Uniqueness Result in the Cauchy Dirichlet Problem via Mehler Kernel
Dhungana, Bishnu P.
2014-09-01
Using the Mehler kernel, a uniqueness theorem in the Cauchy Dirichlet problem for the Hermite heat equation with homogeneous Dirichlet boundary conditions on a class P of bounded functions U( x, t) with certain growth on U x ( x, t) is established.
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.
Das, Moumita; Bhattacharya, Sourabh
2014-01-01
In this paper, using kernel convolution of order based dependent Dirichlet process (Griffin & Steel (2006)) we construct a nonstationary, nonseparable, nonparametric space-time process, which, as we show, satisfies desirable properties, and includes the stationary, separable, parametric processes as special cases. We also investigate the smoothness properties of our proposed model. Since our model entails an infinite random series, for Bayesian model fitting purpose we must either truncate th...
On the Diamond Bessel Heat Kernel
Directory of Open Access Journals (Sweden)
Wanchak Satsanit
2011-01-01
Full Text Available We study the heat equation in n dimensional by Diamond Bessel operator. We find the solution by method of convolution and Fourier transform in distribution theory and also obtain an interesting kernel related to the spectrum and the kernel which is called Bessel heat kernel.
Quantum scalar fields in the half-line. A heat kernel/zeta function approach
Mateos Guilarte, Juan; Muñoz-Castañeda, Jose María; Senosiaín Aramendía, María Jesús
2009-01-01
[EN]In this paper we shall study vacuum fluctuations of a single scalar field with Dirichlet boundary conditions in a finite but very long line. The spectral heat kernel, the heat partition function and the spectral zeta function are calculated in terms of Riemann Theta functions, the error function, and hypergeometric PFQ functions. [ES]En este artículo vamos a estudiar las fluctuaciones en el vacío de un campo escalar con las condiciones de contorno de Dirichlet en una línea finita pero muy...
Rufty, A
2006-01-01
Problems in $\\mathbb{R}^3$ are addressed where the scalar potential of an associated vector field satisfies Laplace's equation in some unbounded external region and is to be approximated by unknown (point) sources contained in the complimentary subregion. Two specific field geometries are considered: $\\mathbb{R}^3$ half-space and the exterior of an $\\mathbb{R}^3$ sphere, which are the two standard settings for geophysical and geoexploration gravitational problems. For these geometries it is shown that a new type of kernel space exists, which is labeled a Dirichlet-integral dual-access collocation-kernel space (DIDACKS) and that is well suited for many applications. The DIDACKS examples studied are related to reproducing kernel Hilbert spaces and they have a replicating kernel (as opposed to a reproducing kernel) that has the ubiquitous form of the inverse of the distance between a field point and a corresponding source point. Underpinning this approach are three basic mathematical relationships of general int...
Heat-kernel approach for scattering
Li, Wen-Du
2015-01-01
An approach for solving scattering problems, based on two quantum field theory methods, the heat kernel method and the scattering spectral method, is constructed. This approach has a special advantage: it is not only one single approach; it is indeed a set of approaches for solving scattering problems. Concretely, we build a bridge between a scattering problem and the heat kernel method, so that each method of calculating heat kernels can be converted into a method of solving a scattering problem. As applications, we construct two approaches for solving scattering problems based on two heat-kernel expansions: the Seeley-DeWitt expansion and the covariant perturbation theory. In order to apply the heat kernel method to scattering problems, we also calculate two off-diagonal heat-kernel expansions in the frames of the Seeley-DeWitt expansion and the covariant perturbation theory, respectively. Moreover, as an alternative application of the relation between heat kernels and partial-wave phase shifts presented in...
Heat Kernel Renormalization on Manifolds with Boundary
Albert, Benjamin I.
2016-01-01
In the monograph Renormalization and Effective Field Theory, Costello gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. In this paper, we extend Costello's renormalization procedure to a class of manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.
Covariant derivative expansion of the heat kernel
Energy Technology Data Exchange (ETDEWEB)
Salcedo, L.L. [Universidad de Granada, Departamento de Fisica Moderna, Granada (Spain)
2004-11-01
Using the technique of labeled operators, compact explicit expressions are given for all traced heat kernel coefficients containing zero, two, four and six covariant derivatives, and for diagonal coefficients with zero, two and four derivatives. The results apply to boundaryless flat space-times and arbitrary non-Abelian scalar and gauge background fields. (orig.)
HEAT KERNEL AND HARDY'S THEOREM FOR JACOBI TRANSFORM
Institute of Scientific and Technical Information of China (English)
T. KAWAZOE; LIU JIANMING(刘建明)
2003-01-01
In this paper, the authors obtain sharp upper and lower bounds for the heat kernel associatedwith Jacobi transform, and get some analogues of Hardy's Theorem for Jacobi transform byusing the sharp estimate of the heat kernel.
Global Heat Kernel Estimates for $\\Delta+\\Delta^{\\alpha/2}$ in Half-space-like domains
Chen, Zhen-Qing; Song, Renming
2011-01-01
Suppose that $d\\ge 1$ and $\\alpha\\in (0, 2)$. In this paper, by using probabilistic methods, we establish sharp two-sided pointwise estimates for the Dirichlet heat kernels of $\\{\\Delta+ a^\\alpha \\Delta^{\\alpha/2}; \\ a\\in (0, 1]\\}$ on half-space-like $C^{1, 1}$ domains in ${\\mathbb R}^d$ for all time $t>0$. The large time estimates for half-space-like domains are very different from those for bounded domains. Our estimates are uniform in $a \\in (0, 1]$ in the sense that the constants in the estimates are independent of $a\\in (0, 1]$. Thus it yields the Dirichlet heat kernel estimates for Brownian motion in half-space-like domains by taking $a\\to 0$. Integrating the heat kernel estimates in time $t$, we obtain uniform sharp two-sided estimates for the Green functions of $\\{\\Delta+ a^\\alpha \\Delta^{\\alpha/2}; \\ a\\in (0, 1]\\}$ in half-space-like $C^{1, 1}$ domains in ${\\mathbb R}^d$.
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...
THE HEAT KERNEL ON THE CAYLEY HEISENBERG GROUP
Institute of Scientific and Technical Information of China (English)
Luan Jingwen; Zhu Fuliu
2005-01-01
The authors obtain an explicit expression of the heat kernel for the Cayley Heisenberg group of order n by using the stochastic integral method of Gaveau. Apart from the standard Heisenberg group and the quaternionic Heisenberg group, this is the only nilpotent Lie group on which an explicit formula for the heat kernel has been obtained.
Heat kernel method and its applications
Avramidi, Ivan G
2015-01-01
The heart of the book is the development of a short-time asymptotic expansion for the heat kernel. This is explained in detail and explicit examples of some advanced calculations are given. In addition some advanced methods and extensions, including path integrals, jump diffusion and others are presented. The book consists of four parts: Analysis, Geometry, Perturbations and Applications. The first part shortly reviews of some background material and gives an introduction to PDEs. The second part is devoted to a short introduction to various aspects of differential geometry that will be needed later. The third part and heart of the book presents a systematic development of effective methods for various approximation schemes for parabolic differential equations. The last part is devoted to applications in financial mathematics, in particular, stochastic differential equations. Although this book is intended for advanced undergraduate or beginning graduate students in, it should also provide a useful reference ...
Index-free Heat Kernel Coefficients
De van Ven, A E M
1998-01-01
Using index-free notation, we present the diagonal values of the first five heat kernel coefficients associated with a general Laplace-type operator on a compact Riemannian space without boundary. The fifth coefficient appears here for the first time. For a flat space with a gauge connection, the sixth coefficient is given too. Also provided are the leading terms for any coefficient, both in ascending and descending powers of the Yang-Mills and Riemann curvatures, to the same order as required for the fourth coefficient. These results are obtained by directly solving the relevant recursion relations, working in Fock-Schwinger gauge and Riemann normal coordinates. Our procedure is thus noncovariant, but we show that for any coefficient the `gauged' respectively `curved' version is found from the corresponding `non-gauged' respectively `flat' coefficient by making some simple covariant substitutions. These substitutions being understood, the coefficients retain their `flat' form and size. In this sense the fift...
Heat kernel measures on random surfaces
Klevtsov, Semyon
2015-01-01
The heat kernel on the symmetric space of positive definite Hermitian matrices is used to endow the spaces of Bergman metrics of degree k on a Riemann surface M with a family of probability measures depending on a choice of the background metric. Under a certain matrix-metric correspondence, each positive definite Hermitian matrix corresponds to a Kahler metric on M. The one and two point functions of the random metric are calculated in a variety of limits as k and t tend to infinity. In the limit when the time t goes to infinity the fluctuations of the random metric around the background metric are the same as the fluctuations of random zeros of holomorphic sections. This is due to the fact that the random zeros form the boundary of the space of Bergman metrics.
Wrapping Brownian motion and heat kernels I: compact Lie groups
Maher, David G
2010-01-01
An important object of study in harmonic analysis is the heat equation. On a Euclidean space, the fundamental solution of the associated semigroup is known as the heat kernel, which is also the law of Brownian motion. Similar statements also hold in the case of a Lie group. By using the wrapping map of Dooley and Wildberger, we show how to wrap a Brownian motion to a compact Lie group from its Lie algebra (viewed as a Euclidean space) and find the heat kernel. This is achieved by considering It\\^o type stochastic differential equations and applying the Feynman-Ka\\v{c} theorem.
Wrapping Brownian motion and heat kernels II: symmetric spaces
Maher, David G
2010-01-01
In this paper we extend our previous results on wrapping Brownian motion and heat kernels onto compact Lie groups to various symmetric spaces, where a global generalisation of Rouvi\\`ere's formula and the $e$-function are considered. Additionally, we extend some of our results to complex Lie groups, and certain non-compact symmetric spaces.
Yan, Yan
2015-01-01
We study a new optimization scheme that generates smooth and robust solutions for Dirichlet velocity boundary control (DVBC) of conjugate heat transfer (CHT) processes. The solutions to the DVBC of the incompressible Navier-Stokes equations are typically nonsmooth, due to the regularity degradation of the boundary stress in the adjoint Navier-Stokes equations. This nonsmoothness is inherited by the solutions to the DVBC of CHT processes, since the CHT process couples the Navier-Stokes equations of fluid motion with the convection-diffusion equations of fluid-solid thermal interaction. Our objective in the CHT boundary control problem is to select optimally the fluid inflow profile that minimizes an objective function that involves the sum of the mismatch between the temperature distribution in the fluid system and a prescribed temperature profile and the cost of the control.Our strategy to resolve the nonsmoothness of the boundary control solution is based on two features, namely, the objective function with a regularization term on the gradient of the control profile on both the continuous and the discrete levels, and the optimization scheme with either explicit or implicit smoothing effects, such as the smoothed Steepest Descent and the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) methods. Our strategy to achieve the robustness of the solution process is based on combining the smoothed optimization scheme with the numerical continuation technique on the regularization parameters in the objective function. In the section of numerical studies, we present two suites of experiments. In the first one, we demonstrate the feasibility and effectiveness of our numerical schemes in recovering the boundary control profile of the standard case of a Poiseuille flow. In the second one, we illustrate the robustness of our optimization schemes via solving more challenging DVBC problems for both the channel flow and the flow past a square cylinder, which use initial
Analysis of Heat Kernel Highlights the Strongly Modular and Heat-Preserving Structure of Proteins
Livi, Lorenzo; Pinna, Andrea; Sadeghian, Alireza; Rizzi, Antonello; Giuliani, Alessandro
2014-01-01
In this paper we study the structure of three types of biochemical networks: protein, metabolic, and gene expression networks, together with simulated archetypical networks acting as probes. We consider both classical topological descriptors, such as the modularity and statistics of the shortest paths, and different interpretations in terms of diffusion provided by the well-known discrete heat kernel. A principal component analysis shows high discrimination among the network types, either by considering the topological and heat kernel based characterizations. Furthermore, a canonical correlation analysis demonstrates the strong agreement among the two characterizations, providing an important justification in terms of interpretability for the heat kernel. Finally, and most importantly, the focused analysis of the heat kernel provides us a way to yield insights on the fact that proteins have to satisfy specific structural design constraints that the other considered biochemical networks do not need to obey.
Heat-kernel coefficients for oblique boundary conditions
Dowker, John S; Kirsten, Klaus
1997-01-01
We calculate the heat-kernel coefficients, up to $a_2$, for a U(1) bundle on the 4-Ball for boundary conditions which are such that the normal derivative of the field at the boundary is related to a first-order operator in boundary derivatives acting on the field. The results are used to place restrictions on the general forms of the coefficients. In the specific case considered, there can be a breakdown of ellipticity.
Harmonic analysis with respect to heat kernel measure
Hall, B C
2000-01-01
I review certain results in harmonic analysis for systems whose configuration space is a compact Lie group. The results described involve a heat kernel measure, which plays the same role as a Gaussian measure on Euclidean space. The main constructions are group analogs of the Hermite expansion, the Segal-Bargmann transform, and the Taylor expansion. The results are related to geometric quantization, to stochastic analysis, and to the quantization of 1+1-dimensional Yang-Mills theory.
Observing integrals of heat kernels from a distance
DEFF Research Database (Denmark)
Heat kernels have integrals such as Brownian motion mean exit time, potential capacity, and torsional rigidity. We show how to obtain bounds on these values - essentially by observing their behaviour in terms of the distance function from a point and then comparing with corresponding values...... in tailor-made warped product spaces. The results will be illustrated by applications to the so-called 'type' problem: How to decide if a given manifold or surface is transient (hyperbolic) or recurrent (parabolic). Specific examples of minimal surfaces and constant pressure dry foams will be shown...
A multi-resolution approach to heat kernels on discrete surfaces
Vaxman, Amir
2010-07-26
Studying the behavior of the heat diffusion process on a manifold is emerging as an important tool for analyzing the geometry of the manifold. Unfortunately, the high complexity of the computation of the heat kernel - the key to the diffusion process - limits this type of analysis to 3D models of modest resolution. We show how to use the unique properties of the heat kernel of a discrete two dimensional manifold to overcome these limitations. Combining a multi-resolution approach with a novel approximation method for the heat kernel at short times results in an efficient and robust algorithm for computing the heat kernels of detailed models. We show experimentally that our method can achieve good approximations in a fraction of the time required by traditional algorithms. Finally, we demonstrate how these heat kernels can be used to improve a diffusion-based feature extraction algorithm. © 2010 ACM.
Nondiagonal Values of the Heat Kernel for Scalars in a Constant Electromagnetic Field
Kalinichenko, I. S.; Kazinski, P. O.
2017-03-01
An original method for finding the nondiagonal values of the heat kernel associated with the wave operator Fourier-transformed in time is proposed for the case of a constant external electromagnetic field. The connection of the trace of such a heat kernel to the one-loop correction to the grand thermodynamic potential is indicated. The structure of its singularities is analyzed.
Heat kernel for non-minimal operators on a Kähler manifold
Alexandrov, S Yu; Alexandrov, Sergei; Vassilevich, Dmitri
1996-01-01
The heat kernel expansion for a general non--minimal operator on the spaces C^\\infty (\\Lambda^k) and C^\\infty (\\Lambda^{p,q}) is studied. The coefficients of the heat kernel asymptotics for this operator are expressed in terms of the Seeley coefficients for the Hodge--de Rham Laplacian.
Heat kernel expansion in the background field formalism
Barvinsky, Andrei
2015-01-01
Heat kernel expansion and background field formalism represent the combination of two calculational methods within the functional approach to quantum field theory. This approach implies construction of generating functionals for matrix elements and expectation values of physical observables. These are functionals of arbitrary external sources or the mean field of a generic configuration -- the background field. Exact calculation of quantum effects on a generic background is impossible. However, a special integral (proper time) representation for the Green's function of the wave operator -- the propagator of the theory -- and its expansion in the ultraviolet and infrared limits of respectively short and late proper time parameter allow one to construct approximations which are valid on generic background fields. Current progress of quantum field theory, its renormalization properties, model building in unification of fundamental physical interactions and QFT applications in high energy physics, gravitation and...
Heat kernel methods for Lifshitz theories arXiv
Barvinsky, Andrei O.; Herrero-Valea, Mario; Nesterov, Dmitry V.; Pérez-Nadal, Guillem; Steinwachs, Christian F.
We study the one-loop covariant effective action of Lifshitz theories using the heat kernel technique. The characteristic feature of Lifshitz theories is an anisotropic scaling between space and time. This is enforced by the existence of a preferred foliation of space-time, which breaks Lorentz invariance. In contrast to the relativistic case, covariant Lifshitz theories are only invariant under diffeomorphisms preserving the foliation structure. We develop a systematic method to reduce the calculation of the effective action for a generic Lifshitz operator to an algorithm acting on known results for relativistic operators. In addition, we present techniques that drastically simplify the calculation for operators with special properties. We demonstrate the efficiency of these methods by explicit applications.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Taking the Lindemann model as a sample system in which there exist chemical reactions, diffusion and heat conduction, we found the theoretical framework of linear stability analysis for a unidimensional nonhomogeneous two-variable system with one end subject to Dirichlet conditions, while the other end no-flux conditions. Furthermore, the conditions for the emergence of temperature waves are found out by the linear stabiliy analysis and verified by a diagram for successive steps of evolution of spatial profile of temperature during a period that is plotted by numerical simulations on a computer. Without doubt, these results are in favor of the heat balance in chemical reactor designs.
Chung, Moo K; Qiu, Anqi; Seo, Seongho; Vorperian, Houri K
2015-05-01
We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel method is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, the method is applied to characterize the localized growth pattern of mandible surfaces obtained in CT images between ages 0 and 20 by regressing the length of displacement vectors with respect to a surface template.
Ho, Gregory S.; Lignères, Vincent L.; Carter, Emily A.
2008-07-01
We derive an analytic form of the Wang-Govind-Carter (WGC) [Wang , Phys. Rev. B 60, 16350 (1999)] kinetic energy density functional (KEDF) with the density-dependent response kernel. A real-space aperiodic implementation of the WGC KEDF is then described and used in linear scaling orbital-free density functional theory (OF-DFT) calculations.
Trace of heat kernel,spectral zeta function and isospectral problem for sub-laplacians
Institute of Scientific and Technical Information of China (English)
CHANG; Der-Chen; YEUNG; Sai-Kee
2009-01-01
In this article,we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in C n+1.Then we survey some results on the spectral zeta function which is induced by the trace of the heat kernel.In the second part of the paper,we discuss an isospectral problem in the CR setting.
Symmetries of the Super Heat Kernel N = 1 and SKdV hierarchy
Energy Technology Data Exchange (ETDEWEB)
Andrea, S.; Restuccia, A. [Departamento de Matematicas, Universidad Simon Bolivar (Venezuela); Sotomayor, A. [Departamento de Ciencias Basicas, Unexpo Luis Caballero Mejias (Venezuela)]. E-mail: sandrea@usb.ve
2006-07-01
A new heat operator with N = 1 supersymmetry is proposed. We study the symmetries of the corresponding heat kernel, which generalizes the bosonic one in a natural way. We used these symmetries to obtain, in the asymptotic limit, the super KdV hierarchy supersymmetric tree version associated with this hierarchy is presented. (Author)
Institute of Scientific and Technical Information of China (English)
E.M.E. ZAYED
2004-01-01
The asymptotic expansion of the heat kernel Θ(t)(∞∑=(i=0))exp (-λi) where({λi}∞i=1) Are the eigen-values of negative Laplacian( -△n=-n∑k=1(θ/θxk)2)in Rn(n=2 or 3) is studied for short-time t for a general bounded domainθΩwith a smooth boundary θΩ.In this paper, we consider the case of a finite number of the Dirichlet conditions φ=0 on Γi (i = J +1,….,J)and the Neumann conditions and (θφ/θ vi) = 0 on Γi (i = J+1,…,k) and the Robin condition (θφ/θ vi+γi) θ=(I=k+1,… m) where γi are piecewise smooth positive impedancem(θφ=mUi=1Γi. )We construct the required asymptotics in the form of a power series over t. The senior coe.cients inthis series are speci.ed as functionals of the geometric shape of the domain Ω.This result is applied to calculatethe one-particle partition function of a "special ideal gas", i.e., the set of non-interacting particles set up in abox with Dirichlet, Neumann and Robin boundary conditions for the appropriate wave function. Calculationof the thermodynamic quantities for the ideal gas such as the internal energy, pressure and speci.c heat revealsthat these quantities alone are incapable of distinguishing between two di.erent shapes of the domain. Thisconclusion seems to be intuitively clear because it is based on a limited information given by a one-particlepartition function; nevertheless, its formal theoretical motivation is of some interest.
Short-time behavior of the heat kernel and Weyl's law on $RCD^*(K, N)$-spaces
Ambrosio, Luigi; Honda, Shouhei; Tewodrose, David
2017-01-01
In this paper, we prove pointwise convergence of heat kernels for mGH-convergent sequences of $RCD^*(K,N)$-spaces. We obtain as a corollary results on the short-time behavior of the heat kernel in $RCD^*(K,N)$-spaces. We use then these results to initiate the study of Weyl's law in the $RCD$ setting
The rate of decay of the Wiener sausage in local Dirichlet space
Gibson, Lee R
2010-01-01
In the context of a heat kernel diffusion which admits a Gaussian type estimate with parameter beta on a local Dirichlet space, we consider the log asymptotic behavior of the negative exponential moments of the Wiener sausage. We show that the log asymptotic behavior up to time t^{beta}V(x,t) is V(x,t), which is analogous to the Euclidean result. Here V(x,t) represents the mass of the ball of radius t about a point x of the local Dirichlet space. The proof uses a known coarse graining technique to obtain the upper asymptotic, but must be adapted to for use without translation invariance in this setting. This result provides the first such asymptotics for several other contexts, including diffusions on complete Riemannian manifolds with non-negative Ricci curvature.
Toeplitz Operators on Dirichlet Spaces
Institute of Scientific and Technical Information of China (English)
Yu Feng LU; Shun Hua SUN
2001-01-01
In this paper we study Toeplitz operators on Dirichlet spaces and describe the boundedness and compactness of Toeplitz operators on Dirichlet spaces. Meanwhile. we give density theorems for Toeplitz operators on Dirichlet spaces
Measurable operators and the asymptotics of heat kernels and zeta functions
Carey, Alan
2012-01-01
In this note we answer some questions inspired by the introduction, by Alain Connes, of the notion of measurable operators using Dixmier traces. These questions concern the relationship of measurability to the asymptotics of $\\zeta-$functions and heat kernels. The answers have remained elusive for some 15 years.
Cowling–Price Theorem and Characterization of Heat Kernel on Symmetric Spaces
Indian Academy of Sciences (India)
Swagato K Ray; Rudra P Sarkar
2004-05-01
We extend the uncertainty principle, the Cowling–Price theorem, on non-compact Riemannian symmetric spaces . We establish a characterization of the heat kernel of the Laplace–Beltrami operator on from integral estimates of the Cowling–Price type.
Oskoueian, Ehsan; Abdullah, Norhani; Idrus, Zulkifli; Ebrahimi, Mahdi; Goh, Yong Meng; SHAKERI, Majid; Oskoueian, Armin
2014-01-01
Background Palm kernel cake (PKC), the most abundant by-product of oil palm industry is believed to contain bioactive compounds with hepatoprotective potential. These compounds may serve as hepatoprotective agents which could help the poultry industry to alleviate adverse effects of heat stress on liver function in chickens. Methods This study was performed to evaluate the hepatoprotective potential of PKC extract in heat-induced oxidative stress in chicken hepatocytes. The nature of the acti...
Heat kernel estimates and spectral properties of a pseudorelativistic operator with magnetic field
Jakubassa-Amundsen, D. H.
2008-03-01
Based on the Mehler heat kernel of the Schrödinger operator for a free electron in a constant magnetic field, an estimate for the kernel of EA=∣α(p-eA)+βm∣ is derived, where EA represents the kinetic energy of a Dirac electron within the pseudorelativistic no-pair Brown-Ravenhall model. This estimate is used to provide the bottom of the essential spectrum for the two-particle Brown-Ravenhall operator, describing the motion of the electrons in a central Coulomb field and a constant magnetic field, if the central charge is restricted to Z ⩽86.
Dirichlet Expression for (1, ) with General Dirichlet Character
Indian Academy of Sciences (India)
V V Rane
2010-02-01
In the famous work of Dirichlet on class number formula, (, ) at =1 has been expressed as a finite sum, where (, ) is the Dirichlet -series of a real Dirichlet character. We show that this expression with obvious modification is valid for the general primitive Dirichlet character .
The heat kernel for two Aharonov-Bohm solenoids in a uniform magnetic field
Šťovíček, Pavel
2017-01-01
A non-relativistic quantum model is considered with a point particle carrying a charge e and moving in the plane pierced by two infinitesimally thin Aharonov-Bohm solenoids and subjected to a perpendicular uniform magnetic field of magnitude B. Relying on a technique originally due to Schulman, Laidlaw and DeWitt which is applicable to Schrödinger operators on multiply connected configuration manifolds a formula is derived for the corresponding heat kernel. As an application of the heat kernel formula, approximate asymptotic expressions are derived for the lowest eigenvalue lying above the first Landau level and for the corresponding eigenfunction while assuming that | eB | R2 /(ħ c) is large, where R is the distance between the two solenoids.
Oskoueian, Ehsan; Abdullah, Norhani; Idrus, Zulkifli; Ebrahimi, Mahdi; Goh, Yong Meng; Shakeri, Majid; Oskoueian, Armin
2014-10-02
Palm kernel cake (PKC), the most abundant by-product of oil palm industry is believed to contain bioactive compounds with hepatoprotective potential. These compounds may serve as hepatoprotective agents which could help the poultry industry to alleviate adverse effects of heat stress on liver function in chickens. This study was performed to evaluate the hepatoprotective potential of PKC extract in heat-induced oxidative stress in chicken hepatocytes. The nature of the active metabolites and elucidation of the possible mechanism involved were also investigated. The PKC extract possessed free radical scavenging activity with values significantly (p Heat-induced oxidative stress in chicken hepatocyte impaired the total protein, lipid peroxidation and antioxidant enzymes activity significantly (p heat-induced hepatocytes with PKC extract (125 μg/ml) and silymarin as positive control increased these values significantly (p stress biomarkers including TNF-like, IFN-γ and IL-1β genes; NF-κB, COX-2, iNOS and Hsp70 proteins expression upon heat stress in chicken hepatocytes. The PKC extract and silymarin were able to alleviate the expression of all of these biomarkers in heat-induced chicken hepatocytes. The gas chromatography-mass spectrometry analysis of PKC extract showed the presence of fatty acids, phenolic compounds, sugar derivatives and other organic compounds such as furfural which could be responsible for the observed hepatoprotective activity. Palm kernel cake extract could be a potential agent to protect hepatocytes function under heat induced oxidative stress.
A Semi-supervised Heat Kernel Pagerank MBO Algorithm for Data Classification
2016-07-01
closed-form expression for the class of each node is derived. Moreover, the authors of [50] describe a semi-supervised method for classifying data using...manifold smoothing and image denoising. In addition to image processing, methods in- volving spectral graph theory [17,56], based on a graphical setting...pagerank and Section 3 presents a model using heat kernel pagerank directly as a classifier . Section 4 formulates the new algorithm as well as provides
An Irreducible Form for the Asymptotic Expansion Coefficients of the Heat Kernel of Fermions
Yajima, S.; Fukuda, M.; Tokuo, S.; Kubota, S.-I.; Higashida, Y.; Kamo, Y.
2008-09-01
We consider the asymptotic coefficients of the heat kernel for a fermion of spin (1)/(2) interacting with all types of non-abelian boson fields, i.e. totally antisymmetric tensor fields, in even dimensional Riemannian space. The coefficients are decomposed by irreducible matrices which are the totally antisymmetric product of the γ-matrices. The form of the coefficients given in our method is useful to evaluate some fermionic anomalies.
One loop partition function of six dimensional conformal gravity using heat kernel on AdS
Energy Technology Data Exchange (ETDEWEB)
Lovreković, Iva [Institute for Theoretical Physics, Technische Universität Wien,Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria)
2016-10-13
We compute the heat kernel for the Laplacians of symmetric transverse traceless fields of arbitrary spin on the AdS background in even number of dimensions using the group theoretic approach introduced in http://dx.doi.org/10.1007/JHEP11(2011)010 and apply it on the partition function of six dimensional conformal gravity. The obtained partition function consists of the Einstein gravity, conformal ghost and two modes that contain mass.
Indian Academy of Sciences (India)
Rudra P Sarkar
2002-11-01
A theorem of Hardy characterizes the Gauss kernel (heat kernel of the Laplacian) on $\\mathbb{R}$ from estimates on the function and its Fourier transform. In this article we establish a full group version of the theorem for $SL_2(\\mathbb{R})$ which can accommodate functions with arbitrary -types. We also consider the `heat equation' of the Casimir operator, which plays the role of the Laplacian for the group. We show that despite the structural difference of the Casimir with the Laplacian on $\\mathbb{R}^n$ or the Laplace-Beltrami operator on the Riemannian symmetric spaces, it is possible to have a heat kernel. This heat kernel for the full group can also be characterized by Hardy-like estimates.
Directory of Open Access Journals (Sweden)
Atangana Abdon
2016-01-01
Full Text Available In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional heat transfer model.
Algebraic Structure on Dirichlet Spaces
Institute of Scientific and Technical Information of China (English)
Xing FANG; Ping HE; Jian Gang YING
2006-01-01
In this short note, we shall give a few equivalent conditions for a closed form to be Markovian, and prove that the closure of a sub-algebra of bounded functions in a Dirichlet space must be Markovian. We also study the regular representation of Dirichlet spaces and the classification of Dirichlet subspaces.
On Segal-Bargmann analysis for finite Coxeter groups and its heat kernel
Sontz, Stephen Bruce
2009-01-01
We prove identities involving the integral kernels of three versions of the Segal-Bargmann transform associated to a Coxeter group (defined by a finite root system) acting on a finite dimensional, real Euclidean space (one of these kernels having been introduced around the same time by Ben Said and Orsted and independently by Soltani) and the Dunkl heat kernel of the Dunkl Laplacian associated with the same Coxeter group, due to Rosler. All but one of our relations are originally due to Hall in the context of standard Segal-Bargmann analysis on Euclidean space. Hall's results (trivial Dunkl structure and arbitrary finite dimension) as well as our own results in mu-deformed quantum mechanics (non-trivial Dunkl structure, dimension one) are particular cases of the results proved here. So we can understand all of these versions of the Segal-Bargmann transform associated to a Coxeter group as Hall type transforms. In particular, we define an analogue of Hall's "Version C" generalized Segal-Bargmann transform whic...
Generalizations and applications of the Onofri heat kernel expansion in quantum field theory
Martin, Louise Claire
2001-07-01
This thesis concerns perturbative quantum field theory. Two aspects of radiative corrections are examined: expansion of the heat kernel, and gauge parameter and metric dependence in quantum corrections in a topological gauge field theory. A novel expansion of the quantum mechanical heat kernel matrix element, introduced by Onofri, is generalized to accommodate Hamiltonians with vector potentials and with arbitrary metrics (i.e. curved space). The expansion is represented in terms of functional derivatives of an expression which solely involves classical variables, this being in some ways complementary to the quantum mechanical Feynman path integral. Ambiguities that arise in implementing the Feynman approach are avoided in this method. Illustrative field theoretic calculations are performed using this expansion. They are: the lowest order term in the Schwinger-DeWitt expansion for the diagonal heat kernel matrix element for a scalar propagating in a curved background, the Adler-Bell-Jackiw anomaly for the VVA (Vector, Vector, Axial-Vector) triangle graph, and, using off-diagonal elements of the heat kernel, a two-loop calculation for a scalar theory in six dimensions. In the second part of this work, in pure non-Abelian Chern-Simons theory, the contribution to the modulus of the one-loop effective action in an arbitrary covariant gauge is computed. It is found that the results depend on both the gauge parameter ( a ) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form a/p2 emlnpl . This is possible because in three dimensions a is dimensionful. A variant of proper time regularization is used to render these integrals well-behaved (although no divergences occur when the regularization is turned off at the end of the calculation). The results are shown to be consistent with the so-called Nielsen identities which predict the explicit gauge parameter dependence using an extension of BRS symmetry
One-loop effective action of QCD at high temperature using the heat kernel method
Energy Technology Data Exchange (ETDEWEB)
Megias, E. [Universidad de Granada (Spain). Dept. de Fisica Moderna]. E-mail: emegias@ugr.es
2004-07-01
Perturbation theory is an important tool to describe the properties of QCD at very high temperatures. Recently a new technique has been proposed to compute the one-loop effective action of QCD at finite temperature by making a gauge covariant derivative expansion, which is fully consistent with topologically small and large gauge transformations (also time dependent transformations). This technique is based on the heat kernel expansion, and the thermal Wilson line plays an essential role. We consider a general SU(N-c) gauge group. (author)
An Irreducible Form of Gamma Matrices for HMDS Coefficients of the Heat Kernel in Higher Dimensions
Fukuda, M.; Yajima, S.; Higashida, Y.; Kubota, S.; Tokuo, S.; Kamo, Y.
2009-05-01
The heat kernel method is used to calculate 1-loop corrections of a fermion interacting with general background fields. To apply the Hadamard-Minakshisundaram-DeWitt-Seeley (HMDS) coefficients a_q(x,x') of the heat kernel to calculate the corrections, it is meaningful to decompose the coefficients into tensorial components with irreducible matrices, which are the totally antisymmetric products of γ matrices. We present formulae for the tensorial forms of the γ-matrix-valued quantities X, tilde{Λ}_{μν} and their product and covariant derivative in terms of the irreducible matrices in higher dimensions. The concrete forms of HMDS coefficients obtained by repeated application of the formulae simplifies the derivation of the loop corrections after the trace calculations, because each term in the coefficients contains one of the irreducible matrices and some of the terms are expressed by commutator and the anticommutator with respect to th e generator of non-abelian gauge groups. The form of the third HMDS coefficient is useful for evaluating some of the fermionic anomalies in 6-dimensional curved space. We show that the new formulae appear in the chiral {U(1)} anomaly when the vector and the third-order tensor gauge fields do not commute.
