynamics. We also determine the anisotropic nonequilibrium attractor of a system subject to this collisional kernel. We find that, when the near-equilibrium relaxation-times in the Anderson-Witting and scalar collisional kernels are matched, the scalar kernel results in a higher degree of momentum-space anisotropy during the system's evolution, given the same initial conditions. Additionally, we find that taking into account Bose enhancement further increases the dynamically generated momentum-space anisotropy.

Exact Heat Kernel on a Hypersphere and Its Applications in Kernel SVM

Directory of Open Access Journals (Sweden)

Chenchao Zhao

2018-01-01

Full Text Available Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector machine compared to other competing similarity measures. Specifically, the idea of using heat diffusion on a hypersphere to measure similarity has been previously proposed and tested by Lafferty and Lebanon [1], demonstrating promising results based on a heuristic heat kernel obtained from the zeroth order parametrix expansion; however, how well this heuristic kernel agrees with the exact hyperspherical heat kernel remains unknown. This paper presents a higher order parametrix expansion of the heat kernel on a unit hypersphere and discusses several problems associated with this expansion method. We then compare the heuristic kernel with an exact form of the heat kernel expressed in terms of a uniformly and absolutely convergent series in high-dimensional angular momentum eigenmodes. Being a natural measure of similarity between sample points dwelling on a hypersphere, the exact kernel often shows superior performance in kernel SVM classifications applied to text mining, tumor somatic mutation imputation, and stock market analysis.

Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces

Science.gov (United States)

Ito, Kazufumi

1987-01-01

The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.

Computing Instantaneous Frequency by normalizing Hilbert Transform

Science.gov (United States)

Huang, Norden E.

2005-05-31

This invention presents Normalized Amplitude Hilbert Transform (NAHT) and Normalized Hilbert Transform(NHT), both of which are new methods for computing Instantaneous Frequency. This method is designed specifically to circumvent the limitation set by the Bedorsian and Nuttal Theorems, and to provide a sharp local measure of error when the quadrature and the Hilbert Transform do not agree. Motivation for this method is that straightforward application of the Hilbert Transform followed by taking the derivative of the phase-angle as the Instantaneous Frequency (IF) leads to a common mistake made up to this date. In order to make the Hilbert Transform method work, the data has to obey certain restrictions.

On the factorization of integral operators on spaces of summable functions

International Nuclear Information System (INIS)

Engibaryan, Norayr B

2009-01-01

We consider the factorization I-K=(I-U + )(I-U - ), where I is the identity operator, K is an integral operator acting on some Banach space of functions summable with respect to a measure μ on (a,b) subset of (-∞,+∞) continuous relative to the Lebesgue measure, (Kf)(x)=∫ a b k(x,t)f(t)μ(dt), x element of (a,b), and U ± are the desired Volterra operators. A necessary and sufficient condition is found for the existence of this factorization for a rather wide class of operators K with positive kernels and for Hilbert-Schmidt operators.

Pure endmember extraction using robust kernel archetypoid analysis for hyperspectral imagery

Science.gov (United States)

Sun, Weiwei; Yang, Gang; Wu, Ke; Li, Weiyue; Zhang, Dianfa

2017-09-01

A robust kernel archetypoid analysis (RKADA) method is proposed to extract pure endmembers from hyperspectral imagery (HSI). The RKADA assumes that each pixel is a sparse linear mixture of all endmembers and each endmember corresponds to a real pixel in the image scene. First, it improves the re8gular archetypal analysis with a new binary sparse constraint, and the adoption of the kernel function constructs the principal convex hull in an infinite Hilbert space and enlarges the divergences between pairwise pixels. Second, the RKADA transfers the pure endmember extraction problem into an optimization problem by minimizing residual errors with the Huber loss function. The Huber loss function reduces the effects from big noises and outliers in the convergence procedure of RKADA and enhances the robustness of the optimization function. Third, the random kernel sinks for fast kernel matrix approximation and the two-stage algorithm for optimizing initial pure endmembers are utilized to improve its computational efficiency in realistic implementations of RKADA, respectively. The optimization equation of RKADA is solved by using the block coordinate descend scheme and the desired pure endmembers are finally obtained. Six state-of-the-art pure endmember extraction methods are employed to make comparisons with the RKADA on both synthetic and real Cuprite HSI datasets, including three geometrical algorithms vertex component analysis (VCA), alternative volume maximization (AVMAX) and orthogonal subspace projection (OSP), and three matrix factorization algorithms the preconditioning for successive projection algorithm (PreSPA), hierarchical clustering based on rank-two nonnegative matrix factorization (H2NMF) and self-dictionary multiple measurement vector (SDMMV). Experimental results show that the RKADA outperforms all the six methods in terms of spectral angle distance (SAD) and root-mean-square-error (RMSE). Moreover, the RKADA has short computational times in offline

Mixture Density Mercer Kernels: A Method to Learn Kernels

Data.gov (United States)

National Aeronautics and Space Administration — This paper presents a method of generating Mercer Kernels from an ensemble of probabilistic mixture models, where each mixture model is generated from a Bayesian...

Exponential Hilbert series of equivariant embeddings

OpenAIRE

Johnson, Wayne A.

2018-01-01

In this article, we study properties of the exponential Hilbert series of a $G$-equivariant projective variety, where $G$ is a semisimple, simply-connected complex linear algebraic group. We prove a relationship between the exponential Hilbert series and the degree and dimension of the variety. We then prove a combinatorial identity for the coefficients of the polynomial representing the exponential Hilbert series. This formula is used in examples to prove further combinatorial identities inv...

Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space

Directory of Open Access Journals (Sweden)

Zhou Yinying

2014-01-01

Full Text Available We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009, Min and Chang (2012, Plubtieng and Punpaeng (2007, S. Takahashi and W. Takahashi (2007, Tada and Takahashi (2007, Gang and Changsong (2009, Ying (2013, Y. Yao and J. C. Yao (2007, and Yong-Cho and Kang (2012.

Gradient descent for robust kernel-based regression

Science.gov (United States)

Guo, Zheng-Chu; Hu, Ting; Shi, Lei

2018-06-01

In this paper, we study the gradient descent algorithm generated by a robust loss function over a reproducing kernel Hilbert space (RKHS). The loss function is defined by a windowing function G and a scale parameter σ, which can include a wide range of commonly used robust losses for regression. There is still a gap between theoretical analysis and optimization process of empirical risk minimization based on loss: the estimator needs to be global optimal in the theoretical analysis while the optimization method can not ensure the global optimality of its solutions. In this paper, we aim to fill this gap by developing a novel theoretical analysis on the performance of estimators generated by the gradient descent algorithm. We demonstrate that with an appropriately chosen scale parameter σ, the gradient update with early stopping rules can approximate the regression function. Our elegant error analysis can lead to convergence in the standard L 2 norm and the strong RKHS norm, both of which are optimal in the mini-max sense. We show that the scale parameter σ plays an important role in providing robustness as well as fast convergence. The numerical experiments implemented on synthetic examples and real data set also support our theoretical results.

Variable kernel density estimation in high-dimensional feature spaces

CSIR Research Space (South Africa)

Van der Walt, Christiaan M

2017-02-01

Full Text Available Estimating the joint probability density function of a dataset is a central task in many machine learning applications. In this work we address the fundamental problem of kernel bandwidth estimation for variable kernel density estimation in high...

Kernels for structured data

CERN Document Server

Gärtner, Thomas

2009-01-01

This book provides a unique treatment of an important area of machine learning and answers the question of how kernel methods can be applied to structured data. Kernel methods are a class of state-of-the-art learning algorithms that exhibit excellent learning results in several application domains. Originally, kernel methods were developed with data in mind that can easily be embedded in a Euclidean vector space. Much real-world data does not have this property but is inherently structured. An example of such data, often consulted in the book, is the (2D) graph structure of molecules formed by

Linked-cluster formulation of electron-hole interaction kernel in real-space representation without using unoccupied states.

Science.gov (United States)

Bayne, Michael G; Scher, Jeremy A; Ellis, Benjamin H; Chakraborty, Arindam

2018-05-21

Electron-hole or quasiparticle representation plays a central role in describing electronic excitations in many-electron systems. For charge-neutral excitation, the electron-hole interaction kernel is the quantity of interest for calculating important excitation properties such as optical gap, optical spectra, electron-hole recombination and electron-hole binding energies. The electron-hole interaction kernel can be formally derived from the density-density correlation function using both Green's function and TDDFT formalism. The accurate determination of the electron-hole interaction kernel remains a significant challenge for precise calculations of optical properties in the GW+BSE formalism. From the TDDFT perspective, the electron-hole interaction kernel has been viewed as a path to systematic development of frequency-dependent exchange-correlation functionals. Traditional approaches, such as MBPT formalism, use unoccupied states (which are defined with respect to Fermi vacuum) to construct the electron-hole interaction kernel. However, the inclusion of unoccupied states has long been recognized as the leading computational bottleneck that limits the application of this approach for larger finite systems. In this work, an alternative derivation that avoids using unoccupied states to construct the electron-hole interaction kernel is presented. The central idea of this approach is to use explicitly correlated geminal functions for treating electron-electron correlation for both ground and excited state wave functions. Using this ansatz, it is derived using both diagrammatic and algebraic techniques that the electron-hole interaction kernel can be expressed only in terms of linked closed-loop diagrams. It is proved that the cancellation of unlinked diagrams is a consequence of linked-cluster theorem in real-space representation. The electron-hole interaction kernel derived in this work was used to calculate excitation energies in many-electron systems and results

Object classification and detection with context kernel descriptors

DEFF Research Database (Denmark)

Pan, Hong; Olsen, Søren Ingvor; Zhu, Yaping

2014-01-01

Context information is important in object representation. By embedding context cue of image attributes into kernel descriptors, we propose a set of novel kernel descriptors called Context Kernel Descriptors (CKD) for object classification and detection. The motivation of CKD is to use spatial...... consistency of image attributes or features defined within a neighboring region to improve the robustness of descriptor matching in kernel space. For feature selection, Kernel Entropy Component Analysis (KECA) is exploited to learn a subset of discriminative CKD. Different from Kernel Principal Component...

Power Spectral Density and Hilbert Transform

Science.gov (United States)

2016-12-01

there is 1.3 W of power. How much bandwidth does a pure sine wave require? The bandwidth of an ideal sine wave is 0 Hz. How do you represent a 1-W...the Hilbert transform. 2.3 Hilbert Transform The Hilbert transform is a math function used to convert a real function into an analytic signal...The math operation minus 2 means to move 2 steps back on the number line. For minus –2, we move 2 steps backwards from –2, which is the same as

Entropy, Topological Theories and Emergent Quantum Mechanics

Directory of Open Access Journals (Sweden)

D. Cabrera

2017-02-01

Full Text Available The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a finite dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological field theory is also discussed in the context of the approach of the emergence of quantum theory, where the concept of entropy plays a key role.

Theory and experiments on Peano and Hilbert curve RFID tags

Science.gov (United States)

McVay, John; Hoorfar, Ahmad; Engheta, Nader

2006-05-01

Recently, there has been considerable interest in the area of Radio Frequency Identification (RFID) and Radio Frequency Tagging (RFTAG). This emerging area of interest can be applied for inventory control (commercial) as well as friend/foe identification (military) to name but a few. The current technology can be broken down into two main groups, namely passive and active RFID tags. Utilization of Space-Filling Curve (SFC) geometries, such as the Peano and Hilbert curves, has been recently investigated for use in completely passive RFID applications [1, 2]. In this work, we give an overview of our work on the space-filling curves and the potential for utilizing the electrically small, resonant characteristics of these curves for use in RFID technologies with an emphasis on the challenging issues involved when attempting to tag conductive objects. In particular, we investigate the possible use of these tags in conjunction with high impedance ground-planes made of Hilbert or Peano curve inclusions [3, 4] to develop electrically small RFID tags that may also radiate efficiently, within close proximity of large conductive objects [5].

Commutators of Integral Operators with Variable Kernels on Hardy ...

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences; Volume 115; Issue 4. Commutators of Integral Operators with Variable Kernels on Hardy Spaces. Pu Zhang Kai Zhao. Volume 115 Issue 4 November 2005 pp 399-410 ... Keywords. Singular and fractional integrals; variable kernel; commutator; Hardy space.

6th Hilbert's problem and S.Lie's infinite groups

International Nuclear Information System (INIS)

Konopleva, N.P.

1999-01-01

The progress in Hilbert's sixth problem solving is demonstrated. That became possible thanks to the gauge field theory in physics and to the geometrical treatment of the gauge fields. It is shown that the fibre bundle spaces geometry is the best basis for solution of the problem being discussed. This talk has been reported at the International Seminar '100 Years after Sophus Lie' (Leipzig, Germany)

Experimental Investigation of a Direct Methanol Fuel Cell with Hilbert Fractal Current Collectors

Directory of Open Access Journals (Sweden)

Jing-Yi Chang

2014-01-01

Full Text Available The Hilbert curve is a continuous type of fractal space-filling curve. This fractal curve visits every point in a square grid with a size of 2×2, 4×4, or any other power of two. This paper presents Hilbert fractal curve application to direct methanol fuel cell (DMFC current collectors. The current collectors are carved following first, second, and third order Hilbert fractal curves. These curves give the current collectors different free open ratios and opening perimeters. We conducted an experimental investigation into DMFC performance as a function of the free open ratio and opening perimeter on the bipolar plates. Nyquist plots of the bipolar plates are made and compared using electrochemical impedance spectroscopy (EIS experiments to understand the phenomena in depth. The results obtained in this paper could be a good reference for future current collector design.

3D Hilbert Space Filling Curves in 3D City Modeling for Faster Spatial Queries

DEFF Research Database (Denmark)

Ujang, Uznir; Antón Castro, Francesc/François; Azri, Suhaibah

2014-01-01

The advantages of three dimensional (3D) city models can be seen in various applications including photogrammetry, urban and regional planning, computer games, etc. They expand the visualization and analysis capabilities of Geographic Information Systems on cities, and they can be developed using...... method, retrieving portions of and especially searching these 3D city models, will not be done optimally. Even though current developments are based on an open data model allotted by the Open Geospatial Consortium (OGC) called CityGML, its XML-based structure makes it challenging to cluster the 3D urban...... objects. In this research, the authors propose an opponent data constellation technique of space-filling curves (3D Hilbert curves) for 3D city model data representation. Unlike previous methods, that try to project 3D or n-dimensional data down to 2D or 3D using Principal Component Analysis (PCA...

Commentaries on Hilbert's Basis Theorem | Apine | Science World ...

African Journals Online (AJOL)

The famous basis theorem of David Hilbert is an important theorem in commutative algebra. In particular the Hilbert's basis theorem is the most important source of Noetherian rings which are by far the most important class of rings in commutative algebra. In this paper we have used Hilbert's theorem to examine their unique ...

The approximate inverse in action: IV. Semi-discrete equations in a Banach space setting

International Nuclear Information System (INIS)

Schuster, T; Schöpfer, F; Rieder, A

2012-01-01

This article concerns the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search for a solution in an infinite-dimensional Banach space having only a finite number of data available. In this sense the situation is applicable to a large variety of applications where a measurement process delivers a discretization of an infinite-dimensional data space. The method of approximate inverse computes scalar products of the data with pre-computed reconstruction kernels which are associated with mollifiers and the dual of the model operator. The convergence, approximation power and regularization property of this method when applied to semi-discrete operator equations in Hilbert spaces has been investigated in three prequels to this paper. Here we extend these results to a Banach space setting. We prove convergence and stability for general Banach spaces and reproduce the results specifically for the integration operator acting on the space of continuous functions. (paper)

Nested Hilbert schemes on surfaces: Virtual fundamental class

DEFF Research Database (Denmark)

Gholampour, Amin; Sheshmani, Artan; Yau, Shing-Tung

We construct natural virtual fundamental classes for nested Hilbert schemes on a nonsingular projective surface S. This allows us to define new invariants of S that recover some of the known important cases such as Poincare invariants of Durr-Kabanov-Okonek and the stable pair invariants of Kool......-Thomas. In the case of the nested Hilbert scheme of points, we can express these invariants in terms of integrals over the products of Hilbert scheme of points on S, and relate them to the vertex operator formulas found by Carlsson-Okounkov. The virtual fundamental classes of the nested Hilbert schemes play a crucial...

Compactly Supported Basis Functions as Support Vector Kernels for Classification.

Science.gov (United States)

Wittek, Peter; Tan, Chew Lim

2011-10-01

Wavelet kernels have been introduced for both support vector regression and classification. Most of these wavelet kernels do not use the inner product of the embedding space, but use wavelets in a similar fashion to radial basis function kernels. Wavelet analysis is typically carried out on data with a temporal or spatial relation between consecutive data points. We argue that it is possible to order the features of a general data set so that consecutive features are statistically related to each other, thus enabling us to interpret the vector representation of an object as a series of equally or randomly spaced observations of a hypothetical continuous signal. By approximating the signal with compactly supported basis functions and employing the inner product of the embedding L2 space, we gain a new family of wavelet kernels. Empirical results show a clear advantage in favor of these kernels.

Index hypergeometric transform and imitation of analysis of Berezin kernels on hyperbolic spaces

International Nuclear Information System (INIS)

Neretin, Yu A

2001-01-01

The index hypergeometric transform (also called the Olevskii transform or the Jacobi transform) generalizes the spherical transform in L 2 on rank 1 symmetric spaces (that is, real, complex, and quaternionic Lobachevskii spaces). The aim of this paper is to obtain properties of the index hypergeometric transform imitating the analysis of Berezin kernels on rank 1 symmetric spaces. The problem of the explicit construction of a unitary operator identifying L 2 and a Berezin space is also discussed. This problem reduces to an integral expression (the Λ-function), which apparently cannot be expressed in a finite form in terms of standard special functions. (Only for certain special values of the parameter can this expression be reduced to the so-called Volterra type special functions.) Properties of this expression are investigated. For some series of symmetric spaces of large rank the above operator of unitary equivalence can be expressed in terms of the determinant of a matrix of Λ-functions

A kernel-based approach to MIMO LPV state-space identification and application to a nonlinear process system

NARCIS (Netherlands)

Rizvi, S.Z.; Mohammadpour, J.; Toth, R.; Meskin, N.

2015-01-01

This paper first describes the development of a nonparametric identification method for linear parameter-varying (LPV) state-space models and then applies it to a nonlinear process system. The proposed method uses kernel-based least-squares support vector machines (LS-SVM). While parametric

The global kernel k-means algorithm for clustering in feature space.

Science.gov (United States)

Tzortzis, Grigorios F; Likas, Aristidis C

2009-07-01

Kernel k-means is an extension of the standard k -means clustering algorithm that identifies nonlinearly separable clusters. In order to overcome the cluster initialization problem associated with this method, we propose the global kernel k-means algorithm, a deterministic and incremental approach to kernel-based clustering. Our method adds one cluster at each stage, through a global search procedure consisting of several executions of kernel k-means from suitable initializations. This algorithm does not depend on cluster initialization, identifies nonlinearly separable clusters, and, due to its incremental nature and search procedure, locates near-optimal solutions avoiding poor local minima. Furthermore, two modifications are developed to reduce the computational cost that do not significantly affect the solution quality. The proposed methods are extended to handle weighted data points, which enables their application to graph partitioning. We experiment with several data sets and the proposed approach compares favorably to kernel k -means with random restarts.

Schroedinger--Dirac spaces of entire functions

International Nuclear Information System (INIS)

De Branges, L.

1977-01-01

A study is made of some Hilbert spaces of entire function which appear in the quantum mechanical theory of the hydrogen atoms. These spaces are examples in the theory of Hilbert spaces whose elements are entire functions and which have certain given properties. 1 reference

Mathematical methods in physics distributions, Hilbert space operators, variational methods, and applications in quantum physics

CERN Document Server

Blanchard, Philippe

2015-01-01

The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas.  The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories.  All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods.   The text is divided into three main parts. Part I is a brief introduction to distribution theory, in which elements from the theories of ultradistributions and hyperfunctions are considered in addition to some deeper results for Schwartz distributions, thus providing a comprehensive introduction to the theory of generalized functions. P...

Sentiment classification with interpolated information diffusion kernels

NARCIS (Netherlands)

Raaijmakers, S.

2007-01-01

Information diffusion kernels - similarity metrics in non-Euclidean information spaces - have been found to produce state of the art results for document classification. In this paper, we present a novel approach to global sentiment classification using these kernels. We carry out a large array of

2D-Zernike Polynomials and Coherent State Quantization of the Unit Disc

Energy Technology Data Exchange (ETDEWEB)

Thirulogasanthar, K., E-mail: santhar@gmail.com [Concordia University, Department of Comuter Science and Software Engineering (Canada); Saad, Nasser, E-mail: nsaad@upei.ca [University of Prince Edward Island, Department of mathematics and Statistics (Canada); Honnouvo, G., E-mail: g-honnouvo@yahoo.fr [McGill University, Department of Mathematics and Statistics (Canada)

2015-12-15

Using the orthonormality of the 2D-Zernike polynomials, reproducing kernels, reproducing kernel Hilbert spaces, and ensuring coherent states attained. With the aid of the so-obtained coherent states, the complex unit disc is quantized. Associated upper symbols, lower symbols and related generalized Berezin transforms also obtained. A number of necessary summation formulas for the 2D-Zernike polynomials proved.

Theoretical foundations of functional data analysis, with an introduction to linear operators

CERN Document Server

Hsing, Tailen

2015-01-01

Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA).The self-contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self-adjoint and non self-adjoint operators. The probabilistic foundation for FDA is described from the

Putting Priors in Mixture Density Mercer Kernels

Science.gov (United States)

Srivastava, Ashok N.; Schumann, Johann; Fischer, Bernd

2004-01-01

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. We describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using predefined kernels. These data adaptive kernels can en- code prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS). The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains template for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic- algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code. The results show that the Mixture Density Mercer-Kernel described here outperforms tree-based classification in distinguishing high-redshift galaxies from low- redshift galaxies by approximately 16% on test data, bagged trees by approximately 7%, and bagged trees built on a much larger sample of data by approximately 2%.

Kernel bundle EPDiff

DEFF Research Database (Denmark)

Sommer, Stefan Horst; Lauze, Francois Bernard; Nielsen, Mads

2011-01-01

In the LDDMM framework, optimal warps for image registration are found as end-points of critical paths for an energy functional, and the EPDiff equations describe the evolution along such paths. The Large Deformation Diffeomorphic Kernel Bundle Mapping (LDDKBM) extension of LDDMM allows scale space...

A new class of Banach spaces

International Nuclear Information System (INIS)

Gill, T L; Zachary, W W

2008-01-01

In this paper, we construct a new class of separable Banach spaces KS p , for 1 ≤ p ≤ ∞, each of which contains all of the standard L p spaces, as well as the space of finitely additive measures, as compact dense embeddings. Equally important is the fact that these spaces contain all Henstock-Kurzweil integrable functions and, in particular, the Feynman kernel and the Dirac measure, as norm bounded elements. As a first application, we construct the elementary path integral in the manner originally intended by Feynman. We then suggest that KS 2 is a more appropriate Hilbert space for quantum theory, in that it satisfies the requirements for the Feynman, Heisenberg and Schroedinger representations, while the conventional choice only satisfies the requirements for the Heisenberg and Schroedinger representations. As a second application, we show that the mixed topology on the space of bounded continuous functions, C b [R n ], used to define the weak generator for a semigroup T(t), is stronger than the norm topology on KS p . (This means that, when extended to KS p , T(t) is strongly continuous, so that the weak generator on C b [R n ] becomes a strong generator on KS p .)

Kernel based orthogonalization for change detection in hyperspectral images

DEFF Research Database (Denmark)

Nielsen, Allan Aasbjerg

function and all quantities needed in the analysis are expressed in terms of this kernel function. This means that we need not know the nonlinear mappings explicitly. Kernel PCA and MNF analyses handle nonlinearities by implicitly transforming data into high (even infinite) dimensional feature space via...... analysis all 126 spectral bands of the HyMap are included. Changes on the ground are most likely due to harvest having taken place between the two acquisitions and solar effects (both solar elevation and azimuth have changed). Both types of kernel analysis emphasize change and unlike kernel PCA, kernel MNF...

Geodesic exponential kernels: When Curvature and Linearity Conflict

DEFF Research Database (Denmark)

Feragen, Aase; Lauze, François; Hauberg, Søren

2015-01-01

manifold, the geodesic Gaussian kernel is only positive definite if the Riemannian manifold is Euclidean. This implies that any attempt to design geodesic Gaussian kernels on curved Riemannian manifolds is futile. However, we show that for spaces with conditionally negative definite distances the geodesic...