Wang, Gang; Wang, Yalin
2017-02-15
In this paper, we propose a heat kernel based regional shape descriptor that may be capable of better exploiting volumetric morphological information than other available methods, thereby improving statistical power on brain magnetic resonance imaging (MRI) analysis. The mechanism of our analysis is driven by the graph spectrum and the heat kernel theory, to capture the volumetric geometry information in the constructed tetrahedral meshes. In order to capture profound brain grey matter shape changes, we first use the volumetric Laplace-Beltrami operator to determine the point pair correspondence between white-grey matter and CSF-grey matter boundary surfaces by computing the streamlines in a tetrahedral mesh. Secondly, we propose multi-scale grey matter morphology signatures to describe the transition probability by random walk between the point pairs, which reflects the inherent geometric characteristics. Thirdly, a point distribution model is applied to reduce the dimensionality of the grey matter morphology signatures and generate the internal structure features. With the sparse linear discriminant analysis, we select a concise morphology feature set with improved classification accuracies. In our experiments, the proposed work outperformed the cortical thickness features computed by FreeSurfer software in the classification of Alzheimer's disease and its prodromal stage, i.e., mild cognitive impairment, on publicly available data from the Alzheimer's Disease Neuroimaging Initiative. The multi-scale and physics based volumetric structure feature may bring stronger statistical power than some traditional methods for MRI-based grey matter morphology analysis.
Heat Kernel Estimate for $\\Delta+\\Delta^{\\alpha/2}$ in $C^{1,1}$ open sets
Chen, Zhen-Qing; Song, Renming
2010-01-01
We consider a family of pseudo differential operators $\\{\\Delta+ a^\\alpha \\Delta^{\\alpha/2}; a\\in (0, 1]\\}$ on $\\bR^d$ for every $d\\geq 1$ that evolves continuously from $\\Delta$ to $\\Delta + \\Delta^{\\alpha/2}$, where $\\alpha \\in (0, 2)$. It gives rise to a family of L\\'evy processes $\\{X^a, a\\in (0, 1]\\}$ in $\\bR^d$, where $X^a$ is the sum of a Brownian motion and an independent symmetric $\\alpha$-stable process with weight $a$. We establish sharp two-sided estimates for the heat kernel of $\\Delta + a^{\\alpha} \\Delta^{\\alpha/2}$ with zero exterior condition in a family of open subsets, including bounded $C^{1, 1}$ (possibly disconnected) open sets. This heat kernel is also the transition density of the sum of a Brownian motion and an independent symmetric $\\alpha$-stable process with weight $a$ in such open sets. Our result is the first sharp two-sided estimates for the transition density of a Markov process with both diffusion and jump components in open sets. Moreover, our result is uniform in $a$ in the s...
Shape-Based Image Matching Using Heat Kernels and Diffusion Maps
Vizilter, Yu. V.; Gorbatsevich, V. S.; Rubis, A. Yu.; Zheltov, S. Yu.
2014-08-01
2D image matching problem is often stated as an image-to-shape or shape-to-shape matching problem. Such shape-based matching techniques should provide the matching of scene image fragments registered in various lighting, weather and season conditions or in different spectral bands. Most popular shape-to-shape matching technique is based on mutual information approach. Another wellknown approach is a morphological image-to-shape matching proposed by Pytiev. In this paper we propose the new image-to-shape matching technique based on heat kernels and diffusion maps. The corresponding Diffusion Morphology is proposed as a new generalization of Pytiev morphological scheme. The fast implementation of morphological diffusion filtering is described. Experimental comparison of new and aforementioned shape-based matching techniques is reported applying to the TV and IR image matching problem.
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
Fast discriminative latent Dirichlet allocation
National Aeronautics and Space Administration — This is the code for fast discriminative latent Dirichlet allocation, which is an algorithm for topic modeling and text classification. The related paper is at...
Diophantine approximation and Dirichlet series
Queffélec, Hervé
2013-01-01
This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...
Optimal heat kernel estimates for Schroedinger operators with magnetic fields in two dimensions
Energy Technology Data Exchange (ETDEWEB)
Loss, M. [Georgia Inst. of Tech., Atlanta (United States). School of Mathematics; Thaller, B. [Institut fuer Mathematik, Universitaet Graz, A-8010 Graz (Austria)
1997-06-01
Sharp smoothing estimates are proven for magnetic Schroedinger semigroups in two dimensions under the assumption that the magnetic field is bounded below by some positive constant B{sub 0}. As a consequence the L{sup {infinity}} norm of the associated integral kernel is bounded by the L{sup {infinity}} norm of the Mehler kernel of the Schroedinger semigroup with the constant magnetic field B{sub 0}. (orig.)
Institute of Scientific and Technical Information of China (English)
Zhao Caidi; Zhou Shengfan; Li Yongsheng
2008-01-01
This note discusses the long time behavior of solutions for nonautonomous weakly dissipative Klein-Gordon-Schrodinger equations with homogeneous Dirichlet bound-ary condition. The authors prove the existence of compact kernel sections for the associated process by using a suitable decomposition of the equations.
New directions in Dirichlet forms
Jost, Jürgen; Mosco, Umberto; Rockner, Michael; Sturm, Karl-Theodor
1998-01-01
The theory of Dirichlet forms brings together methods and insights from the calculus of variations, stochastic analysis, partial differential and difference equations, potential theory, Riemannian geometry and more. This book features contributions by leading experts and provides up-to-date, authoritative accounts on exciting developments in the field and on new research perspectives. Topics covered include the following: stochastic analysis on configuration spaces, specifically a mathematically rigorous approach to the stochastic dynamics of Gibbs measures and infinite interacting particle systems; subelliptic PDE, homogenization, and fractals; geometric aspects of Dirichlet forms on metric spaces and function theory on such spaces; generalized harmonic maps as nonlinear analogues of Dirichlet forms, with an emphasis on non-locally compact situations; and a stochastic approach based on Brownian motion to harmonic maps and their regularity. Various new connections between the topics are featured, and it is de...
Dirichlet Problem on the Upper Half Space
Indian Academy of Sciences (India)
Dewu Yang; Yudong Ren
2014-05-01
In this paper, a solution of the Dirichlet problem on the upper half space for a fast growing continuous boundary function is constructed by the generalized Dirichlet integral with this boundary function.
DEFICIENT FUNCTIONS OF RANDOM DIRICHLET SERIES
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this article, the uniqueness theorem of Dirichlet series is proved. Then the random Dirichlet series in the right half plane is studied, and the result that the random Dirichlet series of finite order has almost surely(a.s.) no deficient functions is proved.
Toeplitz Algebras on Dirichlet Spaces
Institute of Scientific and Technical Information of China (English)
TAN Yan-hua; WANG Xiao-feng
2001-01-01
In the present paper, some properties of Toeplitz algebras on Dirichlet spaces for several complex variables are discussed; in particular, the automorphism group of the Toeplitz C* -algebra, (C1), generated by Toeplitz operators with C1-symbols is discussed. In addition, the first cohomology group of (C1) is computed.
On the Dirichlet's Box Principle
Poon, Kin-Keung; Shiu, Wai-Chee
2008-01-01
In this note, we will focus on several applications on the Dirichlet's box principle in Discrete Mathematics lesson and number theory lesson. In addition, the main result is an innovative game on a triangular board developed by the authors. The game has been used in teaching and learning mathematics in Discrete Mathematics and some high schools in…
Institute of Scientific and Technical Information of China (English)
Chen Li; Ma He-Ping; Cheng Yu-Min
2013-01-01
In this paper,the complex variable reproducing kernel particle (CVRKP) method and the finite element (FE) method are combined as the CVRKP-FE method to solve transient heat conduction problems.The CVRKP-FE method not only conveniently imposes the essential boundary conditions,but also exploits the advantages of the individual methods while avoiding their disadvantages,then the computational efficiency is higher.A hybrid approximation function is applied to combine the CVRKP method with the FE method,and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme.The corresponding formulations of the CVRKP-FE method are presented in detail.Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.
WEIGHTED COMPOSITION OPERATORS BETWEEN DIRICHLET SPACES
Institute of Scientific and Technical Information of China (English)
Wang Maofa
2011-01-01
In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.
Quantum "violation" of Dirichlet boundary condition
Park, I. Y.
2017-02-01
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the 'violation' of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
Quantum violation of Dirichlet boundary condition
Park, I Y
2016-01-01
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a clash between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum corrected solution of the 1PI action no longer obeys the Dirichlet boundary conditions imposed at the classical level. We attribute the violation of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
On Dirichlet's Derivation of the Ellipsoid Potential
Dittrich, W
2016-01-01
Newton's potential of a massive homogeneous ellipsoid is derived via Dirichlet's discontinuous factor. At first we review part of Dirichlet's work in an English translation of the original German, and then continue with an extension of his method into the complex plane. With this trick it becomes possible to first calculate the potential and thereafter the force components exerted on a test mass by the ellipsoid. This is remarkable in so far as all other famous researchers prior to Dirichlet merely calculated the attraction components. Unfortunately, Dirichlet's derivation is to a large extent mathematically unacceptable which, however, can be corrected by treating the problem in the complex plane.
Solution of the Dirichlet Problem for the Poisson's Equation in a Multidimensional Infinite Layer
Directory of Open Access Journals (Sweden)
O. D. Algazin
2015-01-01
Full Text Available The paper considers the multidimensional Poisson equation in the domain bounded by two parallel hyperplanes (in the multidimensional infinite layer. For an n-dimensional half-space method of solving boundary value problems for linear partial differential equations with constant coefficients is a Fourier transform to the variables in the boundary hyperplane. The same method can be used for an infinite layer, as is done in this paper in the case of the Dirichlet problem for the Poisson equation. For strip and infinite layer in three-dimensional space the solutions of this problem are known. And in the three-dimensional case Green's function is written as an infinite series. In this paper, the solution is obtained in the integral form and kernels of integrals are expressed in a finite form in terms of elementary functions and Bessel functions. A recurrence relation between the kernels of integrals for n-dimensional and (n + 2 -dimensional layers was obtained. In particular, is built the Green's function of the Laplace operator for the Dirichlet problem, through which the solution of the problem is recorded. Even in three-dimensional case we obtained new formula compared to the known. It is shown that the kernel of the integral representation of the solution of the Dirichlet problem for a homogeneous Poisson equation (Laplace equation is an approximate identity (δ-shaped system of functions. Therefore, if the boundary values are generalized functions of slow growth, the solution of the Dirichlet problem for the homogeneous equation (Laplace is written as a convolution of kernels with these functions.
Dirichlet Form of Product of Variational Fractals
Institute of Scientific and Technical Information of China (English)
刘源
2003-01-01
Much effort has gone into constructing Dirichlet forms to define Laplacians on self-similar sets. However, the results have only been successful on p.c.f. (post critical finite) fractals. We prove the existence of a Dirichlet form on a class of non-p.c.f. sets that are the product of variational fractals.
Meta-analysis using Dirichlet process.
Muthukumarana, Saman; Tiwari, Ram C
2016-02-01
This article develops a Bayesian approach for meta-analysis using the Dirichlet process. The key aspect of the Dirichlet process in meta-analysis is the ability to assess evidence of statistical heterogeneity or variation in the underlying effects across study while relaxing the distributional assumptions. We assume that the study effects are generated from a Dirichlet process. Under a Dirichlet process model, the study effects parameters have support on a discrete space and enable borrowing of information across studies while facilitating clustering among studies. We illustrate the proposed method by applying it to a dataset on the Program for International Student Assessment on 30 countries. Results from the data analysis, simulation studies, and the log pseudo-marginal likelihood model selection procedure indicate that the Dirichlet process model performs better than conventional alternative methods.
Directory of Open Access Journals (Sweden)
A.R Salari Kia
2014-04-01
Full Text Available Pistachio has a special ranking among Iranian agricultural products. Iran is known as the largest producer and exporter of pistachio in the world. Agricultural products are imposed under different thermal treatments during storage and processing. Designing all these processes requires thermal parameters of the products such as specific heat capacity. Regarding the importance of pistachio processing as an exportable product, in this study the specific heat capacity of nut and kernel of two varieties of Iranian pistachio (Kalle-Ghochi and Badami were investigated at four levels of moisture content (initial moisture content (5%, 15%, 25% and 40% w.b. and three levels of temperature (40, 50 and 60°C. In both varieties, the differences between the data were significant at the 1% of probability; however, the effect of moisture content was greater than that of temperature. The results indicated that the specific heat capacity of both nuts and kernels increase logarithmically with increase of moisture content and also increase linearly with increase of temperature. This parameter has altered for nut and kernel of Kalle-Ghochi and Badami varieties within the range of 1.039-2.936 kJ kg-1 K-1, 1.236-3.320 kJ kg-1 K-1, 0.887-2.773 kJ kg-1 K-1 and 0.811-2.914 kJ kg-1 K-1, respectively. Moreover, for any given level of temperature, the specific heat capacity of kernels was higher than that of nuts. Finally, regression models with high R2 values were developed to predict the specific heat capacity of pistachio varieties as a function of moisture content and temperature
The heat flux from a relativistic kinetic equation with a simplified collision kernel
Sandoval-Villalbazo, A; García-Colin, L S
2009-01-01
We show how using a special relativistic kinetic equation with a BGK- like collision operator the ensuing expression for the heat flux can be casted in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so-called "first order in the gradients theories" contend. Here we calculate explicitly the ensuing transport coefficients and compare them with the results obtained by other authors.
Institute of Scientific and Technical Information of China (English)
E. M. E. ZAYED
2003-01-01
The asymptotic expansions of the trace of the heat kernel Θ(t) = ∑∞ν=1 exp(-tλν) for smallpositive t, where {λν} are the eigenvalues of the negative Laplacian -△n = - ∑n i=1 ( / xi )2 in Rn(n= 2or 3), are studied for a general annular bounded domain Ω with a smooth inner boundary (e)Ω1 and asmooth outer boundary (e)Ω2, where a finite number of piecewise smooth Robin boundary conditions((e)/(e)nj+rj)φ=0 on the components γj(j = 1, ..., k)of (e)Ω1 and on teh components γj(j = 1, ..., m) of (e)Ω2 are considered such that( (e)Ω1+ukj=1 Fj and (e)Ω2=Umj=k+1Fj )and where the coefficients (rj(j=1，…，m))are piecewise smooth positive functions. Some applications of Θ(t) for an ideal gasenclosed in the general annular bounded domain Ω are given. Further results are also obtained.
Voon, C. H.; Lim, B. Y.; Gopinath, S. C. B.; Tan, H. S.; Tony, V. C. S.; Arshad, M. K. Md; Foo, K. L.; Hashim, U.
2016-11-01
Silicon carbide nanomaterials especially silicon carbide nanowhiskers (SiCNWs) has been known for its excellent properties such as high thermal stability, good chemical inertness and excellent electronic properties. In this paper, a green synthesis of SiCNWs by microwave heating of blends of palm kernel shell (PKS) and silica was presented. The effect of ratio of PKS and silica on the synthesis process was also studied and reported. Blends of PKS and silica in different ratio were mixed homogenously in ultrasonic bath for 2 hours using ethanol as liquid medium. The blends were then dried on hotplate to remove the ethanol and compressed into pellets form.. Synthesis was conducted in 2.45 GHz multimode cavity at 1400 °C for 40 minutes. X-ray diffraction revealed that β-SiC was detected for samples synthesized from blends with ratio of PKS to silica of 5:1 and 7:1. FESEM images also show that SiCNWs with the average diameter of 70 nm were successfully formed from blends with ratio of PKS to silica of 5:1 and 7:1. A vapour-liquid-solid (VLS) mechanism was proposed to explain the growth of SiCNWs from blends of PKS and silica.
On extensions of local Dirichlet forms
Robinson, Derek W.
2016-01-01
Let $\\ce$ be a Dirichlet form on $L_2(X\\,;\\mu)$ where $(X,\\mu)$ is locally compact $\\sigma$-compact measure space. Assume $\\ce$ is inner regular, i.e.\\ regular in restriction to functions of compact support, and local in the sense that $\\ce(\\varphi,\\psi)=0$ for all $\\varphi, \\psi\\in D(\\ce)$ with $\\varphi\\,\\psi=0$. We construct two Dirichlet forms $\\ce_m$ and $\\ce_M$ such that $\\ce_m\\leq \\ce\\leq \\ce_M$. These forms are potentially the smallest and largest such Dirichlet forms. In particular $\\...
Estimation in Dirichlet random effects models
Kyung, Minjung; Casella, George; 10.1214/09-AOS731
2010-01-01
We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the multinomial and Dirichlet distributions, and is shown to be an improvement, in terms of operator norm and efficiency, over other commonly used MCMC algorithms. We also investigate methods for the estimation of the precision parameter of the Dirichlet process, finding that maximum likelihood may not be desirable, but a posterior mode is a reasonable approach. Examples are given to show how these models perform on real data. Our results complement both the theoretical basis of the Dirichlet process nonparametric prior and the computational work that has been done to date.
Directory of Open Access Journals (Sweden)
Nesseim, TDT.
2017-01-01
Full Text Available Jatropha curcas is a tropical plant belonging to the Euphorbiaceae family whose cultivation has been largely promoted in recent years for the production of biofuels. The kernel of the seed contains approximately 55% lipid in dry matter and the meal obtained could be an exceptional source of proteins for family poultry farming, after treatments to remove toxic and anti-nutritional compounds. The ingestion and the growth performance of J. curcas kernel meal (JKM, obtained after partial physico-chemical de-oiling combined or not with heating was evaluated in broiler chickens and chicks. Sixty unsexed broiler chickens, 30 day-old, divided into three groups as well as twenty broiler chicks, 1 day-old, divided into two groups were used in two experiments. In experiment 1, jatropha kernel was de-oiled and incorporated into a control fattening feed at 40 and 80g/kg (diets 4JKM1 and 8JM1. In experiment 2, jatropha kernel meal obtained in experiment 1 was heat treated and incorporated into a growing diet at 80g/kg (diet 8JKM2. Daily dietary intakes as well as weight gain of the animals were affected by the incorporation of jatropha kernel meal in the ration. In experiment 1, average daily feed intake (ADFI1 of 139.2, 55.2 and 23.4g/day/animal and also average daily weight gain (ADWG1 of 61.9, 18.5 and -7.7g/animal were obtained respectively for the groups fed with diets 0JKM1, 4JKM1 and 8JKM1. In experiment 2, Average daily feed intake (ADFI2 of 18.7 and 3.1g/day/animal and also average daily weight gain (ADWG2 of 7.1 and 1.9g/animal were obtained respectively for the groups fed with diets 0JKM2 and 8JKM2. In both experiment, feed conversion ratio (FCR was also affected by the dietary treatments and the overall mortality rate showed an increase according to levels of jatropha kernel meal in diet.
Ha, Jae-Won; Kang, Dong-Hyun
2015-07-01
The aim of this study was to investigate the efficacy of near-infrared radiation (NIR) heating combined with lactic acid (LA) sprays for inactivating Salmonella enterica serovar Enteritidis on almond and pine nut kernels and to elucidate the mechanisms of the lethal effect of the NIR-LA combined treatment. Also, the effect of the combination treatment on product quality was determined. Separately prepared S. Enteritidis phage type (PT) 30 and non-PT 30 S. Enteritidis cocktails were inoculated onto almond and pine nut kernels, respectively, followed by treatments with NIR or 2% LA spray alone, NIR with distilled water spray (NIR-DW), and NIR with 2% LA spray (NIR-LA). Although surface temperatures of nuts treated with NIR were higher than those subjected to NIR-DW or NIR-LA treatment, more S. Enteritidis survived after NIR treatment alone. The effectiveness of NIR-DW and NIR-LA was similar, but significantly more sublethally injured cells were recovered from NIR-DW-treated samples. We confirmed that the enhanced bactericidal effect of the NIR-LA combination may not be attributable to cell membrane damage per se. NIR heat treatment might allow S. Enteritidis cells to become permeable to applied LA solution. The NIR-LA treatment (5 min) did not significantly (P > 0.05) cause changes in the lipid peroxidation parameters, total phenolic contents, color values, moisture contents, and sensory attributes of nut kernels. Given the results of the present study, NIR-LA treatment may be a potential intervention for controlling food-borne pathogens on nut kernel products.
Some Properties of Complex Matrix-Variate Generalized Dirichlet Integrals
Indian Academy of Sciences (India)
Joy Jacob; Sebastian George; A M Mathai
2005-08-01
Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive definite or hermitian positive definite, are available [4]. Real scalar variables case of the Dirichlet models are generalized in various directions. One such generalization of the type-2 or inverted Dirichlet is looked into in this article. Matrix-variate analogue, when the matrices are hermitian positive definite, are worked out along with some properties which are mathematically and statistically interesting.
Constructing Weyl group multiple Dirichlet series
Chinta, Gautam; Gunnells, Paul E.
2010-01-01
Let Phi be a reduced root system of rank r . A Weyl group multiple Dirichlet series for Phi is a Dirichlet series in r complex variables s_1,dots,s_r , initially converging for {Re}(s_i) sufficiently large, that has meromorphic continuation to {{C}}^r and satisfies functional equations under the transformations of {{C}}^r corresponding to the Weyl group of Phi . A heuristic definition of such a series was given by Brubaker, Bump, Chinta, Friedberg, and Hoffstein, and they have been investigated in certain special cases by others. In this paper we generalize results by Chinta and Gunnells to construct Weyl group multiple Dirichlet series by a uniform method and show in all cases that they have the expected properties.
Text Categorization with Latent Dirichlet Allocation
Directory of Open Access Journals (Sweden)
ZLACKÝ Daniel
2014-05-01
Full Text Available This paper focuses on the text categorization of Slovak text corpora using latent Dirichlet allocation. Our goal is to build text subcorpora that contain similar text documents. We want to use these better organized text subcorpora to build more robust language models that can be used in the area of speech recognition systems. Our previous research in the area of text categorization showed that we can achieve better results with categorized text corpora. In this paper we used latent Dirichlet allocation for text categorization. We divided initial text corpus into 2, 5, 10, 20 or 100 subcorpora with various iterations and save steps. Language models were built on these subcorpora and adapted with linear interpolation to judicial domain. The experiment results showed that text categorization using latent Dirichlet allocation can improve the system for automatic speech recognition by creating the language models from organized text corpora.
ON THE GROWTH OF INFINITE ORDER DIRICHLET SERIES
Institute of Scientific and Technical Information of China (English)
陈特为; 孙道椿
2003-01-01
In this paper, the property of infinite order Dirichlet series in the half-plane areinvestigated. The more exact growth of infinite order Dirichlet series is obtained withoutusing logarithm argument to the type-function for the first time.
Composition Operators on Dirichlet Spaces and Bloch Space
Institute of Scientific and Technical Information of China (English)
Yuan CHENG; Sanjay KUMAR; Ze Hua ZHOU
2014-01-01
In this paper we give a Carleson measure characterization for the compact composition operators between Dirichlet type spaces. We use this characterization to show that every compact composition operator on Dirichlet type spaces is compact on the Bloch space.
Hyperfinite Dirichlet Forms and Stochastic Processes
Albeverio, Sergio; Herzberg, Frederik
2011-01-01
This monograph treats the theory of Dirichlet forms from a comprehensive point of view, using 'nonstandard analysis'. Thus, it is close in spirit to the discrete classical formulation of Dirichlet space theory by Beurling and Deny (1958). The discrete infinitesimal setup makes it possible to study the diffusion and the jump part using essentially the same methods. This setting has the advantage of being independent of special topological properties of the state space and in this sense is a natural one, valid for both finite- and infinite-dimensional spaces. The present monograph provides a tho
Dirichlet and Related Distributions Theory, Methods and Applications
Ng, Kai Wang; Tang, Man-Lai
2011-01-01
The Dirichlet distribution appears in many areas of application, which include modelling of compositional data, Bayesian analysis, statistical genetics, and nonparametric inference. This book provides a comprehensive review of the Dirichlet distribution and two extended versions, the Grouped Dirichlet Distribution (GDD) and the Nested Dirichlet Distribution (NDD), arising from likelihood and Bayesian analysis of incomplete categorical data and survey data with non-response. The theoretical properties and applications are also reviewed in detail for other related distributions, such as the inve
POSITIVE SOLUTIONS FOR A DIRICHLET PROBLEM
Institute of Scientific and Technical Information of China (English)
周焕松
2001-01-01
In this paper, we study a nonlinear Dirichlet problem on a smooth bounded domain, in which the nonlinear term is asymptotically linear, not superlinear, at infinity and sublinear near the origin. By using Mountain Pass Theorem, we prove that there exist at least two positive solutions under suitable assumptions on the nonlinearity.
Heat kernels on cone of AdS2 and k-wound circular Wilson loop in AdS5 × S5 superstring
Bergamin, R.; Tseytlin, A. A.
2016-04-01
We compute the one-loop world-sheet correction to partition function of {{AdS}}5× {{{S}}}5 superstring that should be representing k-fundamental circular Wilson loop in planar limit. The 2d metric of the minimal surface ending on k-wound circle at the boundary is that of a cone of AdS2 with deficit 2π (1-k). We compute the determinants of 2d fluctuation operators by first constructing heat kernels of scalar and spinor Laplacians on the cone using the Sommerfeld formula. The final expression for the k-dependent part of the one-loop correction has simple integral representation but is different from earlier results.
Bergamin, R
2015-01-01
We compute the one-loop world-sheet correction to partition function of $AdS_5 \\times S^5$ superstring that should be representing $k$-fundamental circular Wilson loop in planar limit. The 2d metric of the minimal surface ending on $k$-wound circle at the boundary is that of a cone of $AdS_2$ with deficit $2\\pi (1-k)$. We compute determinants of 2d fluctuation operators by first constructing heat kernels of scalar and spinor Laplacians on the cone using the Sommerfeld formula. The final expression for the k-dependent part of the one-loop correction has simple integral representation but is different from earlier results.
Hybrid bounds for Dirichlet's L-function
Huxley, M. N.; Watt, N.
2000-11-01
This is a paper about upper bounds for Dirichlet's L-function, L(s, [chi]), on its critical line (s + s¯ = 1). It is to be assumed throughout that, unless otherwise stated, the Dirichlet character, [chi], is periodic modulo a prime, r, and is not the principal character mod r. Our main theorem below shows that, if [epsilon] > 0, thenformula here(where A is an absolute constant), for 0 < [alpha] = (log r)/(log t) [less-than-or-eq, slant] 2/753 [minus sign] [epsilon]. Somewhat weaker bounds are obtained for other cases where 0 < [alpha] [less-than-or-eq, slant] 11/180 [minus sign] [epsilon]. Note that in [13] it was shown that, for 0 < [alpha] [less-than-or-eq, slant] 2/57,formula hereOur main theorem is a corollary of the new bounds we prove for certain exponential sums, S, with a Dirichlet character factor:formula herewhere M2 [less-than-or-eq, slant] 2M and f(x) is a real function whose derivatives satisfy certain conditions restricting their size.
Perpetuity property of the Dirichlet distribution
Hitczenko, Pawel
2012-01-01
Let $X$, $B$ and $Y$ be three Dirichlet, Bernoulli and beta independent random variables such that $X\\sim \\mathcal{D}(a_0,...,a_d),$ such that $\\Pr(B=(0,...,0,1,0,...,0))=a_i/a$ with $a=\\sum_{i=0}^da_i$ and such that $Y\\sim \\beta(1,a).$ We prove that $X\\sim X(1-Y)+BY.$ This gives the stationary distribution of a simple Markov chain on a tetrahedron. We also extend this result to the case when $B$ follows a quasi Bernoulli distribution $\\mathcal{B}_k(a_0,...,a_d)$ on the tetrahedron and when $Y\\sim \\beta(k,a)$. We extend it even more generally to the case where $X$ is a Dirichlet process and $B$ is a quasi Bernoulli random probability. Finally the case where the integer $k$ is replaced by a positive number $c$ is considered when $a_0=...=a_d=1.$ \\textsc{Keywords} \\textit{Perpetuities, Dirichlet process, Ewens distribution, quasi Bernoulli laws, probabilities on a tetrahedron, $T_c$ transform, stationary distribution.} AMS classification 60J05, 60E99.
TOEPLITZ OPERATORS AND ALGEBRAS ON DIRICHLET SPACES
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The automorphism group of the Toeplitz C*- algebra,J(C1),generated by Toeplitz operators with C1-symbols on Dirichlet space D is discussed; the K0,K1-groups and the first cohomology group of J(C1) are computed.In addition,the author proves that the spectra of Toeplitz operators with C1-symbols are always connected,and discusses the algebraic properties of Toeplitz operators.In particular,it is proved that there is no nontrivial selfadjoint Toeplitz operator on D and T* = T if and only if T is a scalar operator.
Modeling Word Burstiness Using the Dirichlet Distribution
DEFF Research Database (Denmark)
Madsen, Rasmus Elsborg; Kauchak, David; Elkan, Charles
2005-01-01
Multinomial distributions are often used to model text documents. However, they do not capture well the phenomenon that words in a document tend to appear in bursts: if a word appears once, it is more likely to appear again. In this paper, we propose the Dirichlet compound multinomial model (DCM......) as an alternative to the multinomial. The DCM model has one additional degree of freedom, which allows it to capture burstiness. We show experimentally that the DCM is substantially better than the multinomial at modeling text data, measured by perplexity. We also show using three standard document collections...
THE PITS PROPERTY OF ENTIRE FUNCTIONS DEFINED BY DIRICHLET SERIES
Institute of Scientific and Technical Information of China (English)
Shang Lina; Gao Zongsheng
2009-01-01
The value distribution of entire functions defined by Dirichlet series are studied in this present article. It is proved that entire functions defined by Dirichlet series have the pits property, which improve the relative results on lacunary Taylor series obtained by Littlewood J.E. and Offord A.C.
Generative supervised classification using Dirichlet process priors.
Davy, Manuel; Tourneret, Jean-Yves
2010-10-01
Choosing the appropriate parameter prior distributions associated to a given bayesian model is a challenging problem. Conjugate priors can be selected for simplicity motivations. However, conjugate priors can be too restrictive to accurately model the available prior information. This paper studies a new generative supervised classifier which assumes that the parameter prior distributions conditioned on each class are mixtures of Dirichlet processes. The motivations for using mixtures of Dirichlet processes is their known ability to model accurately a large class of probability distributions. A Monte Carlo method allowing one to sample according to the resulting class-conditional posterior distributions is then studied. The parameters appearing in the class-conditional densities can then be estimated using these generated samples (following bayesian learning). The proposed supervised classifier is applied to the classification of altimetric waveforms backscattered from different surfaces (oceans, ices, forests, and deserts). This classification is a first step before developing tools allowing for the extraction of useful geophysical information from altimetric waveforms backscattered from nonoceanic surfaces.
Baur, Benedict; Stilgenbauer, Patrik
2011-01-01
We provide a general construction scheme for $\\mathcal L^p$-strong Feller processes on locally compact separable metric spaces. Starting from a regular Dirichlet form and specified regularity assumptions, we construct an associated semigroup and resolvents of kernels having the $\\mathcal L^p$-strong Feller property. They allow us to construct a process which solves the corresponding martingale problem for all starting points from a known set, namely the set where the regularity assumptions hold. We apply this result to construct elliptic diffusions having locally Lipschitz matrix coefficients and singular drifts on general open sets with absorption at the boundary. In this application elliptic regularity results imply the desired regularity assumptions.
On the exact controllability of a nonlinear stochastic heat equation
Directory of Open Access Journals (Sweden)
Bui An Ton
2006-01-01
Full Text Available The exact controllability of a nonlinear stochastic heat equation with null Dirichlet boundary conditions, nonzero initial and target values, and an interior control is established.
Unsupervised Feature Selection for Latent Dirichlet Allocation
Institute of Scientific and Technical Information of China (English)
Xu Weiran; Du Gang; Chen Guang; Guo Jun; Yang Jie
2011-01-01
As a generative model Latent Dirichlet Allocation Model,which lacks optimization of topics' discrimination capability focuses on how to generate data,This paper aims to improve the discrimination capability through unsupervised feature selection.Theoretical analysis shows that the discrimination capability of a topic is limited by the discrimination capability of its representative words.The discrimination capability of a word is approximated by the Information Gain of the word for topics,which is used to distinguish between “general word” and “special word” in LDA topics.Therefore,we add a constraint to the LDA objective function to let the “general words” only happen in “general topics”other than “special topics”.Then a heuristic algorithm is presented to get the solution.Experiments show that this method can not only improve the information gain of topics,but also make the topics easier to understand by human.
Dirichlet problem for a second order singular differential equation
Directory of Open Access Journals (Sweden)
Wenshu Zhou
2006-12-01
Full Text Available This article concerns the existence of positive solutions to the Dirichlet problem for a second order singular differential equation. To prove existence, we use the classical method of elliptic regularization.
Product of Toeplitz Operators on the Harmonic Dirichlet Space
Institute of Scientific and Technical Information of China (English)
Lian Kuo ZHAO
2012-01-01
In this paper,we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space,and show that the product of two Toeplitz operators is another Toeplitz operator only if one factor is constant.
Quantum “violation” of Dirichlet boundary condition
Directory of Open Access Journals (Sweden)
I.Y. Park
2017-02-01
Full Text Available Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the ‘violation’ of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
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...... analysis, looking at the class of subsampled realised kernels and we derive the limit theory for this class of estimators. We find that subsampling is highly advantageous for estimators based on discontinuous kernels, such as the truncated kernel. For kinked kernels, such as the Bartlett kernel, we show...... 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...
Predicting Component Failures Using Latent Dirichlet Allocation
Directory of Open Access Journals (Sweden)
Hailin Liu
2015-01-01
Full Text Available Latent Dirichlet Allocation (LDA is a statistical topic model that has been widely used to abstract semantic information from software source code. Failure refers to an observable error in the program behavior. This work investigates whether semantic information and failures recorded in the history can be used to predict component failures. We use LDA to abstract topics from source code and a new metric (topic failure density is proposed by mapping failures to these topics. Exploring the basic information of topics from neighboring versions of a system, we obtain a similarity matrix. Multiply the Topic Failure Density (TFD by the similarity matrix to get the TFD of the next version. The prediction results achieve an average 77.8% agreement with the real failures by considering the top 3 and last 3 components descending ordered by the number of failures. We use the Spearman coefficient to measure the statistical correlation between the actual and estimated failure rate. The validation results range from 0.5342 to 0.8337 which beats the similar method. It suggests that our predictor based on similarity of topics does a fine job of component failure prediction.
Preparing UO2 kernels by gelcasting
Institute of Scientific and Technical Information of China (English)
GUO Wenli; LIANG Tongxiang; ZHAO Xingyu; HAO Shaochang; LI Chengliang
2009-01-01
A process named gel-casting has been developed for the production of dense UO2 kernels for the high-ten-temperature gas-cooled reactor. Compared with the sol-gel process, the green microspheres can be got by dispersing the U3O8 slurry in gelcasting process, which means that gelcasting is a more facilitative process with less waste in fabricating UO2 kernels. The heat treatment.
Alam, Md. Ashad; Fukumizu, Kenji; Wang, Yu-Ping
2016-01-01
To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). They are sensitive to contaminated data, even when using bounded positive definite kernels. First, we propose robust kernel covariance operator (robust kernel CO) and robust kernel crosscovariance operator (robust kern...
2008-08-01
Berg et al., 1984] has been used in a machine learning context by Cuturi and Vert [2005]. Definition 26 Let (X ,+) be a semigroup .2 A function ϕ : X...R is called pd (in the semigroup sense) if k : X × X → R, defined as k(x, y) = ϕ(x + y), is a pd kernel. Likewise, ϕ is called nd if k is a nd...kernel. Accordingly, these are called semigroup kernels. 7.3 Jensen-Shannon and Tsallis kernels The basic result that allows deriving pd kernels based on
Approximate kernel competitive learning.
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.
Dirichlet Problem for Hermitian-Einstein Equation over Almost Hermitian Manifold
Institute of Scientific and Technical Information of China (English)
Yue WANG; Xi ZHANG
2012-01-01
In this paper,we investigate the Dirichlet problem for Hermitian-Einstein equation on complex vector bundle over almost Hermitian manifold,and we obtain the unique solution of the Dirichlet problem for Hermitian-Einstein equation.
Generalized Dirichlet Normal Ordering in Open Bosonic Strings
Institute of Scientific and Technical Information of China (English)
CAO Zhen-Bin; DUAN Yi-Shi
2009-01-01
Generally, open string boundary conditions play a nontrivial role in string theory. For example, in the presence of an antisymmetric tensor background field, they will lead the spacetime coordinates noncommutative. In this paper, we mainly discuss how to build up a generalized Dirichlet normal ordered product of open bosonic string embedding operators that satisfies both the equations of motion and the generalized Dirichlet boundary conditions at the quantum level in the presence of an antisymmetric background field, as the generalized Neumann case has already been discussed in the literature. Further, we also give a brief cheek of the consistency of the theory under the newly introduced normal ordering.
Optimized Kernel Entropy Components.
Izquierdo-Verdiguier, Emma; Laparra, Valero; Jenssen, Robert; Gomez-Chova, Luis; Camps-Valls, Gustau
2016-02-25
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.
On a stochastic Burgers equation with Dirichlet boundary conditions
Directory of Open Access Journals (Sweden)
Ekaterina T. Kolkovska
2003-01-01
Full Text Available We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.
Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian
Directory of Open Access Journals (Sweden)
Dorota Bors
2014-01-01
Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated. The application of the results to some optimal control problem is presented. The methods applied in the paper make use of the variational structure of the problem.
Stability of nonlinear Dirichlet BVPs governed by fractional Laplacian.
Bors, Dorota
2014-01-01
We consider a class of partial differential equations with the fractional Laplacian and the homogeneous Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated. The application of the results to some optimal control problem is presented. The methods applied in the paper make use of the variational structure of the problem.
A generalized Dirichlet distribution accounting for singularities of the variables
DEFF Research Database (Denmark)
Lewy, Peter
1996-01-01
A multivariate generalized Dirichlet distribution has been formulated for the case where the stochastic variables are allowed to have singularities at 0 and 1. Small sample properties of the estimates of moments of the variables based on maximum likelihood estimates of the parameters have been co...
Commuting Toeplitz and Hankel Operators on Harmonic Dirichlet Spaces
Directory of Open Access Journals (Sweden)
Qian Ding
2017-01-01
Full Text Available On the harmonic Dirichlet space of the unit disk, the commutativity of Toeplitz and Hankel operators is studied. We obtain characterizations of commuting Toeplitz and Hankel operators and essentially commuting (semicommuting Toeplitz and Hankel operators with general symbols.
Augmenting Latent Dirichlet Allocation and Rank Threshold Detection with Ontologies
2010-03-01
Department of Defense, or the United States Government . AFIT/GCS/ENG/10-03 Augmenting Latent Dirichlet Allocation and Rank Threshold Detection with...dog great pyrenees dalmation dog domestic dog canis familiaris dog andiron firedog dog dog-iron frump dog pawl detent click dog chap fellow feller
On the Uniqueness Result for the Dirichlet Problem and Invexity
Directory of Open Access Journals (Sweden)
M. Płócienniczak
2008-08-01
Full Text Available We provide an existence and uniqueness theorem for the Dirichlet problem div Hz(y,Ñx(y=ÑxF(y,x(y.The assumption that both H and F are invex with respect to the second variable is imposed and the direct variational method is applied. The applicationis also shown.
Regularization in kernel learning
Mendelson, Shahar; 10.1214/09-AOS728
2010-01-01
Under mild assumptions on the kernel, we obtain the best known error rates in a regularized learning scenario taking place in the corresponding reproducing kernel Hilbert space (RKHS). The main novelty in the analysis is a proof that one can use a regularization term that grows significantly slower than the standard quadratic growth in the RKHS norm.
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`.
Kernel Affine Projection Algorithms
Directory of Open Access Journals (Sweden)
José C. Príncipe
2008-05-01
Full Text Available The combination of the famed kernel trick and affine projection algorithms (APAs yields powerful nonlinear extensions, named collectively here, KAPA. This paper is a follow-up study of the recently introduced kernel least-mean-square algorithm (KLMS. KAPA inherits the simplicity and online nature of KLMS while reducing its gradient noise, boosting performance. More interestingly, it provides a unifying model for several neural network techniques, including kernel least-mean-square algorithms, kernel adaline, sliding-window kernel recursive-least squares (KRLS, and regularization networks. Therefore, many insights can be gained into the basic relations among them and the tradeoff between computation complexity and performance. Several simulations illustrate its wide applicability.
Kernel Affine Projection Algorithms
Liu, Weifeng; Príncipe, José C.
2008-12-01
The combination of the famed kernel trick and affine projection algorithms (APAs) yields powerful nonlinear extensions, named collectively here, KAPA. This paper is a follow-up study of the recently introduced kernel least-mean-square algorithm (KLMS). KAPA inherits the simplicity and online nature of KLMS while reducing its gradient noise, boosting performance. More interestingly, it provides a unifying model for several neural network techniques, including kernel least-mean-square algorithms, kernel adaline, sliding-window kernel recursive-least squares (KRLS), and regularization networks. Therefore, many insights can be gained into the basic relations among them and the tradeoff between computation complexity and performance. Several simulations illustrate its wide applicability.
Directory of Open Access Journals (Sweden)
R. Lakshmi
2014-06-01
Full Text Available A kernel $J$ of a digraph $D$ is an independent set of vertices of $D$ such that for every vertex $w,in,V(D,setminus,J$ there exists an arc from $w$ to a vertex in $J.$ In this paper, among other results, a characterization of $2$-regular circulant digraph having a kernel is obtained. This characterization is a partial solution to the following problem: Characterize circulant digraphs which have kernels; it appeared in the book {it Digraphs - theory, algorithms and applications}, Second Edition, Springer-Verlag, 2009, by J. Bang-Jensen and G. Gutin.
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
Hierarchical topic modeling with nested hierarchical Dirichlet process
Institute of Scientific and Technical Information of China (English)
Yi-qun DING; Shan-ping LI; Zhen ZHANG; Bin SHEN
2009-01-01
This paper deals with the statistical modeling of latent topic hierarchies in text corpora. The height of the topic tree is assumed as fixed, while the number of topics on each level as unknown a priori and to be inferred from data. Taking a nonparametric Bayesian approach to this problem, we propose a new probabilistic generative model based on the nested hierarchical Dirichlet process (nHDP) and present a Markov chain Monte Carlo sampling algorithm for the inference of the topic tree structure as welt as the word distribution of each topic and topic distribution of each document. Our theoretical analysis and experiment results show that this model can produce a more compact hierarchical topic structure and captures more free-grained topic relationships compared to the hierarchical latent Dirichlet allocation model.
Toeplitz Operators on Dirichlet-Type Space of Unit Ball
Directory of Open Access Journals (Sweden)
Jin Xia
2014-01-01
Full Text Available We construct a function u in L2Bn, dV which is unbounded on any neighborhood of each boundary point of Bn such that Toeplitz operator Tu is a Schatten p-class 0
Dirichlet-type space DBn, dV. Then, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Dirichlet-type space DBn, dV. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. We investigate the zero-product problem for several Toeplitz operators with radial symbols. Furthermore, the corresponding commuting problem of Toeplitz operators whose symbols are of the form ξku is studied, where k ∈ Zn, ξ ∈ ∂Bn, and u is a radial function.
Global properties of Dirichlet forms on discrete spaces
Schmidt, Marcel
2012-01-01
The goal of this Diploma thesis is to study global properties of Dirichlet forms associated with infinite weighted graphs. These include recurrence and transience, stochastic completeness and the question whether the Neumann form on a graph is regular. We show that recurrence of the regular Dirichlet form of a graph is equivalent to recurrence of a certain random walk on it. After that, we prove some general characterizations of the mentioned global properties which allow us to investigate their connections. It turns out that recurrence always implies stochastic completeness and the regularity of the Neumann form. In the case where the underlying $\\ell^2$-space has finite measure, we are able to show that all concepts coincide. Finally, we demonstrate that the above properties are all equivalent to uniqueness of solutions to the eigenvalue problem for the (unbounded) graph Laplacian when considered on the right space.
Locally linear approximation for Kernel methods : the Railway Kernel
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 capability of the pr...
The Dirichlet problem for the minimal surface equation
Williams, Graham H.
1996-01-01
The minimal surface equation is an elliptic equation but it is nonlinear and is not uniformly elliptic. It is the Euler-Lagrange equation for variational problems which involve minimising the area of the graphs of functions. For the most part we will solve the variational problem with Dirichlet boundary values, that is, when the values of the function are prescribed on the boundary of some given set. We will present some existence results using the Direct Method from the Calcul...
On Polya's inequality for torsional rigidity and first Dirichlet eigenvalue
Berg, M. van den; Ferone, V.; Nitsch, C.; Trombetti, C.
2016-01-01
Let $\\Omega$ be an open set in Euclidean space with finite Lebesgue measure $|\\Omega|$. We obtain some properties of the set function $F:\\Omega\\mapsto \\R^+$ defined by $$ F(\\Omega)=\\frac{T(\\Omega)\\lambda_1(\\Omega)}{|\\Omega|} ,$$ where $T(\\Omega)$ and $\\lambda_1(\\Omega)$ are the torsional rigidity and the first eigenvalue of the Dirichlet Laplacian respectively. We improve the classical P\\'olya bound $F(\\Omega)\\le 1,$ and show that $$F(\\Omega)\\le 1- \
ALMOST SURE AND QUASI-SURE GROWTH OF DIRICHLET SERIES
Institute of Scientific and Technical Information of China (English)
YUJIARONG
1996-01-01
For a given Dirichlet series absolutely convergent and of order (R)ρ∈(O, +∞) in the right-halfplan, its terms can be multiplied respectively by the members of a suitable sequence defined in a probability or topological space such that the series obtained is of order (R)ρ on any one of countably infinite horizontal half-lines almost or quasi surely.
Abscissas of weak convergence of vector valued Dirichlet series
2015-01-01
The abscissas of convergence, uniform convergence and absolute convergence of vector valued Dirichlet series with respect to the original topology and with respect to the weak topology $\\sigma(X,X')$ of a locally convex space $X$, in particular of a Banach space $X$, are compared. The relation of their coincidence with geometric or topological properties of the underlying space $X$ is investigated. Cotype in the context of Banach spaces, and nuclearity and certain topological invariants for F...
Kroah-Hartman, Greg
2009-01-01
Linux Kernel in a Nutshell covers the entire range of kernel tasks, starting with downloading the source and making sure that the kernel is in sync with the versions of the tools you need. In addition to configuration and installation steps, the book offers reference material and discussions of related topics such as control of kernel options at runtime.
Weyl group multiple Dirichlet series of type C
Beineke, Jennifer; Frechette, Sharon
2010-01-01
We develop the theory of Weyl group multiple Dirichlet series for root systems of type C. For an arbitrary root system of rank r and a positive integer n, these are Dirichlet series in r complex variables with analytic continuation and functional equations isomorphic to the associated Weyl group. In type C, they conjecturally arise from the Fourier-Whittaker coefficients of minimal parabolic Eisenstein series on an n-fold metaplectic cover of SO(2r+1). For any odd n, we construct an infinite family of Dirichlet series conjecturally satisfying the above analytic properties. The coefficients of these series are exponential sums built from Gelfand-Tsetlin bases of certain highest weight representations. Previous attempts to define such series by Brubaker, Bump, and Friedberg in [6] and [7] required n to be sufficiently large, so that coefficients could be described by Weyl group orbits. We demonstrate that our construction agrees with that of [6] and [7] in the case where both series are defined, and hence inher...
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
Mixture Density Mercer Kernels
National Aeronautics and Space Administration — We present a method of generating Mercer Kernels from an ensemble of probabilistic mixture models, where each mixture model is generated from a Bayesian mixture...
Johno, Hisashi; Nakamoto, Kazunori; Saigo, Tatsuhiko
2015-01-01
Kernel Bayes' rule has been proposed as a nonparametric kernel-based method to realize Bayesian inference in reproducing kernel Hilbert spaces. However, we demonstrate both theoretically and experimentally that the prediction result by kernel Bayes' rule is in some cases unnatural. We consider that this phenomenon is in part due to the fact that the assumptions in kernel Bayes' rule do not hold in general.
Linearized Kernel Dictionary Learning
Golts, Alona; Elad, Michael
2016-06-01
In this paper we present a new approach of incorporating kernels into dictionary learning. The kernel K-SVD algorithm (KKSVD), which has been introduced recently, shows an improvement in classification performance, with relation to its linear counterpart K-SVD. However, this algorithm requires the storage and handling of a very large kernel matrix, which leads to high computational cost, while also limiting its use to setups with small number of training examples. We address these problems by combining two ideas: first we approximate the kernel matrix using a cleverly sampled subset of its columns using the Nystr\\"{o}m method; secondly, as we wish to avoid using this matrix altogether, we decompose it by SVD to form new "virtual samples," on which any linear dictionary learning can be employed. Our method, termed "Linearized Kernel Dictionary Learning" (LKDL) can be seamlessly applied as a pre-processing stage on top of any efficient off-the-shelf dictionary learning scheme, effectively "kernelizing" it. We demonstrate the effectiveness of our method on several tasks of both supervised and unsupervised classification and show the efficiency of the proposed scheme, its easy integration and performance boosting properties.
Indigenous Methods in Preserving Bush Mango Kernels in Cameroon
Directory of Open Access Journals (Sweden)
Zac Tchoundjeu
2005-01-01
Full Text Available Traditional practices for preserving Irvingia wombolu and Irvingia gabonensis (bush mango kernels were assessed in a survey covering twelve villages (Dongo, Bouno, Gribi [East], Elig-Nkouma, Nkom I, Ngoumou [Centre], Bidjap, Nko’ovos, Ondodo [South], Besong-Abang, Ossing and Kembong [Southwest], in the humid lowland forest zone of Cameroon. All the interviewed households that own trees of species were found to preserve kernels in periods of abundance, excluding Elig-Nkouma (87.5%. Eighty nine and 85% did so in periods of scarcity for I. wombolu and I. gabonensis respectively. Seventeen and twenty-nine kernel preservation practices were recorded for I. wombolu and I. gabonensis respectively. Most were based on continuous heating of the kernels or kernel by-products (cakes. The most commonly involved keeping the sun-dried kernels in a plastic bag on a bamboo rack hung above the fireplace in the kitchen. A 78% of interviews households reported preserving I. wombolu kernels for less than one year while 22% preserved it for more than one year with 1.9% for two years, the normal length of the off-season period for trees in the wild. Cakes wrapped with leaves and kept on a bamboo rack hung over the fireplace were reported by households in the East and South provinces to store Irvingia gabonensis longer (more than one year. Further studies on the utilization of heat for preserving and canning bush mango kernels are recommended.
Relations among Dirichlet series whose coefficients are class numbers of binary cubic forms II
Ohno, Yasuo
2011-01-01
As a continuation of the authors and Wakatsuki's previous paper [5], we study relations among Dirichlet series whose coefficients are class numbers of binary cubic forms. We show that for any integral models of the space of binary cubic forms, the associated Dirichlet series satisfies a simple explicit relation to that of the dual other than the usual functional equation. As an application, we write the functional equations of these Dirichlet series in self dual forms.
Contingent kernel density estimation.
Directory of Open Access Journals (Sweden)
Scott Fortmann-Roe
Full Text Available Kernel density estimation is a widely used method for estimating a distribution based on a sample of points drawn from that distribution. Generally, in practice some form of error contaminates the sample of observed points. Such error can be the result of imprecise measurements or observation bias. Often this error is negligible and may be disregarded in analysis. In cases where the error is non-negligible, estimation methods should be adjusted to reduce resulting bias. Several modifications of kernel density estimation have been developed to address specific forms of errors. One form of error that has not yet been addressed is the case where observations are nominally placed at the centers of areas from which the points are assumed to have been drawn, where these areas are of varying sizes. In this scenario, the bias arises because the size of the error can vary among points and some subset of points can be known to have smaller error than another subset or the form of the error may change among points. This paper proposes a "contingent kernel density estimation" technique to address this form of error. This new technique adjusts the standard kernel on a point-by-point basis in an adaptive response to changing structure and magnitude of error. In this paper, equations for our contingent kernel technique are derived, the technique is validated using numerical simulations, and an example using the geographic locations of social networking users is worked to demonstrate the utility of the method.
FDM for Elliptic Equations with Bitsadze-Samarskii-Dirichlet Conditions
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2012-01-01
Full Text Available A numerical method is proposed for solving nonlocal boundary value problem for the multidimensional elliptic partial differential equation with the Bitsadze-Samarskii-Dirichlet condition. The first and second-orders of accuracy stable difference schemes for the approximate solution of this nonlocal boundary value problem are presented. The stability estimates, coercivity, and almost coercivity inequalities for solution of these schemes are established. The theoretical statements for the solutions of these nonlocal elliptic problems are supported by results of numerical examples.
Regularity of spectral fractional Dirichlet and Neumann problems
DEFF Research Database (Denmark)
Grubb, Gerd
2016-01-01
Consider the fractional powers and of the Dirichlet and Neumann realizations of a second-order strongly elliptic differential operator A on a smooth bounded subset Ω of . Recalling the results on complex powers and complex interpolation of domains of elliptic boundary value problems by Seeley...... in the 1970's, we demonstrate how they imply regularity properties in full scales of -Sobolev spaces and Hölder spaces, for the solutions of the associated equations. Extensions to nonsmooth situations for low values of s are derived by use of recent results on -calculus. We also include an overview...
Approximate Solutions of Delay Parabolic Equations with the Dirichlet Condition
Directory of Open Access Journals (Sweden)
Deniz Agirseven
2012-01-01
Full Text Available Finite difference and homotopy analysis methods are used for the approximate solution of the initial-boundary value problem for the delay parabolic partial differential equation with the Dirichlet condition. The convergence estimates for the solution of first and second orders of difference schemes in Hölder norms are obtained. A procedure of modified Gauss elimination method is used for the solution of these difference schemes. Homotopy analysis method is applied. Comparison of finite difference and homotopy analysis methods is given on the problem.
Multidimensional kernel estimation
Milosevic, Vukasin
2015-01-01
Kernel estimation is one of the non-parametric methods used for estimation of probability density function. Its first ROOT implementation, as part of RooFit package, has one major issue, its evaluation time is extremely slow making in almost unusable. The goal of this project was to create a new class (TKNDTree) which will follow the original idea of kernel estimation, greatly improve the evaluation time (using the TKTree class for storing the data and creating different user-controlled modes of evaluation) and add the interpolation option, for 2D case, with the help of the new Delaunnay2D class.
for palm kernel oil extraction
African Journals Online (AJOL)
user
OEE), ... designed (CRD) experimental approach with 4 factor levels and 2 replications was used to determine the effect of kernel .... palm kernels in either a continuous or batch mode ... are fed through the hopper; the screw conveys, crushes,.
ON GENERALIZED ORDERS AND GENERALIZED TYPES OF DIRICHLET SERIES IN THE RIGHT HALF-PLANE
Institute of Scientific and Technical Information of China (English)
Yingying HUO; Yinying KONG
2014-01-01
In the paper, generalized orders and generalized types of Dirichlet series in the right half-plane are given. Some interesting relationships on maximum modulus, the maximum term and the coefficients of entire function defined by Dirichlet series of in the right half-plane are obtained.
A note on the Dirichlet problem for model complex partial differential equations
Ashyralyev, Allaberen; Karaca, Bahriye
2016-08-01
Complex model partial differential equations of arbitrary order are considered. The uniqueness of the Dirichlet problem is studied. It is proved that the Dirichlet problem for higher order of complex partial differential equations with one complex variable has infinitely many solutions.
DEFF Research Database (Denmark)
Sjölander, K.; Karplus, K; Brown, M
1996-01-01
We present a method for condensing the information in multiple alignments of proteins into amixture of Dirichlet densities over amino acid distributions. Dirichlet mixture densities aredesigned to be combined with observed amino acid frequencies to form estimates of expectedamino acid probabiliti...
On Existence and Stability of Solutions for Higher Order Semilinear Dirichlet Problems
Indian Academy of Sciences (India)
Marek Galewski
2008-11-01
We provide existence and stability results for semilinear Dirichlet problems with nonlinearity satisfying general growth conditions. We consider the case when both the coefficients of the differential operator and the nonlinear term depend on the numerical parameter. We show applications for the fourth order semilinear Dirichlet problem.
On the stability of gravity with Dirichlet walls
Andrade, Tomas; Marolf, Donald; Santos, Jorge E
2015-01-01
Dirichlet walls -- timelike boundaries at finite distance from the bulk on which the induced metric is held fixed -- have been used to model AdS spacetimes with a finite cutoff. In the context of gauge/gravity duality, such models are often described as dual to some novel UV-cufoff version of a corresponding CFT that maintains local Lorentz invariance. We study linearized gravity in the presence of such a wall and find it to differ significantly from the seemingly-analogous case of Dirichlet boundary conditions for fields of spins zero and one. In particular, using the Kodama-Ishibashi formalism, the boundary condition that must be imposed on scalar-sector master field with harmonic time dependence depends explicitly on their frequency. That this feature first arises for spin-2 appears to be related to the second-order nature of the equations of motion. It gives rise to a number of novel instabilities, though both global and planar Anti-de Sitter remain (linearly) stable in the presence of large-radius Dirich...
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...
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Hansen, Peter Reinhard; Lunde, Asger
2011-01-01
We propose a multivariate realised kernel to estimate the ex-post covariation of log-prices. We show this new consistent estimator is guaranteed to be positive semi-definite and is robust to measurement error of certain types and can also handle non-synchronous trading. It is the first estimator...
Adaptive metric kernel regression
DEFF Research Database (Denmark)
Goutte, Cyril; Larsen, Jan
2000-01-01
regression by minimising a cross-validation estimate of the generalisation error. This allows to automatically adjust the importance of different dimensions. The improvement in terms of modelling performance is illustrated on a variable selection task where the adaptive metric kernel clearly outperforms...
Adaptive Metric Kernel Regression
DEFF Research Database (Denmark)
Goutte, Cyril; Larsen, Jan
1998-01-01
by minimising a cross-validation estimate of the generalisation error. This allows one to automatically adjust the importance of different dimensions. The improvement in terms of modelling performance is illustrated on a variable selection task where the adaptive metric kernel clearly outperforms the standard...
Characteristics of traditionally processed shea kernels and butter
Honfo, G.F.; Linnemann, A.R.; Akissoe, N.; Soumanou, M.M.; Boekel, van M.A.J.S.
2013-01-01
The traditional production of shea butter requires a heat treatment of the nuts. This study compared the end products derived by two commonly used heat treatments, namely smoking and boiling followed by sun-drying. Neither treatment influenced the moisture content of the kernels (8–10%), but the boi
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...
Multiple Kernel Point Set Registration.
Nguyen, Thanh Minh; Wu, Q M Jonathan
2016-06-01
The finite Gaussian mixture model with kernel correlation is a flexible tool that has recently received attention for point set registration. While there are many algorithms for point set registration presented in the literature, an important issue arising from these studies concerns the mapping of data with nonlinear relationships and the ability to select a suitable kernel. Kernel selection is crucial for effective point set registration. We focus here on multiple kernel point set registration. We make several contributions in this paper. First, each observation is modeled using the Student's t-distribution, which is heavily tailed and more robust than the Gaussian distribution. Second, by automatically adjusting the kernel weights, the proposed method allows us to prune the ineffective kernels. This makes the choice of kernels less crucial. After parameter learning, the kernel saliencies of the irrelevant kernels go to zero. Thus, the choice of kernels is less crucial and it is easy to include other kinds of kernels. Finally, we show empirically that our model outperforms state-of-the-art methods recently proposed in the literature.
Directory of Open Access Journals (Sweden)
Nur Asiah Mohd Makhatar
2016-09-01
Full Text Available A numerical investigation is carried out into the flow and heat transfer within a fully-developed mixed convection flow of water–alumina (Al2O3–water, water–titania (TiO2–water and water–copperoxide (CuO–water in a vertical channel by considering Dirichlet, Neumann and Robin boundary conditions. Actual values of thermophysical quantities are used in arriving at conclusions on the three nanoliquids. The Biot number influences on velocity and temperature distributions are opposite in regions close to the left wall and the right wall. Robin condition is seen to favour symmetry in the flow velocity whereas Dirichlet and Neumann conditions skew the flow distribution and push the point of maximum velocity to the right of the channel. A reversal of role is seen between them in their influence on the flow in the left-half and the right-half of the channel. This leads to related consequences in heat transport. Viscous dissipation is shown to aid flow and heat transport. The present findings reiterate the observation on heat transfer in other configurations that only low concentrations of nanoparticles facilitate enhanced heat transport for all three temperature conditions. Significant change was observed in Neumann condition, whereas the changes are too extreme in Dirichlet condition. It is found that Robin condition is the most stable condition. Further, it is also found that all three nanoliquids have enhanced heat transport compared to that by base liquid, with CuO–water nanoliquid shows higher enhancement in its Nusselt number, compared to Al2O3 and TiO2.
Gamma-Dirichlet Structure and Two Classes of Measure-valued Processes
Feng, Shui
2011-01-01
The Gamma-Dirichlet structure corresponds to the decomposition of the gamma process into the independent product of a gamma random variable and a Dirichlet process. This structure allows us to study the properties of the Dirichlet process through the gamma process and vice versa. In this article, we begin with a brief review of existing results concerning the Gamma-Dirichlet structure. New results are obtained for the large deviations of the jump sizes of the gamma process and the quasi-invariance of the two-parameter Poisson-Dirichlet distribution. The laws of the gamma process and the Dirichlet process are the respective reversible measures of the measure-valued branching diffusion with immigration and the Fleming-Viot process with parent independent mutation. We view the relation between these two classes of measure-valued processes as the dynamical Gamma-Dirichlet structure. Other results of this article include the derivation of the transition function of the Fleming-Viot process with parent independent ...
The Hierarchical Dirichlet Process Hidden Semi-Markov Model
Johnson, Matthew J
2012-01-01
There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the traditional HMM. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi- Markovianity, which has been developed in the parametric setting to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicitduration HDP-HSMM and develop posterior sampling algorithms for efficient inference in both the direct-assignment and weak-limit approximation settings. We demonstrate the utility of the model and our inference methods on synthetic data as well as experiments on a speaker diarization problem and an example of learning the patterns in Morse code.
On Dirichlet eigenvectors for neutral two-dimensional Markov chains
Champagnat, Nicolas; Miclo, Laurent
2012-01-01
We consider a general class of discrete, two-dimensional Markov chains modeling the dynamics of a population with two types, without mutation or immigration, and neutral in the sense that type has no influence on each individual's birth or death parameters. We prove that all the eigenvectors of the corresponding transition matrix or infinitesimal generator \\Pi\\ can be expressed as the product of "universal" polynomials of two variables, depending on each type's size but not on the specific transitions of the dynamics, and functions depending only on the total population size. These eigenvectors appear to be Dirichlet eigenvectors for \\Pi\\ on the complement of triangular subdomains, and as a consequence the corresponding eigenvalues are ordered in a specific way. As an application, we study the quasistationary behavior of finite, nearly neutral, two-dimensional Markov chains, absorbed in the sense that 0 is an absorbing state for each component of the process.
Identification of Novel Type III Effectors Using Latent Dirichlet Allocation
Directory of Open Access Journals (Sweden)
Yang Yang
2012-01-01
Full Text Available Among the six secretion systems identified in Gram-negative bacteria, the type III secretion system (T3SS plays important roles in the disease development of pathogens. T3SS has attracted a great deal of research interests. However, the secretion mechanism has not been fully understood yet. Especially, the identification of effectors (secreted proteins is an important and challenging task. This paper adopts machine learning methods to identify type III secreted effectors (T3SEs. We extract features from amino acid sequences and conduct feature reduction based on latent semantic information by using latent Dirichlet allocation model. The experimental results on Pseudomonas syringae data set demonstrate the good performance of the new methods.
EEG Signal Classification With Super-Dirichlet Mixture Model
DEFF Research Database (Denmark)
Ma, Zhanyu; Tan, Zheng-Hua; Prasad, Swati
2012-01-01
Classification of the Electroencephalogram (EEG) signal is a challengeable task in the brain-computer interface systems. The marginalized discrete wavelet transform (mDWT) coefficients extracted from the EEG signals have been frequently used in researches since they reveal features related to the...... vector machine (SVM) based classifier, the SDMM based classifier performs more stable and shows a promising improvement, with both channel selection strategies....... by the Dirichlet distribution and the distribution of the mDWT coefficients from more than one channels is described by a super-Dirichletmixture model (SDMM). The Fisher ratio and the generalization error estimation are applied to select relevant channels, respectively. Compared to the state-of-the-art support...
A q-Analogue of the Dirichlet L-Function
Institute of Scientific and Technical Information of China (English)
Min-Soo Kim; Jin-Woo Son
2002-01-01
In this paper, we will treat some interesting formulae which are slightly different from Kim's results by more or less the same method in [4-9]. At first, we consider a new definition of a q-analogue of Bernoulli numbers and polynomials.We construct a q-analogue of the Riemann ζ-function, Hurwitz ζ-function, and Dirichlet L-series. Also, we investigate the relation between the q-analogue of generalized Bernoulli numbers and the generalized Euler numbers. As an application, we prove that the q-analogue of Bernoulli numbers occurs in the coefficients of some Stirling type series for the p-adic analytic q-log-gamma function.
Background Subtraction with DirichletProcess Mixture Models.
Haines, Tom S F; Tao Xiang
2014-04-01
Video analysis often begins with background subtraction. This problem is often approached in two steps-a background model followed by a regularisation scheme. A model of the background allows it to be distinguished on a per-pixel basis from the foreground, whilst the regularisation combines information from adjacent pixels. We present a new method based on Dirichlet process Gaussian mixture models, which are used to estimate per-pixel background distributions. It is followed by probabilistic regularisation. Using a non-parametric Bayesian method allows per-pixel mode counts to be automatically inferred, avoiding over-/under- fitting. We also develop novel model learning algorithms for continuous update of the model in a principled fashion as the scene changes. These key advantages enable us to outperform the state-of-the-art alternatives on four benchmarks.
Fast Fourier-Galerkin methods for first-kind logarithmic-kernel integral equations on open arcs
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We propose a fully discrete fast Fourier-Galerkin method for solving an integral equation of the first kind with a logarithmic kernel on a smooth open arc,which is a reformulation of the Dirichlet problem of the Laplace equation in the plane.The optimal convergence order and quasi-linear complexity order of the proposed method are established.A precondition is introduced.Combining this method with an efficient numerical integration algorithm for computing the single-layer potential defined on an open arc,we obtain the solution of the Dirichlet problem on a smooth open arc in the plane.Numerical examples are presented to confirm the theoretical estimates and to demonstrate the efficiency and accuracy of the proposed method.