Input Space Regularization Stabilizes Pre-images for Kernel PCA De-noising

DEFF Research Database (Denmark)

Abrahamsen, Trine Julie; Hansen, Lars Kai

2009-01-01

Solution of the pre-image problem is key to efficient nonlinear de-noising using kernel Principal Component Analysis. Pre-image estimation is inherently ill-posed for typical kernels used in applications and consequently the most widely used estimation schemes lack stability. For de...

q-deformed Minkowski space

International Nuclear Information System (INIS)

Ogievetsky, O.; Pillin, M.; Schmidke, W.B.; Wess, J.; Zumino, B.

1993-01-01

In this lecture I discuss the algebraic structure of a q-deformed four-vector space. It serves as a good example of quantizing Minkowski space. To give a physical interpretation of such a quantized Minkowski space we construct the Hilbert space representation and find that the relevant time and space operators have a discrete spectrum. Thus the q-deformed Minkowski space has a lattice structure. Nevertheless this lattice structure is compatible with the operation of q-deformed Lorentz transformations. The generators of the q-deformed Lorentz group can be represented as linear operators in the same Hilbert space. (orig.)

A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

Science.gov (United States)

Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira

2014-06-01

Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.

A differential equation for Lerch's transcendent and associated symmetric operators in Hilbert space

International Nuclear Information System (INIS)

Kaplitskii, V M

2014-01-01

The function Ψ(x,y,s)=e iy Φ(−e iy ,s,x), where Φ(z,s,v) is Lerch's transcendent, satisfies the following two-dimensional formally self-adjoint second-order hyperbolic differential equation, where s=1/2+iλ. The corresponding differential expression determines a densely defined symmetric operator (the minimal operator) on the Hilbert space L 2 (Π), where Π=(0,1)×(0,2π). We obtain a description of the domains of definition of some symmetric extensions of the minimal operator. We show that formal solutions of the eigenvalue problem for these symmetric extensions are represented by functional series whose structure resembles that of the Fourier series of Ψ(x,y,s). We discuss sufficient conditions for these formal solutions to be eigenfunctions of the resulting symmetric differential operators. We also demonstrate a close relationship between the spectral properties of these symmetric differential operators and the distribution of the zeros of some special analytic functions analogous to the Riemann zeta function. Bibliography: 15 titles

Hilbert schemes of points and infinite dimensional Lie algebras

CERN Document Server

Qin, Zhenbo

2018-01-01

Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes X^{[n]} of collections of n points (zero-dimensional subschemes) in a smooth algebraic surface X. Schemes X^{[n]} turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others. This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of X^{[n]}, including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of X^{[n]} a...

Gradient-based adaptation of general gaussian kernels.

Science.gov (United States)

Glasmachers, Tobias; Igel, Christian

2005-10-01

Gradient-based optimizing of gaussian kernel functions is considered. The gradient for the adaptation of scaling and rotation of the input space is computed to achieve invariance against linear transformations. This is done by using the exponential map as a parameterization of the kernel parameter manifold. By restricting the optimization to a constant trace subspace, the kernel size can be controlled. This is, for example, useful to prevent overfitting when minimizing radius-margin generalization performance measures. The concepts are demonstrated by training hard margin support vector machines on toy data.

Wigner Distribution Functions and the Representation of Canonical Transformations in Time-Dependent Quantum Mechanics

Directory of Open Access Journals (Sweden)

Marcos Moshinsky

2008-07-01

Full Text Available For classical canonical transformations, one can, using the Wigner transformation, pass from their representation in Hilbert space to a kernel in phase space. In this paper it will be discussed how the time-dependence of the uncertainties of the corresponding time-dependent quantum problems can be incorporated into this formalism.

Complexity control in statistical learning

Indian Academy of Sciences (India)

Then we describe how the method of regularization is used to control complexity in learning. We discuss two examples of regularization, one in which the function space used is finite dimensional, and another in which it is a reproducing kernel Hilbert space. Our exposition follows the formulation of Cucker and Smale.

Kernel methods in orthogonalization of multi- and hypervariate data

DEFF Research Database (Denmark)

Nielsen, Allan Aasbjerg

2009-01-01

A kernel version of maximum autocorrelation factor (MAF) analysis is described very briefly and applied to change detection in remotely sensed hyperspectral image (HyMap) data. The kernel version is based on a dual formulation also termed Q-mode analysis in which the data enter into the analysis...... via inner products in the Gram matrix only. In the kernel version the inner products are replaced by inner products between nonlinear mappings into higher dimensional feature space of the original data. Via kernel substitution also known as the kernel trick these inner products between the mappings...... are in turn replaced by a kernel function and all quantities needed in the analysis are expressed in terms of this kernel function. This means that we need not know the nonlinear mappings explicitly. Kernel PCA and MAF analysis handle nonlinearities by implicitly transforming data into high (even infinite...

Projective loop quantum gravity. I. State space

Science.gov (United States)

Lanéry, Suzanne; Thiemann, Thomas

2016-12-01

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In a latter work by Okolów, the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states.

Convexity and the Euclidean Metric of Space-Time

Directory of Open Access Journals (Sweden)

Nikolaos Kalogeropoulos

2017-02-01

Full Text Available We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces.

Control Transfer in Operating System Kernels

Science.gov (United States)

1994-05-13

microkernel system that runs less code in the kernel address space. To realize the performance benefit of allocating stacks in unmapped kseg0 memory, the...review how I modified the Mach 3.0 kernel to use continuations. Because of Mach’s message-passing microkernel structure, interprocess communication was...critical control transfer paths, deeply- nested call chains are undesirable in any case because of the function call overhead. 4.1.3 Microkernel Operating

Adaptive Shape Kernel-Based Mean Shift Tracker in Robot Vision System

Directory of Open Access Journals (Sweden)

Chunmei Liu

2016-01-01

Full Text Available This paper proposes an adaptive shape kernel-based mean shift tracker using a single static camera for the robot vision system. The question that we address in this paper is how to construct such a kernel shape that is adaptive to the object shape. We perform nonlinear manifold learning technique to obtain the low-dimensional shape space which is trained by training data with the same view as the tracking video. The proposed kernel searches the shape in the low-dimensional shape space obtained by nonlinear manifold learning technique and constructs the adaptive kernel shape in the high-dimensional shape space. It can improve mean shift tracker performance to track object position and object contour and avoid the background clutter. In the experimental part, we take the walking human as example to validate that our method is accurate and robust to track human position and describe human contour.

Adaptive Shape Kernel-Based Mean Shift Tracker in Robot Vision System

Science.gov (United States)

2016-01-01

This paper proposes an adaptive shape kernel-based mean shift tracker using a single static camera for the robot vision system. The question that we address in this paper is how to construct such a kernel shape that is adaptive to the object shape. We perform nonlinear manifold learning technique to obtain the low-dimensional shape space which is trained by training data with the same view as the tracking video. The proposed kernel searches the shape in the low-dimensional shape space obtained by nonlinear manifold learning technique and constructs the adaptive kernel shape in the high-dimensional shape space. It can improve mean shift tracker performance to track object position and object contour and avoid the background clutter. In the experimental part, we take the walking human as example to validate that our method is accurate and robust to track human position and describe human contour. PMID:27379165

Approximation of a Common Element of the Fixed Point Sets of Multivalued Strictly Pseudocontractive-Type Mappings and the Set of Solutions of an Equilibrium Problem in Hilbert Spaces

Directory of Open Access Journals (Sweden)

F. O. Isiogugu

2016-01-01

Full Text Available The strong convergence of a hybrid algorithm to a common element of the fixed point sets of multivalued strictly pseudocontractive-type mappings and the set of solutions of an equilibrium problem in Hilbert spaces is obtained using a strict fixed point set condition. The obtained results improve, complement, and extend the results on multivalued and single-valued mappings in the contemporary literature.

Empirical mode decomposition and Hilbert transforms for analysis of oil-film interferograms

International Nuclear Information System (INIS)

Chauhan, Kapil; Ng, Henry C H; Marusic, Ivan

2010-01-01

Oil-film interferometry is rapidly becoming the preferred method for direct measurement of wall shear stress in studies of wall-bounded turbulent flows. Although being widely accepted as the most accurate technique, it does have inherent measurement uncertainties, one of which is associated with determining the fringe spacing. This is the focus of this paper. Conventional analysis methods involve a certain level of user input and thus some subjectivity. In this paper, we consider empirical mode decomposition (EMD) and the Hilbert transform as an alternative tool for analyzing oil-film interferograms. In contrast to the commonly used Fourier-based techniques, this new method is less subjective and, as it is based on the Hilbert transform, is superior for treating amplitude and frequency modulated data. This makes it particularly robust to wide differences in the quality of interferograms

Nonlinear Forecasting With Many Predictors Using Kernel Ridge Regression

DEFF Research Database (Denmark)

Exterkate, Peter; Groenen, Patrick J.F.; Heij, Christiaan

This paper puts forward kernel ridge regression as an approach for forecasting with many predictors that are related nonlinearly to the target variable. In kernel ridge regression, the observed predictor variables are mapped nonlinearly into a high-dimensional space, where estimation of the predi...

Hilbert-Twin – A Novel Hilbert Transform-Based Method To Compute Envelope Of Free Decaying Oscillations Embedded In Noise, And The Logarithmic Decrement In High-Resolution Mechanical Spectroscopy HRMS

Directory of Open Access Journals (Sweden)

Magalas L.B.

2015-06-01

Full Text Available In this work, we present a novel Hilbert-twin method to compute an envelope and the logarithmic decrement, δ, from exponentially damped time-invariant harmonic strain signals embedded in noise. The results obtained from five computing methods: (1 the parametric OMI (Optimization in Multiple Intervals method, two interpolated discrete Fourier transform-based (IpDFT methods: (2 the Yoshida-Magalas (YM method and (3 the classic Yoshida (Y method, (4 the novel Hilbert-twin (H-twin method based on the Hilbert transform, and (5 the conventional Hilbert transform (HT method are analyzed and compared. The fundamental feature of the Hilbert-twin method is the efficient elimination of intrinsic asymmetrical oscillations of the envelope, aHT (t, obtained from the discrete Hilbert transform of analyzed signals. Excellent performance in estimation of the logarithmic decrement from the Hilbert-twin method is comparable to that of the OMI and YM for the low- and high-damping levels. The Hilbert-twin method proved to be robust and effective in computing the logarithmic decrement and the resonant frequency of exponentially damped free decaying signals embedded in experimental noise. The Hilbert-twin method is also appropriate to detect nonlinearities in mechanical loss measurements of metals and alloys.

Semi-supervised learning for ordinal Kernel Discriminant Analysis.

Science.gov (United States)

Pérez-Ortiz, M; Gutiérrez, P A; Carbonero-Ruz, M; Hervás-Martínez, C

2016-12-01

Ordinal classification considers those classification problems where the labels of the variable to predict follow a given order. Naturally, labelled data is scarce or difficult to obtain in this type of problems because, in many cases, ordinal labels are given by a user or expert (e.g. in recommendation systems). Firstly, this paper develops a new strategy for ordinal classification where both labelled and unlabelled data are used in the model construction step (a scheme which is referred to as semi-supervised learning). More specifically, the ordinal version of kernel discriminant learning is extended for this setting considering the neighbourhood information of unlabelled data, which is proposed to be computed in the feature space induced by the kernel function. Secondly, a new method for semi-supervised kernel learning is devised in the context of ordinal classification, which is combined with our developed classification strategy to optimise the kernel parameters. The experiments conducted compare 6 different approaches for semi-supervised learning in the context of ordinal classification in a battery of 30 datasets, showing (1) the good synergy of the ordinal version of discriminant analysis and the use of unlabelled data and (2) the advantage of computing distances in the feature space induced by the kernel function. Copyright © 2016 Elsevier Ltd. All rights reserved.

Fast metabolite identification with Input Output Kernel Regression

Science.gov (United States)

Brouard, Céline; Shen, Huibin; Dührkop, Kai; d'Alché-Buc, Florence; Böcker, Sebastian; Rousu, Juho

2016-01-01

Motivation: An important problematic of metabolomics is to identify metabolites using tandem mass spectrometry data. Machine learning methods have been proposed recently to solve this problem by predicting molecular fingerprint vectors and matching these fingerprints against existing molecular structure databases. In this work we propose to address the metabolite identification problem using a structured output prediction approach. This type of approach is not limited to vector output space and can handle structured output space such as the molecule space. Results: We use the Input Output Kernel Regression method to learn the mapping between tandem mass spectra and molecular structures. The principle of this method is to encode the similarities in the input (spectra) space and the similarities in the output (molecule) space using two kernel functions. This method approximates the spectra-molecule mapping in two phases. The first phase corresponds to a regression problem from the input space to the feature space associated to the output kernel. The second phase is a preimage problem, consisting in mapping back the predicted output feature vectors to the molecule space. We show that our approach achieves state-of-the-art accuracy in metabolite identification. Moreover, our method has the advantage of decreasing the running times for the training step and the test step by several orders of magnitude over the preceding methods. Availability and implementation: Contact: celine.brouard@aalto.fi Supplementary information: Supplementary data are available at Bioinformatics online. PMID:27307628

Linear and kernel methods for multi- and hypervariate change detection

DEFF Research Database (Denmark)

Nielsen, Allan Aasbjerg; Canty, Morton J.

2010-01-01

. Principal component analysis (PCA) as well as maximum autocorrelation factor (MAF) and minimum noise fraction (MNF) analyses of IR-MAD images, both linear and kernel-based (which are nonlinear), may further enhance change signals relative to no-change background. The kernel versions are based on a dual...... formulation, also termed Q-mode analysis, in which the data enter into the analysis via inner products in the Gram matrix only. In the kernel version the inner products of the original data are replaced by inner products between nonlinear mappings into higher dimensional feature space. Via kernel substitution......, also known as the kernel trick, these inner products between the mappings are in turn replaced by a kernel function and all quantities needed in the analysis are expressed in terms of the kernel function. This means that we need not know the nonlinear mappings explicitly. Kernel principal component...

Per-Sample Multiple Kernel Approach for Visual Concept Learning

Directory of Open Access Journals (Sweden)

Ling-Yu Duan

2010-01-01

Full Text Available Learning visual concepts from images is an important yet challenging problem in computer vision and multimedia research areas. Multiple kernel learning (MKL methods have shown great advantages in visual concept learning. As a visual concept often exhibits great appearance variance, a canonical MKL approach may not generate satisfactory results when a uniform kernel combination is applied over the input space. In this paper, we propose a per-sample multiple kernel learning (PS-MKL approach to take into account intraclass diversity for improving discrimination. PS-MKL determines sample-wise kernel weights according to kernel functions and training samples. Kernel weights as well as kernel-based classifiers are jointly learned. For efficient learning, PS-MKL employs a sample selection strategy. Extensive experiments are carried out over three benchmarking datasets of different characteristics including Caltech101, WikipediaMM, and Pascal VOC'07. PS-MKL has achieved encouraging performance, comparable to the state of the art, which has outperformed a canonical MKL.

Per-Sample Multiple Kernel Approach for Visual Concept Learning

Directory of Open Access Journals (Sweden)

Tian Yonghong

2010-01-01

Full Text Available Abstract Learning visual concepts from images is an important yet challenging problem in computer vision and multimedia research areas. Multiple kernel learning (MKL methods have shown great advantages in visual concept learning. As a visual concept often exhibits great appearance variance, a canonical MKL approach may not generate satisfactory results when a uniform kernel combination is applied over the input space. In this paper, we propose a per-sample multiple kernel learning (PS-MKL approach to take into account intraclass diversity for improving discrimination. PS-MKL determines sample-wise kernel weights according to kernel functions and training samples. Kernel weights as well as kernel-based classifiers are jointly learned. For efficient learning, PS-MKL employs a sample selection strategy. Extensive experiments are carried out over three benchmarking datasets of different characteristics including Caltech101, WikipediaMM, and Pascal VOC'07. PS-MKL has achieved encouraging performance, comparable to the state of the art, which has outperformed a canonical MKL.

Multivariate prediction, de Branges spaces, and related extension and inverse problems

CERN Document Server

Arov, Damir Z

2018-01-01

This monograph deals primarily with the prediction of vector valued stochastic processes that are either weakly stationary, or have weakly stationary increments, from finite segments of their past. The main focus is on the analytic counterpart of these problems, which amounts to computing projections onto subspaces of a Hilbert space of p x 1 vector valued functions with an inner product that is defined in terms of the p x p matrix valued spectral density of the process. The strategy is to identify these subspaces as vector valued de Branges spaces and then to express projections in terms of the reproducing kernels of these spaces and/or in terms of a generalized Fourier transform that is obtained from the solution of an associated inverse spectral problem. Subsequently, the projection of the past onto the future and the future onto the past is interpreted in terms of the range of appropriately defined Hankel operators and their adjoints, and, in the last chapter, assorted computations are carried out for rat...

Discriminative kernel feature extraction and learning for object recognition and detection

DEFF Research Database (Denmark)

Pan, Hong; Olsen, Søren Ingvor; Zhu, Yaping

2015-01-01

Feature extraction and learning is critical for object recognition and detection. By embedding context cue of image attributes into the kernel descriptors, we propose a set of novel kernel descriptors called context kernel descriptors (CKD). The motivation of CKD is to use the spatial consistency...... even in high-dimensional space. In addition, the latent connection between Rényi quadratic entropy and the mapping data in kernel feature space further facilitates us to capture the geometric structure as well as the information about the underlying labels of the CKD using CSQMI. Thus the resulting...... codebook and reduced CKD are discriminative. We report superior performance of our algorithm for object recognition on benchmark datasets like Caltech-101 and CIFAR-10, as well as for detection on a challenging chicken feet dataset....

Ensemble Approach to Building Mercer Kernels

Data.gov (United States)

National Aeronautics and Space Administration — This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive...

KINETIC-J: A computational kernel for solving the linearized Vlasov equation applied to calculations of the kinetic, configuration space plasma current for time harmonic wave electric fields

Science.gov (United States)

Green, David L.; Berry, Lee A.; Simpson, Adam B.; Younkin, Timothy R.

2018-04-01

We present the KINETIC-J code, a computational kernel for evaluating the linearized Vlasov equation with application to calculating the kinetic plasma response (current) to an applied time harmonic wave electric field. This code addresses the need for a configuration space evaluation of the plasma current to enable kinetic full-wave solvers for waves in hot plasmas to move beyond the limitations of the traditional Fourier spectral methods. We benchmark the kernel via comparison with the standard k →-space forms of the hot plasma conductivity tensor.

Improved specimen reconstruction by Hilbert phase contrast tomography.

Science.gov (United States)

Barton, Bastian; Joos, Friederike; Schröder, Rasmus R

2008-11-01

The low signal-to-noise ratio (SNR) in images of unstained specimens recorded with conventional defocus phase contrast makes it difficult to interpret 3D volumes obtained by electron tomography (ET). The high defocus applied for conventional tilt series generates some phase contrast but leads to an incomplete transfer of object information. For tomography of biological weak-phase objects, optimal image contrast and subsequently an optimized SNR are essential for the reconstruction of details such as macromolecular assemblies at molecular resolution. The problem of low contrast can be partially solved by applying a Hilbert phase plate positioned in the back focal plane (BFP) of the objective lens while recording images in Gaussian focus. Images recorded with the Hilbert phase plate provide optimized positive phase contrast at low spatial frequencies, and the contrast transfer in principle extends to the information limit of the microscope. The antisymmetric Hilbert phase contrast (HPC) can be numerically converted into isotropic contrast, which is equivalent to the contrast obtained by a Zernike phase plate. Thus, in-focus HPC provides optimal structure factor information without limiting effects of the transfer function. In this article, we present the first electron tomograms of biological specimens reconstructed from Hilbert phase plate image series. We outline the technical implementation of the phase plate and demonstrate that the technique is routinely applicable for tomography. A comparison between conventional defocus tomograms and in-focus HPC volumes shows an enhanced SNR and an improved specimen visibility for in-focus Hilbert tomography.

An Ensemble Approach to Building Mercer Kernels with Prior Information

Science.gov (United States)

Srivastava, Ashok N.; Schumann, Johann; Fischer, Bernd

2005-01-01

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly dimensional feature space. we describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using pre-defined kernels. These data adaptive kernels can encode prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. Specifically, we demonstrate the use of the algorithm in situations with extremely small samples of data. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS) and demonstrate the method's superior performance against standard methods. The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains templates for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic-algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code.

on differential operators on w 1,2 space and fredholm operators

African Journals Online (AJOL)

A selfadjoint differential operator defined over a closed and bounded interval on Sobolev space which is a dense linear subspace of a Hilbert space over the same interval is considered and shown to be a Fredholm operator with index zero. KEY WORDS: Sobolev space, Hilbert space, dense subspace, Fredholm operator

Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

Energy Technology Data Exchange (ETDEWEB)

Groh, Kai

2012-10-15

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement

Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

International Nuclear Information System (INIS)

Groh, Kai

2012-10-01

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of

Terahertz bandwidth all-optical Hilbert transformers based on long-period gratings.

Science.gov (United States)

Ashrafi, Reza; Azaña, José

2012-07-01

A novel, all-optical design for implementing terahertz (THz) bandwidth real-time Hilbert transformers is proposed and numerically demonstrated. An all-optical Hilbert transformer can be implemented using a uniform-period long-period grating (LPG) with a properly designed amplitude-only grating apodization profile, incorporating a single π-phase shift in the middle of the grating length. The designed LPG-based Hilbert transformers can be practically implemented using either fiber-optic or integrated-waveguide technologies. As a generalization, photonic fractional Hilbert transformers are also designed based on the same optical platform. In this general case, the resulting LPGs have multiple π-phase shifts along the grating length. Our numerical simulations confirm that all-optical Hilbert transformers capable of processing arbitrary optical signals with bandwidths well in the THz range can be implemented using feasible fiber/waveguide LPG designs.

Best approximation of the Dunkl Multiplier Operators Tk,ℓ,m

Directory of Open Access Journals (Sweden)

Fethi Soltani

2015-03-01

Full Text Available We study some class of Dunkl multiplier operators Tk,ℓ,m; and we give for them an application of the theory of reproducing kernels to the Tikhonov regularization,which gives the best approximation of the operators Tk,ℓ,m on a Hilbert spaces Hskℓ.

Hilbert-Schmidt expansion for the nucleon-deuteron scattering amplitude

International Nuclear Information System (INIS)

Moeller, K.; Narodetskii, I.M.

1983-01-01

The Hilbert-Schmidt method is used to sum the divergent iterative series for the partial amplitudes of nucleon-deuteron scattering in the energy region above the deuteron breakup threshold. It is observed that the Hilbert-Schmidt series for the partial amplitudes themselves diverges, which is due to the closeness of the logarithmic singularities. But if the first iterations in the series for multiple scattering are subtracted from the amplitude, the Hilbert-Schmidt series for the remainder converges rapidly. The final answer obtained in the present paper is in excellent agreement with the results obtained in exact calculations

Spatiotemporal characteristics of elderly population's traffic accidents in Seoul using space-time cube and space-time kernel density estimation.

Science.gov (United States)

Kang, Youngok; Cho, Nahye; Son, Serin

2018-01-01

The purpose of this study is to analyze how the spatiotemporal characteristics of traffic accidents involving the elderly population in Seoul are changing by time period. We applied kernel density estimation and hotspot analyses to analyze the spatial characteristics of elderly people's traffic accidents, and the space-time cube, emerging hotspot, and space-time kernel density estimation analyses to analyze the spatiotemporal characteristics. In addition, we analyzed elderly people's traffic accidents by dividing cases into those in which the drivers were elderly people and those in which elderly people were victims of traffic accidents, and used the traffic accidents data in Seoul for 2013 for analysis. The main findings were as follows: (1) the hotspots for elderly people's traffic accidents differed according to whether they were drivers or victims. (2) The hourly analysis showed that the hotspots for elderly drivers' traffic accidents are in specific areas north of the Han River during the period from morning to afternoon, whereas the hotspots for elderly victims are distributed over a wide area from daytime to evening. (3) Monthly analysis showed that the hotspots are weak during winter and summer, whereas they are strong in the hiking and climbing areas in Seoul during spring and fall. Further, elderly victims' hotspots are more sporadic than elderly drivers' hotspots. (4) The analysis for the entire period of 2013 indicates that traffic accidents involving elderly people are increasing in specific areas on the north side of the Han River. We expect the results of this study to aid in reducing the number of traffic accidents involving elderly people in the future.

Supervised Kernel Optimized Locality Preserving Projection with Its Application to Face Recognition and Palm Biometrics

Directory of Open Access Journals (Sweden)

Chuang Lin

2015-01-01

Full Text Available Kernel Locality Preserving Projection (KLPP algorithm can effectively preserve the neighborhood structure of the database using the kernel trick. We have known that supervised KLPP (SKLPP can preserve within-class geometric structures by using label information. However, the conventional SKLPP algorithm endures the kernel selection which has significant impact on the performances of SKLPP. In order to overcome this limitation, a method named supervised kernel optimized LPP (SKOLPP is proposed in this paper, which can maximize the class separability in kernel learning. The proposed method maps the data from the original space to a higher dimensional kernel space using a data-dependent kernel. The adaptive parameters of the data-dependent kernel are automatically calculated through optimizing an objective function. Consequently, the nonlinear features extracted by SKOLPP have larger discriminative ability compared with SKLPP and are more adaptive to the input data. Experimental results on ORL, Yale, AR, and Palmprint databases showed the effectiveness of the proposed method.