Dirichlet multinomial mixtures: generative models for microbial metagenomics.
Holmes, Ian; Harris, Keith; Quince, Christopher
2012-01-01
We introduce Dirichlet multinomial mixtures (DMM) for the probabilistic modelling of microbial metagenomics data. This data can be represented as a frequency matrix giving the number of times each taxa is observed in each sample. The samples have different size, and the matrix is sparse, as communities are diverse and skewed to rare taxa. Most methods used previously to classify or cluster samples have ignored these features. We describe each community by a vector of taxa probabilities. These vectors are generated from one of a finite number of Dirichlet mixture components each with different hyperparameters. Observed samples are generated through multinomial sampling. The mixture components cluster communities into distinct 'metacommunities', and, hence, determine envirotypes or enterotypes, groups of communities with a similar composition. The model can also deduce the impact of a treatment and be used for classification. We wrote software for the fitting of DMM models using the 'evidence framework' (http://code.google.com/p/microbedmm/). This includes the Laplace approximation of the model evidence. We applied the DMM model to human gut microbe genera frequencies from Obese and Lean twins. From the model evidence four clusters fit this data best. Two clusters were dominated by Bacteroides and were homogenous; two had a more variable community composition. We could not find a significant impact of body mass on community structure. However, Obese twins were more likely to derive from the high variance clusters. We propose that obesity is not associated with a distinct microbiota but increases the chance that an individual derives from a disturbed enterotype. This is an example of the 'Anna Karenina principle (AKP)' applied to microbial communities: disturbed states having many more configurations than undisturbed. We verify this by showing that in a study of inflammatory bowel disease (IBD) phenotypes, ileal Crohn's disease (ICD) is associated with a more variable
Dirichlet multinomial mixtures: generative models for microbial metagenomics.
Directory of Open Access Journals (Sweden)
Ian Holmes
Full Text Available We introduce Dirichlet multinomial mixtures (DMM for the probabilistic modelling of microbial metagenomics data. This data can be represented as a frequency matrix giving the number of times each taxa is observed in each sample. The samples have different size, and the matrix is sparse, as communities are diverse and skewed to rare taxa. Most methods used previously to classify or cluster samples have ignored these features. We describe each community by a vector of taxa probabilities. These vectors are generated from one of a finite number of Dirichlet mixture components each with different hyperparameters. Observed samples are generated through multinomial sampling. The mixture components cluster communities into distinct 'metacommunities', and, hence, determine envirotypes or enterotypes, groups of communities with a similar composition. The model can also deduce the impact of a treatment and be used for classification. We wrote software for the fitting of DMM models using the 'evidence framework' (http://code.google.com/p/microbedmm/. This includes the Laplace approximation of the model evidence. We applied the DMM model to human gut microbe genera frequencies from Obese and Lean twins. From the model evidence four clusters fit this data best. Two clusters were dominated by Bacteroides and were homogenous; two had a more variable community composition. We could not find a significant impact of body mass on community structure. However, Obese twins were more likely to derive from the high variance clusters. We propose that obesity is not associated with a distinct microbiota but increases the chance that an individual derives from a disturbed enterotype. This is an example of the 'Anna Karenina principle (AKP' applied to microbial communities: disturbed states having many more configurations than undisturbed. We verify this by showing that in a study of inflammatory bowel disease (IBD phenotypes, ileal Crohn's disease (ICD is associated with
Asymptotic Results for the Two-parameter Poisson-Dirichlet Distribution
Feng, Shui
2009-01-01
The two-parameter Poisson-Dirichlet distribution is the law of a sequence of decreasing nonnegative random variables with total sum one. It can be constructed from stable and Gamma subordinators with the two-parameters, $\\alpha$ and $\\theta$, corresponding to the stable component and Gamma component respectively. The moderate deviation principles are established for the two-parameter Poisson-Dirichlet distribution and the corresponding homozygosity when $\\theta$ approaches infinity, and the large deviation principle is established for the two-parameter Poisson-Dirichlet distribution when both $\\alpha$ and $\\theta$ approach zero.
Weyl Group Multiple Dirichlet Series Type A Combinatorial Theory (AM-175)
Brubaker, Ben; Friedberg, Solomon
2011-01-01
Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series an
Testing Monotonicity of Pricing Kernels
Timofeev, Roman
2007-01-01
In this master thesis a mechanism to test mononicity of empirical pricing kernels (EPK) is presented. By testing monotonicity of pricing kernel we can determine whether utility function is concave or not. Strictly decreasing pricing kernel corresponds to concave utility function while non-decreasing EPK means that utility function contains some non-concave regions. Risk averse behavior is usually described by concave utility function and considered to be a cornerstone of classical behavioral ...
7 CFR 51.1415 - Inedible kernels.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Inedible kernels. 51.1415 Section 51.1415 Agriculture... Standards for Grades of Pecans in the Shell 1 Definitions § 51.1415 Inedible kernels. Inedible kernels means that the kernel or pieces of kernels are rancid, moldy, decayed, injured by insects or...
7 CFR 981.8 - Inedible kernel.
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,...
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....
7 CFR 981.408 - Inedible kernel.
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...
Toeplitz operators on Dirichlet space Dp on annulus%圆环的 Dirichlet 空间Dp上的 Toeplitz 算子
Institute of Scientific and Technical Information of China (English)
梁颖志; 王晓峰
2014-01-01
主要研究了圆环M的Dirichlet空间D p （1＜p＜∞）上Toeplitz算子的有界性、紧性和Fredholm性质，计算了D p （ M）上Toeplitz算子的Fredholm指标，并刻画了D p （ M）上Hankel算子的紧性。%In this paper ,the boundedness ,compactness and the Fredholm properties of Toeplitz operators on the Dirichlet space Dp(M)(1
Dirichlet space Dp(M) are computed .We also describe the compactness of Hankel operators on the Dirichlet space Dp(M).
Dirichlet Eigenvalue Ratios for the p-sub-Laplacian in the Carnot Group
Institute of Scientific and Technical Information of China (English)
WEI Na; NIU Pengcheng; LIU Haifeng
2009-01-01
We prove some new Hardy type inequalities on the bounded domain with smooth boundary in the Carnot group. Several estimates of the first and second Dirich-let eigenvalues for the p-sub-Laplacian are established.
THE DYNAMICS OF SINE-GORDON SYSTEM WITH DIRICHLET BOUNDARY CONDITION
Institute of Scientific and Technical Information of China (English)
Liu Yingdong; Li Zhengyuan
2000-01-01
We prove the existence of the global attractor of Sine-Gordon system with Dirichlet boundary condition and show the attractor is the unique steady state when the damping constant and the diffusion constant are sufficiently large.
On the Mean Value of the Complete Trigonometric Sums with Dirichlet Characters
Institute of Scientific and Technical Information of China (English)
Zhe Feng XU
2007-01-01
The main purpose of this paper is, using the analytic method, to study the mean value properties of the complete trigonometric sums with Dirichlet characters, and give an exact calculating formula for its fourth power mean.
Institute of Scientific and Technical Information of China (English)
Ling DING; Chunlei TANG
2013-01-01
The existence and multiplicity of positive solutions are studied for a class of quasilinear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.
A Note on Existence and Stability of Solutions for Semilinear Dirichlet Problems
Indian Academy of Sciences (India)
Marek Galewski
2011-05-01
We provide existence and stability results for a fourth-order semilinear Dirichlet problem in the case when both the coefficients of the differential operator and the nonlinear term depend on the numerical parameter. We use a dual variational method.
Clustering via Kernel Decomposition
DEFF Research Database (Denmark)
Have, Anna Szynkowiak; Girolami, Mark A.; Larsen, Jan
2006-01-01
Methods for spectral clustering have been proposed recently which rely on the eigenvalue decomposition of an affinity matrix. In this work it is proposed that the affinity matrix is created based on the elements of a non-parametric density estimator. This matrix is then decomposed to obtain...... posterior probabilities of class membership using an appropriate form of nonnegative matrix factorization. The troublesome selection of hyperparameters such as kernel width and number of clusters can be obtained using standard cross-validation methods as is demonstrated on a number of diverse data sets....
On the Dirichlet Problem of Mixed Type for Lower Hybrid Waves in Axisymmetric Cold Plasmas
Lupo, Daniela; Monticelli, Dario D.; Payne, Kevin R.
2015-07-01
For a class of linear second order partial differential equations of mixed elliptic-hyperbolic type, which includes a well known model for analyzing possible heating in axisymmetric cold plasmas, we give results on the weak well-posedness of the Dirichlet problem and show that such solutions are characterized by a variational principle. The weak solutions are shown to be saddle points of natural functionals suggested by the divergence form of the PDEs. Moreover, the natural domains of the functionals are the weighted Sobolev spaces to which the solutions belong. In addition, all critical levels will be characterized in terms of global extrema of the functionals restricted to suitable infinite dimensional linear subspaces. These subspaces are defined in terms of a robust spectral theory with weights which is associated to the linear operator and is developed herein. Similar characterizations for the weighted eigenvalue problem and nonlinear variants will also be given. Finally, topological methods are employed to obtain existence results for nonlinear problems including perturbations in the gradient which are then applied to the well-posedness of the linear problem with lower order terms.
Counterterms for the Dirichlet Prescription of the AdS/CFT Correspondence
Mück, W
1999-01-01
We illustrate the Dirichlet prescription of the AdS/CFT correspondence using the example of a massive scalar field and argue that it is the only entirely consistent regularization procedure known so far. Using the Dirichlet prescription, we then calculate the divergent terms for gravity in the cases $d=2,4,6$, which give rise to the Weyl anomaly in the boundary conformal field theory.
Vector-Valued Dirichlet-Type Functions on the Unit Ball of Cn
Institute of Scientific and Technical Information of China (English)
LI Ying-kui; LIU Pei-de
2005-01-01
The vector-valued Dirichlet-type spaces on the unit ball of Cn is introduced. We discuss the pointwise multipliers of Dirichlet-type spaces. Sufficient conditions of the pointwise multipliers of D2μ for 0≤μ＜2 if n=1 or D2μ,q for 0＜μ＜1 if n≥2 are given. Finally, Rademacher p-type space is characterized by vector-valued sequence spaces.
Kernel Phase and Kernel Amplitude in Fizeau Imaging
Pope, Benjamin J S
2016-01-01
Kernel phase interferometry is an approach to high angular resolution imaging which enhances the performance of speckle imaging with adaptive optics. Kernel phases are self-calibrating observables that generalize the idea of closure phases from non-redundant arrays to telescopes with arbitrarily shaped pupils, by considering a matrix-based approximation to the diffraction problem. In this paper I discuss the recent history of kernel phase, in particular in the matrix-based study of sparse arrays, and propose an analogous generalization of the closure amplitude to kernel amplitudes. This new approach can self-calibrate throughput and scintillation errors in optical imaging, which extends the power of kernel phase-like methods to symmetric targets where amplitude and not phase calibration can be a significant limitation, and will enable further developments in high angular resolution astronomy.
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...
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...
Graph kernels between point clouds
Bach, Francis
2007-01-01
Point clouds are sets of points in two or three dimensions. Most kernel methods for learning on sets of points have not yet dealt with the specific geometrical invariances and practical constraints associated with point clouds in computer vision and graphics. In this paper, we present extensions of graph kernels for point clouds, which allow to use kernel methods for such ob jects as shapes, line drawings, or any three-dimensional point clouds. In order to design rich and numerically efficient kernels with as few free parameters as possible, we use kernels between covariance matrices and their factorizations on graphical models. We derive polynomial time dynamic programming recursions and present applications to recognition of handwritten digits and Chinese characters from few training examples.
Kernel Generalized Noise Clustering Algorithm
Institute of Scientific and Technical Information of China (English)
WU Xiao-hong; ZHOU Jian-jiang
2007-01-01
To deal with the nonlinear separable problem, the generalized noise clustering (GNC) algorithm is extended to a kernel generalized noise clustering (KGNC) model. Different from the fuzzy c-means (FCM) model and the GNC model which are based on Euclidean distance, the presented model is based on kernel-induced distance by using kernel method. By kernel method the input data are nonlinearly and implicitly mapped into a high-dimensional feature space, where the nonlinear pattern appears linear and the GNC algorithm is performed. It is unnecessary to calculate in high-dimensional feature space because the kernel function can do itjust in input space. The effectiveness of the proposed algorithm is verified by experiments on three data sets. It is concluded that the KGNC algorithm has better clustering accuracy than FCM and GNC in clustering data sets containing noisy data.
Modeling Information Content Via Dirichlet-Multinomial Regression Analysis.
Ferrari, Alberto
2017-02-16
Shannon entropy is being increasingly used in biomedical research as an index of complexity and information content in sequences of symbols, e.g. languages, amino acid sequences, DNA methylation patterns and animal vocalizations. Yet, distributional properties of information entropy as a random variable have seldom been the object of study, leading to researchers mainly using linear models or simulation-based analytical approach to assess differences in information content, when entropy is measured repeatedly in different experimental conditions. Here a method to perform inference on entropy in such conditions is proposed. Building on results coming from studies in the field of Bayesian entropy estimation, a symmetric Dirichlet-multinomial regression model, able to deal efficiently with the issue of mean entropy estimation, is formulated. Through a simulation study the model is shown to outperform linear modeling in a vast range of scenarios and to have promising statistical properties. As a practical example, the method is applied to a data set coming from a real experiment on animal communication.
Dirichlet-to-Neumann boundary conditions for multiple scattering problems
Grote, Marcus J.; Kirsch, Christoph
2004-12-01
A Dirichlet-to-Neumann (DtN) condition is derived for the numerical solution of time-harmonic multiple scattering problems, where the scatterer consists of several disjoint components. It is obtained by combining contributions from multiple purely outgoing wave fields. The DtN condition yields an exact non-reflecting boundary condition for the situation, where the computational domain and its exterior artificial boundary consist of several disjoint components. Because each sub-scatterer can be enclosed by a separate artificial boundary, the computational effort is greatly reduced and becomes independent of the relative distances between the different sub-domains. The DtN condition naturally fits into a variational formulation of the boundary-value problem for use with the finite element method. Moreover, it immediately yields as a by-product an exact formula for the far-field pattern of the scattered field. Numerical examples show that the DtN condition for multiple scattering is as accurate as the well-known DtN condition for single scattering problems [J. Comput. Phys. 82 (1989) 172; Numerical Methods for Problems in Infinite Domains, Elsevier, Amsterdam, 1992], while being more efficient due to the reduced size of the computational domain.
Flying randomly in $\\mathbb{R}^d$ with Dirichlet displacements
De Gregorio, Alessandro
2011-01-01
Random flights in $\\mathbb{R}^d,d\\geq 2,$ with Dirichlet-distributed displacements and uniformly distributed orientation are analyzed. The explicit characteristic functions of the position $\\underline{\\bf X}_d(t),\\,t>0,$ when the number of changes of direction is fixed are obtained. The probability distributions are derived by inverting the characteristic functions for all dimensions $d$ of $\\mathbb{R}^d$ and many properties of the probabilistic structure of $\\underline{\\bf X}_d(t),t>0,$ are examined. If the number of changes of direction is randomized by means of a fractional Poisson process, we are able to obtain explicit distributions for $P\\{\\underline{\\bf X}_d(t)\\in d\\underline{\\bf x}_d\\}$ for all $d\\geq 2$. A Section is devoted to random flights in $\\mathbb{R}^3$ where the general results are discussed. The existing literature is compared with the results of this paper where in our view the classical Pearson's problem of random flights is resolved by suitably randomizing the step lengths. The random fli...
Modeling healthcare data using multiple-channel latent Dirichlet allocation.
Lu, Hsin-Min; Wei, Chih-Ping; Hsiao, Fei-Yuan
2016-04-01
Information and communications technologies have enabled healthcare institutions to accumulate large amounts of healthcare data that include diagnoses, medications, and additional contextual information such as patient demographics. To gain a better understanding of big healthcare data and to develop better data-driven clinical decision support systems, we propose a novel multiple-channel latent Dirichlet allocation (MCLDA) approach for modeling diagnoses, medications, and contextual information in healthcare data. The proposed MCLDA model assumes that a latent health status group structure is responsible for the observed co-occurrences among diagnoses, medications, and contextual information. Using a real-world research testbed that includes one million healthcare insurance claim records, we investigate the utility of MCLDA. Our empirical evaluation results suggest that MCLDA is capable of capturing the comorbidity structures and linking them with the distribution of medications. Moreover, MCLDA is able to identify the pairing between diagnoses and medications in a record based on the assigned latent groups. MCLDA can also be employed to predict missing medications or diagnoses given partial records. Our evaluation results also show that, in most cases, MCLDA outperforms alternative methods such as logistic regressions and the k-nearest-neighbor (KNN) model for two prediction tasks, i.e., medication and diagnosis prediction. Thus, MCLDA represents a promising approach to modeling healthcare data for clinical decision support.
A Probabilistic Recommendation Method Inspired by Latent Dirichlet Allocation Model
Directory of Open Access Journals (Sweden)
WenBo Xie
2014-01-01
Full Text Available The recent decade has witnessed an increasing popularity of recommendation systems, which help users acquire relevant knowledge, commodities, and services from an overwhelming information ocean on the Internet. Latent Dirichlet Allocation (LDA, originally presented as a graphical model for text topic discovery, now has found its application in many other disciplines. In this paper, we propose an LDA-inspired probabilistic recommendation method by taking the user-item collecting behavior as a two-step process: every user first becomes a member of one latent user-group at a certain probability and each user-group will then collect various items with different probabilities. Gibbs sampling is employed to approximate all the probabilities in the two-step process. The experiment results on three real-world data sets MovieLens, Netflix, and Last.fm show that our method exhibits a competitive performance on precision, coverage, and diversity in comparison with the other four typical recommendation methods. Moreover, we present an approximate strategy to reduce the computing complexity of our method with a slight degradation of the performance.
Bruemmer, David J.
2009-11-17
A robot platform includes perceptors, locomotors, and a system controller. The system controller executes a robot intelligence kernel (RIK) that includes a multi-level architecture and a dynamic autonomy structure. The multi-level architecture includes a robot behavior level for defining robot behaviors, that incorporate robot attributes and a cognitive level for defining conduct modules that blend an adaptive interaction between predefined decision functions and the robot behaviors. The dynamic autonomy structure is configured for modifying a transaction capacity between an operator intervention and a robot initiative and may include multiple levels with at least a teleoperation mode configured to maximize the operator intervention and minimize the robot initiative and an autonomous mode configured to minimize the operator intervention and maximize the robot initiative. Within the RIK at least the cognitive level includes the dynamic autonomy structure.
Nowicki, Dimitri; Siegelmann, Hava
2010-06-11
This paper introduces a new model of associative memory, capable of both binary and continuous-valued inputs. Based on kernel theory, the memory model is on one hand a generalization of Radial Basis Function networks and, on the other, is in feature space, analogous to a Hopfield network. Attractors can be added, deleted, and updated on-line simply, without harming existing memories, and the number of attractors is independent of input dimension. Input vectors do not have to adhere to a fixed or bounded dimensionality; they can increase and decrease it without relearning previous memories. A memory consolidation process enables the network to generalize concepts and form clusters of input data, which outperforms many unsupervised clustering techniques; this process is demonstrated on handwritten digits from MNIST. Another process, reminiscent of memory reconsolidation is introduced, in which existing memories are refreshed and tuned with new inputs; this process is demonstrated on series of morphed faces.
Directory of Open Access Journals (Sweden)
Dimitri Nowicki
Full Text Available This paper introduces a new model of associative memory, capable of both binary and continuous-valued inputs. Based on kernel theory, the memory model is on one hand a generalization of Radial Basis Function networks and, on the other, is in feature space, analogous to a Hopfield network. Attractors can be added, deleted, and updated on-line simply, without harming existing memories, and the number of attractors is independent of input dimension. Input vectors do not have to adhere to a fixed or bounded dimensionality; they can increase and decrease it without relearning previous memories. A memory consolidation process enables the network to generalize concepts and form clusters of input data, which outperforms many unsupervised clustering techniques; this process is demonstrated on handwritten digits from MNIST. Another process, reminiscent of memory reconsolidation is introduced, in which existing memories are refreshed and tuned with new inputs; this process is demonstrated on series of morphed faces.
Mixture Density Mercer Kernels: A Method to Learn Kernels
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...
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,...
(Pre)kernel catchers for cooperative games
Chang, Chih; Driessen, Theo
1995-01-01
The paper provides a new (pre)kernel catcher in that the relevant set always contains the (pre)kernel. This new (pre)kernel catcher gives rise to a better lower bound ɛ*** such that the kernel is included in strong ɛ-cores for all real numbers ɛ not smaller than the relevant bound ɛ***.
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....
FUV Continuum in Flare Kernels Observed by IRIS
Daw, Adrian N.; Kowalski, Adam; Allred, Joel C.; Cauzzi, Gianna
2016-05-01
Fits to Interface Region Imaging Spectrograph (IRIS) spectra observed from bright kernels during the impulsive phase of solar flares are providing long-sought constraints on the UV/white-light continuum emission. Results of fits of continua plus numerous atomic and molecular emission lines to IRIS far ultraviolet (FUV) spectra of bright kernels are presented. Constraints on beam energy and cross sectional area are provided by cotemporaneous RHESSI, FERMI, ROSA/DST, IRIS slit-jaw and SDO/AIA observations, allowing for comparison of the observed IRIS continuum to calculations of non-thermal electron beam heating using the RADYN radiative-hydrodynamic loop model.
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...
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The methods for computing the kemel consistency-based diagnoses and the kernel abductive diagnoses are only suited for the situation where part of the fault behavioral modes of the components are known. The characterization of the kernel model-based diagnosis based on the general causal theory is proposed, which can break through the limitation of the above methods when all behavioral modes of each component are known. Using this method, when observation subsets deduced logically are respectively assigned to the empty or the whole observation set, the kernel consistency-based diagnoses and the kernel abductive diagnoses can deal with all situations. The direct relationship between this diagnostic procedure and the prime implicants/implicates is proved, thus linking theoretical result with implementation.
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.
The density function of the gamma distribution is used as shift kernel in Brownian semistationary processes modelling the timewise behaviour of the velocity in turbulent regimes. This report presents exact and asymptotic properties of the second order structure function under such a model......, and relates these to results of von Karmann and Horwath. But first it is shown that the gamma kernel is interpretable as a Green’s function....
Kernel Rootkits Implement and Detection
Institute of Scientific and Technical Information of China (English)
LI Xianghe; ZHANG Liancheng; LI Shuo
2006-01-01
Rootkits, which unnoticeably reside in your computer, stealthily carry on remote control and software eavesdropping, are a great threat to network and computer security. It' time to acquaint ourselves with their implement and detection. This article pays more attention to kernel rootkits, because they are more difficult to compose and to be identified than useland rootkits. The latest technologies used to write and detect kernel rootkits, along with their advantages and disadvantages, are present in this article.
Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data.
Feischl, M; Page, M; Praetorius, D
2014-01-01
We consider the solution of a second order elliptic PDE with inhomogeneous Dirichlet data by means of adaptive lowest-order FEM. As is usually done in practice, the given Dirichlet data are discretized by nodal interpolation. As model example serves the Poisson equation with mixed Dirichlet-Neumann boundary conditions. For error estimation, we use an edge-based residual error estimator which replaces the volume residual contributions by edge oscillations. For 2D, we prove convergence of the adaptive algorithm even with optimal convergence rate. For 2D and 3D, we show convergence if the nodal interpolation operator is replaced by the [Formula: see text]-projection or the Scott-Zhang quasi-interpolation operator. As a byproduct of the proof, we show that the Scott-Zhang operator converges pointwise to a limiting operator as the mesh is locally refined. This property might be of independent interest besides the current application. Finally, numerical experiments conclude the work.
Estimates of the first Dirichlet eigenvalue from exit time moment spectra
DEFF Research Database (Denmark)
Hurtado, Ana; Markvorsen, Steen; Palmer, Vicente
2013-01-01
We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. This expression implies an estimate as exact as you want for the first Dirichlet eigenvalue of a geodesic ball...... in these rotationally symmetric spaces, including the real space forms of constant curvature. As an application of the model space theory we prove lower and upper bounds for the first Dirichlet eigenvalues of extrinsic metric balls in submanifolds of ambient Riemannian spaces which have model space controlled...... curvatures. Moreover, from this general setting we thereby obtain new generalizations of the classical and celebrated results due to McKean and Cheung--Leung concerning the fundamental tones of Cartan-Hadamard manifolds and the fundamental tones of submanifolds with bounded mean curvature in hyperbolic...
Statistical model of stress corrosion cracking based on extended form of Dirichlet energy
Indian Academy of Sciences (India)
Harry Yosh
2013-12-01
The mechanism of stress corrosion cracking (SCC) has been discussed for decades. Here I propose a model of SCC reflecting the feature of fracture in brittle manner based on the variational principle under approximately supposed thermal equilibrium. In that model the functionals are expressed with extended forms of Dirichlet energy, and Dirichlet principle is applied to them to solve the variational problem that represents SCC and normal extension on pipe surface. Based on the model and the maximum entropy principle, the statistical nature of SCC colony is discussed and it is indicated that the crack has discrete energy and length under ideal isotropy of materials and thermal equilibrium.
Estimates of the first Dirichlet eigenvalue from exit time moment spectra
DEFF Research Database (Denmark)
Hurtado, A.; Markvorsen, Steen; Palmer, V.
2016-01-01
We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. As an application of the model space theory we prove lower and upper bounds for the first Dirichlet eigenvalues...... of extrinsic metric balls in submanifolds of ambient Riemannian spaces which have model space controlled curvatures. Moreover, from this general setting we thereby obtain new generalizations of the classical and celebrated results due to McKean and Cheung–Leung concerning the fundamental tones of Cartan...
Kalvin, Victor
2011-01-01
We establish a limiting absorption principle for Dirichlet Laplacians in quasi-cylindrical domains. Outside a bounded set these domains can be transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet Laplacians model quantum or acoustically-soft waveguides associated with quasi-cylindrical domains. We construct a uniquely solvable problem with perfectly matched layers of finite length. We prove that solutions of the latter problem approximate outgoing or incoming solutions with an error that exponentially tends to zero as the length of layers tends to infinity. Outgoing and incoming solutions are characterized by means of the limiting absorption principle.
R-matrix theory with Dirichlet boundary conditions for integrable electron waveguides
Energy Technology Data Exchange (ETDEWEB)
Lee, Hoshik [Department of Physics, College of William and Mary, Williamsburg, VA 23187 (United States); Reichl, L E, E-mail: hoshik.lee@wm.ed, E-mail: reichl@physics.utexas.ed [Center for Complex Quantum Systems, University of Texas at Austin, Austin, TX 78712 (United States)
2010-10-08
R-matrix theory is used to compute transmission properties of a T-shaped electron waveguide and an electron waveguide-based rotation gate by using Dirichlet boundary conditions for reaction region basis states, even at interfaces with external leads. Such boundary conditions have been known to cause R-matrix convergence problems. We show that an R-matrix obtained using Dirichlet boundary conditions can be convergent for some cases. We also show that R-matrix theory can efficiently reproduce results that were obtained using far more computationally demanding methods such as mode matching techniques, tight-binding Green's function methods or the finite element methods.
An analytic mapping property of the Dirichlet-to-Neumann operator in Helmholtz boundary problems
DEFF Research Database (Denmark)
Karamehmedovic, Mirza
The analytic version of microlocal analysis shows that if the boundary and the Dirichlet datum of a Helmholtz boundary value problem are real-analytic, then so is the corresponding Neumann datum. However, the domain of ana-lytic continuation of the Neumann datum is, in general, unknown. We shall...... here relate, in terms of explicit estimates, the domains of analytic continua-tion of Dirichlet and Neumann boundary data for Helmholtz problems in two or more independent variables, and in neighbourhoods of planar pieces of the boundary. For this purpose, we shall characterise a special subspace...
A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup
Directory of Open Access Journals (Sweden)
Rola Ali Ahmad
2015-01-01
Full Text Available The aim of this work is to study a semidiscrete Crank-Nicolson type scheme in order to approximate numerically the Dirichlet-to-Neumann semigroup. We construct an approximating family of operators for the Dirichlet-to-Neumann semigroup, which satisfies the assumptions of Chernoff’s product formula, and consequently the Crank-Nicolson scheme converges to the exact solution. Finally, we write a P1 finite element scheme for the problem, and we illustrate this convergence by means of a FreeFem++ implementation.
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...
An Approximate Approach to Automatic Kernel Selection.
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.
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...
Integral equations with contrasting kernels
Directory of Open Access Journals (Sweden)
Theodore Burton
2008-01-01
Full Text Available In this paper we study integral equations of the form $x(t=a(t-\\int^t_0 C(t,sx(sds$ with sharply contrasting kernels typified by $C^*(t,s=\\ln (e+(t-s$ and $D^*(t,s=[1+(t-s]^{-1}$. The kernel assigns a weight to $x(s$ and these kernels have exactly opposite effects of weighting. Each type is well represented in the literature. Our first project is to show that for $a\\in L^2[0,\\infty$, then solutions are largely indistinguishable regardless of which kernel is used. This is a surprise and it leads us to study the essential differences. In fact, those differences become large as the magnitude of $a(t$ increases. The form of the kernel alone projects necessary conditions concerning the magnitude of $a(t$ which could result in bounded solutions. Thus, the next project is to determine how close we can come to proving that the necessary conditions are also sufficient. The third project is to show that solutions will be bounded for given conditions on $C$ regardless of whether $a$ is chosen large or small; this is important in real-world problems since we would like to have $a(t$ as the sum of a bounded, but badly behaved function, and a large well behaved function.
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...
Kernel learning algorithms for face recognition
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
A Viscosity Approach to the Dirichlet Problem for Complex Monge-Amp\\`ere Equations
Wang, Yu
2010-01-01
The Dirichlet problem for complex Monge-Amp\\'ere equations with continuous data is considered. In particular, a notion of viscosity solutions is introduced; a comparison principle and a solvability theorem are proved; the equivalence between viscosity and pluripotential solutions is established; and an ABP-type of $L^{\\infty}$-estimate is achieved.
The Graviton in the AdS-CFT correspondence Solution via the Dirichlet Boundary value problem
Mück, W
1998-01-01
Using the AdS-CFT correspondence we calculate the two point function of CFT energy momentum tensors. The AdS gravitons are considered by explicitly solving the Dirichlet boundary value problem for $x_0=\\epsilon$. We consider this treatment as complementary to existing work, with which we make contact.
Dirichlet-Neumann bracketing for boundary-value problems on graphs
Directory of Open Access Journals (Sweden)
Sonja Currie
2005-08-01
Full Text Available We consider the spectral structure of second order boundary-value problems on graphs. A variational formulation for boundary-value problems on graphs is given. As a consequence we can formulate an analogue of Dirichlet-Neumann bracketing for boundary-value problems on graphs. This in turn gives rise to eigenvalue and eigenfunction asymptotic approximations.
Lee, Kuo-Wei
2016-01-01
We prove the existence and uniqueness of the Dirichlet problem for spacelike, spherically symmetric, constant mean curvature equation with symmetric boundary data in the extended Schwarzschild spacetime. As an application, we completely solve the CMC foliation conjecture which is posted by Malec and O Murchadha in 2003.
Lee, Kuo-Wei
2016-09-01
We prove the existence and uniqueness of the Dirichlet problem for the spacelike, spherically symmetric, constant mean curvature equation with symmetric boundary data in the extended Schwarzschild spacetime. As an application, we completely solve the CMC foliation conjecture which is proposed by Malec and Murchadha (2003 Phys. Rev. D 68 124019).
An elementary approach to the meromorphic continuation of some classical Dirichlet series
Indian Academy of Sciences (India)
BISWAJYOTI SAHA
2017-04-01
Here we obtain the meromorphic continuation of some classical Dirichlet series by means of elementary and simple translation formulae for these series. We are also able to determine the poles and the residues by this method. The motivation to our work originates from an idea of Ramanujan which he used to derive the meromorphic continuation of the Riemann zeta function.
Directory of Open Access Journals (Sweden)
Tengfei Shen
2015-12-01
Full Text Available This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained. An example is given to illustrate the main result.
Commuting Dual Toeplitz Operators on the Orthogonal Complement of the Dirichlet Space
Institute of Scientific and Technical Information of China (English)
Tao YU; Shi Yue WU
2009-01-01
In this paper we characterize commuting dual Toeplitz operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We also obtain the sufficient and necessary conditions for the product of two dual Toeplitz operators with harmonic symbols to be a finite rank perturbation of a dual Toeplitz operator.
Self-Commutators of Composition Operators with Monomial Symbols on the Dirichlet Space
Directory of Open Access Journals (Sweden)
A. Abdollahi
2011-01-01
Full Text Available Let (=,∈, for some positive integer and the composition operator on the Dirichlet space induced by . In this paper, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators ∗,∗ and self-commutators of , which expose that the spectrum and point spectrum coincide. We also find the eigenfunctions of the operators.
Directory of Open Access Journals (Sweden)
Maria Transirico
2008-10-01
Full Text Available This paper is concerned with the study of the Dirichlet problem for a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of Ã¢Â„Ân, nÃ¢Â‰Â¥3. We state a regularity result and we can deduce an existence and uniqueness theorem.
Directory of Open Access Journals (Sweden)
Boccia Serena
2008-01-01
Full Text Available This paper is concerned with the study of the Dirichlet problem for a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of , . We state a regularity result and we can deduce an existence and uniqueness theorem.
The Dirichlet Form of a Gradient-type Drift Transformation of a Symmetric Diffusion
Institute of Scientific and Technical Information of China (English)
P.J.FITZSIMMONS
2008-01-01
In the context of a symmetric diffusion process X,we give a precise description of the Dirichlet form of the process obtained by subjecting X to a drift transformation of gradient type.This description relies on boundary-type conditions restricting an associated reflecting Dirichiet form.