Universal Algorithm for Online Trading Based on the Method of Calibration

OpenAIRE

V'yugin, Vladimir; Trunov, Vladimir

2012-01-01

We present a universal algorithm for online trading in Stock Market which performs asymptotically at least as good as any stationary trading strategy that computes the investment at each step using a fixed function of the side information that belongs to a given RKHS (Reproducing Kernel Hilbert Space). Using a universal kernel, we extend this result for any continuous stationary strategy. In this learning process, a trader rationally chooses his gambles using predictions made by a randomized ...

Structured Kernel Dictionary Learning with Correlation Constraint for Object Recognition.

Science.gov (United States)

Wang, Zhengjue; Wang, Yinghua; Liu, Hongwei; Zhang, Hao

2017-06-21

In this paper, we propose a new discriminative non-linear dictionary learning approach, called correlation constrained structured kernel KSVD, for object recognition. The objective function for dictionary learning contains a reconstructive term and a discriminative term. In the reconstructive term, signals are implicitly non-linearly mapped into a space, where a structured kernel dictionary, each sub-dictionary of which lies in the span of the mapped signals from the corresponding class, is established. In the discriminative term, by analyzing the classification mechanism, the correlation constraint is proposed in kernel form, constraining the correlations between different discriminative codes, and restricting the coefficient vectors to be transformed into a feature space, where the features are highly correlated inner-class and nearly independent between-classes. The objective function is optimized by the proposed structured kernel KSVD. During the classification stage, the specific form of the discriminative feature is needless to be known, while the inner product of the discriminative feature with kernel matrix embedded is available, and is suitable for a linear SVM classifier. Experimental results demonstrate that the proposed approach outperforms many state-of-the-art dictionary learning approaches for face, scene and synthetic aperture radar (SAR) vehicle target recognition.

Diagonalization of a self-adjoint operator acting on a Hilbert module

Directory of Open Access Journals (Sweden)

Parfeny P. Saworotnow

1985-01-01

Full Text Available For each bounded self-adjoint operator T on a Hilbert module H over an H*-algebra A there exists a locally compact space m and a certain A-valued measure μ such that H is isomorphic to L2(μ⊗A and T corresponds to a multiplication with a continuous function. There is a similar result for a commuting family of normal operators. A consequence for this result is a representation theorem for generalized stationary processes.

Regularization methods in Banach spaces

CERN Document Server

Schuster, Thomas; Hofmann, Bernd; Kazimierski, Kamil S

2012-01-01

Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert spaces. However, for numerous problems the reasons for using a Hilbert space setting seem to be based rather on conventions than on an approprimate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, sparsity constraints using general Lp-norms or the B

A kernel-based multi-feature image representation for histopathology image classification

International Nuclear Information System (INIS)

Moreno J; Caicedo J Gonzalez F

2010-01-01

This paper presents a novel strategy for building a high-dimensional feature space to represent histopathology image contents. Histogram features, related to colors, textures and edges, are combined together in a unique image representation space using kernel functions. This feature space is further enhanced by the application of latent semantic analysis, to model hidden relationships among visual patterns. All that information is included in the new image representation space. Then, support vector machine classifiers are used to assign semantic labels to images. Processing and classification algorithms operate on top of kernel functions, so that; the structure of the feature space is completely controlled using similarity measures and a dual representation. The proposed approach has shown a successful performance in a classification task using a dataset with 1,502 real histopathology images in 18 different classes. The results show that our approach for histological image classification obtains an improved average performance of 20.6% when compared to a conventional classification approach based on SVM directly applied to the original kernel.

A KERNEL-BASED MULTI-FEATURE IMAGE REPRESENTATION FOR HISTOPATHOLOGY IMAGE CLASSIFICATION

Directory of Open Access Journals (Sweden)

J Carlos Moreno

2010-09-01

Full Text Available This paper presents a novel strategy for building a high-dimensional feature space to represent histopathology image contents. Histogram features, related to colors, textures and edges, are combined together in a unique image representation space using kernel functions. This feature space is further enhanced by the application of Latent Semantic Analysis, to model hidden relationships among visual patterns. All that information is included in the new image representation space. Then, Support Vector Machine classifiers are used to assign semantic labels to images. Processing and classification algorithms operate on top of kernel functions, so that, the structure of the feature space is completely controlled using similarity measures and a dual representation. The proposed approach has shown a successful performance in a classification task using a dataset with 1,502 real histopathology images in 18 different classes. The results show that our approach for histological image classification obtains an improved average performance of 20.6% when compared to a conventional classification approach based on SVM directly applied to the original kernel.

DuSK: A Dual Structure-preserving Kernel for Supervised Tensor Learning with Applications to Neuroimages.

Science.gov (United States)

He, Lifang; Kong, Xiangnan; Yu, Philip S; Ragin, Ann B; Hao, Zhifeng; Yang, Xiaowei

With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning community. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, however structural information within the tensors will be lost. In this paper, we introduce a new scheme to design structure-preserving kernels for supervised tensor learning. Specifically, we demonstrate how to leverage the naturally available structure within the tensorial representation to encode prior knowledge in the kernel. We proposed a tensor kernel that can preserve tensor structures based upon dual-tensorial mapping. The dual-tensorial mapping function can map each tensor instance in the input space to another tensor in the feature space while preserving the tensorial structure. Theoretically, our approach is an extension of the conventional kernels in the vector space to tensor space. We applied our novel kernel in conjunction with SVM to real-world tensor classification problems including brain fMRI classification for three different diseases ( i.e ., Alzheimer's disease, ADHD and brain damage by HIV). Extensive empirical studies demonstrate that our proposed approach can effectively boost tensor classification performances, particularly with small sample sizes.

An Extreme Learning Machine Based on the Mixed Kernel Function of Triangular Kernel and Generalized Hermite Dirichlet Kernel

Directory of Open Access Journals (Sweden)

Senyue Zhang

2016-01-01

Full Text Available According to the characteristics that the kernel function of extreme learning machine (ELM and its performance have a strong correlation, a novel extreme learning machine based on a generalized triangle Hermitian kernel function was proposed in this paper. First, the generalized triangle Hermitian kernel function was constructed by using the product of triangular kernel and generalized Hermite Dirichlet kernel, and the proposed kernel function was proved as a valid kernel function of extreme learning machine. Then, the learning methodology of the extreme learning machine based on the proposed kernel function was presented. The biggest advantage of the proposed kernel is its kernel parameter values only chosen in the natural numbers, which thus can greatly shorten the computational time of parameter optimization and retain more of its sample data structure information. Experiments were performed on a number of binary classification, multiclassification, and regression datasets from the UCI benchmark repository. The experiment results demonstrated that the robustness and generalization performance of the proposed method are outperformed compared to other extreme learning machines with different kernels. Furthermore, the learning speed of proposed method is faster than support vector machine (SVM methods.

A trace ratio maximization approach to multiple kernel-based dimensionality reduction.

Science.gov (United States)

Jiang, Wenhao; Chung, Fu-lai

2014-01-01

Most dimensionality reduction techniques are based on one metric or one kernel, hence it is necessary to select an appropriate kernel for kernel-based dimensionality reduction. Multiple kernel learning for dimensionality reduction (MKL-DR) has been recently proposed to learn a kernel from a set of base kernels which are seen as different descriptions of data. As MKL-DR does not involve regularization, it might be ill-posed under some conditions and consequently its applications are hindered. This paper proposes a multiple kernel learning framework for dimensionality reduction based on regularized trace ratio, termed as MKL-TR. Our method aims at learning a transformation into a space of lower dimension and a corresponding kernel from the given base kernels among which some may not be suitable for the given data. The solutions for the proposed framework can be found based on trace ratio maximization. The experimental results demonstrate its effectiveness in benchmark datasets, which include text, image and sound datasets, for supervised, unsupervised as well as semi-supervised settings. Copyright © 2013 Elsevier Ltd. All rights reserved.

Completion of the Kernel of the Differentiation Operator

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Anatoly N. Morozov

2017-01-01

Full Text Available When investigating piecewise polynomial approximations in spaces \\(L_p, \\; 0~<~p~<~1,\\ the author considered the spreading of k-th derivative (of the operator from Sobolev spaces \\(W_1 ^ k\\ on spaces that are, in a sense, their successors with a low index less than one. In this article, we continue the study of the properties acquired by the differentiation operator \\(\\Lambda\\ with spreading beyond the space \\(W_1^1\\ $$\\Lambda~:~W_1^1~\\mapsto~L_1,\\; \\Lambda f = f^{\\;'} $$.The study is conducted by introducing the family of spaces \\(Y_p^1, \\; 0

kernel.During the spreading of the differentiation operator from the space \\( C ^ 1 \\ on the space \\( W_p ^ 1 \\ the kernel does not change. In the article, it is constructively shown that jump functions and singular functions \\(f\\ belong to all spaces \\( Y_p ^ 1 \\ and \\(\\Lambda f = 0.\\ Consequently, the space of the functions of the bounded variation \\(H_1 ^ 1 \\ is contained in each \\( Y_p ^ 1 ,\\ and the differentiation operator on \\(H_1^1\\ satisfies the relation \\(\\Lambda f = f^{\\; '}.\\Also, we come to the conclusion that every function from the added part of the kernel can be logically named singular.

Spatiotemporal characteristics of elderly population’s traffic accidents in Seoul using space-time cube and space-time kernel density estimation

Science.gov (United States)

Cho, Nahye; Son, Serin

2018-01-01

The purpose of this study is to analyze how the spatiotemporal characteristics of traffic accidents involving the elderly population in Seoul are changing by time period. We applied kernel density estimation and hotspot analyses to analyze the spatial characteristics of elderly people’s traffic accidents, and the space-time cube, emerging hotspot, and space-time kernel density estimation analyses to analyze the spatiotemporal characteristics. In addition, we analyzed elderly people’s traffic accidents by dividing cases into those in which the drivers were elderly people and those in which elderly people were victims of traffic accidents, and used the traffic accidents data in Seoul for 2013 for analysis. The main findings were as follows: (1) the hotspots for elderly people’s traffic accidents differed according to whether they were drivers or victims. (2) The hourly analysis showed that the hotspots for elderly drivers’ traffic accidents are in specific areas north of the Han River during the period from morning to afternoon, whereas the hotspots for elderly victims are distributed over a wide area from daytime to evening. (3) Monthly analysis showed that the hotspots are weak during winter and summer, whereas they are strong in the hiking and climbing areas in Seoul during spring and fall. Further, elderly victims’ hotspots are more sporadic than elderly drivers’ hotspots. (4) The analysis for the entire period of 2013 indicates that traffic accidents involving elderly people are increasing in specific areas on the north side of the Han River. We expect the results of this study to aid in reducing the number of traffic accidents involving elderly people in the future. PMID:29768453

Phase difference estimation method based on data extension and Hilbert transform

International Nuclear Information System (INIS)

Shen, Yan-lin; Tu, Ya-qing; Chen, Lin-jun; Shen, Ting-ao

2015-01-01

To improve the precision and anti-interference performance of phase difference estimation for non-integer periods of sampling signals, a phase difference estimation method based on data extension and Hilbert transform is proposed. Estimated phase difference is obtained by means of data extension, Hilbert transform, cross-correlation, auto-correlation, and weighted phase average. Theoretical analysis shows that the proposed method suppresses the end effects of Hilbert transform effectively. The results of simulations and field experiments demonstrate that the proposed method improves the anti-interference performance of phase difference estimation and has better performance of phase difference estimation than the correlation, Hilbert transform, and data extension-based correlation methods, which contribute to improving the measurement precision of the Coriolis mass flowmeter. (paper)

Kernel Machine SNP-set Testing under Multiple Candidate Kernels

Science.gov (United States)

Wu, Michael C.; Maity, Arnab; Lee, Seunggeun; Simmons, Elizabeth M.; Harmon, Quaker E.; Lin, Xinyi; Engel, Stephanie M.; Molldrem, Jeffrey J.; Armistead, Paul M.

2013-01-01

Joint testing for the cumulative effect of multiple single nucleotide polymorphisms grouped on the basis of prior biological knowledge has become a popular and powerful strategy for the analysis of large scale genetic association studies. The kernel machine (KM) testing framework is a useful approach that has been proposed for testing associations between multiple genetic variants and many different types of complex traits by comparing pairwise similarity in phenotype between subjects to pairwise similarity in genotype, with similarity in genotype defined via a kernel function. An advantage of the KM framework is its flexibility: choosing different kernel functions allows for different assumptions concerning the underlying model and can allow for improved power. In practice, it is difficult to know which kernel to use a priori since this depends on the unknown underlying trait architecture and selecting the kernel which gives the lowest p-value can lead to inflated type I error. Therefore, we propose practical strategies for KM testing when multiple candidate kernels are present based on constructing composite kernels and based on efficient perturbation procedures. We demonstrate through simulations and real data applications that the procedures protect the type I error rate and can lead to substantially improved power over poor choices of kernels and only modest differences in power versus using the best candidate kernel. PMID:23471868

Hilbert's 'Foundations of Physics': Gravitation and electromagnetism within the axiomatic method

Science.gov (United States)

Brading, K. A.; Ryckman, T. A.

2008-01-01

In November and December 1915, Hilbert presented two communications to the Göttingen Academy of Sciences under the common title 'The Foundations of Physics'. Versions of each eventually appeared in the Nachrichten of the Academy. Hilbert's first communication has received significant reconsideration in recent years, following the discovery of printer's proofs of this paper, dated 6 December 1915. The focus has been primarily on the 'priority dispute' over the Einstein field equations. Our contention, in contrast, is that the discovery of the December proofs makes it possible to see the thematic linkage between the material that Hilbert cut from the published version of the first communication and the content of the second, as published in 1917. The latter has been largely either disregarded or misinterpreted, and our aim is to show that (a) Hilbert's two communications should be regarded as part of a wider research program within the overarching framework of 'the axiomatic method' (as Hilbert expressly stated was the case), and (b) the second communication is a fine and coherent piece of work within this framework, whose principal aim is to address an apparent tension between general invariance and causality (in the precise sense of Cauchy determination), pinpointed in Theorem I of the first communication. This is not the same problem as that found in Einstein's 'hole argument'-something that, we argue, never confused Hilbert.

Regularized Pre-image Estimation for Kernel PCA De-noising

DEFF Research Database (Denmark)

Abrahamsen, Trine Julie; Hansen, Lars Kai

2011-01-01

The main challenge in de-noising by kernel Principal Component Analysis (PCA) is the mapping of de-noised feature space points back into input space, also referred to as “the pre-image problem”. Since the feature space mapping is typically not bijective, pre-image estimation is inherently illposed...

DuSK: A Dual Structure-preserving Kernel for Supervised Tensor Learning with Applications to Neuroimages

Science.gov (United States)

He, Lifang; Kong, Xiangnan; Yu, Philip S.; Ragin, Ann B.; Hao, Zhifeng; Yang, Xiaowei

2015-01-01

With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning community. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, however structural information within the tensors will be lost. In this paper, we introduce a new scheme to design structure-preserving kernels for supervised tensor learning. Specifically, we demonstrate how to leverage the naturally available structure within the tensorial representation to encode prior knowledge in the kernel. We proposed a tensor kernel that can preserve tensor structures based upon dual-tensorial mapping. The dual-tensorial mapping function can map each tensor instance in the input space to another tensor in the feature space while preserving the tensorial structure. Theoretically, our approach is an extension of the conventional kernels in the vector space to tensor space. We applied our novel kernel in conjunction with SVM to real-world tensor classification problems including brain fMRI classification for three different diseases (i.e., Alzheimer's disease, ADHD and brain damage by HIV). Extensive empirical studies demonstrate that our proposed approach can effectively boost tensor classification performances, particularly with small sample sizes. PMID:25927014

Hilbert schemes of points and Heisenberg algebras

International Nuclear Information System (INIS)

Ellingsrud, G.; Goettsche, L.

2000-01-01

Let X [n] be the Hilbert scheme of n points on a smooth projective surface X over the complex numbers. In these lectures we describe the action of the Heisenberg algebra on the direct sum of the cohomologies of all the X [n] , which has been constructed by Nakajima. In the second half of the lectures we study the relation of the Heisenberg algebra action and the ring structures of the cohomologies of the X [n] , following recent work of Lehn. In particular we study the Chern and Segre classes of tautological vector bundles on the Hilbert schemes X [n] . (author)

Liquid identification by Hilbert spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Lyatti, M; Divin, Y; Poppe, U; Urban, K, E-mail: M.Lyatti@fz-juelich.d, E-mail: Y.Divin@fz-juelich.d [Forschungszentrum Juelich, 52425 Juelich (Germany)

2009-11-15

Fast and reliable identification of liquids is of great importance in, for example, security, biology and the beverage industry. An unambiguous identification of liquids can be made by electromagnetic measurements of their dielectric functions in the frequency range of their main dispersions, but this frequency range, from a few GHz to a few THz, is not covered by any conventional spectroscopy. We have developed a concept of liquid identification based on our new Hilbert spectroscopy and high- T{sub c} Josephson junctions, which can operate at the intermediate range from microwaves to THz frequencies. A demonstration setup has been developed consisting of a polychromatic radiation source and a compact Hilbert spectrometer integrated in a Stirling cryocooler. Reflection polychromatic spectra of various bottled liquids have been measured at the spectral range of 15-300 GHz with total scanning time down to 0.2 s and identification of liquids has been demonstrated.

Liquid identification by Hilbert spectroscopy

Science.gov (United States)

Lyatti, M.; Divin, Y.; Poppe, U.; Urban, K.

2009-11-01

Fast and reliable identification of liquids is of great importance in, for example, security, biology and the beverage industry. An unambiguous identification of liquids can be made by electromagnetic measurements of their dielectric functions in the frequency range of their main dispersions, but this frequency range, from a few GHz to a few THz, is not covered by any conventional spectroscopy. We have developed a concept of liquid identification based on our new Hilbert spectroscopy and high- Tc Josephson junctions, which can operate at the intermediate range from microwaves to THz frequencies. A demonstration setup has been developed consisting of a polychromatic radiation source and a compact Hilbert spectrometer integrated in a Stirling cryocooler. Reflection polychromatic spectra of various bottled liquids have been measured at the spectral range of 15-300 GHz with total scanning time down to 0.2 s and identification of liquids has been demonstrated.

Liquid identification by Hilbert spectroscopy

International Nuclear Information System (INIS)

Lyatti, M; Divin, Y; Poppe, U; Urban, K

2009-01-01

Fast and reliable identification of liquids is of great importance in, for example, security, biology and the beverage industry. An unambiguous identification of liquids can be made by electromagnetic measurements of their dielectric functions in the frequency range of their main dispersions, but this frequency range, from a few GHz to a few THz, is not covered by any conventional spectroscopy. We have developed a concept of liquid identification based on our new Hilbert spectroscopy and high- T c Josephson junctions, which can operate at the intermediate range from microwaves to THz frequencies. A demonstration setup has been developed consisting of a polychromatic radiation source and a compact Hilbert spectrometer integrated in a Stirling cryocooler. Reflection polychromatic spectra of various bottled liquids have been measured at the spectral range of 15-300 GHz with total scanning time down to 0.2 s and identification of liquids has been demonstrated.

Introducing etch kernels for efficient pattern sampling and etch bias prediction

Science.gov (United States)

Weisbuch, François; Lutich, Andrey; Schatz, Jirka

2018-01-01

Successful patterning requires good control of the photolithography and etch processes. While compact litho models, mainly based on rigorous physics, can predict very well the contours printed in photoresist, pure empirical etch models are less accurate and more unstable. Compact etch models are based on geometrical kernels to compute the litho-etch biases that measure the distance between litho and etch contours. The definition of the kernels, as well as the choice of calibration patterns, is critical to get a robust etch model. This work proposes to define a set of independent and anisotropic etch kernels-"internal, external, curvature, Gaussian, z_profile"-designed to represent the finest details of the resist geometry to characterize precisely the etch bias at any point along a resist contour. By evaluating the etch kernels on various structures, it is possible to map their etch signatures in a multidimensional space and analyze them to find an optimal sampling of structures. The etch kernels evaluated on these structures were combined with experimental etch bias derived from scanning electron microscope contours to train artificial neural networks to predict etch bias. The method applied to contact and line/space layers shows an improvement in etch model prediction accuracy over standard etch model. This work emphasizes the importance of the etch kernel definition to characterize and predict complex etch effects.

Application of Arbitrary-Order Hilbert Spectral Analysis to Passive Scalar Turbulence

International Nuclear Information System (INIS)

Huang, Y X; Lu, Z M; Liu, Y L; Schmitt, F G; Gagne, Y

2011-01-01

In previous work [Huang et al., PRE 82, 26319, 2010], we found that the passive scalar turbulence field maybe less intermittent than what we believed before. Here we apply the same method, namely arbitrary-order Hilbert spectral analysis, to a passive scalar (temperature) time series with a Taylor's microscale Reynolds number Re λ ≅ 3000. We find that with increasing Reynolds number, the discrepancy of scaling exponents between Hilbert ξ θ (q) and Kolmogorov-Obukhov-Corrsin (KOC) theory is increasing, and consequently the discrepancy between Hilbert and structure function could disappear at infinite Reynolds number.

Frames and outer frames for Hilbert C^*-modules

OpenAIRE

Arambašić, Ljiljana; Bakić, Damir

2015-01-01

The goal of the present paper is to extend the theory of frames for countably generated Hilbert $C^*$-modules over arbitrary $C^*$-algebras. In investigating the non-unital case we introduce the concept of outer frame as a sequence in the multiplier module $M(X)$ that has the standard frame property when applied to elements of the ambient module $X$. Given a Hilbert $\\A$-module $X$, we prove that there is a bijective correspondence of the set of all adjointable surjections from the generalize...

Explicit Hilbert-space representations of atomic and molecular photoabsorption spectra: Computational studies of Stieltjes-Tchebycheff functions

International Nuclear Information System (INIS)

Hermann, M.R.; Langhoff, P.W.

1983-01-01

Explicit Hilbert-space techniques are reported for construction of the discrete and continuum Schroedinger states required in atomic and molecular photoexcitation and/or photoionization studies. These developments extend and clarify previously described moment-theory methods for determinations of photoabsorption cross sections from discrete basis-set calculations to include explicit construction of underlying wave functions. The appropriate Stieltjes-Tchebycheff excitation and ionization functions of nth order are defined as Radau-type eigenstates of an appropriate operator in an n-term Cauchy-Lanczos basis. The energies of these states are the Radau quadrature points of the photoabsorption cross section, and their (reciprocal) norms provide the corresponding quadrature weights. Although finite-order Stieltjes-Tchebycheff functions are L 2 integrable, and do not have asymptotic spatial tails in the continuous spectrum, the Radau quadrature weights nevertheless provide information for normalization in the conventional Dirac delta-function sense. Since one Radau point can be placed anywhere in the spectrum, appropriately normalized convergent approximations to any of the discrete or continuum Schroedinger states are obtained from the development. Connections with matrix partitioning methods are established, demonstrating that nth-order Stieltjes-Tchebycheff functions are optical-potential solutions of the matrix Schroedinger equation in the full Cauchy-Lanczos basis

Hilbert-Schmidt method for nucleon-deuteron scattering

International Nuclear Information System (INIS)

Moeller, K.; Narodetskij, I.M.

1983-01-01

The Hilbert-Schmidt technique is used for computing the divergent multiple-scattering series for scattering of nucleons by deuterons at energies above the deuteron breakup. It is found that for each partial amplitude a series of s-channel resonances diverges because of the logarithmic singularities which reflect the t-channel singularities of the total amplitude. However, the convergence of the Hilbert-Schmidt series may be improved by iterating the Faddeev equations thereby extracting the most strong logarithmic singularities. It is shown that the series for the amplitudes with first two iterations subtracted converges rapidly. Final results are in excellent agreement with exact results obtained by a direct matrix technique

A Walk-based Semantically Enriched Tree Kernel Over Distributed Word Representations

DEFF Research Database (Denmark)

Srivastava, Shashank; Hovy, Dirk

2013-01-01

We propose a walk-based graph kernel that generalizes the notion of tree-kernels to continuous spaces. Our proposed approach subsumes a general framework for word-similarity, and in particular, provides a flexible way to incorporate distributed representations. Using vector representations......, such an approach captures both distributional semantic similarities among words as well as the structural relations between them (encoded as the structure of the parse tree). We show an efficient formulation to compute this kernel using simple matrix multiplication operations. We present our results on three...

Independence and totalness of subspaces in phase space methods

Science.gov (United States)

Vourdas, A.

2018-04-01

The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the non-distributivity of the lattice of subspaces, there are various levels of independence, from pairwise independence up to (full) independence. Pairwise totalness, totalness and other intermediate concepts are also introduced, which roughly express that the subspaces overlap strongly among themselves, and they cover the full Hilbert space. A duality between independence and totalness, that involves orthocomplementation (logical NOT operation), is discussed. Another approach to independence is also studied, using Rota's formalism on independent partitions of the Hilbert space. This is used to define informational independence, which is proved to be equivalent to independence. As an application, the pentagram (used in discussions on contextuality) is analysed using these concepts.

Analog forecasting with dynamics-adapted kernels

Science.gov (United States)

Zhao, Zhizhen; Giannakis, Dimitrios

2016-09-01

Analog forecasting is a nonparametric technique introduced by Lorenz in 1969 which predicts the evolution of states of a dynamical system (or observables defined on the states) by following the evolution of the sample in a historical record of observations which most closely resembles the current initial data. Here, we introduce a suite of forecasting methods which improve traditional analog forecasting by combining ideas from kernel methods developed in harmonic analysis and machine learning and state-space reconstruction for dynamical systems. A key ingredient of our approach is to replace single-analog forecasting with weighted ensembles of analogs constructed using local similarity kernels. The kernels used here employ a number of dynamics-dependent features designed to improve forecast skill, including Takens’ delay-coordinate maps (to recover information in the initial data lost through partial observations) and a directional dependence on the dynamical vector field generating the data. Mathematically, our approach is closely related to kernel methods for out-of-sample extension of functions, and we discuss alternative strategies based on the Nyström method and the multiscale Laplacian pyramids technique. We illustrate these techniques in applications to forecasting in a low-order deterministic model for atmospheric dynamics with chaotic metastability, and interannual-scale forecasting in the North Pacific sector of a comprehensive climate model. We find that forecasts based on kernel-weighted ensembles have significantly higher skill than the conventional approach following a single analog.

Topological freeness for Hilbert bimodules

DEFF Research Database (Denmark)

Kwasniewski, Bartosz

2014-01-01

It is shown that topological freeness of Rieffel’s induced representation functor implies that any C*-algebra generated by a faithful covariant representation of a Hilbert bimodule X over a C*-algebra A is canonically isomorphic to the crossed product A ⋊ X ℤ. An ideal lattice description...

Hilbert transform and optical tomography for anisotropic edge enhancement of phase objects

International Nuclear Information System (INIS)

Montes-Perez, Areli; Meneses-Fabian, Cruz; Rodriguez-Zurita, Gustavo

2011-01-01

In phase object tomography a slice reconstruction is related to distribution of refractive index. Typically, this is obtained by applying the filtered back-projection algorithm to the set of projections (sinogram) obtained experimentally, which are sequentially obtained by calculating the phase of the wave emerging from the slice of the object at different angles. In this paper, based on optical implementation of the Hilbert-transform in a 4f Fourier operator, the Hilbert transform of the projections leaving of the object are obtained numerically. When these projection data are captured for a set of viewing angles an unconventional sinogram is eventually obtained, we have called it as an Hilbert-sinogram. The reconstruction obtained by applying the filtered back-projection algorithm is proportional to the Hilbert transform of the distribution of refractive index of the slice and the obtained image shows a typical isotropic edge enhancement. In this manuscript, the theoretical analysis and the numerical implementation of the Hilbert-transform, mathematical model of the edge enhancement reconstructed are extensively detailed.

Online learning control using adaptive critic designs with sparse kernel machines.

Science.gov (United States)

Xu, Xin; Hou, Zhongsheng; Lian, Chuanqiang; He, Haibo

2013-05-01

In the past decade, adaptive critic designs (ACDs), including heuristic dynamic programming (HDP), dual heuristic programming (DHP), and their action-dependent ones, have been widely studied to realize online learning control of dynamical systems. However, because neural networks with manually designed features are commonly used to deal with continuous state and action spaces, the generalization capability and learning efficiency of previous ACDs still need to be improved. In this paper, a novel framework of ACDs with sparse kernel machines is presented by integrating kernel methods into the critic of ACDs. To improve the generalization capability as well as the computational efficiency of kernel machines, a sparsification method based on the approximately linear dependence analysis is used. Using the sparse kernel machines, two kernel-based ACD algorithms, that is, kernel HDP (KHDP) and kernel DHP (KDHP), are proposed and their performance is analyzed both theoretically and empirically. Because of the representation learning and generalization capability of sparse kernel machines, KHDP and KDHP can obtain much better performance than previous HDP and DHP with manually designed neural networks. Simulation and experimental results of two nonlinear control problems, that is, a continuous-action inverted pendulum problem and a ball and plate control problem, demonstrate the effectiveness of the proposed kernel ACD methods.

A relative Hilbert-Mumford criterion

DEFF Research Database (Denmark)

Gulbrandsen, Martin G.; Halle, Lars Halvard; Hulek, Klaus

2015-01-01

We generalize the classical Hilbert-Mumford criteria for GIT (semi-)stability in terms of one parameter subgroups of a linearly reductive group G over a field k, to the relative situation of an equivariant, projective morphism X -> Spec A to a noetherian k-algebra A. We also extend the classical...

Numerical solution of Boltzmann's equation

International Nuclear Information System (INIS)

Sod, G.A.

1976-04-01

The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig

Data-variant kernel analysis

CERN Document Server

Motai, Yuichi

2015-01-01

Describes and discusses the variants of kernel analysis methods for data types that have been intensely studied in recent years This book covers kernel analysis topics ranging from the fundamental theory of kernel functions to its applications. The book surveys the current status, popular trends, and developments in kernel analysis studies. The author discusses multiple kernel learning algorithms and how to choose the appropriate kernels during the learning phase. Data-Variant Kernel Analysis is a new pattern analysis framework for different types of data configurations. The chapters include

A Novel Approach to Calculation of Reproducing Kernel on Infinite Interval and Applications to Boundary Value Problems

Directory of Open Access Journals (Sweden)

Jing Niu

2013-01-01

reproducing kernel on infinite interval is obtained concisely in polynomial form for the first time. Furthermore, as a particular effective application of this method, we give an explicit representation formula for calculation of reproducing kernel in reproducing kernel space with boundary value conditions.

Wavelet Based Hilbert Transform with Digital Design and Application to QCM-SS Watermarking

Directory of Open Access Journals (Sweden)

S. P. Maity

2008-04-01

Full Text Available In recent time, wavelet transforms are used extensively for efficient storage, transmission and representation of multimedia signals. Hilbert transform pairs of wavelets is the basic unit of many wavelet theories such as complex filter banks, complex wavelet and phaselet etc. Moreover, Hilbert transform finds various applications in communications and signal processing such as generation of single sideband (SSB modulation, quadrature carrier multiplexing (QCM and bandpass representation of a signal. Thus wavelet based discrete Hilbert transform design draws much attention of researchers for couple of years. This paper proposes an (i algorithm for generation of low computation cost Hilbert transform pairs of symmetric filter coefficients using biorthogonal wavelets, (ii approximation to its rational coefficients form for its efficient hardware realization and without much loss in signal representation, and finally (iii development of QCM-SS (spread spectrum image watermarking scheme for doubling the payload capacity. Simulation results show novelty of the proposed Hilbert transform design and its application to watermarking compared to existing algorithms.

Notes on Hilbert and Cauchy Matrices

Czech Academy of Sciences Publication Activity Database

Fiedler, Miroslav

2010-01-01

Roč. 432, č. 1 (2010), s. 351-356 ISSN 0024-3795 Institutional research plan: CEZ:AV0Z10300504 Keywords : Hilbert matrix * Cauchy matrix * combined matrix * AT-property Subject RIV: BA - General Mathematics Impact factor: 1.005, year: 2010

Hörmander spaces, interpolation, and elliptic problems

CERN Document Server

Mikhailets, Vladimir A; Malyshev, Peter V

2014-01-01

The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hörmander function spaces. This theory was constructed by the authors in a number of papers published in 2005-2009. It is distinguished by a systematic use of the method of interpolation with a functional parameter of abstract Hilbert spaces and Sobolev inner product spaces. This method, the theory and their applications are expounded for the first time in the monographic literature. The monograph is written in detail and in a

N-body quantum scattering theory in two Hilbert spaces. VII. Real-energy limits

International Nuclear Information System (INIS)

Chandler, C.; Gibson, A.G.

1994-01-01

A study is made of the real-energy limits of approximate solutions of the Chandler--Gibson equations, as well as the real-energy limits of the approximate equations themselves. It is proved that (1) the approximate time-independent transition operator T π (z) and an auxiliary operator M π (z), when restricted to finite energy intervals, are trace class operators and have limits in trace norm for almost all values of the real energy; (2) the basic dynamical equation that determines the operator M π (z), when restricted to the space of trace class operators, has a real-energy limit in trace norm for almost all values of the real energy; (3) the real-energy limit of M π (z) is a solution of the real-energy limit equation; (4) the diagonal (on-shell) elements of the kernels of the real-energy limit of T π (z) and of all solutions of the real-energy limit equation exactly equal the on-shell transition operator, implying that the real-energy limit equation uniquely determines the physical transition amplitude; and (5) a sequence of approximate on-shell transition operators converges strongly to the exact on-shell transition operator. These mathematically rigorous results are believed to be the most general of their type for nonrelativistic N-body quantum scattering theories

Nonparametric evaluation of dynamic disease risk: a spatio-temporal kernel approach.

Directory of Open Access Journals (Sweden)

Zhijie Zhang

Full Text Available Quantifying the distributions of disease risk in space and time jointly is a key element for understanding spatio-temporal phenomena while also having the potential to enhance our understanding of epidemiologic trajectories. However, most studies to date have neglected time dimension and focus instead on the "average" spatial pattern of disease risk, thereby masking time trajectories of disease risk. In this study we propose a new idea titled "spatio-temporal kernel density estimation (stKDE" that employs hybrid kernel (i.e., weight functions to evaluate the spatio-temporal disease risks. This approach not only can make full use of sample data but also "borrows" information in a particular manner from neighboring points both in space and time via appropriate choice of kernel functions. Monte Carlo simulations show that the proposed method performs substantially better than the traditional (i.e., frequency-based kernel density estimation (trKDE which has been used in applied settings while two illustrative examples demonstrate that the proposed approach can yield superior results compared to the popular trKDE approach. In addition, there exist various possibilities for improving and extending this method.

Object classfication from RGB-D images using depth context kernel descriptors

DEFF Research Database (Denmark)

Pan, Hong; Olsen, Søren Ingvor; Zhu, Yaping

2015-01-01

Context cue is important in object classification. By embedding the depth context cue of image attributes into kernel descriptors, we propose a new set of depth image descriptors called depth context kernel descriptors (DCKD) for RGB-D based object classification. The motivation of DCKD is to use...... the depth consistency of image attributes defined within a neighboring region to improve the robustness of descriptor matching in the kernel space. Moreover, a novel joint spatial-depth pooling (JSDP) scheme, which further partitions image sub-regions using the depth cue and pools features in both 2D image...

A framework for multiple kernel support vector regression and its applications to siRNA efficacy prediction.

Science.gov (United States)

Qiu, Shibin; Lane, Terran

2009-01-01

The cell defense mechanism of RNA interference has applications in gene function analysis and promising potentials in human disease therapy. To effectively silence a target gene, it is desirable to select appropriate initiator siRNA molecules having satisfactory silencing capabilities. Computational prediction for silencing efficacy of siRNAs can assist this screening process before using them in biological experiments. String kernel functions, which operate directly on the string objects representing siRNAs and target mRNAs, have been applied to support vector regression for the prediction and improved accuracy over numerical kernels in multidimensional vector spaces constructed from descriptors of siRNA design rules. To fully utilize information provided by string and numerical data, we propose to unify the two in a kernel feature space by devising a multiple kernel regression framework where a linear combination of the kernels is used. We formulate the multiple kernel learning into a quadratically constrained quadratic programming (QCQP) problem, which although yields global optimal solution, is computationally demanding and requires a commercial solver package. We further propose three heuristics based on the principle of kernel-target alignment and predictive accuracy. Empirical results demonstrate that multiple kernel regression can improve accuracy, decrease model complexity by reducing the number of support vectors, and speed up computational performance dramatically. In addition, multiple kernel regression evaluates the importance of constituent kernels, which for the siRNA efficacy prediction problem, compares the relative significance of the design rules. Finally, we give insights into the multiple kernel regression mechanism and point out possible extensions.

Approximate kernel competitive learning.

Science.gov (United States)

Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang

2015-03-01

Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.

Differentiable absorption of Hilbert C*-modules, connections and lifts of unbounded operators

DEFF Research Database (Denmark)

Kaad, Jens

2017-01-01

. The differentiable absorption theorem is then applied to construct densely defined connections (or correpondences) on Hilbert C∗C∗-modules. These connections can in turn be used to define selfadjoint and regular "lifts" of unbounded operators which act on an auxiliary Hilbert C∗C∗-module....

The Hilbert-Schmidt method for nucleon-deuteron scattering

International Nuclear Information System (INIS)

Moeller, K.; Narodetskii, I.M.

1984-01-01

The Hilbert-Schmidt technique is used for computing the divergent multiple-scattering series for scattering of nucleons by deuterons at energies above the deuteron breakup. We have found that for each partial amplitude a series of s-channel resonances diverges because of the logarithmic singularities which reflect the t-channel singularities of the total amplitude. However, the convergence of the Hilbert-Schmidt series may be improved by iterating the Faddeev equations thereby extracting the most strong logarithmic singularities. We show that the series for the amplitudes with the first two iteration subtracted converges rapidly. Our final results are in excellent agreement with exact results obtained by a direct matrix technique. (orig.)

Classification With Truncated Distance Kernel.

Science.gov (United States)

Huang, Xiaolin; Suykens, Johan A K; Wang, Shuning; Hornegger, Joachim; Maier, Andreas

2018-05-01

This brief proposes a truncated distance (TL1) kernel, which results in a classifier that is nonlinear in the global region but is linear in each subregion. With this kernel, the subregion structure can be trained using all the training data and local linear classifiers can be established simultaneously. The TL1 kernel has good adaptiveness to nonlinearity and is suitable for problems which require different nonlinearities in different areas. Though the TL1 kernel is not positive semidefinite, some classical kernel learning methods are still applicable which means that the TL1 kernel can be directly used in standard toolboxes by replacing the kernel evaluation. In numerical experiments, the TL1 kernel with a pregiven parameter achieves similar or better performance than the radial basis function kernel with the parameter tuned by cross validation, implying the TL1 kernel a promising nonlinear kernel for classification tasks.

Measurement of vibration mode shape by using Hilbert transform

International Nuclear Information System (INIS)

Kang, Min Sig

2001-01-01

This paper concerns on modal analysis of mechanical structures by using a continuous scanning laser Doppler vibrometer. In modal analysis the Hilbert transform based approach is superior to the Fourier transform based approach because of its fine accuracy and its flexible experimental settings. In this paper the Hilbert transform based approach is extended to measure area mode shape data of a structure by simply modifying the scanning pattern ranging the entire surface of the structure. The effectiveness of this proposed method is illustrated along with results of numerical simulation for a rectangular plate

New Fukui, dual and hyper-dual kernels as bond reactivity descriptors.

Science.gov (United States)

Franco-Pérez, Marco; Polanco-Ramírez, Carlos-A; Ayers, Paul W; Gázquez, José L; Vela, Alberto

2017-06-21

We define three new linear response indices with promising applications for bond reactivity using the mathematical framework of τ-CRT (finite temperature chemical reactivity theory). The τ-Fukui kernel is defined as the ratio between the fluctuations of the average electron density at two different points in the space and the fluctuations in the average electron number and is designed to integrate to the finite-temperature definition of the electronic Fukui function. When this kernel is condensed, it can be interpreted as a site-reactivity descriptor of the boundary region between two atoms. The τ-dual kernel corresponds to the first order response of the Fukui kernel and is designed to integrate to the finite temperature definition of the dual descriptor; it indicates the ambiphilic reactivity of a specific bond and enriches the traditional dual descriptor by allowing one to distinguish between the electron-accepting and electron-donating processes. Finally, the τ-hyper dual kernel is defined as the second-order derivative of the Fukui kernel and is proposed as a measure of the strength of ambiphilic bonding interactions. Although these quantities have never been proposed, our results for the τ-Fukui kernel and for τ-dual kernel can be derived in zero-temperature formulation of the chemical reactivity theory with, among other things, the widely-used parabolic interpolation model.

Multiple Kernel Learning for adaptive graph regularized nonnegative matrix factorization

KAUST Repository

Wang, Jim Jing-Yan; AbdulJabbar, Mustafa Abdulmajeed

2012-01-01

Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define parts-based, and linear representation of non-negative data. Recently, Graph regularized NMF (GrNMF) is proposed to find a compact representation, which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In GNMF, an affinity graph is constructed from the original data space to encode the geometrical information. In this paper, we propose a novel idea which engages a Multiple Kernel Learning approach into refining the graph structure that reflects the factorization of the matrix and the new data space. The GrNMF is improved by utilizing the graph refined by the kernel learning, and then a novel kernel learning method is introduced under the GrNMF framework. Our approach shows encouraging results of the proposed algorithm in comparison to the state-of-the-art clustering algorithms like NMF, GrNMF, SVD etc.

Kernel Bayesian ART and ARTMAP.

Science.gov (United States)

Masuyama, Naoki; Loo, Chu Kiong; Dawood, Farhan

2018-02-01

Adaptive Resonance Theory (ART) is one of the successful approaches to resolving "the plasticity-stability dilemma" in neural networks, and its supervised learning model called ARTMAP is a powerful tool for classification. Among several improvements, such as Fuzzy or Gaussian based models, the state of art model is Bayesian based one, while solving the drawbacks of others. However, it is known that the Bayesian approach for the high dimensional and a large number of data requires high computational cost, and the covariance matrix in likelihood becomes unstable. This paper introduces Kernel Bayesian ART (KBA) and ARTMAP (KBAM) by integrating Kernel Bayes' Rule (KBR) and Correntropy Induced Metric (CIM) to Bayesian ART (BA) and ARTMAP (BAM), respectively, while maintaining the properties of BA and BAM. The kernel frameworks in KBA and KBAM are able to avoid the curse of dimensionality. In addition, the covariance-free Bayesian computation by KBR provides the efficient and stable computational capability to KBA and KBAM. Furthermore, Correntropy-based similarity measurement allows improving the noise reduction ability even in the high dimensional space. The simulation experiments show that KBA performs an outstanding self-organizing capability than BA, and KBAM provides the superior classification ability than BAM, respectively. Copyright © 2017 Elsevier Ltd. All rights reserved.

Stochastic Moyal product on the Wiener space

International Nuclear Information System (INIS)

Dito, Giuseppe; Leandre, Remi

2007-01-01

We propose a stochastic extension of deformation quantization on a Hilbert space. The Moyal product is defined in this context on the space of functionals belonging to all of the Sobolev spaces of the Malliavin calculus

PKI, Gamma Radiation Reactor Shielding Calculation by Point-Kernel Method

International Nuclear Information System (INIS)

Li Chunhuai; Zhang Liwu; Zhang Yuqin; Zhang Chuanxu; Niu Xihua

1990-01-01

1 - Description of program or function: This code calculates radiation shielding problem of gamma-ray in geometric space. 2 - Method of solution: PKI uses a point kernel integration technique, describes radiation shielding geometric space by using geometric space configuration method and coordinate conversion, and makes use of calculation result of reactor primary shielding and flow regularity in loop system for coolant

Quantum Hilbert matrices and orthogonal polynomials

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Berg, Christian

2009-01-01

Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|<1 , and for the special value they are closely related to Hankel matrice...

Noise properties of Hilbert transform evaluation

Czech Academy of Sciences Publication Activity Database

Pavlíček, Pavel; Svak, V.

2015-01-01

Roč. 26, č. 8 (2015), s. 085207 ISSN 0957-0233 R&D Projects: GA ČR GA13-12301S Institutional support: RVO:68378271 Keywords : Hilbert transform * noise * measurement uncertainty * white -light interferometry * fringe-pattern analysis Subject RIV: BH - Optics, Masers, Lasers Impact factor: 1.492, year: 2015

Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

Directory of Open Access Journals (Sweden)

Akbulut Ali

2016-01-01

Full Text Available In this paper, we study the boundedness of fractional multilinear integral operators with rough kernels TΩ,αA1,A2,…,Ak,$T_{\\Omega ,\\alpha }^{{A_1},{A_2}, \\ldots ,{A_k}},$ which is a generalization of the higher-order commutator of the rough fractional integral on the generalized weighted Morrey spaces Mp,ϕ (w. We find the sufficient conditions on the pair (ϕ1, ϕ2 with w ∈ Ap,q which ensures the boundedness of the operators TΩ,αA1,A2,…,Ak,$T_{\\Omega ,\\alpha }^{{A_1},{A_2}, \\ldots ,{A_k}},$ from Mp,φ1wptoMp,φ2wq${M_{p,{\\varphi _1}}}\\left( {{w^p}} \\right\\,{\\rm{to}}\\,{M_{p,{\\varphi _2}}}\\left( {{w^q}} \\right$ for 1 < p < q < ∞. In all cases the conditions for the boundedness of the operator TΩ,αA1,A2,…,Ak,$T_{\\Omega ,\\alpha }^{{A_1},{A_2}, \\ldots ,{A_k}},$ are given in terms of Zygmund-type integral inequalities on (ϕ1, ϕ2 and w, which do not assume any assumption on monotonicity of ϕ1 (x,r, ϕ2(x, r in r.

Terahertz bandwidth photonic Hilbert transformers based on synthesized planar Bragg grating fabrication.

Science.gov (United States)

Sima, Chaotan; Gates, J C; Holmes, C; Mennea, P L; Zervas, M N; Smith, P G R

2013-09-01

Terahertz bandwidth photonic Hilbert transformers are proposed and experimentally demonstrated. The integrated device is fabricated via a direct UV grating writing technique in a silica-on-silicon platform. The photonic Hilbert transformer operates at bandwidths of up to 2 THz (~16 nm) in the telecom band, a 10-fold greater bandwidth than any previously reported experimental approaches. Achieving this performance requires detailed knowledge of the system transfer function of the direct UV grating writing technique; this allows improved linearity and yields terahertz bandwidth Bragg gratings with improved spectral quality. By incorporating a flat-top reflector and Hilbert grating with a waveguide coupler, an ultrawideband all-optical single-sideband filter is demonstrated.

Subsampling Realised Kernels

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Hansen, Peter Reinhard; Lunde, Asger

2011-01-01

In a recent paper we have introduced the class of realised kernel estimators of the increments of quadratic variation in the presence of noise. We showed that this estimator is consistent and derived its limit distribution under various assumptions on the kernel weights. In this paper we extend our...... that subsampling is impotent, in the sense that subsampling has no effect on the asymptotic distribution. Perhaps surprisingly, for the efficient smooth kernels, such as the Parzen kernel, we show that subsampling is harmful as it increases the asymptotic variance. We also study the performance of subsampled...

Metabolite identification through multiple kernel learning on fragmentation trees.

Science.gov (United States)

Shen, Huibin; Dührkop, Kai; Böcker, Sebastian; Rousu, Juho

2014-06-15

Metabolite identification from tandem mass spectrometric data is a key task in metabolomics. Various computational methods have been proposed for the identification of metabolites from tandem mass spectra. Fragmentation tree methods explore the space of possible ways in which the metabolite can fragment, and base the metabolite identification on scoring of these fragmentation trees. Machine learning methods have been used to map mass spectra to molecular fingerprints; predicted fingerprints, in turn, can be used to score candidate molecular structures. Here, we combine fragmentation tree computations with kernel-based machine learning to predict molecular fingerprints and identify molecular structures. We introduce a family of kernels capturing the similarity of fragmentation trees, and combine these kernels using recently proposed multiple kernel learning approaches. Experiments on two large reference datasets show that the new methods significantly improve molecular fingerprint prediction accuracy. These improvements result in better metabolite identification, doubling the number of metabolites ranked at the top position of the candidates list. © The Author 2014. Published by Oxford University Press.