The Growth of Random Dirichlet Series%随机Richlet级数的增长性
Institute of Scientific and Technical Information of China (English)
霍颖莹; 孙道椿
2008-01-01
For a known random Dirichlet series of infinite order Oil the whole plane,the authors construct a Dirirchlet series such that the growth of both series referring to the type function is the same.Thus one can study the growth of the former by studying the coefficient and exponent of the latter.
Dual variational formulas for the first Dirichlet eigenvalue on half-line
Institute of Scientific and Technical Information of China (English)
Chen; Mufa(陈木法); ZHANG; Yuhui(张余辉); ZHAO; Xiaoliang(赵晓亮)
2003-01-01
The aim of the paper is to establish two dual variational formulas for the first Dirichlet eigenvalue of the second order elliptic operators on half-line. Some explicit bounds of the eigenvalue depending only on the coefficients of the operators are presented. Moreover, the corresponding problems in the discrete case and the higher-order eigenvalues in the continuous case are also studied.
T, M P Ramirez
2012-01-01
Using a conjecture that allows to approach separable-variables conductivity functions, the elements of the Modern Pseudoanalytic Function Theory are used, for the first time, to numerically solve the Dirichlet boundary value problem of the two-dimensional Electrical Impedance Equation, when the conductivity function arises from geometrical figures, located within bounded domains.
Directory of Open Access Journals (Sweden)
Suzanne Daoud
1992-05-01
Full Text Available In this paper, we consider the space X of all Entire functions represented by Dirichlet series equipped with various topologies. The main result is concerned with finding certain continuous linear operators which are used to determine the proper bases in X.
DEFF Research Database (Denmark)
Walder, Christian; Henao, Ricardo; Mørup, Morten
We present three generalisations of Kernel Principal Components Analysis (KPCA) which incorporate knowledge of the class labels of a subset of the data points. The first, MV-KPCA, penalises within class variances similar to Fisher discriminant analysis. The second, LSKPCA is a hybrid of least...... squares regression and kernel PCA. The final LR-KPCA is an iteratively reweighted version of the previous which achieves a sigmoid loss function on the labeled points. We provide a theoretical risk bound as well as illustrative experiments on real and toy data sets....
Congruence Kernels of Orthoimplication Algebras
Directory of Open Access Journals (Sweden)
I. Chajda
2007-10-01
Full Text Available Abstracting from certain properties of the implication operation in Boolean algebras leads to so-called orthoimplication algebras. These are in a natural one-to-one correspondence with families of compatible orthomodular lattices. It is proved that congruence kernels of orthoimplication algebras are in a natural one-to-one correspondence with families of compatible p-filters on the corresponding orthomodular lattices. Finally, it is proved that the lattice of all congruence kernels of an orthoimplication algebra is relatively pseudocomplemented and a simple description of the relative pseudocomplement is given.
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...
Bergman kernel on generalized exceptional Hua domain
Institute of Scientific and Technical Information of China (English)
YIN; weipng(殷慰萍); ZHAO; zhengang(赵振刚)
2002-01-01
We have computed the Bergman kernel functions explicitly for two types of generalized exceptional Hua domains, and also studied the asymptotic behavior of the Bergman kernel function of exceptional Hua domain near boundary points, based on Appell's multivariable hypergeometric function.
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....
Random Feature Maps for Dot Product Kernels
Kar, Purushottam; Karnick, Harish
2012-01-01
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear Euclidean spaces. We base our results on a classical result in harmonic analysis characterizing all dot product kernels and use it to define randomized feature maps into explic...
ks: Kernel Density Estimation and Kernel Discriminant Analysis for Multivariate Data in R
Directory of Open Access Journals (Sweden)
Tarn Duong
2007-09-01
Full Text Available Kernel smoothing is one of the most widely used non-parametric data smoothing techniques. We introduce a new R package ks for multivariate kernel smoothing. Currently it contains functionality for kernel density estimation and kernel discriminant analysis. It is a comprehensive package for bandwidth matrix selection, implementing a wide range of data-driven diagonal and unconstrained bandwidth selectors.
Local Observed-Score Kernel Equating
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…
Computations of Bergman Kernels on Hua Domains
Institute of Scientific and Technical Information of China (English)
殷慰萍; 王安; 赵振刚; 赵晓霞; 管冰辛
2001-01-01
@@The Bergman kernel function plays an important ro1e in several complex variables.There exists the Bergman kernel function on any bounded domain in Cn. But we can get the Bergman kernel functions in explicit formulas for a few types of domains only,for example:the bounded homogeneous domains and the egg domain in some cases.
Veto-Consensus Multiple Kernel Learning
Y. Zhou; N. Hu; C.J. Spanos
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 propose
Accelerating the Original Profile Kernel.
Directory of Open Access Journals (Sweden)
Tobias Hamp
Full Text Available One of the most accurate multi-class protein classification systems continues to be the profile-based SVM kernel introduced by the Leslie group. Unfortunately, its CPU requirements render it too slow for practical applications of large-scale classification tasks. Here, we introduce several software improvements that enable significant acceleration. Using various non-redundant data sets, we demonstrate that our new implementation reaches a maximal speed-up as high as 14-fold for calculating the same kernel matrix. Some predictions are over 200 times faster and render the kernel as possibly the top contender in a low ratio of speed/performance. Additionally, we explain how to parallelize various computations and provide an integrative program that reduces creating a production-quality classifier to a single program call. The new implementation is available as a Debian package under a free academic license and does not depend on commercial software. For non-Debian based distributions, the source package ships with a traditional Makefile-based installer. Download and installation instructions can be found at https://rostlab.org/owiki/index.php/Fast_Profile_Kernel. Bugs and other issues may be reported at https://rostlab.org/bugzilla3/enter_bug.cgi?product=fastprofkernel.
Adaptive wiener image restoration kernel
Yuan, Ding
2007-06-05
A method and device for restoration of electro-optical image data using an adaptive Wiener filter begins with constructing imaging system Optical Transfer Function, and the Fourier Transformations of the noise and the image. A spatial representation of the imaged object is restored by spatial convolution of the image using a Wiener restoration kernel.
Random Feature Maps for Dot Product Kernels
Kar, Purushottam
2012-01-01
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear Euclidean spaces. We base our results on a classical result in harmonic analysis characterizing all dot product kernels and use it to define randomized feature maps into explicit low dimensional Euclidean spaces in which the native dot product provides an approximation to the dot product kernel with high confidence.
PERI - Auto-tuning Memory Intensive Kernels for Multicore
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H; Williams, Samuel; Datta, Kaushik; Carter, Jonathan; Oliker, Leonid; Shalf, John; Yelick, Katherine; Bailey, David H
2008-06-24
We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of search-based performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to Sparse Matrix Vector Multiplication (SpMV), the explicit heat equation PDE on a regular grid (Stencil), and a lattice Boltzmann application (LBMHD). We explore one of the broadest sets of multicore architectures in the HPC literature, including the Intel Xeon Clovertown, AMD Opteron Barcelona, Sun Victoria Falls, and the Sony-Toshiba-IBM (STI) Cell. Rather than hand-tuning each kernel for each system, we develop a code generator for each kernel that allows us to identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our auto-tuned kernel applications often achieve a better than 4X improvement compared with the original code. Additionally, we analyze a Roofline performance model for each platform to reveal hardware bottlenecks and software challenges for future multicore systems and applications.
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....
Speech Enhancement Using Kernel and Normalized Kernel Affine Projection Algorithm
Directory of Open Access Journals (Sweden)
Bolimera Ravi
2013-08-01
Full Text Available The goal of this paper is to investigate the speech signal enhancement using Kernel Affine ProjectionAlgorithm (KAPA and Normalized KAPA. The removal of background noise is very important in manyapplications like speech recognition, telephone conversations, hearing aids, forensic, etc. Kernel adaptivefilters shown good performance for removal of noise. If the evaluation of background noise is more slowlythan the speech, i.e., noise signal is more stationary than the speech, we can easily estimate the noiseduring the pauses in speech. Otherwise it is more difficult to estimate the noise which results indegradation of speech. In order to improve the quality and intelligibility of speech, unlike time andfrequency domains, we can process the signal in new domain like Reproducing Kernel Hilbert Space(RKHS for high dimensional to yield more powerful nonlinear extensions. For experiments, we have usedthe database of noisy speech corpus (NOIZEUS. From the results, we observed the removal noise in RKHShas great performance in signal to noise ratio values in comparison with conventional adaptive filters.
A sign-changing solution for a superlinear Dirichlet problem, II
Directory of Open Access Journals (Sweden)
Alfonso Castro
2003-02-01
Full Text Available In previous work by Castro, Cossio, and Neuberger cite{ccn}, it was shown that a superlinear Dirichlet problem has at least three nontrivial solutions when the derivative of the nonlinearity at zero is less than the first eigenvalue of $-Delta$ with zero Dirichlet boundry condition. One of these solutions changes sign exactly-once and the other two are of one sign. In this paper we show that when this derivative is between the $k$-th and $k+1$-st eigenvalues there still exists a solution which changes sign at most $k$ times. In particular, when $k=1$ the sign-changing {it exactly-once} solution persists although one-sign solutions no longer exist.
A second eigenvalue bound for the Dirichlet Schrodinger equation wtih a radially symmetric potential
Directory of Open Access Journals (Sweden)
Craig Haile
2000-01-01
Full Text Available We study the time-independent Schrodinger equation with radially symmetric potential $k|x|^alpha$, $k ge 0$, $k in mathbb{R}, alpha ge 2$ on a bounded domain $Omega$ in $mathbb{R}^n$, $(n ge 2$ with Dirichlet boundary conditions. In particular, we compare the eigenvalue $lambda_2(Omega$ of the operator $-Delta + k |x|^alpha $ on $Omega$ with the eigenvalue $lambda_2(S_1$ of the same operator $-Delta +kr^alpha$ on a ball $S_1$, where $S_1$ has radius such that the first eigenvalues are the same ($lambda_1(Omega = lambda_1(S_1$. The main result is to show $lambda_2(Omega le lambda_2(S_1$. We also give an extension of the main result to the case of a more general elliptic eigenvalue problem on a bounded domain $Omega$ with Dirichlet boundary conditions.
On the 2-th Power Mean of Dirichlet -Functions with the Weight of Trigonometric Sums
Indian Academy of Sciences (India)
Rong Ma; Junhuai Zhang; Yulong Zhang
2009-09-01
Let be a prime, denote the Dirichlet character modulo $p,f(x)=a_0+a_1 x+\\cdots+a_kx^k$ is a -degree polynomial with integral coefficients such that $(p, a_0,a_1,\\ldots,a_k)=1$, for any integer , we study the asymptotic property of \\begin{equation*}\\sum\\limits_{≠ _0}\\left| \\sum\\limits^{p-1}_{a=1}(a)e\\left( \\frac{f(a)}{p}\\right)\\right|^2 |L(1,)|^{2m},\\end{equation*} where $e(y)=e^{2 iy}$. The main purpose is to use the analytic method to study the $2m$-th power mean of Dirichlet -functions with the weight of the general trigonometric sums and give an interesting asymptotic formula. This result is an extension of the previous results.
The growth of double Dirichlet series%二重Dirichlet级数的增长性
Institute of Scientific and Technical Information of China (English)
高国妮
2011-01-01
Under the condition that there is not restrict that the three pairs of convergence coordinates of double entire Dirichlet series are equal,it is studied the relationship between the growth of double entire Dirichlet Series and coefficient in two-dimensional after plane by Knopp-Kojima method, then, a necessary and sufficient condition of θ order is got and the strict proof is given.%采用Knopp-Kojima的方法,在不限制二重整Dirichlet级数的三对收敛坐标都相等的条件下,研究了二重整Dirichlet级数在二维复平面上增长性与系数的关系,得到了θ级的一个充要条件,并给出了严格证明.
The Dirichlet problem with L2-boundary data for elliptic linear equations
Chabrowski, Jan
1991-01-01
The Dirichlet problem has a very long history in mathematics and its importance in partial differential equations, harmonic analysis, potential theory and the applied sciences is well-known. In the last decade the Dirichlet problem with L2-boundary data has attracted the attention of several mathematicians. The significant features of this recent research are the use of weighted Sobolev spaces, existence results for elliptic equations under very weak regularity assumptions on coefficients, energy estimates involving L2-norm of a boundary data and the construction of a space larger than the usual Sobolev space W1,2 such that every L2-function on the boundary of a given set is the trace of a suitable element of this space. The book gives a concise account of main aspects of these recent developments and is intended for researchers and graduate students. Some basic knowledge of Sobolev spaces and measure theory is required.
On selecting a prior for the precision parameter of Dirichlet process mixture models
Dorazio, R.M.
2009-01-01
In hierarchical mixture models the Dirichlet process is used to specify latent patterns of heterogeneity, particularly when the distribution of latent parameters is thought to be clustered (multimodal). The parameters of a Dirichlet process include a precision parameter ?? and a base probability measure G0. In problems where ?? is unknown and must be estimated, inferences about the level of clustering can be sensitive to the choice of prior assumed for ??. In this paper an approach is developed for computing a prior for the precision parameter ?? that can be used in the presence or absence of prior information about the level of clustering. This approach is illustrated in an analysis of counts of stream fishes. The results of this fully Bayesian analysis are compared with an empirical Bayes analysis of the same data and with a Bayesian analysis based on an alternative commonly used prior.
Minimization of the k-th eigenvalue of the Dirichlet Laplacian
Bucur, Dorin
2012-12-01
For every {k in {N}}, we prove the existence of a quasi-open set minimizing the k-th eigenvalue of the Dirichlet Laplacian among all sets of prescribed Lebesgue measure. Moreover, we prove that every minimizer is bounded and has a finite perimeter. The key point is the observation that such quasi-open sets are shape subsolutions for an energy minimizing free boundary problem.
Exact Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls
Institute of Scientific and Technical Information of China (English)
Tatsien LI; Bopeng RAO
2013-01-01
In this paper,the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced.By means of the exact null controllability of a reduced coupled system,under certain conditions of compatibility,the exact synchronization,the exact synchronization by groups,and the exact null controllability and synchronization by groups are all realized by suitable boundary controls.
Algebraic Properties of Dual Toeplitz Operators on the Orthogonal Complement of the Dirichlet Space
Institute of Scientific and Technical Information of China (English)
Tao YU; Shi Yue WU
2008-01-01
In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space.We completely characterize commuting dual Toeplitz operators with harmonic symbols,and show that a dual Toeplitz operator commutes with a nonconstant analytic dual Toeplitz operator if and only if its symbol is analytic.We also obtain the sufficient and necessary conditions on the harmonic symbols for SψSψ=Sψψ.
调和Dirichlet空间上的Toeplitz代数%Toeplitz Algebra on the Harmonic Dirichlet Space
Institute of Scientific and Technical Information of China (English)
张正亮; 赵连阔
2008-01-01
Compact Toeplitz operators on the harmonic Dirichlet space are studied by their matrix representation. Applying this result, the short exact sequence associated with the Toeplitz algebra is established.%在调和Dirichlet空间上,利用Toeplitz算子的矩阵表达式对紧算子进行研究.并应用所得结论,建立了与Toeplitz代数相关的短正合列.
Order of Dirichlet Series in the Whole Plane and Remainder Estimation
Institute of Scientific and Technical Information of China (English)
HUANG Hui-jun; NING Ju-hong
2015-01-01
In this paper, firstly, theρorder andρβorder of Dirichlet series which converges in the whole plane are studied. Secondly, the equivalence relation between remainder logarithm ln En−1(f,α), ln Rn(f,α) and coeﬃcients logarithm ln|an|is discussed respectively. Finally, the theory of applying remainder to estimateρorder andρβ order can be obtained by using the equivalence relation.
Existence of Positive Solutions to Semipositone Singular Dirichlet Boundary Value Problems
Institute of Scientific and Technical Information of China (English)
Svatoslav STAN(E)K
2006-01-01
The paper presents the conditions which guarantee that for some positive value of μ there are positive solutions of the differential equation (φ(x'))' +μQ(t, x, x') = 0 satisfying the Dirichlet boundary conditions x(0) = x(T) = 0. Here Q is a continuous function on the set [0, T] × (0, ∞) × (R \\ {0}) of the semipositone type and Q is singular at the value zero of its phase variables.
Littelmann patterns and Weyl group multiple Dirichlet series of type D
Chinta, Gautam
2009-01-01
We formulate a conjecture for the local parts of Weyl group multiple Dirichlet series attached to root systems of type D. Our conjecture is analogous to the description of the local parts of type A series given by Brubaker, Bump, Friedberg, and Hoffstein in terms of Gelfand--Tsetlin patterns. Our conjecture is given in terms of patterns for irreducible representations of even orthogonal Lie algebras developed by Littelmann.
Institute of Scientific and Technical Information of China (English)
Wang Zhigang; Li Yachun
2012-01-01
The aim of this paper is to prove the well-posedness (existence and uniqueness)of the Lp entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with Lp initial value.We use the device of doubling variables and some technical analysis to prove the uniqueness result.Moreover we can prove that the Lp entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.
Quantum singular operator limits of thin Dirichlet tubes via $\\Gamma$-convergence
de Oliveira, Cesar R.
2010-01-01
The $\\Gamma$-convergence of lower bounded quadratic forms is used to study the singular operator limit of thin tubes (i.e., the vanishing of the cross section diameter) of the Laplace operator with Dirichlet boundary conditions; a procedure to obtain the effective Schr\\"odinger operator (in different subspaces) is proposed, generalizing recent results in case of compact tubes. Finally, after scaling curvature and torsion the limit of a broken line is briefly investigated.
Javili, A.; Saeb, S.; Steinmann, P.
2016-10-01
In the past decades computational homogenization has proven to be a powerful strategy to compute the overall response of continua. Central to computational homogenization is the Hill-Mandel condition. The Hill-Mandel condition is fulfilled via imposing displacement boundary conditions (DBC), periodic boundary conditions (PBC) or traction boundary conditions (TBC) collectively referred to as canonical boundary conditions. While DBC and PBC are widely implemented, TBC remains poorly understood, with a few exceptions. The main issue with TBC is the singularity of the stiffness matrix due to rigid body motions. The objective of this manuscript is to propose a generic strategy to implement TBC in the context of computational homogenization at finite strains. To eliminate rigid body motions, we introduce the concept of semi-Dirichlet boundary conditions. Semi-Dirichlet boundary conditions are non-homogeneous Dirichlet-type constraints that simultaneously satisfy the Neumann-type conditions. A key feature of the proposed methodology is its applicability for both strain-driven as well as stress-driven homogenization. The performance of the proposed scheme is demonstrated via a series of numerical examples.
Analyses of Developmental Rate Isomorphy in Ectotherms: Introducing the Dirichlet Regression.
Directory of Open Access Journals (Sweden)
David S Boukal
Full Text Available Temperature drives development in insects and other ectotherms because their metabolic rate and growth depends directly on thermal conditions. However, relative durations of successive ontogenetic stages often remain nearly constant across a substantial range of temperatures. This pattern, termed 'developmental rate isomorphy' (DRI in insects, appears to be widespread and reported departures from DRI are generally very small. We show that these conclusions may be due to the caveats hidden in the statistical methods currently used to study DRI. Because the DRI concept is inherently based on proportional data, we propose that Dirichlet regression applied to individual-level data is an appropriate statistical method to critically assess DRI. As a case study we analyze data on five aquatic and four terrestrial insect species. We find that results obtained by Dirichlet regression are consistent with DRI violation in at least eight of the studied species, although standard analysis detects significant departure from DRI in only four of them. Moreover, the departures from DRI detected by Dirichlet regression are consistently much larger than previously reported. The proposed framework can also be used to infer whether observed departures from DRI reflect life history adaptations to size- or stage-dependent effects of varying temperature. Our results indicate that the concept of DRI in insects and other ectotherms should be critically re-evaluated and put in a wider context, including the concept of 'equiproportional development' developed for copepods.
Prior Design for Dependent Dirichlet Processes: An Application to Marathon Modeling.
Directory of Open Access Journals (Sweden)
Melanie F Pradier
Full Text Available This paper presents a novel application of Bayesian nonparametrics (BNP for marathon data modeling. We make use of two well-known BNP priors, the single-p dependent Dirichlet process and the hierarchical Dirichlet process, in order to address two different problems. First, we study the impact of age, gender and environment on the runners' performance. We derive a fair grading method that allows direct comparison of runners regardless of their age and gender. Unlike current grading systems, our approach is based not only on top world records, but on the performances of all runners. The presented methodology for comparison of densities can be adopted in many other applications straightforwardly, providing an interesting perspective to build dependent Dirichlet processes. Second, we analyze the running patterns of the marathoners in time, obtaining information that can be valuable for training purposes. We also show that these running patterns can be used to predict finishing time given intermediate interval measurements. We apply our models to New York City, Boston and London marathons.
Javili, A.; Saeb, S.; Steinmann, P.
2017-01-01
In the past decades computational homogenization has proven to be a powerful strategy to compute the overall response of continua. Central to computational homogenization is the Hill-Mandel condition. The Hill-Mandel condition is fulfilled via imposing displacement boundary conditions (DBC), periodic boundary conditions (PBC) or traction boundary conditions (TBC) collectively referred to as canonical boundary conditions. While DBC and PBC are widely implemented, TBC remains poorly understood, with a few exceptions. The main issue with TBC is the singularity of the stiffness matrix due to rigid body motions. The objective of this manuscript is to propose a generic strategy to implement TBC in the context of computational homogenization at finite strains. To eliminate rigid body motions, we introduce the concept of semi-Dirichlet boundary conditions. Semi-Dirichlet boundary conditions are non-homogeneous Dirichlet-type constraints that simultaneously satisfy the Neumann-type conditions. A key feature of the proposed methodology is its applicability for both strain-driven as well as stress-driven homogenization. The performance of the proposed scheme is demonstrated via a series of numerical examples.
Nonlinear Deep Kernel Learning for Image Annotation.
Jiu, Mingyuan; Sahbi, Hichem
2017-02-08
Multiple kernel learning (MKL) is a widely used technique for kernel design. Its principle consists in learning, for a given support vector classifier, the most suitable convex (or sparse) linear combination of standard elementary kernels. However, these combinations are shallow and often powerless to capture the actual similarity between highly semantic data, especially for challenging classification tasks such as image annotation. In this paper, we redefine multiple kernels using deep multi-layer networks. In this new contribution, a deep multiple kernel is recursively defined as a multi-layered combination of nonlinear activation functions, each one involves a combination of several elementary or intermediate kernels, and results into a positive semi-definite deep kernel. We propose four different frameworks in order to learn the weights of these networks: supervised, unsupervised, kernel-based semisupervised and Laplacian-based semi-supervised. When plugged into support vector machines (SVMs), the resulting deep kernel networks show clear gain, compared to several shallow kernels for the task of image annotation. Extensive experiments and analysis on the challenging ImageCLEF photo annotation benchmark, the COREL5k database and the Banana dataset validate the effectiveness of the proposed method.
Nonlinear projection trick in kernel methods: an alternative to the kernel trick.
Kwak, Nojun
2013-12-01
In kernel methods such as kernel principal component analysis (PCA) and support vector machines, the so called kernel trick is used to avoid direct calculations in a high (virtually infinite) dimensional kernel space. In this brief, based on the fact that the effective dimensionality of a kernel space is less than the number of training samples, we propose an alternative to the kernel trick that explicitly maps the input data into a reduced dimensional kernel space. This is easily obtained by the eigenvalue decomposition of the kernel matrix. The proposed method is named as the nonlinear projection trick in contrast to the kernel trick. With this technique, the applicability of the kernel methods is widened to arbitrary algorithms that do not use the dot product. The equivalence between the kernel trick and the nonlinear projection trick is shown for several conventional kernel methods. In addition, we extend PCA-L1, which uses L1-norm instead of L2-norm (or dot product), into a kernel version and show the effectiveness of the proposed approach.
Theory of reproducing kernels and applications
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...
Filters, reproducing kernel, and adaptive meshfree method
You, Y.; Chen, J.-S.; Lu, H.
Reproducing kernel, with its intrinsic feature of moving averaging, can be utilized as a low-pass filter with scale decomposition capability. The discrete convolution of two nth order reproducing kernels with arbitrary support size in each kernel results in a filtered reproducing kernel function that has the same reproducing order. This property is utilized to separate the numerical solution into an unfiltered lower order portion and a filtered higher order portion. As such, the corresponding high-pass filter of this reproducing kernel filter can be used to identify the locations of high gradient, and consequently serves as an operator for error indication in meshfree analysis. In conjunction with the naturally conforming property of the reproducing kernel approximation, a meshfree adaptivity method is also proposed.
Kernel principal component analysis for change detection
DEFF Research Database (Denmark)
Nielsen, Allan Aasbjerg; Morton, J.C.
2008-01-01
region acquired at two different time points. If change over time does not dominate the scene, the projection of the original two bands onto the second eigenvector will show change over time. In this paper a kernel version of PCA is used to carry out the analysis. Unlike ordinary PCA, kernel PCA...... with a Gaussian kernel successfully finds the change observations in a case where nonlinearities are introduced artificially....
Tame Kernels of Pure Cubic Fields
Institute of Scientific and Technical Information of China (English)
Xiao Yun CHENG
2012-01-01
In this paper,we study the p-rank of the tame kernels of pure cubic fields.In particular,we prove that for a fixed positive integer m,there exist infinitely many pure cubic fields whose 3-rank of the tame kernel equal to m.As an application,we determine the 3-rank of their tame kernels for some special pure cubic fields.
Kernel Factor Analysis Algorithm with Varimax
Institute of Scientific and Technical Information of China (English)
Xia Guoen; Jin Weidong; Zhang Gexiang
2006-01-01
Kernal factor analysis (KFA) with varimax was proposed by using Mercer kernel function which can map the data in the original space to a high-dimensional feature space, and was compared with the kernel principle component analysis (KPCA). The results show that the best error rate in handwritten digit recognition by kernel factor analysis with varimax (4.2%) was superior to KPCA (4.4%). The KFA with varimax could more accurately image handwritten digit recognition.
Convergence of barycentric coordinates to barycentric kernels
Kosinka, Jiří
2016-02-12
We investigate the close correspondence between barycentric coordinates and barycentric kernels from the point of view of the limit process when finer and finer polygons converge to a smooth convex domain. We show that any barycentric kernel is the limit of a set of barycentric coordinates and prove that the convergence rate is quadratic. Our convergence analysis extends naturally to barycentric interpolants and mappings induced by barycentric coordinates and kernels. We verify our theoretical convergence results numerically on several examples.
Efficient classification for additive kernel SVMs.
Maji, Subhransu; Berg, Alexander C; Malik, Jitendra
2013-01-01
We show that a class of nonlinear kernel SVMs admits approximate classifiers with runtime and memory complexity that is independent of the number of support vectors. This class of kernels, which we refer to as additive kernels, includes widely used kernels for histogram-based image comparison like intersection and chi-squared kernels. Additive kernel SVMs can offer significant improvements in accuracy over linear SVMs on a wide variety of tasks while having the same runtime, making them practical for large-scale recognition or real-time detection tasks. We present experiments on a variety of datasets, including the INRIA person, Daimler-Chrysler pedestrians, UIUC Cars, Caltech-101, MNIST, and USPS digits, to demonstrate the effectiveness of our method for efficient evaluation of SVMs with additive kernels. Since its introduction, our method has become integral to various state-of-the-art systems for PASCAL VOC object detection/image classification, ImageNet Challenge, TRECVID, etc. The techniques we propose can also be applied to settings where evaluation of weighted additive kernels is required, which include kernelized versions of PCA, LDA, regression, k-means, as well as speeding up the inner loop of SVM classifier training algorithms.
Institute of Scientific and Technical Information of China (English)
王斐; 史闯; 殷钟意; 郑旭煦
2016-01-01
The heating process of peony seed kernel oil(PSKO)was simulated by oven method,and the effects of different heating conditions on the fatty acids composition,acid value and peroxide value of PSKO were evaluat-ed using home-made PSKO as raw material. The results showed that the quality of PSKO were susceptible to heating temperature and time,the total amounts of trans fatty acids and the peroxide value of PSKO were in-creased but the acid value was basically unchanged with the increasing of heating temperature or heating time. The PSKO were heated at 50℃not more than 1h or heated at 100℃not more than 0.5 h respectively,the total amount of trans fatty acids could be less than the requirements of national standard (0.3 g/100 g),and in such condition,the acid value and the peroxide value of PSKO could be less than the requirements of national stan-dard.%以自制的牡丹籽仁油为原料，利用油浴加热模拟牡丹籽仁油的加热过程，研究不同加热条件对牡丹籽仁油脂肪酸组成、酸值和过氧化值的影响。结果表明，牡丹籽仁油品质易受加热温度和加热时间的影响，随着加热温度的升高或加热时间的延长，牡丹籽仁油中的反式脂肪酸总含量、过氧化值均增加，但酸值基本不变；牡丹籽仁油于50℃下加热不超过1 h或于100℃下加热不超过0.5 h，其反式脂肪酸总含量可达到国家标准（0.3 g/100 g）要求；在该条件下，牡丹籽仁油的酸值和过氧化值均能达到国家标准要求。
The Regular Growth of Dirichlet Series on the Whole Plane%Dirichlet级数在全平面上的正规增长性
Institute of Scientific and Technical Information of China (English)
古振东; 孙道椿
2011-01-01
该文引用Knopp-Kojima的方法,定义了Dirichlet级数的级及正规增长级,并以此研究了Dirichlet级数在全平面的正规增长性,得到了Dirichlet级数在全平面的正规增长级的等价条件.%By the method of Knopp-Kojima, the authors define the order of Dirichlet series and the order of regular growth of Dirichlet series, and study the regular growth of Dirichlet series on the whole plane, and obtain an equivalent condition of the order of regular growth of Dirichlet series.
Molecular hydrodynamics from memory kernels
Lesnicki, Dominika; Carof, Antoine; Rotenberg, Benjamin
2016-01-01
The memory kernel for a tagged particle in a fluid, computed from molecular dynamics simulations, decays algebraically as $t^{-3/2}$. We show how the hydrodynamic Basset-Boussinesq force naturally emerges from this long-time tail and generalize the concept of hydrodynamic added mass. This mass term is negative in the present case of a molecular solute, at odds with incompressible hydrodynamics predictions. We finally discuss the various contributions to the friction, the associated time scales and the cross-over between the molecular and hydrodynamic regimes upon increasing the solute radius.
Hilbertian kernels and spline functions
Atteia, M
1992-01-01
In this monograph, which is an extensive study of Hilbertian approximation, the emphasis is placed on spline functions theory. The origin of the book was an effort to show that spline theory parallels Hilbertian Kernel theory, not only for splines derived from minimization of a quadratic functional but more generally for splines considered as piecewise functions type. Being as far as possible self-contained, the book may be used as a reference, with information about developments in linear approximation, convex optimization, mechanics and partial differential equations.
Differentiable Kernels in Generalized Matrix Learning Vector Quantization
Kästner, M.; Nebel, D.; Riedel, M.; Biehl, M.; Villmann, T.
2013-01-01
In the present paper we investigate the application of differentiable kernel for generalized matrix learning vector quantization as an alternative kernel-based classifier, which additionally provides classification dependent data visualization. We show that the concept of differentiable kernels allo
Kernel current source density method.
Potworowski, Jan; Jakuczun, Wit; Lȩski, Szymon; Wójcik, Daniel
2012-02-01
Local field potentials (LFP), the low-frequency part of extracellular electrical recordings, are a measure of the neural activity reflecting dendritic processing of synaptic inputs to neuronal populations. To localize synaptic dynamics, it is convenient, whenever possible, to estimate the density of transmembrane current sources (CSD) generating the LFP. In this work, we propose a new framework, the kernel current source density method (kCSD), for nonparametric estimation of CSD from LFP recorded from arbitrarily distributed electrodes using kernel methods. We test specific implementations of this framework on model data measured with one-, two-, and three-dimensional multielectrode setups. We compare these methods with the traditional approach through numerical approximation of the Laplacian and with the recently developed inverse current source density methods (iCSD). We show that iCSD is a special case of kCSD. The proposed method opens up new experimental possibilities for CSD analysis from existing or new recordings on arbitrarily distributed electrodes (not necessarily on a grid), which can be obtained in extracellular recordings of single unit activity with multiple electrodes.
Filtering algorithms using shiftable kernels
Chaudhury, Kunal Narayan
2011-01-01
It was recently demonstrated in [4][arxiv:1105.4204] that the non-linear bilateral filter \\cite{Tomasi} can be efficiently implemented using an O(1) or constant-time algorithm. At the heart of this algorithm was the idea of approximating the Gaussian range kernel of the bilateral filter using trigonometric functions. In this letter, we explain how the idea in [4] can be extended to few other linear and non-linear filters [18,21,2]. While some of these filters have received a lot of attention in recent years, they are known to be computationally intensive. To extend the idea in \\cite{Chaudhury2011}, we identify a central property of trigonometric functions, called shiftability, that allows us to exploit the redundancy inherent in the filtering operations. In particular, using shiftable kernels, we show how certain complex filtering can be reduced to simply that of computing the moving sum of a stack of images. Each image in the stack is obtained through an elementary pointwise transform of the input image. Thi...
Kernel parameter dependence in spatial factor analysis
DEFF Research Database (Denmark)
Nielsen, Allan Aasbjerg
2010-01-01
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...
Improving the Bandwidth Selection in Kernel Equating
Andersson, Björn; von Davier, Alina A.