Magnetomyographic recording and identification of uterine contractions using Hilbert-wavelet transforms

International Nuclear Information System (INIS)

Furdea, A; Wilson, J D; Eswaran, H; Lowery, C L; Govindan, R B; Preissl, H

2009-01-01

We propose a multi-stage approach using Wavelet and Hilbert transforms to identify uterine contraction bursts in magnetomyogram (MMG) signals measured using a 151 magnetic sensor array. In the first stage, we decompose the MMG signals by wavelet analysis into multilevel approximate and detail coefficients. In each level, the signals are reconstructed using the detail coefficients followed by the computation of the Hilbert transform. The Hilbert amplitude of the reconstructed signals from different frequency bands (0.1–1 Hz) is summed up over all the sensors to increase the signal-to-noise ratio. Using a novel clustering technique, affinity propagation, the contractile bursts are distinguished from the noise level. The method is applied on simulated MMG data, using a simple stochastic model to determine its robustness and to seven MMG datasets

Functional equations in matrix normed spaces

Indian Academy of Sciences (India)

The abstract characterization given for linear spaces of bounded Hilbert space operators in terms of ... effect on operator algebra theory (see [12]). .... of functional equations for the proof of new fixed point theorems with applications. By.

Kernel abortion in maize. II. Distribution of 14C among kernel carboydrates

International Nuclear Information System (INIS)

Hanft, J.M.; Jones, R.J.

1986-01-01

This study was designed to compare the uptake and distribution of 14 C among fructose, glucose, sucrose, and starch in the cob, pedicel, and endosperm tissues of maize (Zea mays L.) kernels induced to abort by high temperature with those that develop normally. Kernels cultured in vitro at 309 and 35 0 C were transferred to [ 14 C]sucrose media 10 days after pollination. Kernels cultured at 35 0 C aborted prior to the onset of linear dry matter accumulation. Significant uptake into the cob, pedicel, and endosperm of radioactivity associated with the soluble and starch fractions of the tissues was detected after 24 hours in culture on atlageled media. After 8 days in culture on [ 14 C]sucrose media, 48 and 40% of the radioactivity associated with the cob carbohydrates was found in the reducing sugars at 30 and 35 0 C, respectively. Of the total carbohydrates, a higher percentage of label was associated with sucrose and lower percentage with fructose and glucose in pedicel tissue of kernels cultured at 35 0 C compared to kernels cultured at 30 0 C. These results indicate that sucrose was not cleaved to fructose and glucose as rapidly during the unloading process in the pedicel of kernels induced to abort by high temperature. Kernels cultured at 35 0 C had a much lower proportion of label associated with endosperm starch (29%) than did kernels cultured at 30 0 C (89%). Kernels cultured at 35 0 C had a correspondingly higher proportion of 14 C in endosperm fructose, glucose, and sucrose

Supersymmetric gauge theories, quantization of Mflat, and conformal field theory

International Nuclear Information System (INIS)

Teschner, J.; Vartanov, G.S.

2013-02-01

We propose a derivation of the correspondence between certain gauge theories with N=2 supersymmetry and conformal field theory discovered by Alday, Gaiotto and Tachikawa in the spirit of Seiberg-Witten theory. Based on certain results from the literature we argue that the quantum theory of the moduli spaces of flat SL(2,R)-connections represents a nonperturbative ''skeleton'' of the gauge theory, protected by supersymmetry. It follows that instanton partition functions can be characterized as solutions to a Riemann-Hilbert type problem. In order to solve it, we describe the quantization of the moduli spaces of flat connections explicitly in terms of two natural sets of Darboux coordinates. The kernel describing the relation between the two pictures represents the solution to the Riemann Hilbert problem, and is naturally identified with the Liouville conformal blocks.

Critical Assessment Of The Issues In The Application Of Hilbert Transform To Compute The Logarithmic Decrement

Directory of Open Access Journals (Sweden)

Majewski M.

2015-06-01

Full Text Available The parametric OMI (Optimization in Multiple Intervals, the Yoshida-Magalas (YM and a novel Hilbert-twin (H-twin methods are advocated for computing the logarithmic decrement in the field of internal friction and mechanical spectroscopy of solids. It is shown that dispersion in experimental points results mainly from the selection of the computing methods, the number of oscillations, and noise. It is demonstrated that conventional Hilbert transform method suffers from high dispersion in internal friction values. It is unequivocally demonstrated that the Hilbert-twin method, which yields a ‘true envelope’ for exponentially damped harmonic oscillations is superior to conventional Hilbert transform method. The ‘true envelope’ of free decaying strain signals calculated from the Hilbert-twin method yields excellent estimation of the logarithmic decrement in metals, alloys, and solids.

Short-term traffic flow prediction model using particle swarm optimization–based combined kernel function-least squares support vector machine combined with chaos theory

Directory of Open Access Journals (Sweden)

Qiang Shang

2016-08-01

Full Text Available Short-term traffic flow prediction is an important part of intelligent transportation systems research and applications. For further improving the accuracy of short-time traffic flow prediction, a novel hybrid prediction model (multivariate phase space reconstruction–combined kernel function-least squares support vector machine based on multivariate phase space reconstruction and combined kernel function-least squares support vector machine is proposed. The C-C method is used to determine the optimal time delay and the optimal embedding dimension of traffic variables’ (flow, speed, and occupancy time series for phase space reconstruction. The G-P method is selected to calculate the correlation dimension of attractor which is an important index for judging chaotic characteristics of the traffic variables’ series. The optimal input form of combined kernel function-least squares support vector machine model is determined by multivariate phase space reconstruction, and the model’s parameters are optimized by particle swarm optimization algorithm. Finally, case validation is carried out using the measured data of an expressway in Xiamen, China. The experimental results suggest that the new proposed model yields better predictions compared with similar models (combined kernel function-least squares support vector machine, multivariate phase space reconstruction–generalized kernel function-least squares support vector machine, and phase space reconstruction–combined kernel function-least squares support vector machine, which indicates that the new proposed model exhibits stronger prediction ability and robustness.

NINJA data analysis with a detection pipeline based on the Hilbert-Huang transform

International Nuclear Information System (INIS)

Stroeer, Alexander; Camp, Jordan

2009-01-01

The NINJA data analysis challenge allowed the study of the sensitivity of data analysis pipelines to binary black hole numerical relativity waveforms in simulated Gaussian noise at the design level of the LIGO observatory and the VIRGO observatory. We analyzed NINJA data with a pipeline based on the Hilbert-Huang transform, utilizing a detection stage and a characterization stage: detection is performed by triggering on excess instantaneous power, characterization is performed by displaying the kernel density enhanced (KD) time-frequency trace of the signal. Using the simulated data based on the two LIGO detectors, we were able to detect 77 signals out of 126 above signal-to-noise ratio, SNR 5 in coincidence, with 43 missed events characterized by SNR < 10. Characterization of the detected signals revealed the merger part of the waveform in high time and frequency resolution, free from time-frequency uncertainty. We estimated the timelag of the signals between the detectors based on the optimal overlap of the individual KD time-frequency maps, yielding estimates accurate within a fraction of a millisecond for half of the events. A coherent addition of the data sets according to the estimated timelag eventually was used in a final characterization of the event.

Optimized Kernel Entropy Components.

Science.gov (United States)

Izquierdo-Verdiguier, Emma; Laparra, Valero; Jenssen, Robert; Gomez-Chova, Luis; Camps-Valls, Gustau

2017-06-01

This brief addresses two main issues of the standard kernel entropy component analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of the importance of kernel eigenvectors by entropy instead of variance, as in the kernel principal components analysis. In this brief, we propose an extension of the KECA method, named optimized KECA (OKECA), that directly extracts the optimal features retaining most of the data entropy by means of compacting the information in very few features (often in just one or two). The proposed method produces features which have higher expressive power. In particular, it is based on the independent component analysis framework, and introduces an extra rotation to the eigen decomposition, which is optimized via gradient-ascent search. This maximum entropy preservation suggests that OKECA features are more efficient than KECA features for density estimation. In addition, a critical issue in both the methods is the selection of the kernel parameter, since it critically affects the resulting performance. Here, we analyze the most common kernel length-scale selection criteria. The results of both the methods are illustrated in different synthetic and real problems. Results show that OKECA returns projections with more expressive power than KECA, the most successful rule for estimating the kernel parameter is based on maximum likelihood, and OKECA is more robust to the selection of the length-scale parameter in kernel density estimation.

Feature selection and multi-kernel learning for adaptive graph regularized nonnegative matrix factorization

KAUST Repository

Wang, Jim Jing-Yan

2014-09-20

Nonnegative matrix factorization (NMF), a popular part-based representation technique, does not capture the intrinsic local geometric structure of the data space. Graph regularized NMF (GNMF) was recently proposed to avoid this limitation by regularizing NMF with a nearest neighbor graph constructed from the input data set. However, GNMF has two main bottlenecks. First, using the original feature space directly to construct the graph is not necessarily optimal because of the noisy and irrelevant features and nonlinear distributions of data samples. Second, one possible way to handle the nonlinear distribution of data samples is by kernel embedding. However, it is often difficult to choose the most suitable kernel. To solve these bottlenecks, we propose two novel graph-regularized NMF methods, AGNMFFS and AGNMFMK, by introducing feature selection and multiple-kernel learning to the graph regularized NMF, respectively. Instead of using a fixed graph as in GNMF, the two proposed methods learn the nearest neighbor graph that is adaptive to the selected features and learned multiple kernels, respectively. For each method, we propose a unified objective function to conduct feature selection/multi-kernel learning, NMF and adaptive graph regularization simultaneously. We further develop two iterative algorithms to solve the two optimization problems. Experimental results on two challenging pattern classification tasks demonstrate that the proposed methods significantly outperform state-of-the-art data representation methods.

On Λ-Type Duality of Frames in Banach Spaces

Directory of Open Access Journals (Sweden)

Renu Chugh

2013-11-01

Full Text Available Frames are redundant system which are useful in the reconstruction of certain classes of spaces. The dual of a frame (Hilbert always exists and can be obtained in a natural way. Due to the presence of three Banach spaces in the definition of retro Banach frames (or Banach frames duality of frames in Banach spaces is not similar to frames for Hilbert spaces. In this paper we introduce the notion of Λ-type duality of retro Banach frames. This can be generalized to Banach frames in Banach spaces. Necessary and sufficient conditions for the existence of the dual of retro Banach frames are obtained. A special class of retro Banach frames which always admit a dual frame is discussed.

Nonclassical Problem for Ultraparabolic Equation in Abstract Spaces

Directory of Open Access Journals (Sweden)

Gia Avalishvili

2016-01-01

Full Text Available Nonclassical problem for ultraparabolic equation with nonlocal initial condition with respect to one time variable is studied in abstract Hilbert spaces. We define the space of square integrable vector-functions with values in Hilbert spaces corresponding to the variational formulation of the nonlocal problem for ultraparabolic equation and prove trace theorem, which allows one to interpret initial conditions of the nonlocal problem. We obtain suitable a priori estimates and prove the existence and uniqueness of solution of the nonclassical problem and continuous dependence upon the data of the solution to the nonlocal problem. We consider an application of the obtained abstract results to nonlocal problem for ultraparabolic partial differential equation with second-order elliptic operator and obtain well-posedness result in Sobolev spaces.

Notes on qubit phase space and discrete symplectic structures

International Nuclear Information System (INIS)

Livine, Etera R

2010-01-01

We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite-dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the Moyal product and the differential calculus on these discrete phase spaces. In particular, the qubit phase space provides the simplest example of a four-point non-commutative phase space. We give an explicit expression of the Moyal bracket as a differential operator. We then compare the quantum dynamics encoded by the Moyal bracket to the classical dynamics: we show that the classical Poisson bracket does not satisfy the Jacobi identity thus leaving the Moyal bracket as the only consistent symplectic structure. We finally generalize our analysis to Hilbert spaces of prime dimensions d and their associated d x d phase spaces.

A novel adaptive kernel method with kernel centers determined by a support vector regression approach

NARCIS (Netherlands)

Sun, L.G.; De Visser, C.C.; Chu, Q.P.; Mulder, J.A.

2012-01-01

The optimality of the kernel number and kernel centers plays a significant role in determining the approximation power of nearly all kernel methods. However, the process of choosing optimal kernels is always formulated as a global optimization task, which is hard to accomplish. Recently, an

Protein Subcellular Localization with Gaussian Kernel Discriminant Analysis and Its Kernel Parameter Selection.

Science.gov (United States)

Wang, Shunfang; Nie, Bing; Yue, Kun; Fei, Yu; Li, Wenjia; Xu, Dongshu

2017-12-15

Kernel discriminant analysis (KDA) is a dimension reduction and classification algorithm based on nonlinear kernel trick, which can be novelly used to treat high-dimensional and complex biological data before undergoing classification processes such as protein subcellular localization. Kernel parameters make a great impact on the performance of the KDA model. Specifically, for KDA with the popular Gaussian kernel, to select the scale parameter is still a challenging problem. Thus, this paper introduces the KDA method and proposes a new method for Gaussian kernel parameter selection depending on the fact that the differences between reconstruction errors of edge normal samples and those of interior normal samples should be maximized for certain suitable kernel parameters. Experiments with various standard data sets of protein subcellular localization show that the overall accuracy of protein classification prediction with KDA is much higher than that without KDA. Meanwhile, the kernel parameter of KDA has a great impact on the efficiency, and the proposed method can produce an optimum parameter, which makes the new algorithm not only perform as effectively as the traditional ones, but also reduce the computational time and thus improve efficiency.

Exact calculation of the time convolutionless master equation generator: Application to the nonequilibrium resonant level model

Science.gov (United States)

Kidon, Lyran; Wilner, Eli Y.; Rabani, Eran

2015-12-01

The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima-Zwanzig-Mori time-convolution (TC) and the other on the Tokuyama-Mori time-convolutionless (TCL) formulations provide a starting point to describe the time-evolution of the reduced density matrix. A key in both approaches is to obtain the so called "memory kernel" or "generator," going beyond second or fourth order perturbation techniques. While numerically converged techniques are available for the TC memory kernel, the canonical approach to obtain the TCL generator is based on inverting a super-operator in the full Hilbert space, which is difficult to perform and thus, nearly all applications of the TCL approach rely on a perturbative scheme of some sort. Here, the TCL generator is expressed using a reduced system propagator which can be obtained from system observables alone and requires the calculation of super-operators and their inverse in the reduced Hilbert space rather than the full one. This makes the formulation amenable to quantum impurity solvers or to diagrammatic techniques, such as the nonequilibrium Green's function. We implement the TCL approach for the resonant level model driven away from equilibrium and compare the time scales for the decay of the generator with that of the memory kernel in the TC approach. Furthermore, the effects of temperature, source-drain bias, and gate potential on the TCL/TC generators are discussed.

Calculation and Verification of a Planar Pencil Beam Kernel Through the Hankel Transform of Measured OARs for a Radiosurgery System with Cones

International Nuclear Information System (INIS)

Vargas Verdesoto, Milton X.; Alvarez Romero, Jose T.

2010-01-01

A planar multienergetic pencil beam kernel with rotational symmetry is calculated for a stereotactic radiosurgery system, SRS, BrainLAB with cones, employing the deconvolution method of the off axis ratio profile, OAR, corresponding to the cone of 35 mm in diameter for a 6 MV photon beam produced by a linear accelerator Varian 2100 C/D. Before the deconvolution, the experimental OAR is corrected for beam divergence and variations of the spectral fluence Φ, using a boundary function BF. The function BF and the fluence Φ are transformed to the conjugate space with the zero order Hankel function, which is the appropriate transform due to the radial symmetry of the circular beams generated by the cones. The kernel in the conjugate space is obtained as the ratio of the transform of BF to the transform of Φ, therefore the kernel in the real space is calculated as the inverse transform of the kernel in the conjugate space. To validate the kernel in the real space, it is convolved with the fluence of the cones of 7.5, 12.5, 15, 17.5, 20, 22.5, 25, 30 and 35 mm in diameter. The comparison of the OARs calculated and measured shows a maximum difference of 4.5% in the zones of high gradient of dose, and a difference less than 2% in the regions of low gradient of dose. Finally, the expanded uncertainty of the kernel is estimated and reported.

Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics

Science.gov (United States)

Corry, Leo

2018-04-01

The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932. This article is part of the theme issue `Hilbert's sixth problem'.

Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics.

Science.gov (United States)

Corry, Leo

2018-04-28

The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

7 CFR 981.7 - Edible kernel.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Edible kernel. 981.7 Section 981.7 Agriculture... Regulating Handling Definitions § 981.7 Edible kernel. Edible kernel means a kernel, piece, or particle of almond kernel that is not inedible. [41 FR 26852, June 30, 1976] ...

Analytic properties of the Virasoro modular kernel

Energy Technology Data Exchange (ETDEWEB)

Nemkov, Nikita [Moscow Institute of Physics and Technology (MIPT), Dolgoprudny (Russian Federation); Institute for Theoretical and Experimental Physics (ITEP), Moscow (Russian Federation); National University of Science and Technology MISIS, The Laboratory of Superconducting metamaterials, Moscow (Russian Federation)

2017-06-15

On the space of generic conformal blocks the modular transformation of the underlying surface is realized as a linear integral transformation. We show that the analytic properties of conformal block implied by Zamolodchikov's formula are shared by the kernel of the modular transformation and illustrate this by explicit computation in the case of the one-point toric conformal block. (orig.)

Time-frequency analysis of non-stationary fusion plasma signals using an improved Hilbert-Huang transform

International Nuclear Information System (INIS)

Liu, Yangqing; Tan, Yi; Xie, Huiqiao; Wang, Wenhao; Gao, Zhe

2014-01-01

An improved Hilbert-Huang transform method is developed to the time-frequency analysis of non-stationary signals in tokamak plasmas. Maximal overlap discrete wavelet packet transform rather than wavelet packet transform is proposed as a preprocessor to decompose a signal into various narrow-band components. Then, a correlation coefficient based selection method is utilized to eliminate the irrelevant intrinsic mode functions obtained from empirical mode decomposition of those narrow-band components. Subsequently, a time varying vector autoregressive moving average model instead of Hilbert spectral analysis is performed to compute the Hilbert spectrum, i.e., a three-dimensional time-frequency distribution of the signal. The feasibility and effectiveness of the improved Hilbert-Huang transform method is demonstrated by analyzing a non-stationary simulated signal and actual experimental signals in fusion plasmas

Quantum de Finetti theorem in phase-space representation

International Nuclear Information System (INIS)

Leverrier, Anthony; Cerf, Nicolas J.

2009-01-01

The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).

Application of Hilbert-Huang Transform in Generating Spectrum-Compatible Earthquake Time Histories

OpenAIRE

Ni, Shun-Hao; Xie, Wei-Chau; Pandey, Mahesh

2011-01-01

Spectrum-compatible earthquake time histories have been widely used for seismic analysis and design. In this paper, a data processing method, Hilbert-Huang transform, is applied to generate earthquake time histories compatible with the target seismic design spectra based on multiple actual earthquake records. Each actual earthquake record is decomposed into several components of time-dependent amplitude and frequency by Hilbert-Huang transform. The spectrum-compatible earthquake time history ...

Model Selection in Kernel Ridge Regression

DEFF Research Database (Denmark)

Exterkate, Peter

Kernel ridge regression is gaining popularity as a data-rich nonlinear forecasting tool, which is applicable in many different contexts. This paper investigates the influence of the choice of kernel and the setting of tuning parameters on forecast accuracy. We review several popular kernels......, including polynomial kernels, the Gaussian kernel, and the Sinc kernel. We interpret the latter two kernels in terms of their smoothing properties, and we relate the tuning parameters associated to all these kernels to smoothness measures of the prediction function and to the signal-to-noise ratio. Based...... on these interpretations, we provide guidelines for selecting the tuning parameters from small grids using cross-validation. A Monte Carlo study confirms the practical usefulness of these rules of thumb. Finally, the flexible and smooth functional forms provided by the Gaussian and Sinc kernels makes them widely...

Penetuan Bilangan Iodin pada Hydrogenated Palm Kernel Oil (HPKO) dan Refined Bleached Deodorized Palm Kernel Oil (RBDPKO)

OpenAIRE

Sitompul, Monica Angelina

2015-01-01

Have been conducted Determination of Iodin Value by method titration to some Hydrogenated Palm Kernel Oil (HPKO) and Refined Bleached Deodorized Palm Kernel Oil (RBDPKO). The result of analysis obtained the Iodin Value in Hydrogenated Palm Kernel Oil (A) = 0,16 gr I2/100gr, Hydrogenated Palm Kernel Oil (B) = 0,20 gr I2/100gr, Hydrogenated Palm Kernel Oil (C) = 0,24 gr I2/100gr. And in Refined Bleached Deodorized Palm Kernel Oil (A) = 17,51 gr I2/100gr, Refined Bleached Deodorized Palm Kernel ...

7 CFR 981.8 - Inedible kernel.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Inedible kernel. 981.8 Section 981.8 Agriculture... Regulating Handling Definitions § 981.8 Inedible kernel. Inedible kernel means a kernel, piece, or particle of almond kernel with any defect scored as serious damage, or damage due to mold, gum, shrivel, or...

Supersymmetric gauge theories, quantization of M{sub flat}, and conformal field theory

Energy Technology Data Exchange (ETDEWEB)

Teschner, J.; Vartanov, G.S.

2013-02-15

We propose a derivation of the correspondence between certain gauge theories with N=2 supersymmetry and conformal field theory discovered by Alday, Gaiotto and Tachikawa in the spirit of Seiberg-Witten theory. Based on certain results from the literature we argue that the quantum theory of the moduli spaces of flat SL(2,R)-connections represents a nonperturbative ''skeleton'' of the gauge theory, protected by supersymmetry. It follows that instanton partition functions can be characterized as solutions to a Riemann-Hilbert type problem. In order to solve it, we describe the quantization of the moduli spaces of flat connections explicitly in terms of two natural sets of Darboux coordinates. The kernel describing the relation between the two pictures represents the solution to the Riemann Hilbert problem, and is naturally identified with the Liouville conformal blocks.

7 CFR 981.408 - Inedible kernel.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Inedible kernel. 981.408 Section 981.408 Agriculture... Administrative Rules and Regulations § 981.408 Inedible kernel. Pursuant to § 981.8, the definition of inedible kernel is modified to mean a kernel, piece, or particle of almond kernel with any defect scored as...

Model selection in kernel ridge regression

DEFF Research Database (Denmark)

Exterkate, Peter

2013-01-01

Kernel ridge regression is a technique to perform ridge regression with a potentially infinite number of nonlinear transformations of the independent variables as regressors. This method is gaining popularity as a data-rich nonlinear forecasting tool, which is applicable in many different contexts....... The influence of the choice of kernel and the setting of tuning parameters on forecast accuracy is investigated. Several popular kernels are reviewed, including polynomial kernels, the Gaussian kernel, and the Sinc kernel. The latter two kernels are interpreted in terms of their smoothing properties......, and the tuning parameters associated to all these kernels are related to smoothness measures of the prediction function and to the signal-to-noise ratio. Based on these interpretations, guidelines are provided for selecting the tuning parameters from small grids using cross-validation. A Monte Carlo study...

LZW-Kernel: fast kernel utilizing variable length code blocks from LZW compressors for protein sequence classification.

Science.gov (United States)

Filatov, Gleb; Bauwens, Bruno; Kertész-Farkas, Attila

2018-05-07

Bioinformatics studies often rely on similarity measures between sequence pairs, which often pose a bottleneck in large-scale sequence analysis. Here, we present a new convolutional kernel function for protein sequences called the LZW-Kernel. It is based on code words identified with the Lempel-Ziv-Welch (LZW) universal text compressor. The LZW-Kernel is an alignment-free method, it is always symmetric, is positive, always provides 1.0 for self-similarity and it can directly be used with Support Vector Machines (SVMs) in classification problems, contrary to normalized compression distance (NCD), which often violates the distance metric properties in practice and requires further techniques to be used with SVMs. The LZW-Kernel is a one-pass algorithm, which makes it particularly plausible for big data applications. Our experimental studies on remote protein homology detection and protein classification tasks reveal that the LZW-Kernel closely approaches the performance of the Local Alignment Kernel (LAK) and the SVM-pairwise method combined with Smith-Waterman (SW) scoring at a fraction of the time. Moreover, the LZW-Kernel outperforms the SVM-pairwise method when combined with BLAST scores, which indicates that the LZW code words might be a better basis for similarity measures than local alignment approximations found with BLAST. In addition, the LZW-Kernel outperforms n-gram based mismatch kernels, hidden Markov model based SAM and Fisher kernel, and protein family based PSI-BLAST, among others. Further advantages include the LZW-Kernel's reliance on a simple idea, its ease of implementation, and its high speed, three times faster than BLAST and several magnitudes faster than SW or LAK in our tests. LZW-Kernel is implemented as a standalone C code and is a free open-source program distributed under GPLv3 license and can be downloaded from https://github.com/kfattila/LZW-Kernel. akerteszfarkas@hse.ru. Supplementary data are available at Bioinformatics Online.

Kernel learning algorithms for face recognition

CERN Document Server

Li, Jun-Bao; Pan, Jeng-Shyang

2013-01-01

Kernel Learning Algorithms for Face Recognition covers the framework of kernel based face recognition. This book discusses the advanced kernel learning algorithms and its application on face recognition. This book also focuses on the theoretical deviation, the system framework and experiments involving kernel based face recognition. Included within are algorithms of kernel based face recognition, and also the feasibility of the kernel based face recognition method. This book provides researchers in pattern recognition and machine learning area with advanced face recognition methods and its new

Neuronal model with distributed delay: analysis and simulation study for gamma distribution memory kernel.

Science.gov (United States)

Karmeshu; Gupta, Varun; Kadambari, K V

2011-06-01

A single neuronal model incorporating distributed delay (memory)is proposed. The stochastic model has been formulated as a Stochastic Integro-Differential Equation (SIDE) which results in the underlying process being non-Markovian. A detailed analysis of the model when the distributed delay kernel has exponential form (weak delay) has been carried out. The selection of exponential kernel has enabled the transformation of the non-Markovian model to a Markovian model in an extended state space. For the study of First Passage Time (FPT) with exponential delay kernel, the model has been transformed to a system of coupled Stochastic Differential Equations (SDEs) in two-dimensional state space. Simulation studies of the SDEs provide insight into the effect of weak delay kernel on the Inter-Spike Interval(ISI) distribution. A measure based on Jensen-Shannon divergence is proposed which can be used to make a choice between two competing models viz. distributed delay model vis-á-vis LIF model. An interesting feature of the model is that the behavior of (CV(t))((ISI)) (Coefficient of Variation) of the ISI distribution with respect to memory kernel time constant parameter η reveals that neuron can switch from a bursting state to non-bursting state as the noise intensity parameter changes. The membrane potential exhibits decaying auto-correlation structure with or without damped oscillatory behavior depending on the choice of parameters. This behavior is in agreement with empirically observed pattern of spike count in a fixed time window. The power spectral density derived from the auto-correlation function is found to exhibit single and double peaks. The model is also examined for the case of strong delay with memory kernel having the form of Gamma distribution. In contrast to fast decay of damped oscillations of the ISI distribution for the model with weak delay kernel, the decay of damped oscillations is found to be slower for the model with strong delay kernel.

Novel microwave photonic fractional hilbert transformer using a ring resonator-based optical all-pass filter

NARCIS (Netherlands)

Zhuang, L.; Khan, M.R.H.; Beeker, Willem; Beeker, W.P.; Leinse, Arne; Heideman, Rene; Roeloffzen, C.G.H.

2012-01-01

We propose and demonstrate a novel wideband microwave photonic fractional Hilbert transformer implemented using a ring resonatorbased optical all-pass filter. The full programmability of the ring resonator allows variable and arbitrary fractional order of the Hilbert transformer. The performance

Quantized kernel least mean square algorithm.

Science.gov (United States)

Chen, Badong; Zhao, Songlin; Zhu, Pingping; Príncipe, José C

2012-01-01

In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.

Partial Deconvolution with Inaccurate Blur Kernel.

Science.gov (United States)

Ren, Dongwei; Zuo, Wangmeng; Zhang, David; Xu, Jun; Zhang, Lei

2017-10-17

Most non-blind deconvolution methods are developed under the error-free kernel assumption, and are not robust to inaccurate blur kernel. Unfortunately, despite the great progress in blind deconvolution, estimation error remains inevitable during blur kernel estimation. Consequently, severe artifacts such as ringing effects and distortions are likely to be introduced in the non-blind deconvolution stage. In this paper, we tackle this issue by suggesting: (i) a partial map in the Fourier domain for modeling kernel estimation error, and (ii) a partial deconvolution model for robust deblurring with inaccurate blur kernel. The partial map is constructed by detecting the reliable Fourier entries of estimated blur kernel. And partial deconvolution is applied to wavelet-based and learning-based models to suppress the adverse effect of kernel estimation error. Furthermore, an E-M algorithm is developed for estimating the partial map and recovering the latent sharp image alternatively. Experimental results show that our partial deconvolution model is effective in relieving artifacts caused by inaccurate blur kernel, and can achieve favorable deblurring quality on synthetic and real blurry images.Most non-blind deconvolution methods are developed under the error-free kernel assumption, and are not robust to inaccurate blur kernel. Unfortunately, despite the great progress in blind deconvolution, estimation error remains inevitable during blur kernel estimation. Consequently, severe artifacts such as ringing effects and distortions are likely to be introduced in the non-blind deconvolution stage. In this paper, we tackle this issue by suggesting: (i) a partial map in the Fourier domain for modeling kernel estimation error, and (ii) a partial deconvolution model for robust deblurring with inaccurate blur kernel. The partial map is constructed by detecting the reliable Fourier entries of estimated blur kernel. And partial deconvolution is applied to wavelet-based and learning

Kernel methods for deep learning

OpenAIRE

Cho, Youngmin

2012-01-01

We introduce a new family of positive-definite kernels that mimic the computation in large neural networks. We derive the different members of this family by considering neural networks with different activation functions. Using these kernels as building blocks, we also show how to construct other positive-definite kernels by operations such as composition, multiplication, and averaging. We explore the use of these kernels in standard models of supervised learning, such as support vector mach...

Remarks on the formulation of quantum mechanics on noncommutative phase spaces

International Nuclear Information System (INIS)

Muthukumar, Balasundaram

2007-01-01

We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and also with canonically conjugate momenta. With a postulated normalized distribution function in the quantum domain, the square of the Dirac delta density distribution in the classical case is properly realised in noncommutative phase space and it serves as the quantum condition. With only these inputs, we pull out the entire formalisms of noncommutative quantum mechanics in phase space and in Hilbert space, and elegantly establish the link between classical and quantum formalisms and between Hilbert space and phase space formalisms of noncommutative quantum mechanics. Also, we show that the distribution function in this case possesses 'twisted' Galilean symmetry

A Hilbert space structure on Banach algebras

International Nuclear Information System (INIS)

Mohammad, N.; Thaheem, A.B.

1988-08-01

In this note we define an inner product on ''reduced'' Banach *-algebras via a measure on the set of positive functionals. It is shown here that the resultant inner product space is a topological algebra and also a completeness condition is obtained. (author). 9 refs

Generalized noncommutative Hardy and Hardy-Hilbert type inequalities

DEFF Research Database (Denmark)

Hansen, Frank; Krulic, Kristina; Pecaric, Josip

2010-01-01

We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it ...

Hilbert's Grand Hotel with a series twist

Science.gov (United States)

Wijeratne, Chanakya; Mamolo, Ami; Zazkis, Rina

2014-08-01

This paper presents a new twist on a familiar paradox, linking seemingly disparate ideas under one roof. Hilbert's Grand Hotel, a paradox which addresses infinite set comparisons is adapted and extended to incorporate ideas from calculus - namely infinite series. We present and resolve several variations, and invite the reader to explore his or her own variations.

Efficiently GPU-accelerating long kernel convolutions in 3-D DIRECT TOF PET reconstruction via memory cache optimization

Energy Technology Data Exchange (ETDEWEB)

Ha, Sungsoo; Mueller, Klaus [Stony Brook Univ., NY (United States). Center for Visual Computing; Matej, Samuel [Pennsylvania Univ., Philadelphia, PA (United States). Dept. of Radiology

2011-07-01

The DIRECT represents a novel approach for 3-D Time-of-Flight (TOF) PET reconstruction. Its novelty stems from the fact that it performs all iterative predictor-corrector operations directly in image space. The projection operations now amount to convolutions in image space, using long TOF (resolution) kernels. While for spatially invariant kernels the computational complexity can be algorithmically overcome by replacing spatial convolution with multiplication in Fourier space, spatially variant kernels cannot use this shortcut. Therefore in this paper, we describe a GPU-accelerated approach for this task. However, the intricate parallel architecture of GPUs poses its own challenges, and careful memory and thread management is the key to obtaining optimal results. As convolution is mainly memory-bound we focus on the former, proposing two types of memory caching schemes that warrant best cache memory re-use by the parallel threads. In contrast to our previous two-stage algorithm, the schemes presented here are both single-stage which is more accurate. (orig.)

7 CFR 981.9 - Kernel weight.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Kernel weight. 981.9 Section 981.9 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing Agreements... Regulating Handling Definitions § 981.9 Kernel weight. Kernel weight means the weight of kernels, including...

Channel identification machines.

Science.gov (United States)

Lazar, Aurel A; Slutskiy, Yevgeniy B

2012-01-01

We present a formal methodology for identifying a channel in a system consisting of a communication channel in cascade with an asynchronous sampler. The channel is modeled as a multidimensional filter, while models of asynchronous samplers are taken from neuroscience and communications and include integrate-and-fire neurons, asynchronous sigma/delta modulators and general oscillators in cascade with zero-crossing detectors. We devise channel identification algorithms that recover a projection of the filter(s) onto a space of input signals loss-free for both scalar and vector-valued test signals. The test signals are modeled as elements of a reproducing kernel Hilbert space (RKHS) with a Dirichlet kernel. Under appropriate limiting conditions on the bandwidth and the order of the test signal space, the filter projection converges to the impulse response of the filter. We show that our results hold for a wide class of RKHSs, including the space of finite-energy bandlimited signals. We also extend our channel identification results to noisy circuits.

Channel Identification Machines

Directory of Open Access Journals (Sweden)

Aurel A. Lazar

2012-01-01

Full Text Available We present a formal methodology for identifying a channel in a system consisting of a communication channel in cascade with an asynchronous sampler. The channel is modeled as a multidimensional filter, while models of asynchronous samplers are taken from neuroscience and communications and include integrate-and-fire neurons, asynchronous sigma/delta modulators and general oscillators in cascade with zero-crossing detectors. We devise channel identification algorithms that recover a projection of the filter(s onto a space of input signals loss-free for both scalar and vector-valued test signals. The test signals are modeled as elements of a reproducing kernel Hilbert space (RKHS with a Dirichlet kernel. Under appropriate limiting conditions on the bandwidth and the order of the test signal space, the filter projection converges to the impulse response of the filter. We show that our results hold for a wide class of RKHSs, including the space of finite-energy bandlimited signals. We also extend our channel identification results to noisy circuits.

Veto-Consensus Multiple Kernel Learning

NARCIS (Netherlands)

Zhou, Y.; Hu, N.; Spanos, C.J.

2016-01-01

We propose Veto-Consensus Multiple Kernel Learning (VCMKL), a novel way of combining multiple kernels such that one class of samples is described by the logical intersection (consensus) of base kernelized decision rules, whereas the other classes by the union (veto) of their complements. The

7 CFR 51.2295 - Half kernel.

Science.gov (United States)

2010-01-01

... 7 Agriculture 2 2010-01-01 2010-01-01 false Half kernel. 51.2295 Section 51.2295 Agriculture... Standards for Shelled English Walnuts (Juglans Regia) Definitions § 51.2295 Half kernel. Half kernel means the separated half of a kernel with not more than one-eighth broken off. ...

All-optical Hilbert transformer based on a single phase-shifted fiber Bragg grating: design and analysis.

Science.gov (United States)

Asghari, Mohammad H; Azaña, José

2009-02-01

A simple all-fiber design for implementing an all-optical temporal Hilbert transformer is proposed and numerically demonstrated. We show that an all-optical Hilbert transformer can be implemented using a uniform-period fiber Bragg grating (FBG) with a properly designed amplitude-only grating apodization profile incorporating a single pi phase shift in the middle of the grating length. All-optical Hilbert transformers capable of processing arbitrary optical waveforms with bandwidths up to a few hundreds of gigahertz can be implemented using feasible FBGs.

Adaptive kernel regression for freehand 3D ultrasound reconstruction

Science.gov (United States)

Alshalalfah, Abdel-Latif; Daoud, Mohammad I.; Al-Najar, Mahasen

2017-03-01

Freehand three-dimensional (3D) ultrasound imaging enables low-cost and flexible 3D scanning of arbitrary-shaped organs, where the operator can freely move a two-dimensional (2D) ultrasound probe to acquire a sequence of tracked cross-sectional images of the anatomy. Often, the acquired 2D ultrasound images are irregularly and sparsely distributed in the 3D space. Several 3D reconstruction algorithms have been proposed to synthesize 3D ultrasound volumes based on the acquired 2D images. A challenging task during the reconstruction process is to preserve the texture patterns in the synthesized volume and ensure that all gaps in the volume are correctly filled. This paper presents an adaptive kernel regression algorithm that can effectively reconstruct high-quality freehand 3D ultrasound volumes. The algorithm employs a kernel regression model that enables nonparametric interpolation of the voxel gray-level values. The kernel size of the regression model is adaptively adjusted based on the characteristics of the voxel that is being interpolated. In particular, when the algorithm is employed to interpolate a voxel located in a region with dense ultrasound data samples, the size of the kernel is reduced to preserve the texture patterns. On the other hand, the size of the kernel is increased in areas that include large gaps to enable effective gap filling. The performance of the proposed algorithm was compared with seven previous interpolation approaches by synthesizing freehand 3D ultrasound volumes of a benign breast tumor. The experimental results show that the proposed algorithm outperforms the other interpolation approaches.

Induced quantum torsion

International Nuclear Information System (INIS)

Denardo, G.; Spallucci, E.

1985-07-01

We study pregeometry in the framework of a Poincare gauge field theory. The Riemann-Cartan space-time is shown to be an ''effective geometry'' for this model in the low energy limit. By using Heat Kernel techniques we find the induced action for curvature and torsion. We obtain in this way the usual Einstein-Hilbert action plus an axial Maxwell term describing the propagation of a massless, axial vector torsion field. (author)

Explicit solution of Riemann-Hilbert problems for the Ernst equation

Science.gov (United States)

Klein, C.; Richter, O.

1998-01-01

Riemann-Hilbert problems are an important solution technique for completely integrable differential equations. They are used to introduce a free function in the solutions which can be used at least in principle to solve initial or boundary value problems. But even if the initial or boundary data can be translated into a Riemann-Hilbert problem, it is in general impossible to obtain explicit solutions. In the case of the Ernst equation, however, this is possible for a large class because the matrix problem can be shown to be gauge equivalent to a scalar one on a hyperelliptic Riemann surface that can be solved in terms of theta functions. As an example we discuss the rigidly rotating dust disk.

An Approximate Approach to Automatic Kernel Selection.

Science.gov (United States)

Ding, Lizhong; Liao, Shizhong

2016-02-02

Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.

Iterative software kernels

Energy Technology Data Exchange (ETDEWEB)

Duff, I.

1994-12-31

This workshop focuses on kernels for iterative software packages. Specifically, the three speakers discuss various aspects of sparse BLAS kernels. Their topics are: `Current status of user lever sparse BLAS`; Current status of the sparse BLAS toolkit`; and `Adding matrix-matrix and matrix-matrix-matrix multiply to the sparse BLAS toolkit`.

Analyticity spaces of self-adjoint operators subjected to perturbations with applications to Hankel invariant distribution spaces

NARCIS (Netherlands)

Eijndhoven, van S.J.L.; Graaf, de J.

1986-01-01

A new theory of generalized functions has been developed by one of the authors (de Graaf). In this theory the analyticity domain of each positive self-adjoint unbounded operator $\\mathcal{A}$ in a Hilbert space $X$ is regarded as a test space denoted by $\\mathcal{S}_{x,\\mathcal{A}} $. In the first

Viscozyme L pretreatment on palm kernels improved the aroma of palm kernel oil after kernel roasting.

Science.gov (United States)

Zhang, Wencan; Leong, Siew Mun; Zhao, Feifei; Zhao, Fangju; Yang, Tiankui; Liu, Shaoquan

2018-05-01

With an interest to enhance the aroma of palm kernel oil (PKO), Viscozyme L, an enzyme complex containing a wide range of carbohydrases, was applied to alter the carbohydrates in palm kernels (PK) to modulate the formation of volatiles upon kernel roasting. After Viscozyme treatment, the content of simple sugars and free amino acids in PK increased by 4.4-fold and 4.5-fold, respectively. After kernel roasting and oil extraction, significantly more 2,5-dimethylfuran, 2-[(methylthio)methyl]-furan, 1-(2-furanyl)-ethanone, 1-(2-furyl)-2-propanone, 5-methyl-2-furancarboxaldehyde and 2-acetyl-5-methylfuran but less 2-furanmethanol and 2-furanmethanol acetate were found in treated PKO; the correlation between their formation and simple sugar profile was estimated by using partial least square regression (PLS1). Obvious differences in pyrroles and Strecker aldehydes were also found between the control and treated PKOs. Principal component analysis (PCA) clearly discriminated the treated PKOs from that of control PKOs on the basis of all volatile compounds. Such changes in volatiles translated into distinct sensory attributes, whereby treated PKO was more caramelic and burnt after aqueous extraction and more nutty, roasty, caramelic and smoky after solvent extraction. Copyright © 2018 Elsevier Ltd. All rights reserved.

KNBD: A Remote Kernel Block Server for Linux

Science.gov (United States)

Becker, Jeff

1999-01-01

I am developing a prototype of a Linux remote disk block server whose purpose is to serve as a lower level component of a parallel file system. Parallel file systems are an important component of high performance supercomputers and clusters. Although supercomputer vendors such as SGI and IBM have their own custom solutions, there has been a void and hence a demand for such a system on Beowulf-type PC Clusters. Recently, the Parallel Virtual File System (PVFS) project at Clemson University has begun to address this need (1). Although their system provides much of the functionality of (and indeed was inspired by) the equivalent file systems in the commercial supercomputer market, their system is all in user-space. Migrating their 10 services to the kernel could provide a performance boost, by obviating the need for expensive system calls. Thanks to Pavel Machek, the Linux kernel has provided the network block device (2) with kernels 2.1.101 and later. You can configure this block device to redirect reads and writes to a remote machine's disk. This can be used as a building block for constructing a striped file system across several nodes.

Treatment of electrochemical noise data by the Hilbert-Huang transform

International Nuclear Information System (INIS)

Rahier, A.

2009-01-01

Most of the classical approaches for treating electro-chemical noise (ECN) data suffer from the non-linear and non steady-state character of the delivered signal. Very often, the link between time and the local corrosion events supposedly responsible for ECN data signatures is lost during treatment, as is obvious when using the classical Fourier Transform (FT), followed by an analysis of the response in the frequency domain. In this particular case, the information directly related to the corrosion events is distributed into the full spectra, thereby preventing the operator to derive clear and precise conclusions. In 2005, we suggested an alternative data treatment based on the Hilbert-Huang transform (HHT). The latter keeps track of the time variable and copes with non-linear and non steady-state behaviours of the system under examination. In 2006, we demonstrated the applicability of the newly proposed data treatment in the case of ECN data collected under BWR (Boiling Water Reactor) conditions. In 2007, we collected additional ECN data and started a preliminary investigation of two mathematical restrictions that are susceptible to impair the interpretation of the results. We discovered a possible modification of the Hilbert transform allowing generating controlled phase shifts that are different from pi/2 as is always the case for the Hilbert transform

The kernel G1(x,x') and the quantum equivalence principle

International Nuclear Information System (INIS)

Ceccatto, H.; Foussats, A.; Giacomini, H.; Zandron, O.

1981-01-01

In this paper, it is re-examined the formulation of the quantum equivalence principle (QEP) and its compatibility with the conditions which must be fulfilled by the kernel G 1 (x,x') is discussed. It is also determined the base of solutions which give the particle model in a curved space-time in terms of Cauchy's data for such a kernel. Finally, it is analyzed the creation of particles in this model by studying the time evolution of creation and annihilation operators. This method is an alternative to one that uses Bogoliubov's transformation as a mechanism of creation. (author)

Experimental validation of a structural damage detection method based on marginal Hilbert spectrum

Science.gov (United States)

Banerji, Srishti; Roy, Timir B.; Sabamehr, Ardalan; Bagchi, Ashutosh

2017-04-01

Structural Health Monitoring (SHM) using dynamic characteristics of structures is crucial for early damage detection. Damage detection can be performed by capturing and assessing structural responses. Instrumented structures are monitored by analyzing the responses recorded by deployed sensors in the form of signals. Signal processing is an important tool for the processing of the collected data to diagnose anomalies in structural behavior. The vibration signature of the structure varies with damage. In order to attain effective damage detection, preservation of non-linear and non-stationary features of real structural responses is important. Decomposition of the signals into Intrinsic Mode Functions (IMF) by Empirical Mode Decomposition (EMD) and application of Hilbert-Huang Transform (HHT) addresses the time-varying instantaneous properties of the structural response. The energy distribution among different vibration modes of the intact and damaged structure depicted by Marginal Hilbert Spectrum (MHS) detects location and severity of the damage. The present work investigates damage detection analytically and experimentally by employing MHS. The testing of this methodology for different damage scenarios of a frame structure resulted in its accurate damage identification. The sensitivity of Hilbert Spectral Analysis (HSA) is assessed with varying frequencies and damage locations by means of calculating Damage Indices (DI) from the Hilbert spectrum curves of the undamaged and damaged structures.

The master space of N = 1 gauge theories

International Nuclear Information System (INIS)

Forcella, Davide; Hanany, Amihay; He Yanghui; Zaffaroni, Alberto

2008-01-01

The full moduli space M of a class of N = 1 supersymmetric gauge theories is studied. For gauge theories living on a stack of D3-branes at Calabi-Yau singularities X, M is a combination of the mesonic and baryonic branches. In consonance with the mathematical literature, the single brane moduli space is called the master space F b . Illustrating with a host of explicit examples, we exhibit many algebro-geometric properties of the master space such as when F b is toric Calabi-Yau, behaviour of its Hilbert series, its irreducible components and its symmetries. In conjunction with the plethystic programme, we investigate the counting of BPS gauge invariants, baryonic and mesonic, using the geometry of F b and show how its refined Hilbert series not only engenders the generating functions for the counting but also beautifully encode 'hidden' global symmetries of the gauge theory which manifest themselves as symmetries of the complete moduli space M for N number of branes.

7 CFR 51.1441 - Half-kernel.

Science.gov (United States)

2010-01-01

... 7 Agriculture 2 2010-01-01 2010-01-01 false Half-kernel. 51.1441 Section 51.1441 Agriculture... Standards for Grades of Shelled Pecans Definitions § 51.1441 Half-kernel. Half-kernel means one of the separated halves of an entire pecan kernel with not more than one-eighth of its original volume missing...

Foundations of phase-space quantum mechanics

International Nuclear Information System (INIS)

Guz, W.

1984-01-01

In the present paper a general concept of a phase-space representation of the ordinary Hilbert-space quantum theory is formulated, and then, by using some elementary facts of functional analysis, several equivalent forms of that concept are analyzed. Several important physical examples are presented in Section 3 of the paper. (author)

Local Observed-Score Kernel Equating

Science.gov (United States)

Wiberg, Marie; van der Linden, Wim J.; von Davier, Alina A.

2014-01-01

Three local observed-score kernel equating methods that integrate methods from the local equating and kernel equating frameworks are proposed. The new methods were compared with their earlier counterparts with respect to such measures as bias--as defined by Lord's criterion of equity--and percent relative error. The local kernel item response…

Detecting periodicities with Gaussian processes

Directory of Open Access Journals (Sweden)

Nicolas Durrande

2016-04-01

Full Text Available We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression, which provides a flexible non-parametric framework for modelling periodic data. We introduce a novel decomposition of the covariance function as the sum of periodic and aperiodic kernels. This decomposition allows for the creation of sub-models which capture the periodic nature of the signal and its complement. To quantify the periodicity of the signal, we derive a periodicity ratio which reflects the uncertainty in the fitted sub-models. Although the method can be applied to many kernels, we give a special emphasis to the Matérn family, from the expression of the reproducing kernel Hilbert space inner product to the implementation of the associated periodic kernels in a Gaussian process toolkit. The proposed method is illustrated by considering the detection of periodically expressed genes in the arabidopsis genome.

Credit scoring analysis using kernel discriminant

Science.gov (United States)

Widiharih, T.; Mukid, M. A.; Mustafid

2018-05-01

Credit scoring model is an important tool for reducing the risk of wrong decisions when granting credit facilities to applicants. This paper investigate the performance of kernel discriminant model in assessing customer credit risk. Kernel discriminant analysis is a non- parametric method which means that it does not require any assumptions about the probability distribution of the input. The main ingredient is a kernel that allows an efficient computation of Fisher discriminant. We use several kernel such as normal, epanechnikov, biweight, and triweight. The models accuracy was compared each other using data from a financial institution in Indonesia. The results show that kernel discriminant can be an alternative method that can be used to determine who is eligible for a credit loan. In the data we use, it shows that a normal kernel is relevant to be selected for credit scoring using kernel discriminant model. Sensitivity and specificity reach to 0.5556 and 0.5488 respectively.

Oversampling the Minority Class in the Feature Space.