2014-01-01
We investigate the current bandwidth selection methods in kernel equating and propose a method based on Silverman's rule of thumb for selecting the bandwidth parameters. In kernel equating, the bandwidth parameters have previously been obtained by minimizing a penalty function. This minimization process has been criticized by practitioners…
Ranking Support Vector Machine with Kernel Approximation.
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.
Generalized Derivative Based Kernelized Learning Vector Quantization
Schleif, Frank-Michael; Villmann, Thomas; Hammer, Barbara; Schneider, Petra; Biehl, Michael; Fyfe, Colin; Tino, Peter; Charles, Darryl; Garcia-Osoro, Cesar; Yin, Hujun
2010-01-01
We derive a novel derivative based version of kernelized Generalized Learning Vector Quantization (KGLVQ) as an effective, easy to interpret, prototype based and kernelized classifier. It is called D-KGLVQ and we provide generalization error bounds, experimental results on real world data, showing t
PALM KERNEL SHELL AS AGGREGATE FOR LIGHT
African Journals Online (AJOL)
of cement, sand, gravel andpalm kernel shells respectively gave the highest compressive strength of ... Keywords: Aggregate, Cement, Concrete, Sand, Palm Kernel Shell. ... delivered to the jOb Slte in a plastic ... structures, breakwaters, piers and docks .... related to cement content at a .... sheet and the summary is shown.
Panel data specifications in nonparametric kernel regression
DEFF Research Database (Denmark)
Czekaj, Tomasz Gerard; Henningsen, Arne
parametric panel data estimators to analyse the production technology of Polish crop farms. The results of our nonparametric kernel regressions generally differ from the estimates of the parametric models but they only slightly depend on the choice of the kernel functions. Based on economic reasoning, we...
Institute of Scientific and Technical Information of China (English)
岳超; 孙道椿
2011-01-01
By the method from Knopp - Kojima, the growths of Dirichlet series and random Dirichlet series in the right half plane are studied.The necessary and sufficient conditions of the orders, which are expressed by the coefficients, are obtained.It is shown that the growth of random Dirichlet series in the right half plane is almost the same as what in the horizontal half zone under some conditions.%采用Knopp-Kojima的方法,研究了Diriehlet级数与随机Diriehlet级数在右半平面内的增长性,得到了级由系数表示的充分必要条件.并且得到了随机Dirichlet级数在右半平面内的级与任意水平半带形内的级在一定条件下几乎必然相等的结论.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A kernel-based discriminant analysis method called kernel direct discriminant analysis is employed, which combines the merit of direct linear discriminant analysis with that of kernel trick. In order to demonstrate its better robustness to the complex and nonlinear variations of real face images, such as illumination, facial expression, scale and pose variations, experiments are carried out on the Olivetti Research Laboratory, Yale and self-built face databases. The results indicate that in contrast to kernel principal component analysis and kernel linear discriminant analysis, the method can achieve lower (7%) error rate using only a very small set of features. Furthermore, a new corrected kernel model is proposed to improve the recognition performance. Experimental results confirm its superiority (1% in terms of recognition rate) to other polynomial kernel models.
Parameter-Free Spectral Kernel Learning
Mao, Qi
2012-01-01
Due to the growing ubiquity of unlabeled data, learning with unlabeled data is attracting increasing attention in machine learning. In this paper, we propose a novel semi-supervised kernel learning method which can seamlessly combine manifold structure of unlabeled data and Regularized Least-Squares (RLS) to learn a new kernel. Interestingly, the new kernel matrix can be obtained analytically with the use of spectral decomposition of graph Laplacian matrix. Hence, the proposed algorithm does not require any numerical optimization solvers. Moreover, by maximizing kernel target alignment on labeled data, we can also learn model parameters automatically with a closed-form solution. For a given graph Laplacian matrix, our proposed method does not need to tune any model parameter including the tradeoff parameter in RLS and the balance parameter for unlabeled data. Extensive experiments on ten benchmark datasets show that our proposed two-stage parameter-free spectral kernel learning algorithm can obtain comparable...
Statistical model of stress corrosion cracking based on extended form of Dirichlet energy: Part 2
Indian Academy of Sciences (India)
HARRY YOSH
2016-10-01
In the previous paper ({\\it Pramana – J. Phys.} 81(6), 1009 (2013)), the mechanism of stress corrosion cracking (SCC) based on non-quadratic form of Dirichlet energy was proposed and its statistical features were discussed. Following those results, we discuss here how SCC propagates on pipe wall statistically. It reveals that SCC growth distribution is described with Cauchy problem of time-dependent first-order partial differential equation characterized by the convolution of the initial distribution of SCC over time. We also discuss the extension of the above results to the SCC in two-dimensional space and its statistical features with a simple example.
A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions
Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.
2014-01-01
We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.
Directory of Open Access Journals (Sweden)
Ishfaq Ahmad Ganaie
2014-01-01
Full Text Available Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme.
A formalized proof of Dirichlet's theorem on primes in arithmetic progression
Directory of Open Access Journals (Sweden)
John Harrison
2009-01-01
Full Text Available We describe the formalization using the HOL Light theorem prover of Dirichlet's theorem on primes in arithmetic progression. The proof turned out to be more straightforward than expected, but this depended on a careful choice of an informal proof to use as a starting-point. The goal of this paper iis twofold. First we describe a simple and efficient proof of the theorem informally, which iis otherwise difficult to find in one self-contained place at an elementary level. We also describe its, largely routine, HOL Light formalization, a task that took only a few days.
A three dimensional Dirichlet-to-Neumann map for surface waves over topography
Nachbin, Andre; Andrade, David
2016-11-01
We consider three dimensional surface water waves in the potential theory regime. The bottom topography can have a quite general profile. In the case of linear waves the Dirichlet-to-Neumann operator is formulated in a matrix decomposition form. Computational simulations illustrate the performance of the method. Two dimensional periodic bottom variations are considered in both the Bragg resonance regime as well as the rapidly varying (homogenized) regime. In the three-dimensional case we use the Luneburg lens-shaped submerged mound, which promotes the focusing of the underlying rays. FAPERJ Cientistas do Nosso Estado Grant 102917/2011 and ANP/PRH-32.
Directory of Open Access Journals (Sweden)
Т. Horsin
2014-01-01
Full Text Available We consider an optimal control problem associated to Dirichlet boundary valueproblem for linear elliptic equations on a bounded domain Ω. We take the matrixvalued coecients A(x of such system as a control in L1(Ω;RN RN. One of the important features of the admissible controls is the fact that the coecient matrices A(x are non-symmetric, unbounded on Ω, and eigenvalues of the symmetric part Asym = (A + At=2 may vanish in Ω.
REARRANGEMENT OF THE COEFFICIENTS OF DIRICHLET SERIES%Dirichlet级数系数的重排
Institute of Scientific and Technical Information of China (English)
岳超; 孙道椿
2012-01-01
本文研究了Dirichlet级数系数的重排与此级数的收敛横坐标的关系.利用KnoppKojima的方法,获得了在Knopp-Kojima公式下绝对收敛横坐标保持不变的重排特征.%In this article, we study the relation between rearrangement of the coefficients of Dirichlet series and its abscissa of convergence. By the method of Knopp-Kojima, the rearrangement characteristics of keeping the abscissa of absolute convergence given by Knopp-Kojima formual is obtained.
Imitation learning of Non-Linear Point-to-Point Robot Motions using Dirichlet Processes
DEFF Research Database (Denmark)
Krüger, Volker; Tikhanoff, Vadim; Natale, Lorenzo
2012-01-01
In this paper we discuss the use of the infinite Gaussian mixture model and Dirichlet processes for learning robot movements from demonstrations. Starting point of this work is an earlier paper where the authors learn a non-linear dynamic robot movement model from a small number of observations....... The model in that work is learned using a classical finite Gaussian mixture model (FGMM) where the Gaussian mixtures are appropriately constrained. The problem with this approach is that one needs to make a good guess for how many mixtures the FGMM should use. In this work, we generalize this approach...
Proof of generalized Riemann hypothesis for Dedekind zetas and Dirichlet L-functions
Mcadrecki, Andrzej
2007-01-01
A short proof of the generalized Riemann hypothesis (gRH in short) for zeta functions $\\zeta_{k}$ of algebraic number fields $k$ - based on the Hecke's proof of the functional equation for $\\zeta_{k}$ and the method of the proof of the Riemann hypothesis derived in [$M_{A}$] (algebraic proof of the Riemann hypothesis) is given. The generalized Riemann hypothesis for Dirichlet L-functions is an immediately consequence of (gRH) for $\\zeta_{k}$ and suitable product formula which connects the Dedekind zetas with L-functions.
Sobolev spaces of maps and the Dirichlet problem for harmonic maps
Pigola, Stefano; Veronelli, Giona
2014-01-01
In this paper we prove the existence of a solution to the Dirichlet problem for harmonic maps into a geodesic ball on which the squared distance function from the origin is strictly convex. This improves a celebrated theorem obtained by S. Hildebrandt, H. Kaul and K. Widman in 1977. In particular no curvature assumptions on the target are required. Our proof relies on a careful analysis of the Sobolev spaces of maps involved in the variational process, and on a deformation result which permit...
Ramos, I C
2015-01-01
We present the adaptation to non--free boundary conditions of a pseudospectral method based on the (complex) Fourier transform. The method is applied to the numerical integration of the Oberbeck--Boussinesq equations in a Rayleigh--B\\'enard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature. We show the first results of a 2D numerical simulation of dry air convection at high Rayleigh number ($R\\sim10^9$). These results are the basis for the later study, by the same method, of wet convection in a solar still.
Stability and Bifurcation in a Delayed Reaction-Diffusion Equation with Dirichlet Boundary Condition
Guo, Shangjiang; Ma, Li
2016-04-01
In this paper, we study the dynamics of a diffusive equation with time delay subject to Dirichlet boundary condition in a bounded domain. The existence of spatially nonhomogeneous steady-state solution is investigated by applying Lyapunov-Schmidt reduction. The existence of Hopf bifurcation at the spatially nonhomogeneous steady-state solution is derived by analyzing the distribution of the eigenvalues. The direction of Hopf bifurcation and stability of the bifurcating periodic solution are also investigated by means of normal form theory and center manifold reduction. Moreover, we illustrate our general results by applications to the Nicholson's blowflies models with one- dimensional spatial domain.
Estimates for the resolvent kernel of the Laplacian on p.c.f. self similar fractals and blowups
Rogers, Luke G
2010-01-01
We provide a method for obtaining upper estimates of the resolvent kernel of the Laplacian on a post-critically finite self-similar fractal that relies on a self-similar series decomposition of the resolvent. Decay estimates on the positive real axis are proved by analyzing functions satisfying an interior eigenfunction condition with positive eigenvalue. These lead to estimates on the complement of the negative real axis via the Phragmen-Lindelof theorem. Applications are given to kernels for functions of the Laplacian, including the heat kernel, and to proving the existence of a self-similar series decomposition for the Laplacian resolvent on fractal blowups.
Li, Rui; Zhang, Shuang; Kou, Xiaoxi; Ling, Bo; Wang, Shaojin
2017-02-10
To develop advanced pasteurization treatments based on radio frequency (RF) or microwave (MW) energy, dielectric properties of almond kernels were measured by using an open-ended coaxial-line probe and impedance analyzer at frequencies between 10 and 3000 MHz, moisture contents between 4.2% to 19.6% w.b. and temperatures between 20 and 90 °C. The results showed that both dielectric constant and loss factor of the almond kernels decreased sharply with increasing frequency over the RF range (10-300 MHz), but gradually over the measured MW range (300-3000 MHz). Both dielectric constant and loss factor of almond kernels increased with increasing temperature and moisture content, and largely enhanced at higher temperature and moisture levels. Quadratic polynomial equations were developed to best fit the relationship between dielectric constant or loss factor at 27, 40, 915 or 2450 MHz and sample temperature/moisture content with R(2) greater than 0.967. Penetration depth of electromagnetic wave into samples decreased with increasing frequency (27-2450 MHz), moisture content (4.2-19.6% w.b.) and temperature (20-90 °C). The temperature profiles of RF heated almond kernels under three moisture levels were made using experiment and computer simulation based on measured dielectric properties. Based on the result of this study, RF treatment has potential to be practically used for pasteurization of almond kernels with acceptable heating uniformity.
Contextual learning in ground-penetrating radar data using Dirichlet process priors
Ratto, Christopher R.; Morton, Kenneth D., Jr.; Collins, Leslie M.; Torrione, Peter A.
2011-06-01
In landmine detection applications, fluctuation of environmental and operating conditions can limit the performance of sensors based on ground-penetrating radar (GPR) technology. As these conditions vary, the classification and fusion rules necessary for achieving high detection and low false alarm rates may change. Therefore, context-dependent learning algorithms that exploit contextual variations of GPR data to alter decision rules have been considered for improving the performance of landmine detection systems. Past approaches to contextual learning have used both generative and discriminative methods to learn a probabilistic mixture of contexts, such as a Gaussian mixture, fuzzy c-means clustering, or a mixture of random sets. However, in these approaches the number of mixture components is pre-defined, which could be problematic if the number of contexts in a data collection is unknown a priori. In this work, a generative context model is proposed which requires no a priori knowledge in the number of mixture components. This was achieved through modeling the contextual distribution in a physics-based feature space with a Gaussian mixture, while also incorporating a Dirichlet process prior to model uncertainty in the number of mixture components. This Dirichlet process Gaussian mixture model (DPGMM) was then incorporated in the previously-developed Context-Dependent Feature Selection (CDFS) framework for fusion of multiple landmine detection algorithms. Experimental results suggest that when the DPGMM was incorporated into CDFS, the degree of performance improvement over conventional fusion was greater than when a conventional fixed-order context model was used.
Directory of Open Access Journals (Sweden)
Pretorius Albertus
2003-03-01
Full Text Available Abstract In the case of the mixed linear model the random effects are usually assumed to be normally distributed in both the Bayesian and classical frameworks. In this paper, the Dirichlet process prior was used to provide nonparametric Bayesian estimates for correlated random effects. This goal was achieved by providing a Gibbs sampler algorithm that allows these correlated random effects to have a nonparametric prior distribution. A sampling based method is illustrated. This method which is employed by transforming the genetic covariance matrix to an identity matrix so that the random effects are uncorrelated, is an extension of the theory and the results of previous researchers. Also by using Gibbs sampling and data augmentation a simulation procedure was derived for estimating the precision parameter M associated with the Dirichlet process prior. All needed conditional posterior distributions are given. To illustrate the application, data from the Elsenburg Dormer sheep stud were analysed. A total of 3325 weaning weight records from the progeny of 101 sires were used.
Zhou, Yan; Brinkmann, Henner; Rodrigue, Nicolas; Lartillot, Nicolas; Philippe, Hervé
2010-02-01
Heterotachy, the variation of substitution rate at a site across time, is a prevalent phenomenon in nucleotide and amino acid alignments, which may mislead probabilistic-based phylogenetic inferences. The covarion model is a special case of heterotachy, in which sites change between the "ON" state (allowing substitutions according to any particular model of sequence evolution) and the "OFF" state (prohibiting substitutions). In current implementations, the switch rates between ON and OFF states are homogeneous across sites, a hypothesis that has never been tested. In this study, we developed an infinite mixture model, called the covarion mixture (CM) model, which allows the covarion parameters to vary across sites, controlled by a Dirichlet process prior. Moreover, we combine the CM model with other approaches. We use a second independent Dirichlet process that models the heterogeneities of amino acid equilibrium frequencies across sites, known as the CAT model, and general rate-across-site heterogeneity is modeled by a gamma distribution. The application of the CM model to several large alignments demonstrates that the covarion parameters are significantly heterogeneous across sites. We describe posterior predictive discrepancy tests and use these to demonstrate the importance of these different elements of the models.
An Inverse Eigenvalue Problem for a Vibrating String with Two Dirichlet Spectra
Rundell, William
2013-04-23
A classical inverse problem is "can you hear the density of a string clamped at both ends?" The mathematical model gives rise to an inverse Sturm-Liouville problem for the unknown density ñ, and it is well known that the answer is negative: the Dirichlet spectrum from the clamped end-point conditions is insufficient. There are many known ways to add additional information to gain a positive answer, and these include changing one of the boundary conditions and recomputing the spectrum or giving the energy in each eigenmode-the so-called norming constants. We make the assumption that neither of these changes are possible. Instead we will add known mass-densities to the string in a way we can prescribe and remeasure the Dirichlet spectrum. We will not be able to answer the uniqueness question in its most general form, but will give some insight to what "added masses" should be chosen and how this can lead to a reconstruction of the original string density. © 2013 Society for Industrial and Applied Mathematics.
Ideal regularization for learning kernels from labels.
Pan, Binbin; Lai, Jianhuang; Shen, Lixin
2014-08-01
In this paper, we propose a new form of regularization that is able to utilize the label information of a data set for learning kernels. The proposed regularization, referred to as ideal regularization, is a linear function of the kernel matrix to be learned. The ideal regularization allows us to develop efficient algorithms to exploit labels. Three applications of the ideal regularization are considered. Firstly, we use the ideal regularization to incorporate the labels into a standard kernel, making the resulting kernel more appropriate for learning tasks. Next, we employ the ideal regularization to learn a data-dependent kernel matrix from an initial kernel matrix (which contains prior similarity information, geometric structures, and labels of the data). Finally, we incorporate the ideal regularization to some state-of-the-art kernel learning problems. With this regularization, these learning problems can be formulated as simpler ones which permit more efficient solvers. Empirical results show that the ideal regularization exploits the labels effectively and efficiently.
Kernel score statistic for dependent data.
Malzahn, Dörthe; Friedrichs, Stefanie; Rosenberger, Albert; Bickeböller, Heike
2014-01-01
The kernel score statistic is a global covariance component test over a set of genetic markers. It provides a flexible modeling framework and does not collapse marker information. We generalize the kernel score statistic to allow for familial dependencies and to adjust for random confounder effects. With this extension, we adjust our analysis of real and simulated baseline systolic blood pressure for polygenic familial background. We find that the kernel score test gains appreciably in power through the use of sequencing compared to tag-single-nucleotide polymorphisms for very rare single nucleotide polymorphisms with <1% minor allele frequency.
Kernel-based Maximum Entropy Clustering
Institute of Scientific and Technical Information of China (English)
JIANG Wei; QU Jiao; LI Benxi
2007-01-01
With the development of Support Vector Machine (SVM),the "kernel method" has been studied in a general way.In this paper,we present a novel Kernel-based Maximum Entropy Clustering algorithm (KMEC).By using mercer kernel functions,the proposed algorithm is firstly map the data from their original space to high dimensional space where the data are expected to be more separable,then perform MEC clustering in the feature space.The experimental results show that the proposed method has better performance in the non-hyperspherical and complex data structure.
Kernel adaptive filtering a comprehensive introduction
Liu, Weifeng; Haykin, Simon
2010-01-01
Online learning from a signal processing perspective There is increased interest in kernel learning algorithms in neural networks and a growing need for nonlinear adaptive algorithms in advanced signal processing, communications, and controls. Kernel Adaptive Filtering is the first book to present a comprehensive, unifying introduction to online learning algorithms in reproducing kernel Hilbert spaces. Based on research being conducted in the Computational Neuro-Engineering Laboratory at the University of Florida and in the Cognitive Systems Laboratory at McMaster University, O
Multiple Operator-valued Kernel Learning
Kadri, Hachem; Bach, Francis; Preux, Philippe
2012-01-01
This paper addresses the problem of learning a finite linear combination of operator-valued kernels. We study this problem in the case of kernel ridge regression for functional responses with a lr-norm constraint on the combination coefficients. We propose a multiple operator-valued kernel learning algorithm based on solving a system of linear operator equations by using a block coordinate descent procedure. We experimentally validate our approach on a functional regression task in the context of finger movement prediction in Brain-Computer Interface (BCI).
Polynomial Kernelizations for $\\MINF_1$ and $\\MNP$
Kratsch, Stefan
2009-01-01
The relation of constant-factor approximability to fixed-parameter tractability and kernelization is a long-standing open question. We prove that two large classes of constant-factor approximable problems, namely $\\MINF_1$ and $\\MNP$, including the well-known subclass $\\MSNP$, admit polynomial kernelizations for their natural decision versions. This extends results of Cai and Chen (JCSS 1997), stating that the standard parameterizations of problems in $\\MSNP$ and $\\MINF_1$ are fixed-parameter tractable, and complements recent research on problems that do not admit polynomial kernelizations (Bodlaender et al. ICALP 2008).
Approximating W projection as a separable kernel
Merry, Bruce
2015-01-01
W projection is a commonly-used approach to allow interferometric imaging to be accelerated by Fast Fourier Transforms (FFTs), but it can require a huge amount of storage for convolution kernels. The kernels are not separable, but we show that they can be closely approximated by separable kernels. The error scales with the fourth power of the field of view, and so is small enough to be ignored at mid to high frequencies. We also show that hybrid imaging algorithms combining W projection with ...
Approximating W projection as a separable kernel
Merry, Bruce
2016-02-01
W projection is a commonly used approach to allow interferometric imaging to be accelerated by fast Fourier transforms, but it can require a huge amount of storage for convolution kernels. The kernels are not separable, but we show that they can be closely approximated by separable kernels. The error scales with the fourth power of the field of view, and so is small enough to be ignored at mid- to high frequencies. We also show that hybrid imaging algorithms combining W projection with either faceting, snapshotting, or W stacking allow the error to be made arbitrarily small, making the approximation suitable even for high-resolution wide-field instruments.
Extension of Wirtinger's Calculus in Reproducing Kernel Hilbert Spaces and the Complex Kernel LMS
Bouboulis, Pantelis
2010-01-01
Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space. However, so far, the emphasis has been on batch techniques. It is only recently, that online techniques have been considered in the context of adaptive signal processing tasks. Moreover, these efforts have only been focussed on and real valued data sequences. To the best of our knowledge, no kernel-based strategy has been developed, so far, that is able to deal with complex valued signals. In this paper, we present a general framework to attack the problem of adaptive filtering of complex signals, using either real reproducing kernels, taking advantage of a technique called \\textit{complexification} of real RKHSs, or complex reproducing kernels, highlighting the use of the complex gaussian kernel. In order to derive gradients of operators that need to be defined on the associat...
Kernel map compression for speeding the execution of kernel-based methods.
Arif, Omar; Vela, Patricio A
2011-06-01
The use of Mercer kernel methods in statistical learning theory provides for strong learning capabilities, as seen in kernel principal component analysis and support vector machines. Unfortunately, after learning, the computational complexity of execution through a kernel is of the order of the size of the training set, which is quite large for many applications. This paper proposes a two-step procedure for arriving at a compact and computationally efficient execution procedure. After learning in the kernel space, the proposed extension exploits the universal approximation capabilities of generalized radial basis function neural networks to efficiently approximate and replace the projections onto the empirical kernel map used during execution. Sample applications demonstrate significant compression of the kernel representation with graceful performance loss.
The Linux kernel as flexible product-line architecture
Jonge, M. de
2002-01-01
The 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 component they real
7 CFR 51.2296 - Three-fourths half kernel.
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...
7 CFR 981.401 - Adjusted kernel weight.
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...
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...
7 CFR 51.1403 - Kernel color classification.
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...
NLO corrections to the Kernel of the BKP-equations
Energy Technology Data Exchange (ETDEWEB)
Bartels, J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Fadin, V.S. [Budker Institute of Nuclear Physics, Novosibirsk (Russian Federation); Novosibirskij Gosudarstvennyj Univ., Novosibirsk (Russian Federation); Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg (Russian Federation); Vacca, G.P. [INFN, Sezione di Bologna (Italy)
2012-10-02
We present results for the NLO kernel of the BKP equations for composite states of three reggeized gluons in the Odderon channel, both in QCD and in N=4 SYM. The NLO kernel consists of the NLO BFKL kernel in the color octet representation and the connected 3{yields}3 kernel, computed in the tree approximation.
Heat Trace and Functional Determinant in One Dimension
Avramidi, Ivan G
2014-01-01
We study the spectral properties of the Laplace type operator in one dimension. We discuss various approximations for the heat trace, the zeta function and the zeta-regularized determinant. We obtain a differential equation for the heat kernel diagonal and a recursive system for the diagonal heat kernel coefficients, which enables us to find closed formulas for the heat trace and the determinant. The relation to the generalized KdV hiearchy is discussed as well.
Relative n-widths of periodic convolution classes with NCVD-kernel and B-kernel
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper,we consider the relative n-widths of two kinds of periodic convolution classes,Kp(K) and Bp(G),whose convolution kernels are NCVD-kernel K and B-kernel G. The asymptotic estimations of Kn(Kp(K),Kp(K))q and Kn(Bp(G),Bp(G))q are obtained for p=1 and ∞,1≤ q≤∞.
Reproducing Kernel for D2(Ω, ρ) and Metric Induced by Reproducing Kernel
Institute of Scientific and Technical Information of China (English)
ZHAO Zhen Gang
2009-01-01
An important property of the reproducing kernel of D2(Ω, ρ) is obtained and the reproducing kernels for D2(Ω, ρ) are calculated when Ω = Bn × Bn and ρ are some special functions. A reproducing kernel is used to construct a semi-positive definite matrix and a distance function defined on Ω×Ω. An inequality is obtained about the distance function and the pseudodistance induced by the matrix.
Discriminant Kernel Assignment for Image Coding.
Deng, Yue; Zhao, Yanyu; Ren, Zhiquan; Kong, Youyong; Bao, Feng; Dai, Qionghai
2017-06-01
This paper proposes discriminant kernel assignment (DKA) in the bag-of-features framework for image representation. DKA slightly modifies existing kernel assignment to learn width-variant Gaussian kernel functions to perform discriminant local feature assignment. When directly applying gradient-descent method to solve DKA, the optimization may contain multiple time-consuming reassignment implementations in iterations. Accordingly, we introduce a more practical way to locally linearize the DKA objective and the difficult task is cast as a sequence of easier ones. Since DKA only focuses on the feature assignment part, it seamlessly collaborates with other discriminative learning approaches, e.g., discriminant dictionary learning or multiple kernel learning, for even better performances. Experimental evaluations on multiple benchmark datasets verify that DKA outperforms other image assignment approaches and exhibits significant efficiency in feature coding.
Multiple Kernel Spectral Regression for Dimensionality Reduction
Directory of Open Access Journals (Sweden)
Bing Liu
2013-01-01
Full Text Available Traditional manifold learning algorithms, such as locally linear embedding, Isomap, and Laplacian eigenmap, only provide the embedding results of the training samples. To solve the out-of-sample extension problem, spectral regression (SR solves the problem of learning an embedding function by establishing a regression framework, which can avoid eigen-decomposition of dense matrices. Motivated by the effectiveness of SR, we incorporate multiple kernel learning (MKL into SR for dimensionality reduction. The proposed approach (termed MKL-SR seeks an embedding function in the Reproducing Kernel Hilbert Space (RKHS induced by the multiple base kernels. An MKL-SR algorithm is proposed to improve the performance of kernel-based SR (KSR further. Furthermore, the proposed MKL-SR algorithm can be performed in the supervised, unsupervised, and semi-supervised situation. Experimental results on supervised classification and semi-supervised classification demonstrate the effectiveness and efficiency of our algorithm.
Quantum kernel applications in medicinal chemistry.
Huang, Lulu; Massa, Lou
2012-07-01
Progress in the quantum mechanics of biological molecules is being driven by computational advances. The notion of quantum kernels can be introduced to simplify the formalism of quantum mechanics, making it especially suitable for parallel computation of very large biological molecules. The essential idea is to mathematically break large biological molecules into smaller kernels that are calculationally tractable, and then to represent the full molecule by a summation over the kernels. The accuracy of the kernel energy method (KEM) is shown by systematic application to a great variety of molecular types found in biology. These include peptides, proteins, DNA and RNA. Examples are given that explore the KEM across a variety of chemical models, and to the outer limits of energy accuracy and molecular size. KEM represents an advance in quantum biology applicable to problems in medicine and drug design.
Kernel method-based fuzzy clustering algorithm
Institute of Scientific and Technical Information of China (English)
Wu Zhongdong; Gao Xinbo; Xie Weixin; Yu Jianping
2005-01-01
The fuzzy C-means clustering algorithm(FCM) to the fuzzy kernel C-means clustering algorithm(FKCM) to effectively perform cluster analysis on the diversiform structures are extended, such as non-hyperspherical data, data with noise, data with mixture of heterogeneous cluster prototypes, asymmetric data, etc. Based on the Mercer kernel, FKCM clustering algorithm is derived from FCM algorithm united with kernel method. The results of experiments with the synthetic and real data show that the FKCM clustering algorithm is universality and can effectively unsupervised analyze datasets with variform structures in contrast to FCM algorithm. It is can be imagined that kernel-based clustering algorithm is one of important research direction of fuzzy clustering analysis.
Kernel representations for behaviors over finite rings
Kuijper, M.; Pinto, R.; Polderman, J.W.; Yamamoto, Y.
2006-01-01
In this paper we consider dynamical systems finite rings. The rings that we study are the integers modulo a power of a given prime. We study the theory of representations for such systems, in particular kernel representations.
Ensemble Approach to Building Mercer Kernels
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...
Convolution kernels for multi-wavelength imaging
National Research Council Canada - National Science Library
Boucaud, Alexandre; Bocchio, Marco; Abergel, Alain; Orieux, François; Dole, Hervé; Hadj-Youcef, Mohamed Amine
2016-01-01
.... Given the knowledge of the PSF in each band, a straightforward way of processing images is to homogenise them all to a target PSF using convolution kernels, so that they appear as if they had been...
Difference image analysis: Automatic kernel design using information criteria
Bramich, D M; Alsubai, K A; Bachelet, E; Mislis, D; Parley, N
2015-01-01
We present a selection of methods for automatically constructing an optimal kernel model for difference image analysis which require very few external parameters to control the kernel design. Each method consists of two components; namely, a kernel design algorithm to generate a set of candidate kernel models, and a model selection criterion to select the simplest kernel model from the candidate models that provides a sufficiently good fit to the target image. We restricted our attention to the case of solving for a spatially-invariant convolution kernel composed of delta basis functions, and we considered 19 different kernel solution methods including six employing kernel regularisation. We tested these kernel solution methods by performing a comprehensive set of image simulations and investigating how their performance in terms of model error, fit quality, and photometric accuracy depends on the properties of the reference and target images. We find that the irregular kernel design algorithm employing unreg...
A Note on a Singular Dirichlet Problem%关于一个奇异Dirichlet问题的注记
Institute of Scientific and Technical Information of China (English)
王俊禹; 高文杰
2005-01-01
The Dirichlet problem to a second order differential equation with some singularities is studied. Some existence results are established to the problem which generalize some results recently obtained by D. O'Regan by eliminating some superfluous constrains to the problem. Also, some new results have been proven which may provide more useful information for the study of the problem.
Meulenbroek, B.J.; Ebert, U.; Schäfer, L.
2005-01-01
The dynamics of ionization fronts that generate a conducting body, are in simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact
Directory of Open Access Journals (Sweden)
Nguyen Anh Dao
2016-11-01
Full Text Available We prove the existence and uniqueness of singular solutions (fundamental solution, very singular solution, and large solution of quasilinear parabolic equations with absorption for Dirichlet boundary condition. We also show the short time behavior of singular solutions as t tends to 0.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Dirichlet boundary value problems for perturbed second-order differential equations on a half line are investigated in this paper. The methods mainly depend on the calculus of variations to the classical functionals. Sufficient conditions are obtained for the existence of the solutions.
Directory of Open Access Journals (Sweden)
Tomasz S. Zabawa
2005-01-01
Full Text Available The Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations of elliptic type is considered. It is shown the existence of solutions to this problem. The result is based on Chaplygin's method of lower and upper functions.
The Bergman kernel functions on Hua domains
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
We get the Bergman kernel functions in explicit formulas on four types of Hua domain.There are two key steps: First, we give the holomorphic automorphism groups of four types of Hua domain; second, we introduce the concept of semi-Reinhardt domain and give their complete orthonormal systems. Based on these two aspects we obtain the Bergman kernel function in explicit formulas on Hua domains.
Fractal Weyl law for Linux Kernel Architecture
Ermann, L; Shepelyansky, D L
2010-01-01
We study the properties of spectrum and eigenstates of the Google matrix of a directed network formed by the procedure calls in the Linux Kernel. Our results obtained for various versions of the Linux Kernel show that the spectrum is characterized by the fractal Weyl law established recently for systems of quantum chaotic scattering and the Perron-Frobenius operators of dynamical maps. The fractal Weyl exponent is found to be $\
Varying kernel density estimation on ℝ+
Mnatsakanov, Robert; Sarkisian, Khachatur
2015-01-01
In this article a new nonparametric density estimator based on the sequence of asymmetric kernels is proposed. This method is natural when estimating an unknown density function of a positive random variable. The rates of Mean Squared Error, Mean Integrated Squared Error, and the L1-consistency are investigated. Simulation studies are conducted to compare a new estimator and its modified version with traditional kernel density construction. PMID:26740729
Adaptively Learning the Crowd Kernel
Tamuz, Omer; Belongie, Serge; Shamir, Ohad; Kalai, Adam Tauman
2011-01-01
We introduce an algorithm that, given n objects, learns a similarity matrix over all n^2 pairs, from crowdsourced data alone. The algorithm samples responses to adaptively chosen triplet-based relative-similarity queries. Each query has the form "is object 'a' more similar to 'b' or to 'c'?" and is chosen to be maximally informative given the preceding responses. The output is an embedding of the objects into Euclidean space (like MDS); we refer to this as the "crowd kernel." The runtime (empirically observed to be linear) and cost (about $0.15 per object) of the algorithm are small enough to permit its application to databases of thousands of objects. The distance matrix provided by the algorithm allows for the development of an intuitive and powerful sequential, interactive search algorithm which we demonstrate for a variety of visual stimuli. We present quantitative results that demonstrate the benefit in cost and time of our approach compared to a nonadaptive approach. We also show the ability of our appr...
Evaluating the Gradient of the Thin Wire Kernel
Wilton, Donald R.; Champagne, Nathan J.
2008-01-01
Recently, a formulation for evaluating the thin wire kernel was developed that employed a change of variable to smooth the kernel integrand, canceling the singularity in the integrand. Hence, the typical expansion of the wire kernel in a series for use in the potential integrals is avoided. The new expression for the kernel is exact and may be used directly to determine the gradient of the wire kernel, which consists of components that are parallel and radial to the wire axis.
On the Inclusion Relation of Reproducing Kernel Hilbert Spaces
Zhang, Haizhang; Zhao, Liang
2011-01-01
To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established. A full table of inclusion relations among widely-used translation invariant kernels is given. Concrete examples for Hilbert-Schmidt kernels are presented as well. We also discuss the preservation of such a relation under various operations of ...
On the formation of new ignition kernels in the chemically active dispersed mixtures
Ivanov, M. F.; Kiverin, A. D.
2015-11-01
The specific features of the combustion waves propagating through the channels filled with chemically active gaseous mixture and non-uniformly suspended micro particles are studied numerically. It is shown that the heat radiated by the hot products, absorbed by the micro particles and then transferred to the environmental fresh mixture can be the source of new ignition kernels in the regions of particles' clusters. Herewith the spatial distribution of the particles determines the features of combustion regimes arising in these kernels. One can highlight the multi-kernel ignition in the polydisperse mixtures and ignition of the combustion regimes with shocks and detonation formation in the mixtures with pronounced gradients of microparticles concentration.
Non-parametric method for separating domestic hot water heating spikes and space heating
DEFF Research Database (Denmark)
Bacher, Peder; de Saint-Aubain, Philip Anton; Christiansen, Lasse Engbo;
2016-01-01
In this paper a method for separating spikes from a noisy data series, where the data change and evolve over time, is presented. The method is applied on measurements of the total heat load for a single family house. It relies on the fact that the domestic hot water heating is a process generating...... short-lived spikes in the time series, while the space heating changes in slower patterns during the day dependent on the climate and user behavior. The challenge is to separate the domestic hot water heating spikes from the space heating without affecting the natural noise in the space heating...... measurements. The assumption behind the developed method is that the space heating can be estimated by a non-parametric kernel smoother, such that every value significantly above this kernel smoother estimate is identified as a domestic hot water heating spike. First, it is showed how a basic kernel smoothing...
Yang, Zhiguo; Rong, Zhijian; Wang, Bo; Zhang, Baile
2015-01-01
In this paper, we present an efficient spectral-element method (SEM) for solving general two-dimensional Helmholtz equations in anisotropic media, with particular applications in accurate simulation of polygonal invisibility cloaks, concentrators and circular rotators arisen from the field of transformation electromagnetics (TE). In practice, we adopt a transparent boundary condition (TBC) characterized by the Dirichlet-to-Neumann (DtN) map to reduce wave propagation in an unbounded domain to a bounded domain. We then introduce a semi-analytic technique to integrate the global TBC with local curvilinear elements seamlessly, which is accomplished by using a novel elemental mapping and analytic formulas for evaluating global Fourier coefficients on spectral-element grids exactly. From the perspective of TE, an invisibility cloak is devised by a singular coordinate transformation of Maxwell's equations that leads to anisotropic materials coating the cloaked region to render any object inside invisible to observe...
Bloch waves in an arbitrary two-dimensional lattice of subwavelength Dirichlet scatterers
Schnitzer, Ory
2016-01-01
We study waves governed by the planar Helmholtz equation, propagating in an infinite lattice of subwavelength Dirichlet scatterers, the periodicity being comparable to the wavelength. Applying the method of matched asymptotic expansions, the scatterers are effectively replaced by asymptotic point constraints. The resulting coarse-grained Bloch-wave dispersion problem is solved by a generalised Fourier series, whose singular asymptotics in the vicinities of scatterers yield the dispersion relation governing modes that are strongly perturbed from plane-wave solutions existing in the absence of the scatterers; there are also empty-lattice waves that are only weakly perturbed. Characterising the latter is useful in interpreting and potentially designing the dispersion diagrams of such lattices. The method presented, that simplifies and expands on Krynkin & McIver [Waves Random Complex, 19 347 2009], could be applied in the future to study more sophisticated designs entailing resonant subwavelength elements di...
Anandkumar, Animashree; Hsu, Daniel; Kakade, Sham M; Liu, Yi-Kai
2012-01-01
Topic models can be seen as a generalization of the clustering problem, in that they posit that observations are generated due to multiple latent factors (e.g. the words in each document are generated as a mixture of several active topics, as opposed to just one). This increased representational power comes at the cost of a more challenging unsupervised learning problem of estimating the topic probability vectors (the distributions over words for each topic), when only the words are observed and the corresponding topics are hidden. We provide a simple and efficient learning procedure that is guaranteed to recover the parameters for a wide class of mixture models, including the popular latent Dirichlet allocation (LDA) model. For LDA, the procedure correctly recovers both the topic probability vectors and the prior over the topics, using only trigram statistics (i.e. third order moments, which may be estimated with documents containing just three words). The method, termed Excess Correlation Analysis (ECA), is...
Investigating brand loyalty using Dirichlet benchmarks: The case of light dairy products
DEFF Research Database (Denmark)
Krystallis, Athanasios; Chrysochou, Polymeros
of consumer loyalty to the light dairy sub-category compared to other sub-categories that exist within the wider dairy categories under investigation. The total market share of light brands is found to be directly comparable with that of full fat brands. The importance of the light sub-category is indicated......During the last years, a strong consumer interest appears for food products with low caloric content ("light" products). Due to their popularity, the real success of these products in the marketplace is a worth-investigating issue. The creation of buyers that are loyal to light food brands...... constitutes an indication of this success. The present work aims to investigate consumer loyalty to light dairy (milk and yoghurt) brands. First, basic Brand Performance Measures (BPMs) are empirically estimated to describe market structure of the dairy categories under investigation. Then, the Dirichlet...
Derivation of dissipative Boussinesq equations using the Dirichlet-to-Neumann operator approach
Dutykh, Denys
2011-01-01
The water wave theory traditionally assumes the fluid to be perfect, thus neglecting all effects of the viscosity. However, the explanation of several experimental data sets requires the explicit inclusion of dissipative effects. In order to meet these practical problems, the theory of visco-potential flows has been developed (see P.-F. Liu & A. Orfila (2004) and D. Dutykh & F. Dias (2007)). Then, usually this formulation is further simplified by developing the potential in an entire series in the vertical coordinate and by introducing thus, the long wave approximation. In the present study we propose a derivation of dissipative Boussinesq equations which is based on asymptotic expansions of the Dirichlet-to-Neumann (D2N) operator. Both employed methods yield the same system by different ways.
Tangent unit-vector fields: Nonabelian homotopy invariants and the Dirichlet energy
Majumdar, Apala
2009-10-01
Let O be a closed geodesic polygon in S2. Maps from O into S2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S2, we evaluate the infimum Dirichlet energy, E (H), for continuous tangent maps of arbitrary homotopy type H. The expression for E (H) involves a topological invariant - the spelling length - associated with the (nonabelian) fundamental group of the n-times punctured two-sphere, π1 (S2 - {s1, ..., sn}, *). These results have applications for the theoretical modelling of nematic liquid crystal devices. To cite this article: A. Majumdar et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences.
Investigating brand loyalty using Dirichlet benchmarks: The case of light dairy products
DEFF Research Database (Denmark)
Krystallis, Athanasios; Chrysochou, Polymeros
During the last years, a strong consumer interest appears for food products with low caloric content ("light" products). Due to their popularity, the real success of these products in the marketplace is a worth-investigating issue. The creation of buyers that are loyal to light food brands...... constitutes an indication of this success. The present work aims to investigate consumer loyalty to light dairy (milk and yoghurt) brands. First, basic Brand Performance Measures (BPMs) are empirically estimated to describe market structure of the dairy categories under investigation. Then, the Dirichlet...... model (Ehrenberg et al., 2004) was fitted to the empirical data, pointing out to theoretical category loyalty measures. Grouping of the dairy categories under investigation according to their purchase frequency and brand penetration then follows. The work concludes with the overall estimation...
Valle, Denis; Baiser, Benjamin; Woodall, Christopher W; Chazdon, Robin
2014-12-01
We propose a novel multivariate method to analyse biodiversity data based on the Latent Dirichlet Allocation (LDA) model. LDA, a probabilistic model, reduces assemblages to sets of distinct component communities. It produces easily interpretable results, can represent abrupt and gradual changes in composition, accommodates missing data and allows for coherent estimates of uncertainty. We illustrate our method using tree data for the eastern United States and from a tropical successional chronosequence. The model is able to detect pervasive declines in the oak community in Minnesota and Indiana, potentially due to fire suppression, increased growing season precipitation and herbivory. The chronosequence analysis is able to delineate clear successional trends in species composition, while also revealing that site-specific factors significantly impact these successional trajectories. The proposed method provides a means to decompose and track the dynamics of species assemblages along temporal and spatial gradients, including effects of global change and forest disturbances.
Directory of Open Access Journals (Sweden)
Marco Biroli
2007-12-01
Full Text Available We consider a measure valued map α(u deﬁned on D where D is a subspace of L^p(X,m with X a locally compact Hausdorff topological space with a distance under which it is a space of homogeneous type. Under assumptions of convexity, Gateaux differentiability and other assumptions on α which generalize the properties of the energy measure of a Dirichlet form, we prove the Holder continuity of the local solution u of the problem ∫Xµ(u,v(dx = 0 for each v belonging to a suitable space of test functions, where µ(u,v =< α'(u,v >.
Moist turbulent Rayleigh-Benard convection with Neumann and Dirichlet boundary conditions
Weidauer, Thomas
2012-01-01
Turbulent Rayleigh-Benard convection with phase changes in an extended layer between two parallel impermeable planes is studied by means of three-dimensional direct numerical simulations for Rayleigh numbers between 10^4 and 1.5\\times 10^7 and for Prandtl number Pr=0.7. Two different sets of boundary conditions of temperature and total water content are compared: imposed constant amplitudes which translate into Dirichlet boundary conditions for the scalar field fluctuations about the quiescent diffusive equilibrium and constant imposed flux boundary conditions that result in Neumann boundary conditions. Moist turbulent convection is in the conditionally unstable regime throughout this study for which unsaturated air parcels are stably and saturated air parcels unstably stratified. A direct comparison of both sets of boundary conditions with the same parameters requires to start the turbulence simulations out of differently saturated equilibrium states. Similar to dry Rayleigh-Benard convection the differences...
INFINITELY MANY SOLUTIONS OF DIRICHLET PROBLEM FOR p－MEAN CURVATURE OPERATOR
Institute of Scientific and Technical Information of China (English)
ChenZhihui; ShenYaotian
2003-01-01
The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator:{-div((1+|△↓u|2)p-2/2△↓u)=f(x,u),x∈Ω. u∈W1-p 0(Ω）. is considered,where Ωis a bounded domain in Rn(n>P>1)with smooth boundary δΩ.Under some natural conditions together with some conditions weaker than(AR)condition,we prove that the above problem has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if f(x,u)/|u|p-2 u→+∞asu→∞.
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2010-01-01
Full Text Available We study a Dirichlet boundary value problem for Langevin equation involving two fractional orders. Langevin equation has been widely used to describe the evolution of physical phenomena in fluctuating environments. However, ordinary Langevin equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractal medium, numerous generalizations of Langevin equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Langevin equation. This gives rise to the fractional Langevin equation with a single index. Recently, a new type of Langevin equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.
Directory of Open Access Journals (Sweden)
I. C. Ramos
2015-10-01
Full Text Available We present the adaptation to non-free boundary conditions of a pseudospectral method based on the (complex Fourier transform. The method is applied to the numerical integration of the Oberbeck-Boussinesq equations in a Rayleigh-Bénard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature. We show the first results of a 2D numerical simulation of dry air convection at high Rayleigh number (. These results are the basis for the later study, by the same method, of wet convection in a solar still. Received: 20 Novembre 2014, Accepted: 15 September 2015; Edited by: C. A. Condat, G. J. Sibona; DOI:http://dx.doi.org/10.4279/PIP.070015 Cite as: I C Ramos, C B Briozzo, Papers in Physics 7, 070015 (2015
Energy Technology Data Exchange (ETDEWEB)
Andrzejewski, D; Zhu, X; Craven, M; Recht, B
2011-01-18
Topic models have been used successfully for a variety of problems, often in the form of application-specific extensions of the basic Latent Dirichlet Allocation (LDA) model. Because deriving these new models in order to encode domain knowledge can be difficult and time-consuming, we propose the Fold-all model, which allows the user to specify general domain knowledge in First-Order Logic (FOL). However, combining topic modeling with FOL can result in inference problems beyond the capabilities of existing techniques. We have therefore developed a scalable inference technique using stochastic gradient descent which may also be useful to the Markov Logic Network (MLN) research community. Experiments demonstrate the expressive power of Fold-all, as well as the scalability of our proposed inference method.
Predictive Distribution of the Dirichlet Mixture Model by the Local Variational Inference Method
DEFF Research Database (Denmark)
Ma, Zhanyu; Leijon, Arne; Tan, Zheng-Hua;
2014-01-01
In Bayesian analysis of a statistical model, the predictive distribution is obtained by marginalizing over the parameters with their posterior distributions. Compared to the frequently used point estimate plug-in method, the predictive distribution leads to a more reliable result in calculating...... the predictive likelihood of the new upcoming data, especially when the amount of training data is small. The Bayesian estimation of a Dirichlet mixture model (DMM) is, in general, not analytically tractable. In our previous work, we have proposed a global variational inference-based method for approximately...... calculating the posterior distributions of the parameters in the DMM analytically. In this paper, we extend our previous study for the DMM and propose an algorithm to calculate the predictive distribution of the DMM with the local variational inference (LVI) method. The true predictive distribution of the DMM...
Hanft, J M; Jones, R J
1986-06-01
Kernels cultured in vitro were induced to abort by high temperature (35 degrees C) and by culturing six kernels/cob piece. Aborting kernels failed to enter a linear phase of dry mass accumulation and had a final mass that was less than 6% of nonaborting field-grown kernels. Kernels induced to abort by high temperature failed to synthesize starch in the endosperm and had elevated sucrose concentrations and low fructose and glucose concentrations in the pedicel during early growth compared to nonaborting kernels. Kernels induced to abort by high temperature also had much lower pedicel soluble acid invertase activities than did nonaborting kernels. These results suggest that high temperature during the lag phase of kernel growth may impair the process of sucrose unloading in the pedicel by indirectly inhibiting soluble acid invertase activity and prevent starch synthesis in the endosperm. Kernels induced to abort by culturing six kernels/cob piece had reduced pedicel fructose, glucose, and sucrose concentrations compared to kernels from field-grown ears. These aborting kernels also had a lower pedicel soluble acid invertase activity compared to nonaborting kernels from the same cob piece and from field-grown ears. The low invertase activity in pedicel tissue of the aborting kernels was probably caused by a lack of substrate (sucrose) for the invertase to cleave due to the intense competition for available assimilates. In contrast to kernels cultured at 35 degrees C, aborting kernels from cob pieces containing all six kernels accumulated starch in a linear fashion. These results indicate that kernels cultured six/cob piece abort because of an inadequate supply of sugar and are similar to apical kernels from field-grown ears that often abort prior to the onset of linear growth.
Selection and properties of alternative forming fluids for TRISO fuel kernel production
Energy Technology Data Exchange (ETDEWEB)
Baker, M.P. [Colorado School of Mines, 1500 Illinois St., Golden, CO 80401 (United States); King, J.C., E-mail: kingjc@mines.edu [Colorado School of Mines, 1500 Illinois St., Golden, CO 80401 (United States); Gorman, B.P. [Colorado School of Mines, 1500 Illinois St., Golden, CO 80401 (United States); Marshall, D.W. [Idaho National Laboratory, 2525 N. Fremont Avenue, P.O. Box 1625, Idaho Falls, ID 83415 (United States)
2013-01-15
Highlights: Black-Right-Pointing-Pointer Forming fluid selection criteria developed for TRISO kernel production. Black-Right-Pointing-Pointer Ten candidates selected for further study. Black-Right-Pointing-Pointer Density, viscosity, and surface tension measured for first time. Black-Right-Pointing-Pointer Settling velocity and heat transfer rates calculated. Black-Right-Pointing-Pointer Three fluids recommended for kernel production testing. - Abstract: Current Very High Temperature Reactor (VHTR) designs incorporate TRi-structural ISOtropic (TRISO) fuel, which consists of a spherical fissile fuel kernel surrounded by layers of pyrolytic carbon and silicon carbide. An internal sol-gel process forms the fuel kernel using wet chemistry to produce uranium oxyhydroxide gel spheres by dropping a cold precursor solution into a hot column of trichloroethylene (TCE). Over time, gelation byproducts inhibit complete gelation, and the TCE must be purified or discarded. The resulting TCE waste stream contains both radioactive and hazardous materials and is thus considered a mixed hazardous waste. Changing the forming fluid to a non-hazardous alternative could greatly improve the economics of TRISO fuel kernel production. Selection criteria for a replacement forming fluid narrowed a list of {approx}10,800 chemicals to yield ten potential replacement forming fluids: 1-bromododecane, 1-bromotetradecane, 1-bromoundecane, 1-chlorooctadecane, 1-chlorotetradecane, 1-iododecane, 1-iodododecane, 1-iodohexadecane, 1-iodooctadecane, and squalane. The density, viscosity, and surface tension for each potential replacement forming fluid were measured as a function of temperature between 25 Degree-Sign C and 80 Degree-Sign C. Calculated settling velocities and heat transfer rates give an overall column height approximation. 1-bromotetradecane, 1-chlorooctadecane, and 1-iodododecane show the greatest promise as replacements, and future tests will verify their ability to form satisfactory
Directory of Open Access Journals (Sweden)
Daniel Ting
2010-04-01
Full Text Available Distributions of the backbone dihedral angles of proteins have been studied for over 40 years. While many statistical analyses have been presented, only a handful of probability densities are publicly available for use in structure validation and structure prediction methods. The available distributions differ in a number of important ways, which determine their usefulness for various purposes. These include: 1 input data size and criteria for structure inclusion (resolution, R-factor, etc.; 2 filtering of suspect conformations and outliers using B-factors or other features; 3 secondary structure of input data (e.g., whether helix and sheet are included; whether beta turns are included; 4 the method used for determining probability densities ranging from simple histograms to modern nonparametric density estimation; and 5 whether they include nearest neighbor effects on the distribution of conformations in different regions of the Ramachandran map. In this work, Ramachandran probability distributions are presented for residues in protein loops from a high-resolution data set with filtering based on calculated electron densities. Distributions for all 20 amino acids (with cis and trans proline treated separately have been determined, as well as 420 left-neighbor and 420 right-neighbor dependent distributions. The neighbor-independent and neighbor-dependent probability densities have been accurately estimated using Bayesian nonparametric statistical analysis based on the Dirichlet process. In particular, we used hierarchical Dirichlet process priors, which allow sharing of information between densities for a particular residue type and different neighbor residue types. The resulting distributions are tested in a loop modeling benchmark with the program Rosetta, and are shown to improve protein loop conformation prediction significantly. The distributions are available at http://dunbrack.fccc.edu/hdp.
Ngono Mbarga, M. C.; Bup Nde, D.; Mohagir, A.; Kapseu, C.; Elambo Nkeng, G.
2017-01-01
A neem tree growing abundantly in India as well as in some regions of Asia and Africa gives fruits whose kernels have about 40-50% oil. This oil has high therapeutic and cosmetic qualities and is recently projected to be an important raw material for the production of biodiesel. Its seed is harvested at high moisture contents, which leads tohigh post-harvest losses. In the paper, the sorption isotherms are determined by the static gravimetric method at 40, 50, and 60°C to establish a database useful in defining drying and storage conditions of neem kernels. Five different equations are validated for modeling the sorption isotherms of neem kernels. The properties of sorbed water, such as the monolayer moisture content, surface area of adsorbent, number of adsorbed monolayers, and the percent of bound water are also defined. The critical moisture content necessary for the safe storage of dried neem kernels is shown to range from 5 to 10% dry basis, which can be obtained at a relative humidity less than 65%. The isosteric heats of sorption at 5% moisture content are 7.40 and 22.5 kJ/kg for the adsorption and desorption processes, respectively. This work is the first, to the best of our knowledge, to give the important parameters necessary for drying and storage of neem kernels, a potential raw material for the production of oil to be used in pharmaceutics, cosmetics, and biodiesel manufacturing.
Single pass kernel -means clustering method
Indian Academy of Sciences (India)
T Hitendra Sarma; P Viswanath; B Eswara Reddy
2013-06-01
In unsupervised classiﬁcation, kernel -means clustering method has been shown to perform better than conventional -means clustering method in identifying non-isotropic clusters in a data set. The space and time requirements of this method are $O(n^2)$, where is the data set size. Because of this quadratic time complexity, the kernel -means method is not applicable to work with large data sets. The paper proposes a simple and faster version of the kernel -means clustering method, called single pass kernel k-means clustering method. The proposed method works as follows. First, a random sample $\\mathcal{S}$ is selected from the data set $\\mathcal{D}$. A partition $\\Pi_{\\mathcal{S}}$ is obtained by applying the conventional kernel -means method on the random sample $\\mathcal{S}$. The novelty of the paper is, for each cluster in $\\Pi_{\\mathcal{S}}$, the exact cluster center in the input space is obtained using the gradient descent approach. Finally, each unsampled pattern is assigned to its closest exact cluster center to get a partition of the entire data set. The proposed method needs to scan the data set only once and it is much faster than the conventional kernel -means method. The time complexity of this method is $O(s^2+t+nk)$ where is the size of the random sample $\\mathcal{S}$, is the number of clusters required, and is the time taken by the gradient descent method (to ﬁnd exact cluster centers). The space complexity of the method is $O(s^2)$. The proposed method can be easily implemented and is suitable for large data sets, like those in data mining applications. Experimental results show that, with a small loss of quality, the proposed method can signiﬁcantly reduce the time taken than the conventional kernel -means clustering method. The proposed method is also compared with other recent similar methods.
Kernel-Based Reconstruction of Graph Signals
Romero, Daniel; Ma, Meng; Giannakis, Georgios B.
2017-02-01
A number of applications in engineering, social sciences, physics, and biology involve inference over networks. In this context, graph signals are widely encountered as descriptors of vertex attributes or features in graph-structured data. Estimating such signals in all vertices given noisy observations of their values on a subset of vertices has been extensively analyzed in the literature of signal processing on graphs (SPoG). This paper advocates kernel regression as a framework generalizing popular SPoG modeling and reconstruction and expanding their capabilities. Formulating signal reconstruction as a regression task on reproducing kernel Hilbert spaces of graph signals permeates benefits from statistical learning, offers fresh insights, and allows for estimators to leverage richer forms of prior information than existing alternatives. A number of SPoG notions such as bandlimitedness, graph filters, and the graph Fourier transform are naturally accommodated in the kernel framework. Additionally, this paper capitalizes on the so-called representer theorem to devise simpler versions of existing Thikhonov regularized estimators, and offers a novel probabilistic interpretation of kernel methods on graphs based on graphical models. Motivated by the challenges of selecting the bandwidth parameter in SPoG estimators or the kernel map in kernel-based methods, the present paper further proposes two multi-kernel approaches with complementary strengths. Whereas the first enables estimation of the unknown bandwidth of bandlimited signals, the second allows for efficient graph filter selection. Numerical tests with synthetic as well as real data demonstrate the merits of the proposed methods relative to state-of-the-art alternatives.
A new Mercer sigmoid kernel for clinical data classification.
Carrington, André M; Fieguth, Paul W; Chen, Helen H
2014-01-01
In classification with Support Vector Machines, only Mercer kernels, i.e. valid kernels, such as the Gaussian RBF kernel, are widely accepted and thus suitable for clinical data. Practitioners would also like to use the sigmoid kernel, a non-Mercer kernel, but its range of validity is difficult to determine, and even within range its validity is in dispute. Despite these shortcomings the sigmoid kernel is used by some, and two kernels in the literature attempt to emulate and improve upon it. We propose the first Mercer sigmoid kernel, that is therefore trustworthy for the classification of clinical data. We show the similarity between the Mercer sigmoid kernel and the sigmoid kernel and, in the process, identify a normalization technique that improves the classification accuracy of the latter. The Mercer sigmoid kernel achieves the best mean accuracy on three clinical data sets, detecting melanoma in skin lesions better than the most popular kernels; while with non-clinical data sets it has no significant difference in median accuracy as compared with the Gaussian RBF kernel. It consistently classifies some points correctly that the Gaussian RBF kernel does not and vice versa.
Pattern Classification of Signals Using Fisher Kernels
Directory of Open Access Journals (Sweden)
Yashodhan Athavale
2012-01-01
Full Text Available The intention of this study is to gauge the performance of Fisher kernels for dimension simplification and classification of time-series signals. Our research work has indicated that Fisher kernels have shown substantial improvement in signal classification by enabling clearer pattern visualization in three-dimensional space. In this paper, we will exhibit the performance of Fisher kernels for two domains: financial and biomedical. The financial domain study involves identifying the possibility of collapse or survival of a company trading in the stock market. For assessing the fate of each company, we have collected financial time-series composed of weekly closing stock prices in a common time frame, using Thomson Datastream software. The biomedical domain study involves knee signals collected using the vibration arthrometry technique. This study uses the severity of cartilage degeneration for classifying normal and abnormal knee joints. In both studies, we apply Fisher Kernels incorporated with a Gaussian mixture model (GMM for dimension transformation into feature space, which is created as a three-dimensional plot for visualization and for further classification using support vector machines. From our experiments we observe that Fisher Kernel usage fits really well for both kinds of signals, with low classification error rates.
Analog forecasting with dynamics-adapted kernels
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.
Solution of the two- dimensional heat equation for a rectangular plate
Directory of Open Access Journals (Sweden)
Nurcan BAYKUŞ SAVAŞANERİL
2015-11-01
Full Text Available Laplace equation is a fundamental equation of applied mathematics. Important phenomena in engineering and physics, such as steady-state temperature distribution, electrostatic potential and fluid flow, are modeled by means of this equation. The Laplace equation which satisfies boundary values is known as the Dirichlet problem. The solutions to the Dirichlet problem form one of the most celebrated topics in the area of applied mathematics. In this study, a novel method is presented for the solution of two-dimensional heat equation for a rectangular plate. In this alternative method, the solution function of the problem is based on the Green function, and therefore on elliptic functions.
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...
OS X and iOS Kernel Programming
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
The scalar field kernel in cosmological spaces
Energy Technology Data Exchange (ETDEWEB)
Koksma, Jurjen F; Prokopec, Tomislav [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Rigopoulos, Gerasimos I [Helsinki Institute of Physics, University of Helsinki, PO Box 64, FIN-00014 (Finland)], E-mail: J.F.Koksma@phys.uu.nl, E-mail: T.Prokopec@phys.uu.nl, E-mail: gerasimos.rigopoulos@helsinki.fi
2008-06-21
We construct the quantum-mechanical evolution operator in the functional Schroedinger picture-the kernel-for a scalar field in spatially homogeneous FLRW spacetimes when the field is (a) free and (b) coupled to a spacetime-dependent source term. The essential element in the construction is the causal propagator, linked to the commutator of two Heisenberg picture scalar fields. We show that the kernels can be expressed solely in terms of the causal propagator and derivatives of the causal propagator. Furthermore, we show that our kernel reveals the standard light cone structure in FLRW spacetimes. We finally apply the result to Minkowski spacetime, to de Sitter spacetime and calculate the forward time evolution of the vacuum in a general FLRW spacetime.
Robust Visual Tracking via Fuzzy Kernel Representation
Directory of Open Access Journals (Sweden)
Zhiqiang Wen
2013-05-01
Full Text Available A robust visual kernel tracking approach is presented for solving the problem of existing background pixels in object model. At first, after definition of fuzzy set on image is given, a fuzzy factor is embedded into object model to form the fuzzy kernel representation. Secondly, a fuzzy membership functions are generated by center-surround approach and log likelihood ratio of feature distributions. Thirdly, details about fuzzy kernel tracking algorithm is provided. After that, methods of parameter selection and performance evaluation for tracking algorithm are proposed. At last, a mass of experimental results are done to show our method can reduce the influence of the incomplete representation of object model via integrating both color features and background features.
Fractal Weyl law for Linux Kernel architecture
Ermann, L.; Chepelianskii, A. D.; Shepelyansky, D. L.
2011-01-01
We study the properties of spectrum and eigenstates of the Google matrix of a directed network formed by the procedure calls in the Linux Kernel. Our results obtained for various versions of the Linux Kernel show that the spectrum is characterized by the fractal Weyl law established recently for systems of quantum chaotic scattering and the Perron-Frobenius operators of dynamical maps. The fractal Weyl exponent is found to be ν ≈ 0.65 that corresponds to the fractal dimension of the network d ≈ 1.3. An independent computation of the fractal dimension by the cluster growing method, generalized for directed networks, gives a close value d ≈ 1.4. The eigenmodes of the Google matrix of Linux Kernel are localized on certain principal nodes. We argue that the fractal Weyl law should be generic for directed networks with the fractal dimension d < 2.
Optoacoustic inversion via Volterra kernel reconstruction
Melchert, O; Roth, B
2016-01-01
In this letter we address the numeric inversion of optoacoustic signals to initial stress profiles. Therefore we put under scrutiny the optoacoustic kernel reconstruction problem in the paraxial approximation of the underlying wave-equation. We apply a Fourier-series expansion of the optoacoustic Volterra kernel and obtain the respective expansion coefficients for a given "apparative" setup by performing a gauge procedure using synthetic input data. The resulting effective kernel is subsequently used to solve the optoacoustic source reconstruction problem for general signals. We verify the validity of the proposed inversion protocol for synthetic signals and explore the feasibility of our approach to also account for the diffraction transformation of signals beyond the paraxial approximation.
Tile-Compressed FITS Kernel for IRAF
Seaman, R.
2011-07-01
The Flexible Image Transport System (FITS) is a ubiquitously supported standard of the astronomical community. Similarly, the Image Reduction and Analysis Facility (IRAF), developed by the National Optical Astronomy Observatory, is a widely used astronomical data reduction package. IRAF supplies compatibility with FITS format data through numerous tools and interfaces. The most integrated of these is IRAF's FITS image kernel that provides access to FITS from any IRAF task that uses the basic IMIO interface. The original FITS kernel is a complex interface of purpose-built procedures that presents growing maintenance issues and lacks recent FITS innovations. A new FITS kernel is being developed at NOAO that is layered on the CFITSIO library from the NASA Goddard Space Flight Center. The simplified interface will minimize maintenance headaches as well as add important new features such as support for the FITS tile-compressed (fpack) format.
Existence and non-existence results for a nonlinear heat equation
Directory of Open Access Journals (Sweden)
Canan Celik
2007-02-01
Full Text Available In this study, we consider the nonlinear heat equation $$displaylines{ u_{t}(x,t = Delta u(x,t + u(x,t^p quad hbox{in } Omega imes (0,T,cr Bu(x,t = 0 quad hbox{on } partialOmega imes (0,T,cr u(x,0 = u_0(x quad hbox{in } Omega,}$$ with Dirichlet and mixed boundary conditions, where $Omega subset mathbb{R}^n$ is a smooth bounded domain and $p = 1+ 2 /n$ is the critical exponent. For an initial condition $u_0 in L^1$, we prove the non-existence of local solution in $L^1$ for the mixed boundary condition. Our proof is based on comparison principle for Dirichlet and mixed boundary value problems. We also establish the global existence in $L^{1+epsilon}$ to the Dirichlet problem, for any fixed $epsilon > 0$ with $|u_0|_{1+epsilon}$ sufficiently small.
Hill, Peter; Dudson, Ben
2016-01-01
We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference scheme for $\
A kernel-based approach for biomedical named entity recognition.
Patra, Rakesh; Saha, Sujan Kumar
2013-01-01
Support vector machine (SVM) is one of the popular machine learning techniques used in various text processing tasks including named entity recognition (NER). The performance of the SVM classifier largely depends on the appropriateness of the kernel function. In the last few years a number of task-specific kernel functions have been proposed and used in various text processing tasks, for example, string kernel, graph kernel, tree kernel and so on. So far very few efforts have been devoted to the development of NER task specific kernel. In the literature we found that the tree kernel has been used in NER task only for entity boundary detection or reannotation. The conventional tree kernel is unable to execute the complete NER task on its own. In this paper we have proposed a kernel function, motivated by the tree kernel, which is able to perform the complete NER task. To examine the effectiveness of the proposed kernel, we have applied the kernel function on the openly available JNLPBA 2004 data. Our kernel executes the complete NER task and achieves reasonable accuracy.