Science.gov (United States)

Perez-Ortiz, Maria; Gutierrez, Pedro Antonio; Tino, Peter; Hervas-Martinez, Cesar

2016-09-01

The imbalanced nature of some real-world data is one of the current challenges for machine learning researchers. One common approach oversamples the minority class through convex combination of its patterns. We explore the general idea of synthetic oversampling in the feature space induced by a kernel function (as opposed to input space). If the kernel function matches the underlying problem, the classes will be linearly separable and synthetically generated patterns will lie on the minority class region. Since the feature space is not directly accessible, we use the empirical feature space (EFS) (a Euclidean space isomorphic to the feature space) for oversampling purposes. The proposed method is framed in the context of support vector machines, where the imbalanced data sets can pose a serious hindrance. The idea is investigated in three scenarios: 1) oversampling in the full and reduced-rank EFSs; 2) a kernel learning technique maximizing the data class separation to study the influence of the feature space structure (implicitly defined by the kernel function); and 3) a unified framework for preferential oversampling that spans some of the previous approaches in the literature. We support our investigation with extensive experiments over 50 imbalanced data sets.

Strong consistency of nonparametric Bayes density estimation on compact metric spaces with applications to specific manifolds.

Science.gov (United States)

Bhattacharya, Abhishek; Dunson, David B

2012-08-01

This article considers a broad class of kernel mixture density models on compact metric spaces and manifolds. Following a Bayesian approach with a nonparametric prior on the location mixing distribution, sufficient conditions are obtained on the kernel, prior and the underlying space for strong posterior consistency at any continuous density. The prior is also allowed to depend on the sample size n and sufficient conditions are obtained for weak and strong consistency. These conditions are verified on compact Euclidean spaces using multivariate Gaussian kernels, on the hypersphere using a von Mises-Fisher kernel and on the planar shape space using complex Watson kernels.

Covariant Spectator Theory of heavy–light and heavy mesons and the predictive power of covariant interaction kernels

Energy Technology Data Exchange (ETDEWEB)

Leitão, Sofia, E-mail: sofia.leitao@tecnico.ulisboa.pt [CFTP, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal); Stadler, Alfred, E-mail: stadler@uevora.pt [Departamento de Física, Universidade de Évora, 7000-671 Évora (Portugal); CFTP, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal); Peña, M.T., E-mail: teresa.pena@tecnico.ulisboa.pt [Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal); CFTP, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal); Biernat, Elmar P., E-mail: elmar.biernat@tecnico.ulisboa.pt [CFTP, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal)

2017-01-10

The Covariant Spectator Theory (CST) is used to calculate the mass spectrum and vertex functions of heavy–light and heavy mesons in Minkowski space. The covariant kernel contains Lorentz scalar, pseudoscalar, and vector contributions. The numerical calculations are performed in momentum space, where special care is taken to treat the strong singularities present in the confining kernel. The observed meson spectrum is very well reproduced after fitting a small number of model parameters. Remarkably, a fit to a few pseudoscalar meson states only, which are insensitive to spin–orbit and tensor forces and do not allow to separate the spin–spin from the central interaction, leads to essentially the same model parameters as a more general fit. This demonstrates that the covariance of the chosen interaction kernel is responsible for the very accurate prediction of the spin-dependent quark–antiquark interactions.

Formal truncations of connected kernel equations

International Nuclear Information System (INIS)

Dixon, R.M.

1977-01-01

The Connected Kernel Equations (CKE) of Alt, Grassberger and Sandhas (AGS); Kouri, Levin and Tobocman (KLT); and Bencze, Redish and Sloan (BRS) are compared against reaction theory criteria after formal channel space and/or operator truncations have been introduced. The Channel Coupling Class concept is used to study the structure of these CKE's. The related wave function formalism of Sandhas, of L'Huillier, Redish and Tandy and of Kouri, Krueger and Levin are also presented. New N-body connected kernel equations which are generalizations of the Lovelace three-body equations are derived. A method for systematically constructing fewer body models from the N-body BRS and generalized Lovelace (GL) equations is developed. The formally truncated AGS, BRS, KLT and GL equations are analyzed by employing the criteria of reciprocity and two-cluster unitarity. Reciprocity considerations suggest that formal truncations of BRS, KLT and GL equations can lead to reciprocity-violating results. This study suggests that atomic problems should employ three-cluster connected truncations and that the two-cluster connected truncations should be a useful starting point for nuclear systems

T^{\\sigma}_{\\rho}(G) Theories and Their Hilbert Series

CERN Document Server

Cremonesi, Stefano; Mekareeya, Noppadol; Zaffaroni, Alberto

2015-01-01

We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3d N=4 superconformal gauge theories T^{\\sigma}_{\\rho}(G) corresponding to a set of D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical group, \\sigma is a partition of G and \\rho a partition of the dual group G^\\vee. In deriving such a formula we make use of the recently discovered formula for the Hilbert series of the quantum Coulomb branch of N=4 superconformal theories. The result can be expressed in terms of a generalization of a class of symmetric functions, the Hall-Littlewood polynomials, and can be interpreted in mathematical language in terms of localization. We mainly consider the case G=SU(N) but some interesting results are also given for orthogonal and symplectic groups.

Geometric approach to evolution problems in metric spaces

NARCIS (Netherlands)

Stojković, Igor

2011-01-01

This PhD thesis contains four chapters where research material is presented. In the second chapter the extension of the product formulas for semigroups induced by convex functionals, from the classical Hilbert space setting to the setting of general CAT(0) spaces. In the third chapter, the

Ridge Regression and Other Kernels for Genomic Selection with R Package rrBLUP

Directory of Open Access Journals (Sweden)

Jeffrey B. Endelman

2011-11-01

Full Text Available Many important traits in plant breeding are polygenic and therefore recalcitrant to traditional marker-assisted selection. Genomic selection addresses this complexity by including all markers in the prediction model. A key method for the genomic prediction of breeding values is ridge regression (RR, which is equivalent to best linear unbiased prediction (BLUP when the genetic covariance between lines is proportional to their similarity in genotype space. This additive model can be broadened to include epistatic effects by using other kernels, such as the Gaussian, which represent inner products in a complex feature space. To facilitate the use of RR and nonadditive kernels in plant breeding, a new software package for R called rrBLUP has been developed. At its core is a fast maximum-likelihood algorithm for mixed models with a single variance component besides the residual error, which allows for efficient prediction with unreplicated training data. Use of the rrBLUP software is demonstrated through several examples, including the identification of optimal crosses based on superior progeny value. In cross-validation tests, the prediction accuracy with nonadditive kernels was significantly higher than RR for wheat ( L. grain yield but equivalent for several maize ( L. traits.

Multiple Kernel Learning with Data Augmentation

Science.gov (United States)

2016-11-22

JMLR: Workshop and Conference Proceedings 63:49–64, 2016 ACML 2016 Multiple Kernel Learning with Data Augmentation Khanh Nguyen nkhanh@deakin.edu.au...University, Australia Editors: Robert J. Durrant and Kee-Eung Kim Abstract The motivations of multiple kernel learning (MKL) approach are to increase... kernel expres- siveness capacity and to avoid the expensive grid search over a wide spectrum of kernels . A large amount of work has been proposed to

OS X and iOS Kernel Programming

CERN Document Server

Halvorsen, Ole Henry

2011-01-01

OS X and iOS Kernel Programming combines essential operating system and kernel architecture knowledge with a highly practical approach that will help you write effective kernel-level code. You'll learn fundamental concepts such as memory management and thread synchronization, as well as the I/O Kit framework. You'll also learn how to write your own kernel-level extensions, such as device drivers for USB and Thunderbolt devices, including networking, storage and audio drivers. OS X and iOS Kernel Programming provides an incisive and complete introduction to the XNU kernel, which runs iPhones, i

Model selection for Gaussian kernel PCA denoising

DEFF Research Database (Denmark)

Jørgensen, Kasper Winther; Hansen, Lars Kai

2012-01-01

We propose kernel Parallel Analysis (kPA) for automatic kernel scale and model order selection in Gaussian kernel PCA. Parallel Analysis [1] is based on a permutation test for covariance and has previously been applied for model order selection in linear PCA, we here augment the procedure to also...... tune the Gaussian kernel scale of radial basis function based kernel PCA.We evaluate kPA for denoising of simulated data and the US Postal data set of handwritten digits. We find that kPA outperforms other heuristics to choose the model order and kernel scale in terms of signal-to-noise ratio (SNR...

How were the Hilbert-Einstein equations discovered?

International Nuclear Information System (INIS)

Logunov, Anatolii A; Mestvirishvili, Mirian A; Petrov, Vladimir A

2004-01-01

The ways in which Albert Einstein and David Hilbert independently arrived at the gravitational field equations are traced. A critical analysis is presented of a number of papers in which the history of the derivation of the equations is viewed in a way that 'radically differs from the standard point of view'. The conclusions of these papers are shown to be totally unfounded. (from the history of physics)

The Einstein-Hilbert gravitation with minimum length

Science.gov (United States)

Louzada, H. L. C.

2018-05-01

We study the Einstein-Hilbert gravitation with the deformed Heisenberg algebra leading to the minimum length, with the intention to find and estimate the corrections in this theory, clarifying whether or not it is possible to obtain, by means of the minimum length, a theory, in D=4, which is causal, unitary and provides a massive graviton. Therefore, we will calculate and analyze the dispersion relationships of the considered theory.

Hilbert Series and Mixed Branches of T[SU(N)] theories

Energy Technology Data Exchange (ETDEWEB)

Carta, Federico [Departamento de Física Teórica and Instituto de Física Teórica UAM-CSIC,Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Hayashi, Hirotaka [Departamento de Física Teórica and Instituto de Física Teórica UAM-CSIC,Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Tokai University,4-1-1 Kitakaname, Hiratsuka, Kanagawa 259-1292 (Japan)

2017-02-07

We consider mixed branches of 3dN=4T[SU(N)] theory. We compute the Hilbert series of the Coulomb branch part of the mixed branch from a restriction rule acting on the Hilbert series of the full Coulomb branch that will truncate the magnetic charge summation only to the subset of BPS dressed monopole operators that arise in the Coulomb branch sublocus where the mixed branch stems. This restriction can be understood directly from the type IIB brane picture by a relation between the magnetic charges of the monopoles and brane position moduli. We also apply the restriction rule to the Higgs branch part of a given mixed branch by exploiting 3d mirror symmetry. Both cases show complete agreement with the results calculated by different methods.

Paramecium: An Extensible Object-Based Kernel

NARCIS (Netherlands)

van Doorn, L.; Homburg, P.; Tanenbaum, A.S.

1995-01-01

In this paper we describe the design of an extensible kernel, called Paramecium. This kernel uses an object-based software architecture which together with instance naming, late binding and explicit overrides enables easy reconfiguration. Determining which components reside in the kernel protection

7 CFR 981.401 - Adjusted kernel weight.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Adjusted kernel weight. 981.401 Section 981.401... Administrative Rules and Regulations § 981.401 Adjusted kernel weight. (a) Definition. Adjusted kernel weight... kernels in excess of five percent; less shells, if applicable; less processing loss of one percent for...

An unconventional canonical quantization of local scalar fields over quantum space-time

International Nuclear Information System (INIS)

Banai, M.

1985-12-01

An unconventional extension of the canonical quantization method is presented for a classical local field theory. The proposed canonical commutation relations have a solution in the A-valued Hilbert space where A is the algebra of the bounded operators of the Hilbert space Lsup(2) (IRsup(3)). The canonical equations as operator equations are equivalent formally with the classical field equations, and are well defined for interacting systems, too. This model of quantized field lacks some of the difficulties of the conventional approach. Examples satisfying the asymptotic condition provide examples for Haag-Kastler's axioms, however, they satisfy Wightman's axioms only partially. (author)

Performance analysis and kernel size study of the Lynx real-time operating system

Science.gov (United States)

Liu, Yuan-Kwei; Gibson, James S.; Fernquist, Alan R.

1993-01-01

This paper analyzes the Lynx real-time operating system (LynxOS), which has been selected as the operating system for the Space Station Freedom Data Management System (DMS). The features of LynxOS are compared to other Unix-based operating system (OS). The tools for measuring the performance of LynxOS, which include a high-speed digital timer/counter board, a device driver program, and an application program, are analyzed. The timings for interrupt response, process creation and deletion, threads, semaphores, shared memory, and signals are measured. The memory size of the DMS Embedded Data Processor (EDP) is limited. Besides, virtual memory is not suitable for real-time applications because page swap timing may not be deterministic. Therefore, the DMS software, including LynxOS, has to fit in the main memory of an EDP. To reduce the LynxOS kernel size, the following steps are taken: analyzing the factors that influence the kernel size; identifying the modules of LynxOS that may not be needed in an EDP; adjusting the system parameters of LynxOS; reconfiguring the device drivers used in the LynxOS; and analyzing the symbol table. The reductions in kernel disk size, kernel memory size and total kernel size reduction from each step mentioned above are listed and analyzed.

Nonlinear association criterion, nonlinear Granger causality and related issues with applications to neuroimage studies.

Science.gov (United States)

Tao, Chenyang; Feng, Jianfeng

2016-03-15

Quantifying associations in neuroscience (and many other scientific disciplines) is often challenged by high-dimensionality, nonlinearity and noisy observations. Many classic methods have either poor power or poor scalability on data sets of the same or different scales such as genetical, physiological and image data. Based on the framework of reproducing kernel Hilbert spaces we proposed a new nonlinear association criteria (NAC) with an efficient numerical algorithm and p-value approximation scheme. We also presented mathematical justification that links the proposed method to related methods such as kernel generalized variance, kernel canonical correlation analysis and Hilbert-Schmidt independence criteria. NAC allows the detection of association between arbitrary input domain as long as a characteristic kernel is defined. A MATLAB package was provided to facilitate applications. Extensive simulation examples and four real world neuroscience examples including functional MRI causality, Calcium imaging and imaging genetic studies on autism [Brain, 138(5):13821393 (2015)] and alcohol addiction [PNAS, 112(30):E4085-E4093 (2015)] are used to benchmark NAC. It demonstrates the superior performance over the existing procedures we tested and also yields biologically significant results for the real world examples. NAC beats its linear counterparts when nonlinearity is presented in the data. It also shows more robustness against different experimental setups compared with its nonlinear counterparts. In this work we presented a new and robust statistical approach NAC for measuring associations. It could serve as an interesting alternative to the existing methods for datasets where nonlinearity and other confounding factors are present. Copyright © 2016 Elsevier B.V. All rights reserved.

Clustering in Hilbert simplex geometry

KAUST Repository

Nielsen, Frank

2017-04-03

Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.

Testing Infrastructure for Operating System Kernel Development

DEFF Research Database (Denmark)

Walter, Maxwell; Karlsson, Sven

2014-01-01

Testing is an important part of system development, and to test effectively we require knowledge of the internal state of the system under test. Testing an operating system kernel is a challenge as it is the operating system that typically provides access to this internal state information. Multi......-core kernels pose an even greater challenge due to concurrency and their shared kernel state. In this paper, we present a testing framework that addresses these challenges by running the operating system in a virtual machine, and using virtual machine introspection to both communicate with the kernel...... and obtain information about the system. We have also developed an in-kernel testing API that we can use to develop a suite of unit tests in the kernel. We are using our framework for for the development of our own multi-core research kernel....

7 CFR 51.1403 - Kernel color classification.

Science.gov (United States)

2010-01-01

... 7 Agriculture 2 2010-01-01 2010-01-01 false Kernel color classification. 51.1403 Section 51.1403... STANDARDS) United States Standards for Grades of Pecans in the Shell 1 Kernel Color Classification § 51.1403 Kernel color classification. (a) The skin color of pecan kernels may be described in terms of the color...

Encoding Dissimilarity Data for Statistical Model Building.

Science.gov (United States)

Wahba, Grace

2010-12-01

We summarize, review and comment upon three papers which discuss the use of discrete, noisy, incomplete, scattered pairwise dissimilarity data in statistical model building. Convex cone optimization codes are used to embed the objects into a Euclidean space which respects the dissimilarity information while controlling the dimension of the space. A "newbie" algorithm is provided for embedding new objects into this space. This allows the dissimilarity information to be incorporated into a Smoothing Spline ANOVA penalized likelihood model, a Support Vector Machine, or any model that will admit Reproducing Kernel Hilbert Space components, for nonparametric regression, supervised learning, or semi-supervised learning. Future work and open questions are discussed. The papers are: F. Lu, S. Keles, S. Wright and G. Wahba 2005. A framework for kernel regularization with application to protein clustering. Proceedings of the National Academy of Sciences 102, 12332-1233.G. Corrada Bravo, G. Wahba, K. Lee, B. Klein, R. Klein and S. Iyengar 2009. Examining the relative influence of familial, genetic and environmental covariate information in flexible risk models. Proceedings of the National Academy of Sciences 106, 8128-8133F. Lu, Y. Lin and G. Wahba. Robust manifold unfolding with kernel regularization. TR 1008, Department of Statistics, University of Wisconsin-Madison.

Concerning the Hilbert 16th problem

CERN Document Server

Ilyashenko, Yu; Il'yashenko, Yu

1995-01-01

This book examines qualitative properties of vector fields in the plane, in the spirit of Hilbert's Sixteenth Problem. Two principal topics explored are bifurcations of limit cycles of planar vector fields and desingularization of singular points for individual vector fields and for analytic families of such fields. In addition to presenting important new developments in this area, this book contains an introductory paper which outlines the general context and describes connections between the papers in the volume. The book will appeal to researchers and graduate students working in the qualit

The definition of kernel Oz

OpenAIRE

Smolka, Gert

1994-01-01

Oz is a concurrent language providing for functional, object-oriented, and constraint programming. This paper defines Kernel Oz, a semantically complete sublanguage of Oz. It was an important design requirement that Oz be definable by reduction to a lean kernel language. The definition of Kernel Oz introduces three essential abstractions: the Oz universe, the Oz calculus, and the actor model. The Oz universe is a first-order structure defining the values and constraints Oz computes with. The ...

Fabrication of Uranium Oxycarbide Kernels for HTR Fuel

International Nuclear Information System (INIS)

Barnes, Charles; Richardson, Clay; Nagley, Scott; Hunn, John; Shaber, Eric

2010-01-01

Babcock and Wilcox (B and W) has been producing high quality uranium oxycarbide (UCO) kernels for Advanced Gas Reactor (AGR) fuel tests at the Idaho National Laboratory. In 2005, 350-(micro)m, 19.7% 235U-enriched UCO kernels were produced for the AGR-1 test fuel. Following coating of these kernels and forming the coated-particles into compacts, this fuel was irradiated in the Advanced Test Reactor (ATR) from December 2006 until November 2009. B and W produced 425-(micro)m, 14% enriched UCO kernels in 2008, and these kernels were used to produce fuel for the AGR-2 experiment that was inserted in ATR in 2010. B and W also produced 500-(micro)m, 9.6% enriched UO2 kernels for the AGR-2 experiments. Kernels of the same size and enrichment as AGR-1 were also produced for the AGR-3/4 experiment. In addition to fabricating enriched UCO and UO2 kernels, B and W has produced more than 100 kg of natural uranium UCO kernels which are being used in coating development tests. Successive lots of kernels have demonstrated consistent high quality and also allowed for fabrication process improvements. Improvements in kernel forming were made subsequent to AGR-1 kernel production. Following fabrication of AGR-2 kernels, incremental increases in sintering furnace charge size have been demonstrated. Recently small scale sintering tests using a small development furnace equipped with a residual gas analyzer (RGA) has increased understanding of how kernel sintering parameters affect sintered kernel properties. The steps taken to increase throughput and process knowledge have reduced kernel production costs. Studies have been performed of additional modifications toward the goal of increasing capacity of the current fabrication line to use for production of first core fuel for the Next Generation Nuclear Plant (NGNP) and providing a basis for the design of a full scale fuel fabrication facility.

Ranking Support Vector Machine with Kernel Approximation.

Science.gov (United States)

Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.

Ranking Support Vector Machine with Kernel Approximation

Directory of Open Access Journals (Sweden)

Kai Chen

2017-01-01

Full Text Available Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels can give higher accuracy than linear RankSVM (RankSVM with a linear kernel for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.

Dose point kernels for beta-emitting radioisotopes

International Nuclear Information System (INIS)

Prestwich, W.V.; Chan, L.B.; Kwok, C.S.; Wilson, B.

1986-01-01

Knowledge of the dose point kernel corresponding to a specific radionuclide is required to calculate the spatial dose distribution produced in a homogeneous medium by a distributed source. Dose point kernels for commonly used radionuclides have been calculated previously using as a basis monoenergetic dose point kernels derived by numerical integration of a model transport equation. The treatment neglects fluctuations in energy deposition, an effect which has been later incorporated in dose point kernels calculated using Monte Carlo methods. This work describes new calculations of dose point kernels using the Monte Carlo results as a basis. An analytic representation of the monoenergetic dose point kernels has been developed. This provides a convenient method both for calculating the dose point kernel associated with a given beta spectrum and for incorporating the effect of internal conversion. An algebraic expression for allowed beta spectra has been accomplished through an extension of the Bethe-Bacher approximation, and tested against the exact expression. Simplified expression for first-forbidden shape factors have also been developed. A comparison of the calculated dose point kernel for 32 P with experimental data indicates good agreement with a significant improvement over the earlier results in this respect. An analytic representation of the dose point kernel associated with the spectrum of a single beta group has been formulated. 9 references, 16 figures, 3 tables

Rare variant testing across methods and thresholds using the multi-kernel sequence kernel association test (MK-SKAT).

Science.gov (United States)

Urrutia, Eugene; Lee, Seunggeun; Maity, Arnab; Zhao, Ni; Shen, Judong; Li, Yun; Wu, Michael C

Analysis of rare genetic variants has focused on region-based analysis wherein a subset of the variants within a genomic region is tested for association with a complex trait. Two important practical challenges have emerged. First, it is difficult to choose which test to use. Second, it is unclear which group of variants within a region should be tested. Both depend on the unknown true state of nature. Therefore, we develop the Multi-Kernel SKAT (MK-SKAT) which tests across a range of rare variant tests and groupings. Specifically, we demonstrate that several popular rare variant tests are special cases of the sequence kernel association test which compares pair-wise similarity in trait value to similarity in the rare variant genotypes between subjects as measured through a kernel function. Choosing a particular test is equivalent to choosing a kernel. Similarly, choosing which group of variants to test also reduces to choosing a kernel. Thus, MK-SKAT uses perturbation to test across a range of kernels. Simulations and real data analyses show that our framework controls type I error while maintaining high power across settings: MK-SKAT loses power when compared to the kernel for a particular scenario but has much greater power than poor choices.

Hilbert-Schmidt quantum coherence in multi-qudit systems

Science.gov (United States)

Maziero, Jonas

2017-11-01

Using Bloch's parametrization for qudits ( d-level quantum systems), we write the Hilbert-Schmidt distance (HSD) between two generic n-qudit states as an Euclidean distance between two vectors of observables mean values in R^{Π_{s=1}nds2-1}, where ds is the dimension for qudit s. Then, applying the generalized Gell-Mann's matrices to generate SU(ds), we use that result to obtain the Hilbert-Schmidt quantum coherence (HSC) of n-qudit systems. As examples, we consider in detail one-qubit, one-qutrit, two-qubit, and two copies of one-qubit states. In this last case, the possibility for controlling local and non-local coherences by tuning local populations is studied, and the contrasting behaviors of HSC, l1-norm coherence, and relative entropy of coherence in this regard are noticed. We also investigate the decoherent dynamics of these coherence functions under the action of qutrit dephasing and dissipation channels. At last, we analyze the non-monotonicity of HSD under tensor products and report the first instance of a consequence (for coherence quantification) of this kind of property of a quantum distance measure.

Polynomial approximation of functions in Sobolev spaces

International Nuclear Information System (INIS)

Dupont, T.; Scott, R.

1980-01-01

Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces

Metabolic network prediction through pairwise rational kernels.

Science.gov (United States)

Roche-Lima, Abiel; Domaratzki, Michael; Fristensky, Brian

2014-09-26

Metabolic networks are represented by the set of metabolic pathways. Metabolic pathways are a series of biochemical reactions, in which the product (output) from one reaction serves as the substrate (input) to another reaction. Many pathways remain incompletely characterized. One of the major challenges of computational biology is to obtain better models of metabolic pathways. Existing models are dependent on the annotation of the genes. This propagates error accumulation when the pathways are predicted by incorrectly annotated genes. Pairwise classification methods are supervised learning methods used to classify new pair of entities. Some of these classification methods, e.g., Pairwise Support Vector Machines (SVMs), use pairwise kernels. Pairwise kernels describe similarity measures between two pairs of entities. Using pairwise kernels to handle sequence data requires long processing times and large storage. Rational kernels are kernels based on weighted finite-state transducers that represent similarity measures between sequences or automata. They have been effectively used in problems that handle large amount of sequence information such as protein essentiality, natural language processing and machine translations. We create a new family of pairwise kernels using weighted finite-state transducers (called Pairwise Rational Kernel (PRK)) to predict metabolic pathways from a variety of biological data. PRKs take advantage of the simpler representations and faster algorithms of transducers. Because raw sequence data can be used, the predictor model avoids the errors introduced by incorrect gene annotations. We then developed several experiments with PRKs and Pairwise SVM to validate our methods using the metabolic network of Saccharomyces cerevisiae. As a result, when PRKs are used, our method executes faster in comparison with other pairwise kernels. Also, when we use PRKs combined with other simple kernels that include evolutionary information, the accuracy

Relativistic resonances as non-orthogonal states in Hilbert space

CERN Document Server

Blum, W

2003-01-01

We analyze the energy-momentum properties of relativistic short-lived particles with the result that they are characterized by two 4-vectors: in addition to the familiar energy-momentum vector (timelike) there is an energy-momentum 'spread vector' (spacelike). The wave functions in space and time for unstable particles are constructed. For the relativistic properties of unstable states we refer to Wigner's method of Poincare group representations that are induced by representations of the space-time translation and rotation groups. If stable particles, unstable particles and resonances are treated as elementary objects that are not fundamentally different one has to take into account that they will not generally be orthogonal to each other in their state space. The scalar product between a stable and an unstable state with otherwise identical properties is calculated in a particular Lorentz frame. The spin of an unstable particle is not infinitely sharp but has a 'spin spread' giving rise to 'spin neighbors'....

Stochastic quantization of topological field theory: generalized Langevin equation with memory kernel

International Nuclear Information System (INIS)

Menezes, G.; Svaiter, N.F.

2006-04-01

We use the method of stochastic quantization in a topological field theory defined in an Euclidean space, assuming a Langevin equation with a memory kernel. We show that our procedure for the Abelian Chern-Simons theory converges regardless of the nature of the Chern-Simons coefficient. (author)

Moduli Spaces for Linear Differential Equations and the Painlevé Equations

NARCIS (Netherlands)

Put, Marius van der; Saito, Masa-Hiko

2009-01-01

A systematic construction of isomonodromic families of connections of rank two on the Riemarm sphere is obtained by considering the analytic Riemann-Hilbert map RH : M -> R, where M is a moduli space of connections and 72, the monodromy space, is a moduli space for analytic data (i.e., ordinary

Influence Function and Robust Variant of Kernel Canonical Correlation Analysis

OpenAIRE

Alam, Md. Ashad; Fukumizu, Kenji; Wang, Yu-Ping

2017-01-01

Many unsupervised kernel methods rely on the estimation of the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both kernel CO and kernel CCO are sensitive to contaminated data, even when bounded positive definite kernels are used. To the best of our knowledge, there are few well-founded robust kernel methods for statistical unsupervised learning. In addition, while the influence function (IF) of an estimator can characterize its robustness, asymptotic ...

The Linux kernel as flexible product-line architecture

NARCIS (Netherlands)

M. de Jonge (Merijn)

2002-01-01

textabstractThe Linux kernel source tree is huge ($>$ 125 MB) and inflexible (because it is difficult to add new kernel components). We propose to make this architecture more flexible by assembling kernel source trees dynamically from individual kernel components. Users then, can select what

Exploiting graph kernels for high performance biomedical relation extraction.

Science.gov (United States)

Panyam, Nagesh C; Verspoor, Karin; Cohn, Trevor; Ramamohanarao, Kotagiri

2018-01-30

Relation extraction from biomedical publications is an important task in the area of semantic mining of text. Kernel methods for supervised relation extraction are often preferred over manual feature engineering methods, when classifying highly ordered structures such as trees and graphs obtained from syntactic parsing of a sentence. Tree kernels such as the Subset Tree Kernel and Partial Tree Kernel have been shown to be effective for classifying constituency parse trees and basic dependency parse graphs of a sentence. Graph kernels such as the All Path Graph kernel (APG) and Approximate Subgraph Matching (ASM) kernel have been shown to be suitable for classifying general graphs with cycles, such as the enhanced dependency parse graph of a sentence. In this work, we present a high performance Chemical-Induced Disease (CID) relation extraction system. We present a comparative study of kernel methods for the CID task and also extend our study to the Protein-Protein Interaction (PPI) extraction task, an important biomedical relation extraction task. We discuss novel modifications to the ASM kernel to boost its performance and a method to apply graph kernels for extracting relations expressed in multiple sentences. Our system for CID relation extraction attains an F-score of 60%, without using external knowledge sources or task specific heuristic or rules. In comparison, the state of the art Chemical-Disease Relation Extraction system achieves an F-score of 56% using an ensemble of multiple machine learning methods, which is then boosted to 61% with a rule based system employing task specific post processing rules. For the CID task, graph kernels outperform tree kernels substantially, and the best performance is obtained with APG kernel that attains an F-score of 60%, followed by the ASM kernel at 57%. The performance difference between the ASM and APG kernels for CID sentence level relation extraction is not significant. In our evaluation of ASM for the PPI task, ASM

A Novel Approach for Microgrid Protection Based upon Combined ANFIS and Hilbert Space-Based Power Setting

Directory of Open Access Journals (Sweden)

Ali Hadi Abdulwahid

2016-12-01

Full Text Available Nowadays, the use of distributed generation (DG has increased because of benefits such as increased reliability, reduced losses, improvement in the line capacity, and less environmental pollution. The protection of microgrids, which consist of generation sources, is one of the most crucial concerns of basic distribution operators. One of the key issues in this field is the protection of microgrids against permanent and temporary failures by improving the safety and reliability of the network. The traditional method has a number of disadvantages. The reliability and stability of a power system in a microgrid depend to a great extent on the efficiency of the protection scheme. The application of Artificial Intelligence approaches was introduced recently in the protection of distribution networks. The fault detection method depends on differential relay based on Hilbert Space-Based Power (HSBP theory to achieve fastest primary protection. It is backed up by a total harmonic distortion (THD detection method that takes over in case of a failure in the primary method. The backup protection would be completely independent of the main protection. This is rarely attained in practice. This paper proposes a new algorithm to improve protection performance by adaptive network-based fuzzy inference system (ANFIS. The protection can be obtained in a novel way based on this theory. An advantage of this algorithm is that the protection system operates in fewer than two cycles after the occurrence of the fault. Another advantage is that the error detection is not dependent on the selection of threshold values, and all types of internal fault can identify and show that the algorithm operates correctly for all types of faults while preventing unwanted tripping, even if the data were distorted by current transformer (CT saturation or by data mismatches. The simulation results show that the proposed circuit can identify the faulty phase in the microgrid quickly and

Intelligent Control of a Sensor-Actuator System via Kernelized Least-Squares Policy Iteration

Directory of Open Access Journals (Sweden)

Bo Liu

2012-02-01

Full Text Available In this paper a new framework, called Compressive Kernelized Reinforcement Learning (CKRL, for computing near-optimal policies in sequential decision making with uncertainty is proposed via incorporating the non-adaptive data-independent Random Projections and nonparametric Kernelized Least-squares Policy Iteration (KLSPI. Random Projections are a fast, non-adaptive dimensionality reduction framework in which high-dimensionality data is projected onto a random lower-dimension subspace via spherically random rotation and coordination sampling. KLSPI introduce kernel trick into the LSPI framework for Reinforcement Learning, often achieving faster convergence and providing automatic feature selection via various kernel sparsification approaches. In this approach, policies are computed in a low-dimensional subspace generated by projecting the high-dimensional features onto a set of random basis. We first show how Random Projections constitute an efficient sparsification technique and how our method often converges faster than regular LSPI, while at lower computational costs. Theoretical foundation underlying this approach is a fast approximation of Singular Value Decomposition (SVD. Finally, simulation results are exhibited on benchmark MDP domains, which confirm gains both in computation time and in performance in large feature spaces.

Riesz Representation Theorem on Bilinear Spaces of Truncated Laurent Series

Directory of Open Access Journals (Sweden)

Sabarinsyah

2017-06-01

Full Text Available In this study a generalization of the Riesz representation theorem on non-degenerate bilinear spaces, particularly on spaces of truncated Laurent series, was developed. It was shown that any linear functional on a non-degenerate bilinear space is representable by a unique element of the space if and only if its kernel is closed. Moreover an explicit equivalent condition can be identified for the closedness property of the kernel when the bilinear space is a space of truncated Laurent series.

Second order evolution inclusions governed by sweeping process in Banach spaces

Directory of Open Access Journals (Sweden)

A. G. Ibrahim

2009-11-01

Full Text Available In this paper we prove two existence theorems concerning the existence of solutions for second order evolution inclusions governed by sweeping process with closed convex sets depending on time and state in Banach spaces. This work extends some recent existence theorems cncerning sweeping process from Hilbert spaces to Banach spaces.

Predicting complex traits using a diffusion kernel on genetic markers with an application to dairy cattle and wheat data

Science.gov (United States)

2013-01-01

Background Arguably, genotypes and phenotypes may be linked in functional forms that are not well addressed by the linear additive models that are standard in quantitative genetics. Therefore, developing statistical learning models for predicting phenotypic values from all available molecular information that are capable of capturing complex genetic network architectures is of great importance. Bayesian kernel ridge regression is a non-parametric prediction model proposed for this purpose. Its essence is to create a spatial distance-based relationship matrix called a kernel. Although the set of all single nucleotide polymorphism genotype configurations on which a model is built is finite, past research has mainly used a Gaussian kernel. Results We sought to investigate the performance of a diffusion kernel, which was specifically developed to model discrete marker inputs, using Holstein cattle and wheat data. This kernel can be viewed as a discretization of the Gaussian kernel. The predictive ability of the diffusion kernel was similar to that of non-spatial distance-based additive genomic relationship kernels in the Holstein data, but outperformed the latter in the wheat data. However, the difference in performance between the diffusion and Gaussian kernels was negligible. Conclusions It is concluded that the ability of a diffusion kernel to capture the total genetic variance is not better than that of a Gaussian kernel, at least for these data. Although the diffusion kernel as a choice of basis function may have potential for use in whole-genome prediction, our results imply that embedding genetic markers into a non-Euclidean metric space has very small impact on prediction. Our results suggest that use of the black box Gaussian kernel is justified, given its connection to the diffusion kernel and its similar predictive performance. PMID:23763755

GRIM : Leveraging GPUs for Kernel integrity monitoring

NARCIS (Netherlands)

Koromilas, Lazaros; Vasiliadis, Giorgos; Athanasopoulos, Ilias; Ioannidis, Sotiris

2016-01-01

Kernel rootkits can exploit an operating system and enable future accessibility and control, despite all recent advances in software protection. A promising defense mechanism against rootkits is Kernel Integrity Monitor (KIM) systems, which inspect the kernel text and data to discover any malicious

Space-filling Curves

Indian Academy of Sciences (India)

void hilbert(int r, int d, int t, int u, int i, int h, int &x, int &y). { if(i >0). { i- -; hilbert ( d,r, u,e ,i,h,x,y); move(r ,h,x,y); hilbert(r,d,t,u,i,h,x,y); move ( d,h,x,y); hilbert(r,d,e,u,i ...

7 CFR 51.2296 - Three-fourths half kernel.

Science.gov (United States)

2010-01-01

... 7 Agriculture 2 2010-01-01 2010-01-01 false Three-fourths half kernel. 51.2296 Section 51.2296 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards...-fourths half kernel. Three-fourths half kernel means a portion of a half of a kernel which has more than...

Greedy Algorithms for Reduced Bases in Banach Spaces

KAUST Repository

DeVore, Ronald

2013-02-26

Given a Banach space X and one of its compact sets F, we consider the problem of finding a good n-dimensional space X n⊂X which can be used to approximate the elements of F. The best possible error we can achieve for such an approximation is given by the Kolmogorov width dn(F)X. However, finding the space which gives this performance is typically numerically intractable. Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method for solving a parametric family of PDEs. The performance of this greedy algorithm was initially analyzed in Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) in the case X=H is a Hilbert space. The results of Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) were significantly improved upon in Binev et al. (SIAM J. Math. Anal. 43:1457-1472, 2011). The purpose of the present paper is to give a new analysis of the performance of such greedy algorithms. Our analysis not only gives improved results for the Hilbert space case but can also be applied to the same greedy procedure in general Banach spaces. © 2013 Springer Science+Business Media New York.

Equivalence of quotient Hilbert modules

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

w), that is, γ is an anti-holomorphic frame for E. In the case of n > 1, a similar construction of an anti-holomorphic hermitian vector bundle of rank n can be given. In our case, it is easy to verify that K(·, w), the reproducing kernel at w, is a common ...

Cutting force response in milling of Inconel: analysis by wavelet and Hilbert-Huang Transforms

Directory of Open Access Journals (Sweden)

Grzegorz Litak

Full Text Available We study the milling process of Inconel. By continuously increasing the cutting depth we follow the system response and appearance of oscillations of larger amplitude. The cutting force amplitude and frequency analysis has been done by means of wavelets and Hilbert-Huang transform. We report that in our system the force oscillations are closely related to the rotational motion of the tool and advocate for a regenerative mechanism of chatter vibrations. To identify vibrations amplitudes occurrence in time scale we apply wavelet and Hilbert-Huang transforms.

On the discovery of the gravitational field equations by Einstein and Hilbert: new materials

International Nuclear Information System (INIS)

Vizgin, Vladimir P

2001-01-01

This article describes the history of discovery of the equations of gravitational field by Albert Einstein and David Hilbert in November 1915. The proof sheet of Hilbert's lecture report, made on 20 November 1915 and published in March 1916, rediscovered in 1997 in the archive of the university of Goettingen, throws new light on the history of this discovery. We also discuss the early history of the general theory of relativity that led to the expression of the general covariant equations of gravitational field. (from the history of physics)

Revisiting the definition of local hardness and hardness kernel.

Science.gov (United States)

Polanco-Ramírez, Carlos A; Franco-Pérez, Marco; Carmona-Espíndola, Javier; Gázquez, José L; Ayers, Paul W

2017-05-17

An analysis of the hardness kernel and local hardness is performed to propose new definitions for these quantities that follow a similar pattern to the one that characterizes the quantities associated with softness, that is, we have derived new definitions for which the integral of the hardness kernel over the whole space of one of the variables leads to local hardness, and the integral of local hardness over the whole space leads to global hardness. A basic aspect of the present approach is that global hardness keeps its identity as the second derivative of energy with respect to the number of electrons. Local hardness thus obtained depends on the first and second derivatives of energy and electron density with respect to the number of electrons. When these derivatives are approximated by a smooth quadratic interpolation of energy, the expression for local hardness reduces to the one intuitively proposed by Meneses, Tiznado, Contreras and Fuentealba. However, when one combines the first directional derivatives with smooth second derivatives one finds additional terms that allow one to differentiate local hardness for electrophilic attack from the one for nucleophilic attack. Numerical results related to electrophilic attacks on substituted pyridines, substituted benzenes and substituted ethenes are presented to show the overall performance of the new definition.

Continuous spin mean-field models : Limiting kernels and Gibbs properties of local transforms

NARCIS (Netherlands)

Kulske, Christof; Opoku, Alex A.

2008-01-01

We extend the notion of Gibbsianness for mean-field systems to the setup of general (possibly continuous) local state spaces. We investigate the Gibbs properties of systems arising from an initial mean-field Gibbs measure by application of given local transition kernels. This generalizes previous

Examining Potential Boundary Bias Effects in Kernel Smoothing on Equating: An Introduction for the Adaptive and Epanechnikov Kernels.

Science.gov (United States)

Cid, Jaime A; von Davier, Alina A

2015-05-01

Test equating is a method of making the test scores from different test forms of the same assessment comparable. In the equating process, an important step involves continuizing the discrete score distributions. In traditional observed-score equating, this step is achieved using linear interpolation (or an unscaled uniform kernel). In the kernel equating (KE) process, this continuization process involves Gaussian kernel smoothing. It has been suggested that the choice of bandwidth in kernel smoothing controls the trade-off between variance and bias. In the literature on estimating density functions using kernels, it has also been suggested that the weight of the kernel depends on the sample size, and therefore, the resulting continuous distribution exhibits bias at the endpoints, where the samples are usually smaller. The purpose of this article is (a) to explore the potential effects of atypical scores (spikes) at the extreme ends (high and low) on the KE method in distributions with different degrees of asymmetry using the randomly equivalent groups equating design (Study I), and (b) to introduce the Epanechnikov and adaptive kernels as potential alternative approaches to reducing boundary bias in smoothing (Study II). The beta-binomial model is used to simulate observed scores reflecting a range of different skewed shapes.

Adaptive Kernel in Meshsize Boosting Algorithm in KDE ...

African Journals Online (AJOL)

This paper proposes the use of adaptive kernel in a meshsize boosting algorithm in kernel density estimation. The algorithm is a bias reduction scheme like other existing schemes but uses adaptive kernel instead of the regular fixed kernels. An empirical study for this scheme is conducted and the findings are comparatively ...

Should I stay or should I go? A habitat-dependent dispersal kernel improves prediction of movement.

Directory of Open Access Journals (Sweden)

Fabrice Vinatier

Full Text Available The analysis of animal movement within different landscapes may increase our understanding of how landscape features affect the perceptual range of animals. Perceptual range is linked to movement probability of an animal via a dispersal kernel, the latter being generally considered as spatially invariant but could be spatially affected. We hypothesize that spatial plasticity of an animal's dispersal kernel could greatly modify its distribution in time and space. After radio tracking the movements of walking insects (Cosmopolites sordidus in banana plantations, we considered the movements of individuals as states of a Markov chain whose transition probabilities depended on the habitat characteristics of current and target locations. Combining a likelihood procedure and pattern-oriented modelling, we tested the hypothesis that dispersal kernel depended on habitat features. Our results were consistent with the concept that animal dispersal kernel depends on habitat features. Recognizing the plasticity of animal movement probabilities will provide insight into landscape-level ecological processes.

Should I stay or should I go? A habitat-dependent dispersal kernel improves prediction of movement.

Science.gov (United States)

Vinatier, Fabrice; Lescourret, Françoise; Duyck, Pierre-François; Martin, Olivier; Senoussi, Rachid; Tixier, Philippe

2011-01-01

The analysis of animal movement within different landscapes may increase our understanding of how landscape features affect the perceptual range of animals. Perceptual range is linked to movement probability of an animal via a dispersal kernel, the latter being generally considered as spatially invariant but could be spatially affected. We hypothesize that spatial plasticity of an animal's dispersal kernel could greatly modify its distribution in time and space. After radio tracking the movements of walking insects (Cosmopolites sordidus) in banana plantations, we considered the movements of individuals as states of a Markov chain whose transition probabilities depended on the habitat characteristics of current and target locations. Combining a likelihood procedure and pattern-oriented modelling, we tested the hypothesis that dispersal kernel depended on habitat features. Our results were consistent with the concept that animal dispersal kernel depends on habitat features. Recognizing the plasticity of animal movement probabilities will provide insight into landscape-level ecological processes.

A kernel version of multivariate alteration detection

DEFF Research Database (Denmark)

Nielsen, Allan Aasbjerg; Vestergaard, Jacob Schack

2013-01-01

Based on the established methods kernel canonical correlation analysis and multivariate alteration detection we introduce a kernel version of multivariate alteration detection. A case study with SPOT HRV data shows that the kMAD variates focus on extreme change observations.......Based on the established methods kernel canonical correlation analysis and multivariate alteration detection we introduce a kernel version of multivariate alteration detection. A case study with SPOT HRV data shows that the kMAD variates focus on extreme change observations....

Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter.

Science.gov (United States)

Zhuang, Leimeng; Khan, Muhammad Rezaul; Beeker, Willem; Leinse, Arne; Heideman, René; Roeloffzen, Chris

2012-11-19

We propose and demonstrate a novel wideband microwave photonic fractional Hilbert transformer implemented using a ring resonator-based optical all-pass filter. The full programmability of the ring resonator allows variable and arbitrary fractional order of the Hilbert transformer. The performance analysis in both frequency and time domain validates that the proposed implementation provides a good approximation to an ideal fractional Hilbert transformer. This is also experimentally verified by an electrical S21 response characterization performed on a waveguide realization of a ring resonator. The waveguide-based structure allows the proposed Hilbert transformer to be integrated together with other building blocks on a photonic integrated circuit to create various system-level functionalities for on-chip microwave photonic signal processors. As an example, a circuit consisting of a splitter and a ring resonator has been realized which can perform on-chip phase control of microwave signals generated by means of optical heterodyning, and simultaneous generation of in-phase and quadrature microwave signals for a wide frequency range. For these functionalities, this simple and on-chip solution is considered to be practical, particularly when operating together with a dual-frequency laser. To our best knowledge, this is the first-time on-chip demonstration where ring resonators are employed to perform phase control functionalities for optical generation of microwave signals by means of optical heterodyning.

Symmetry-adapted Liouville space. Pt. 7

International Nuclear Information System (INIS)

Temme, F.P.

1990-01-01

In examining nuclear spin dynamics of NMR spin clusters in density operator/generalized torque formalisms over vertical strokekqv>> operator bases of Liouville space, it is necessary to consider the symmetry mappings and carrier spaces under a specialized group for such (k i = 1) nuclear spin clusters. The SU2 X S n group provides the essential mappings and the form of H carrier space, which allows one to: (a) draw comparisons with Hilbert space duality, and (b) outline the form of the Coleman-Kotani genealogical hierarchy under induced S n -symmetry. (orig.)

A Proof of the Hilbert-Smith Conjecture

OpenAIRE

McAuley, Louis F.

2001-01-01

The Hilbert-Smith Conjecture states that if G is a locally compact group which acts effectively on a connected manifold as a topological transformation group, then G is a Lie group. A rather straightforward proof of this conjecture is given. The motivation is work of Cernavskii (``Finite-to-one mappings of manifolds'', Trans. of Math. Sk. 65 (107), 1964.) His work is generalized to the orbit map of an effective action of a p-adic group on compact connected n-manifolds with the aid of some new...

Uranium kernel formation via internal gelation

International Nuclear Information System (INIS)

Hunt, R.D.; Collins, J.L.

2004-01-01

In the 1970s and 1980s, U.S. Department of Energy (DOE) conducted numerous studies on the fabrication of nuclear fuel particles using the internal gelation process. These amorphous kernels were prone to flaking or breaking when gases tried to escape from the kernels during calcination and sintering. These earlier kernels would not meet today's proposed specifications for reactor fuel. In the interim, the internal gelation process has been used to create hydrous metal oxide microspheres for the treatment of nuclear waste. With the renewed interest in advanced nuclear fuel by the DOE, the lessons learned from the nuclear waste studies were recently applied to the fabrication of uranium kernels, which will become tri-isotropic (TRISO) fuel particles. These process improvements included equipment modifications, small changes to the feed formulations, and a new temperature profile for the calcination and sintering. The modifications to the laboratory-scale equipment and its operation as well as small changes to the feed composition increased the product yield from 60% to 80%-99%. The new kernels were substantially less glassy, and no evidence of flaking was found. Finally, key process parameters were identified, and their effects on the uranium microspheres and kernels are discussed. (orig.)

Quantum mechanics in phase space

DEFF Research Database (Denmark)

Hansen, Frank

1984-01-01

A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered....... Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations...

Kernel learning at the first level of inference.

Science.gov (United States)

Cawley, Gavin C; Talbot, Nicola L C

2014-05-01

Kernel learning methods, whether Bayesian or frequentist, typically involve multiple levels of inference, with the coefficients of the kernel expansion being determined at the first level and the kernel and regularisation parameters carefully tuned at the second level, a process known as model selection. Model selection for kernel machines is commonly performed via optimisation of a suitable model selection criterion, often based on cross-validation or theoretical performance bounds. However, if there are a large number of kernel parameters, as for instance in the case of automatic relevance determination (ARD), there is a substantial risk of over-fitting the model selection criterion, resulting in poor generalisation performance. In this paper we investigate the possibility of learning the kernel, for the Least-Squares Support Vector Machine (LS-SVM) classifier, at the first level of inference, i.e. parameter optimisation. The kernel parameters and the coefficients of the kernel expansion are jointly optimised at the first level of inference, minimising a training criterion with an additional regularisation term acting on the kernel parameters. The key advantage of this approach is that the values of only two regularisation parameters need be determined in model selection, substantially alleviating the problem of over-fitting the model selection criterion. The benefits of this approach are demonstrated using a suite of synthetic and real-world binary classification benchmark problems, where kernel learning at the first level of inference is shown to be statistically superior to the conventional approach, improves on our previous work (Cawley and Talbot, 2007) and is competitive with Multiple Kernel Learning approaches, but with reduced computational expense. Copyright © 2014 Elsevier Ltd. All rights reserved.

Global Polynomial Kernel Hazard Estimation

DEFF Research Database (Denmark)

Hiabu, Munir; Miranda, Maria Dolores Martínez; Nielsen, Jens Perch

2015-01-01

This paper introduces a new bias reducing method for kernel hazard estimation. The method is called global polynomial adjustment (GPA). It is a global correction which is applicable to any kernel hazard estimator. The estimator works well from a theoretical point of view as it asymptotically redu...