Full Waveform Inversion Using Waveform Sensitivity Kernels
Schumacher, Florian; Friederich, Wolfgang
2013-04-01
We present a full waveform inversion concept for applications ranging from seismological to enineering contexts, in which the steps of forward simulation, computation of sensitivity kernels, and the actual inversion are kept separate of each other. We derive waveform sensitivity kernels from Born scattering theory, which for unit material perturbations are identical to the Born integrand for the considered path between source and receiver. The evaluation of such a kernel requires the calculation of Green functions and their strains for single forces at the receiver position, as well as displacement fields and strains originating at the seismic source. We compute these quantities in the frequency domain using the 3D spectral element code SPECFEM3D (Tromp, Komatitsch and Liu, 2008) and the 1D semi-analytical code GEMINI (Friederich and Dalkolmo, 1995) in both, Cartesian and spherical framework. We developed and implemented the modularized software package ASKI (Analysis of Sensitivity and Kernel Inversion) to compute waveform sensitivity kernels from wavefields generated by any of the above methods (support for more methods is planned), where some examples will be shown. As the kernels can be computed independently from any data values, this approach allows to do a sensitivity and resolution analysis first without inverting any data. In the context of active seismic experiments, this property may be used to investigate optimal acquisition geometry and expectable resolution before actually collecting any data, assuming the background model is known sufficiently well. The actual inversion step then, can be repeated at relatively low costs with different (sub)sets of data, adding different smoothing conditions. Using the sensitivity kernels, we expect the waveform inversion to have better convergence properties compared with strategies that use gradients of a misfit function. Also the propagation of the forward wavefield and the backward propagation from the receiver
Inverse of the String Theory KLT Kernel
Mizera, Sebastian
2016-01-01
The field theory Kawai-Lewellen-Tye (KLT) kernel, which relates scattering amplitudes of gravitons and gluons, turns out to be the inverse of a matrix whose components are bi-adjoint scalar partial amplitudes. In this note we propose an analogous construction for the string theory KLT kernel. We present simple diagrammatic rules for the computation of the $\\alpha'$-corrected bi-adjoint scalar amplitudes that are exact in $\\alpha'$. We find compact expressions in terms of graphs, where the standard Feynman propagators $1/p^2$ are replaced by either $1/\\sin (\\pi \\alpha' p^2)$ or $1/\\tan (\\pi \\alpha' p^2)$, which is determined by a recursive procedure.
Reduced multiple empirical kernel learning machine.
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
Volatile compound formation during argan kernel roasting.
El Monfalouti, Hanae; Charrouf, Zoubida; Giordano, Manuela; Guillaume, Dominique; Kartah, Badreddine; Harhar, Hicham; Gharby, Saïd; Denhez, Clément; Zeppa, Giuseppe
2013-01-01
Virgin edible argan oil is prepared by cold-pressing argan kernels previously roasted at 110 degrees C for up to 25 minutes. The concentration of 40 volatile compounds in virgin edible argan oil was determined as a function of argan kernel roasting time. Most of the volatile compounds begin to be formed after 15 to 25 minutes of roasting. This suggests that a strictly controlled roasting time should allow the modulation of argan oil taste and thus satisfy different types of consumers. This could be of major importance considering the present booming use of edible argan oil.
Learning Rates for -Regularized Kernel Classifiers
Directory of Open Access Journals (Sweden)
Hongzhi Tong
2013-01-01
Full Text Available We consider a family of classification algorithms generated from a regularization kernel scheme associated with -regularizer and convex loss function. Our main purpose is to provide an explicit convergence rate for the excess misclassification error of the produced classifiers. The error decomposition includes approximation error, hypothesis error, and sample error. We apply some novel techniques to estimate the hypothesis error and sample error. Learning rates are eventually derived under some assumptions on the kernel, the input space, the marginal distribution, and the approximation error.
Face Recognition Using Kernel Discriminant Analysis
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Linear Discrimiant Analysis (LDA) has demonstrated their success in face recognition. But LDA is difficult to handle the high nonlinear problems, such as changes of large viewpoint and illumination in face recognition. In order to overcome these problems, we investigate Kernel Discriminant Analysis (KDA) for face recognition. This approach adopts the kernel functions to replace the dot products of nonlinear mapping in the high dimensional feature space, and then the nonlinear problem can be solved in the input space conveniently without explicit mapping. Two face databases are used to test KDA approach. The results show that our approach outperforms the conventional PCA(Eigenface) and LDA(Fisherface) approaches.
GROWTH OF RANDOM DIRICHLET SERIES IN THE WHOLE PLANE%随机Dirichlet级数在全平面上的增长性
Institute of Scientific and Technical Information of China (English)
刘伟群; 孙道椿
2012-01-01
In this article, we study the growth of random Dirichlet series on the whole plane. By using Knopp-Kojima method, we prove several lemmas and the two theorems, and the types of two random Dirichlet series are obtained.%本文研究了全平面上随机Dirichlet级数的增长性.应用Knopp-Kojima方法,得到了两类随机Dirichlet级数关于型的两个结果.
Regularization techniques for PSF-matching kernels - I. Choice of kernel basis
Becker, A. C.; Homrighausen, D.; Connolly, A. J.; Genovese, C. R.; Owen, R.; Bickerton, S. J.; Lupton, R. H.
2012-09-01
We review current methods for building point spread function (PSF)-matching kernels for the purposes of image subtraction or co-addition. Such methods use a linear decomposition of the kernel on a series of basis functions. The correct choice of these basis functions is fundamental to the efficiency and effectiveness of the matching - the chosen bases should represent the underlying signal using a reasonably small number of shapes, and/or have a minimum number of user-adjustable tuning parameters. We examine methods whose bases comprise multiple Gauss-Hermite polynomials, as well as a form-free basis composed of delta-functions. Kernels derived from delta-functions are unsurprisingly shown to be more expressive; they are able to take more general shapes and perform better in situations where sum-of-Gaussian methods are known to fail. However, due to its many degrees of freedom (the maximum number allowed by the kernel size) this basis tends to overfit the problem and yields noisy kernels having large variance. We introduce a new technique to regularize these delta-function kernel solutions, which bridges the gap between the generality of delta-function kernels and the compactness of sum-of-Gaussian kernels. Through this regularization we are able to create general kernel solutions that represent the intrinsic shape of the PSF-matching kernel with only one degree of freedom, the strength of the regularization λ. The role of λ is effectively to exchange variance in the resulting difference image with variance in the kernel itself. We examine considerations in choosing the value of λ, including statistical risk estimators and the ability of the solution to predict solutions for adjacent areas. Both of these suggest moderate strengths of λ between 0.1 and 1.0, although this optimization is likely data set dependent. This model allows for flexible representations of the convolution kernel that have significant predictive ability and will prove useful in implementing
van yen, Romain Nguyen; Schneider, Kai
2012-01-01
We report the results of a detailed study of the spectral properties of Laplace and Stokes operators, modified with a volume penalization term designed to approximate Dirichlet conditions in the limit when a penalization parameter, $\\eta$, tends to zero. The eigenvalues and eigenfunctions are determined either analytically or numerically as functions of $\\eta$, both in the continuous case and after applying Fourier or finite difference discretization schemes. For fixed $\\eta$, we find that only the part of the spectrum corresponding to eigenvalues $\\lambda \\lesssim \\eta^{-1}$ approaches Dirichlet boundary conditions, while the remainder of the spectrum is made of uncontrolled, spurious wall modes. The penalization error for the controlled eigenfunctions is estimated as a function of $\\eta$ and $\\lambda$. Surprisingly, in the Stokes case, we show that the eigenfunctions approximately satisfy, with a precision $O(\\eta)$, Navier slip boundary conditions with slip length equal to $\\sqrt{\\eta}$. Moreover, for a gi...
Kernel methods and minimum contrast estimators for empirical deconvolution
Delaigle, Aurore
2010-01-01
We survey classical kernel methods for providing nonparametric solutions to problems involving measurement error. In particular we outline kernel-based methodology in this setting, and discuss its basic properties. Then we point to close connections that exist between kernel methods and much newer approaches based on minimum contrast techniques. The connections are through use of the sinc kernel for kernel-based inference. This `infinite order' kernel is not often used explicitly for kernel-based deconvolution, although it has received attention in more conventional problems where measurement error is not an issue. We show that in a comparison between kernel methods for density deconvolution, and their counterparts based on minimum contrast, the two approaches give identical results on a grid which becomes increasingly fine as the bandwidth decreases. In consequence, the main numerical differences between these two techniques are arguably the result of different approaches to choosing smoothing parameters.
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...
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...
Gustin, Jeffery L; Jackson, Sean; Williams, Chekeria; Patel, Anokhee; Armstrong, Paul; Peter, Gary F; Settles, A Mark
2013-11-20
Maize kernel density affects milling quality of the grain. Kernel density of bulk samples can be predicted by near-infrared reflectance (NIR) spectroscopy, but no accurate method to measure individual kernel density has been reported. This study demonstrates that individual kernel density and volume are accurately measured using X-ray microcomputed tomography (μCT). Kernel density was significantly correlated with kernel volume, air space within the kernel, and protein content. Embryo density and volume did not influence overall kernel density. Partial least-squares (PLS) regression of μCT traits with single-kernel NIR spectra gave stable predictive models for kernel density (R(2) = 0.78, SEP = 0.034 g/cm(3)) and volume (R(2) = 0.86, SEP = 2.88 cm(3)). Density and volume predictions were accurate for data collected over 10 months based on kernel weights calculated from predicted density and volume (R(2) = 0.83, SEP = 24.78 mg). Kernel density was significantly correlated with bulk test weight (r = 0.80), suggesting that selection of dense kernels can translate to improved agronomic performance.
Marco Pedro Ramirez-Tachiquin; Cesar Marco Antonio Robles Gonzalez; Rogelio Adrian Hernandez-Becerril; Ariana Guadalupe Bucio Ramirez
2013-01-01
Based upon the elements of the modern pseudoanalytic function theory, we analyze a new method for numerically solving the forward Dirichlet boundary value problem corresponding to the two-dimensional electrical impedance equation. The analysis is performed by introducing interpolating piecewise separable-variables conductivity functions in the unit circle. To warrant the effectiveness of the posed method, we consider several examples of conductivity functions, whose boundary condi...
Energy Technology Data Exchange (ETDEWEB)
Sharapov, T F [Bashkir State Pedagogical University, Ufa (Russian Federation)
2014-10-31
We consider an elliptic operator in a multidimensional domain with frequently changing boundary conditions in the case when the homogenized operator contains the Dirichlet boundary condition. We prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and obtain estimates for the rate of convergence. A complete asymptotic expansion is constructed for the resolvent when it acts on sufficiently smooth functions. Bibliography: 41 titles.
Heat kernel for Newton-Cartan trace anomalies
Energy Technology Data Exchange (ETDEWEB)
Auzzi, Roberto [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Musei 41, Brescia, 25121 (Italy); INFN Sezione di Perugia, Via A. Pascoli, Perugia, 06123 (Italy); Nardelli, Giuseppe [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Musei 41, Brescia, 25121 (Italy); TIFPA - INFN, Università di Trento,c/o Dipartimento di Fisica, Povo, TN, 38123 (Italy)
2016-07-11
We compute the leading part of the trace anomaly for a free non-relativistic scalar in 2+1 dimensions coupled to a background Newton-Cartan metric. The anomaly is proportional to 1/m, where m is the mass of the scalar. We comment on the implications of a conjectured a-theorem for non-relativistic theories with boost invariance.
One Point Isometric Matching with the Heat Kernel
Ovsjanikov, Maks
2010-09-21
A common operation in many geometry processing algorithms consists of finding correspondences between pairs of shapes by finding structure-preserving maps between them. A particularly useful case of such maps is isometries, which preserve geodesic distances between points on each shape. Although several algorithms have been proposed to find approximately isometric maps between a pair of shapes, the structure of the space of isometries is not well understood. In this paper, we show that under mild genericity conditions, a single correspondence can be used to recover an isometry defined on entire shapes, and thus the space of all isometries can be parameterized by one correspondence between a pair of points. Perhaps surprisingly, this result is general, and does not depend on the dimensionality or the genus, and is valid for compact manifolds in any dimension. Moreover, we show that both the initial correspondence and the isometry can be recovered efficiently in practice. This allows us to devise an algorithm to find intrinsic symmetries of shapes, match shapes undergoing isometric deformations, as well as match partial and incomplete models efficiently. Journal compilation © 2010 The Eurographics Association and Blackwell Publishing Ltd.
Kernel Partial Least Squares for Nonlinear Regression and Discrimination
Rosipal, Roman; Clancy, Daniel (Technical Monitor)
2002-01-01
This paper summarizes recent results on applying the method of partial least squares (PLS) in a reproducing kernel Hilbert space (RKHS). A previously proposed kernel PLS regression model was proven to be competitive with other regularized regression methods in RKHS. The family of nonlinear kernel-based PLS models is extended by considering the kernel PLS method for discrimination. Theoretical and experimental results on a two-class discrimination problem indicate usefulness of the method.
Mitigation of artifacts in rtm with migration kernel decomposition
Zhan, Ge
2012-01-01
The migration kernel for reverse-time migration (RTM) can be decomposed into four component kernels using Born scattering and migration theory. Each component kernel has a unique physical interpretation and can be interpreted differently. In this paper, we present a generalized diffraction-stack migration approach for reducing RTM artifacts via decomposition of migration kernel. The decomposition leads to an improved understanding of migration artifacts and, therefore, presents us with opportunities for improving the quality of RTM images.
Sparse Event Modeling with Hierarchical Bayesian Kernel Methods
2016-01-05
the kernel function which depends on the application and the model user. This research uses the most popular kernel function, the radial basis...an important role in the nation’s economy. Unfortunately, the system’s reliability is declining due to the aging components of the network [Grier...kernel function. Gaussian Bayesian kernel models became very popular recently and were extended and applied to a number of classification problems. An
Yusop, Nur Syaza Mohd; Mohamed, Nurul Akmal
2017-05-01
Boundary Element Method (BEM) is a numerical way to approximate the solutions of a Boundary Value Problem (BVP). The potential problem which involves the Laplace's equation on the square shape domain will be considered where the boundary is divided into four sets of linear boundary elements. We study the derivation system of equation for mixed BVP with one Dirichlet Boundary Condition (BC) is prescribed on one element of the boundary and Neumann BC on the other three elements. The mixed BVP will be reduced to a Boundary Integral Equation (BIE) by using a direct method which involves Green's second identity representation formula. Then, linear interpolation is used where the boundary will be discretized into some linear elements. As the result, we then obtain the system of linear equations. In conclusion, the specific element in the mixed BVP will have the specific prescribe value depends on the type of boundary condition. For Dirichlet BC, it has only one value at each node but for the Neumann BC, there will be different values at the corner nodes due to outward normal. Therefore, the assembly process for the system of equations related to the mixed BVP may not be as straight forward as Dirichlet BVP and Neumann BVP. For the future research, we will consider the different shape domains for mixed BVP with different prescribed boundary conditions.
CFT dual of the AdS Dirichlet problem : Fluid/Gravity on cut-off surfaces
Brattan, Daniel K; Loganayagam, R; Rangamani, Mukund
2011-01-01
We study the gravitational Dirichlet problem in AdS spacetimes with a view to understanding the boundary CFT interpretation. We define the problem as bulk Einstein's equations with Dirichlet boundary conditions on fixed timelike cut-off hypersurface. Using the fluid/gravity correspondence, we argue that one can determine non-linear solutions to this problem in the long wavelength regime. On the boundary we find a conformal fluid with Dirichlet constitutive relations, viz., the fluid propagates on a `dynamical' background metric which depends on the local fluid velocities and temperature. This boundary fluid can be re-expressed as an emergent hypersurface fluid which is non-conformal but has the same value of the shear viscosity as the boundary fluid. The hypersurface dynamics arises as a collective effect, wherein effects of the background are transmuted into the fluid degrees of freedom. Furthermore, we demonstrate that this collective fluid is forced to be non-relativistic below a critical cut-off radius in...
An Extended Ockham Algebra with Endomorphism Kernel Property
Institute of Scientific and Technical Information of China (English)
Jie FANG
2007-01-01
An algebraic structure (∮) is said to have the endomorphism kernel property if every congruence on (∮) , other than the universal congruence, is the kernel of an endomorphism on (∮) .Inthis paper, we consider the EKP (that is, endomorphism kernel property) for an extended Ockham algebra (∮) . In particular, we describe the structure of the finite symmetric extended de Morgan algebras having EKP.
End-use quality of soft kernel durum wheat
Kernel texture is a major determinant of end-use quality of wheat. Durum wheat has very hard kernels. We developed soft kernel durum wheat via Ph1b-mediated homoeologous recombination. The Hardness locus was transferred from Chinese Spring to Svevo durum wheat via back-crossing. ‘Soft Svevo’ had SKC...
7 CFR 981.61 - Redetermination of kernel weight.
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Redetermination of kernel weight. 981.61 Section 981... GROWN IN CALIFORNIA Order Regulating Handling Volume Regulation § 981.61 Redetermination of kernel weight. The Board, on the basis of reports by handlers, shall redetermine the kernel weight of...
Multiple spectral kernel learning and a gaussian complexity computation.
Reyhani, Nima
2013-07-01
Multiple kernel learning (MKL) partially solves the kernel selection problem in support vector machines and similar classifiers by minimizing the empirical risk over a subset of the linear combination of given kernel matrices. For large sample sets, the size of the kernel matrices becomes a numerical issue. In many cases, the kernel matrix is of low-efficient rank. However, the low-rank property is not efficiently utilized in MKL algorithms. Here, we suggest multiple spectral kernel learning that efficiently uses the low-rank property by finding a kernel matrix from a set of Gram matrices of a few eigenvectors from all given kernel matrices, called a spectral kernel set. We provide a new bound for the gaussian complexity of the proposed kernel set, which depends on both the geometry of the kernel set and the number of Gram matrices. This characterization of the complexity implies that in an MKL setting, adding more kernels may not monotonically increase the complexity, while previous bounds show otherwise.
A Fast and Simple Graph Kernel for RDF
de Vries, G.K.D.; de Rooij, S.
2013-01-01
In this paper we study a graph kernel for RDF based on constructing a tree for each instance and counting the number of paths in that tree. In our experiments this kernel shows comparable classification performance to the previously introduced intersection subtree kernel, but is significantly faster
7 CFR 981.60 - Determination of kernel weight.
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Determination of kernel weight. 981.60 Section 981.60... Regulating Handling Volume Regulation § 981.60 Determination of kernel weight. (a) Almonds for which settlement is made on kernel weight. All lots of almonds, whether shelled or unshelled, for which...
21 CFR 176.350 - Tamarind seed kernel powder.
2010-04-01
... 21 Food and Drugs 3 2010-04-01 2009-04-01 true Tamarind seed kernel powder. 176.350 Section 176... Substances for Use Only as Components of Paper and Paperboard § 176.350 Tamarind seed kernel powder. Tamarind seed kernel powder may be safely used as a component of articles intended for use in...
Stable Kernel Representations as Nonlinear Left Coprime Factorizations
Paice, A.D.B.; Schaft, A.J. van der
1994-01-01
A representation of nonlinear systems based on the idea of representing the input-output pairs of the system as elements of the kernel of a stable operator has been recently introduced. This has been denoted the kernel representation of the system. In this paper it is demonstrated that the kernel
Kernel Temporal Differences for Neural Decoding
Directory of Open Access Journals (Sweden)
Jihye Bae
2015-01-01
Full Text Available We study the feasibility and capability of the kernel temporal difference (KTD(λ algorithm for neural decoding. KTD(λ is an online, kernel-based learning algorithm, which has been introduced to estimate value functions in reinforcement learning. This algorithm combines kernel-based representations with the temporal difference approach to learning. One of our key observations is that by using strictly positive definite kernels, algorithm’s convergence can be guaranteed for policy evaluation. The algorithm’s nonlinear functional approximation capabilities are shown in both simulations of policy evaluation and neural decoding problems (policy improvement. KTD can handle high-dimensional neural states containing spatial-temporal information at a reasonable computational complexity allowing real-time applications. When the algorithm seeks a proper mapping between a monkey’s neural states and desired positions of a computer cursor or a robot arm, in both open-loop and closed-loop experiments, it can effectively learn the neural state to action mapping. Finally, a visualization of the coadaptation process between the decoder and the subject shows the algorithm’s capabilities in reinforcement learning brain machine interfaces.
Bergman kernel and complex singularity exponent
Institute of Scientific and Technical Information of China (English)
LEE; HanJin
2009-01-01
We give a precise estimate of the Bergman kernel for the model domain defined by Ω F={(z,w) ∈ C n+1:Im w |F (z)| 2 > 0},where F=(f 1,...,f m) is a holomorphic map from C n to C m,in terms of the complex singularity exponent of F.
Kernel based subspace projection of hyperspectral images
DEFF Research Database (Denmark)
Larsen, Rasmus; Nielsen, Allan Aasbjerg; Arngren, Morten
In hyperspectral image analysis an exploratory approach to analyse the image data is to conduct subspace projections. As linear projections often fail to capture the underlying structure of the data, we present kernel based subspace projections of PCA and Maximum Autocorrelation Factors (MAF...
Analytic properties of the Virasoro modular kernel
Nemkov, Nikita
2016-01-01
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.
A Cubic Kernel for Feedback Vertex Set
Bodlaender, H.L.
2006-01-01
The FEEDBACK VERTEX SET problem on unweighted, undirected graphs is considered. Improving upon a result by Burrage et al. [7], we show that this problem has a kernel with O(κ3) vertices, i.e., there is a polynomial time algorithm, that given a graph G and an integer κ, finds a graph G' and integer
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.)
Hyperbolic L2-modules with Reproducing Kernels
Institute of Scientific and Technical Information of China (English)
David EELPODE; Frank SOMMEN
2006-01-01
Abstract In this paper, the Dirac operator on the Klein model for the hyperbolic space is considered. A function space containing L2-functions on the sphere Sm-1 in (R)m, which are boundary values of solutions for this operator, is defined, and it is proved that this gives rise to a Hilbert module with a reproducing kernel.
Protein Structure Prediction Using String Kernels
2006-03-03
Prediction using String Kernels 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER...consists of 4352 sequences from SCOP version 1.53 extracted from the Astral database, grouped into families and superfamilies. The dataset is processed
Bergman kernel and complex singularity exponent
Institute of Scientific and Technical Information of China (English)
CHEN BoYong; LEE HanJin
2009-01-01
We give a precise estimate of the Bergman kernel for the model domain defined by Ω_F = {(z,w) ∈ C~(n+1) : Imw - |F(z)|~2 > 0},where F = (f_1,... ,f_m) is a holomorphic map from C~n to C~m,in terms of the complex singularity exponent of F.
Symbol recognition with kernel density matching.
Zhang, Wan; Wenyin, Liu; Zhang, Kun
2006-12-01
We propose a novel approach to similarity assessment for graphic symbols. Symbols are represented as 2D kernel densities and their similarity is measured by the Kullback-Leibler divergence. Symbol orientation is found by gradient-based angle searching or independent component analysis. Experimental results show the outstanding performance of this approach in various situations.
Developing Linux kernel space device driver
Institute of Scientific and Technical Information of China (English)
Zheng Wei; Wang Qinruo; Wu Naiyou
2003-01-01
This thesis introduces how to develop kernel level device drivers on Linux platform in detail. On the basis of comparing proc file system with dev file system, we choose PCI devices and USB devices as instances to introduce the method of writing device drivers for character devices by using these two file systems.
Convolution kernels for multi-wavelength imaging
Boucaud, A.; Bocchio, M.; Abergel, A.; Orieux, F.; Dole, H.; Hadj-Youcef, M. A.
2016-12-01
Astrophysical images issued from different instruments and/or spectral bands often require to be processed together, either for fitting or comparison purposes. However each image is affected by an instrumental response, also known as point-spread function (PSF), that depends on the characteristics of the instrument as well as the wavelength and the observing strategy. Given the knowledge of the PSF in each band, a straightforward way of processing images is to homogenise them all to a target PSF using convolution kernels, so that they appear as if they had been acquired by the same instrument. We propose an algorithm that generates such PSF-matching kernels, based on Wiener filtering with a tunable regularisation parameter. This method ensures all anisotropic features in the PSFs to be taken into account. We compare our method to existing procedures using measured Herschel/PACS and SPIRE PSFs and simulated JWST/MIRI PSFs. Significant gains up to two orders of magnitude are obtained with respect to the use of kernels computed assuming Gaussian or circularised PSFs. A software to compute these kernels is available at https://github.com/aboucaud/pypher
Dielectric properties of almond kernels associated with radio frequency and microwave pasteurization
Li, Rui; Zhang, Shuang; Kou, Xiaoxi; Ling, Bo; Wang, Shaojin
2017-01-01
To develop advanced pasteurization treatments based on radio frequency (RF) or microwave (MW) energy, dielectric properties of almond kernels were measured by using an open-ended coaxial-line probe and impedance analyzer at frequencies between 10 and 3000 MHz, moisture contents between 4.2% to 19.6% w.b. and temperatures between 20 and 90 °C. The results showed that both dielectric constant and loss factor of the almond kernels decreased sharply with increasing frequency over the RF range (10–300 MHz), but gradually over the measured MW range (300–3000 MHz). Both dielectric constant and loss factor of almond kernels increased with increasing temperature and moisture content, and largely enhanced at higher temperature and moisture levels. Quadratic polynomial equations were developed to best fit the relationship between dielectric constant or loss factor at 27, 40, 915 or 2450 MHz and sample temperature/moisture content with R2 greater than 0.967. Penetration depth of electromagnetic wave into samples decreased with increasing frequency (27–2450 MHz), moisture content (4.2–19.6% w.b.) and temperature (20–90 °C). The temperature profiles of RF heated almond kernels under three moisture levels were made using experiment and computer simulation based on measured dielectric properties. Based on the result of this study, RF treatment has potential to be practically used for pasteurization of almond kernels with acceptable heating uniformity. PMID:28186149
Dielectric properties of almond kernels associated with radio frequency and microwave pasteurization
Li, Rui; Zhang, Shuang; Kou, Xiaoxi; Ling, Bo; Wang, Shaojin
2017-02-01
To develop advanced pasteurization treatments based on radio frequency (RF) or microwave (MW) energy, dielectric properties of almond kernels were measured by using an open-ended coaxial-line probe and impedance analyzer at frequencies between 10 and 3000 MHz, moisture contents between 4.2% to 19.6% w.b. and temperatures between 20 and 90 °C. The results showed that both dielectric constant and loss factor of the almond kernels decreased sharply with increasing frequency over the RF range (10–300 MHz), but gradually over the measured MW range (300–3000 MHz). Both dielectric constant and loss factor of almond kernels increased with increasing temperature and moisture content, and largely enhanced at higher temperature and moisture levels. Quadratic polynomial equations were developed to best fit the relationship between dielectric constant or loss factor at 27, 40, 915 or 2450 MHz and sample temperature/moisture content with R2 greater than 0.967. Penetration depth of electromagnetic wave into samples decreased with increasing frequency (27–2450 MHz), moisture content (4.2–19.6% w.b.) and temperature (20–90 °C). The temperature profiles of RF heated almond kernels under three moisture levels were made using experiment and computer simulation based on measured dielectric properties. Based on the result of this study, RF treatment has potential to be practically used for pasteurization of almond kernels with acceptable heating uniformity.
Kusumaningrum, Retno; Wei, Hong; Manurung, Ruli; Murni, Aniati
2014-01-01
Scene classification based on latent Dirichlet allocation (LDA) is a more general modeling method known as a bag of visual words, in which the construction of a visual vocabulary is a crucial quantization process to ensure success of the classification. A framework is developed using the following new aspects: Gaussian mixture clustering for the quantization process, the use of an integrated visual vocabulary (IVV), which is built as the union of all centroids obtained from the separate quantization process of each class, and the usage of some features, including edge orientation histogram, CIELab color moments, and gray-level co-occurrence matrix (GLCM). The experiments are conducted on IKONOS images with six semantic classes (tree, grassland, residential, commercial/industrial, road, and water). The results show that the use of an IVV increases the overall accuracy (OA) by 11 to 12% and 6% when it is implemented on the selected and all features, respectively. The selected features of CIELab color moments and GLCM provide a better OA than the implementation over CIELab color moment or GLCM as individuals. The latter increases the OA by only ˜2 to 3%. Moreover, the results show that the OA of LDA outperforms the OA of C4.5 and naive Bayes tree by ˜20%.
Multi-view methods for protein structure comparison using latent dirichlet allocation.
Shivashankar, S; Srivathsan, S; Ravindran, B; Tendulkar, Ashish V
2011-07-01
With rapidly expanding protein structure databases, efficiently retrieving structures similar to a given protein is an important problem. It involves two major issues: (i) effective protein structure representation that captures inherent relationship between fragments and facilitates efficient comparison between the structures and (ii) effective framework to address different retrieval requirements. Recently, researchers proposed vector space model of proteins using bag of fragments representation (FragBag), which corresponds to the basic information retrieval model. In this article, we propose an improved representation of protein structures using latent dirichlet allocation topic model. Another important requirement is to retrieve proteins, whether they are either close or remote homologs. In order to meet diverse objectives, we propose multi-viewpoint based framework that combines multiple representations and retrieval techniques. We compare the proposed representation and retrieval framework on the benchmark dataset developed by Kolodny and co-workers. The results indicate that the proposed techniques outperform state-of-the-art methods. http://www.cse.iitm.ac.in/~ashishvt/research/protein-lda/. ashishvt@cse.iitm.ac.in.
Smith, Keith; Ricaud, Benjamin; Shahid, Nauman; Rhodes, Stephen; Starr, John M.; Ibáñez, Augustin; Parra, Mario A.; Escudero, Javier; Vandergheynst, Pierre
2017-02-01
Visual short-term memory binding tasks are a promising early marker for Alzheimer’s disease (AD). To uncover functional deficits of AD in these tasks it is meaningful to first study unimpaired brain function. Electroencephalogram recordings were obtained from encoding and maintenance periods of tasks performed by healthy young volunteers. We probe the task’s transient physiological underpinnings by contrasting shape only (Shape) and shape-colour binding (Bind) conditions, displayed in the left and right sides of the screen, separately. Particularly, we introduce and implement a novel technique named Modular Dirichlet Energy (MDE) which allows robust and flexible analysis of the functional network with unprecedented temporal precision. We find that connectivity in the Bind condition is less integrated with the global network than in the Shape condition in occipital and frontal modules during the encoding period of the right screen condition. Using MDE we are able to discern driving effects in the occipital module between 100–140 ms, coinciding with the P100 visually evoked potential, followed by a driving effect in the frontal module between 140–180 ms, suggesting that the differences found constitute an information processing difference between these modules. This provides temporally precise information over a heterogeneous population in promising tasks for the detection of AD.
Latent Dirichlet Allocation (LDA) for Sentiment Analysis Toward Tourism Review in Indonesia
Putri, IR; Kusumaningrum, R.
2017-01-01
The tourism industry is one of foreign exchange sector, which has considerable potential development in Indonesia. Compared to other Southeast Asia countries such as Malaysia with 18 million tourists and Singapore 20 million tourists, Indonesia which is the largest Southeast Asia’s country have failed to attract higher tourist numbers compared to its regional peers. Indonesia only managed to attract 8,8 million foreign tourists in 2013, with the value of foreign tourists each year which is likely to decrease. Apart from the infrastructure problems, marketing and managing also form of obstacles for tourism growth. An evaluation and self-analysis should be done by the stakeholder to respond toward this problem and capture opportunities that related to tourism satisfaction from tourists review. Recently, one of technology to answer this problem only relying on the subjective of statistical data which collected by voting or grading from user randomly. So the result is still not to be accountable. Thus, we proposed sentiment analysis with probabilistic topic model using Latent Dirichlet Allocation (LDA) method to be applied for reading general tendency from tourist review into certain topics that can be classified toward positive and negative sentiment.
Gross, Alexander; Murthy, Dhiraj
2014-10-01
This paper explores a variety of methods for applying the Latent Dirichlet Allocation (LDA) automated topic modeling algorithm to the modeling of the structure and behavior of virtual organizations found within modern social media and social networking environments. As the field of Big Data reveals, an increase in the scale of social data available presents new challenges which are not tackled by merely scaling up hardware and software. Rather, they necessitate new methods and, indeed, new areas of expertise. Natural language processing provides one such method. This paper applies LDA to the study of scientific virtual organizations whose members employ social technologies. Because of the vast data footprint in these virtual platforms, we found that natural language processing was needed to 'unlock' and render visible latent, previously unseen conversational connections across large textual corpora (spanning profiles, discussion threads, forums, and other social media incarnations). We introduce variants of LDA and ultimately make the argument that natural language processing is a critical interdisciplinary methodology to make better sense of social 'Big Data' and we were able to successfully model nested discussion topics from forums and blog posts using LDA. Importantly, we found that LDA can move us beyond the state-of-the-art in conventional Social Network Analysis techniques. Copyright © 2014 Elsevier Ltd. All rights reserved.
Vargas-Magaña, Rosa; Panayotaros, Panayotis
2015-11-01
We study the problem of wave propagation in a long-wave asymptotic regime over variable bottom of an ideal irrotational fluid in the framework of the Hamiltonian formulation in which the non-local Dirichlet-Neumann (DtN) operator appears explicitly in the Hamiltonian. We propose a non-local Hamiltonian model for bidirectional wave propagation in shallow water that involves pseudodifferential operators that approximate the DtN operator for variable depth. These models generalize the Boussinesq system as they include the exact dispersion relation in the case of constant depth. We present results for the normal modes and eigenfrequencies of the linearized problem. We see that variable topography introduces effects such as steepening of normal modes with increasing variation of depth, as well as amplitude modulation of the normal modes in certain wavelength ranges. Numerical integration shows that the constant depth nonlocal Boussinesq model with quadratic nonlinearity can capture the evolution obtained with higher order approximations of the DtN operator. In the case of variable depth we observe certain oscillations in width of the crest and also some interesting textures in the evolution of wave crests during the passage from obstacles.
Kojima, Takeo
2009-01-01
We study the time and temperature dependent correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions $\\langle \\psi(x_1,0)\\psi^\\dagger(x_2,t)\\rangle _{\\pm,T}$. We derive the Fredholm determinant formulae for the correlation functions, by means of the Bethe Ansatz. For the special case $x_1=0$, we express correlation functions with Neumann boundary conditions $\\langle\\psi(0,0)\\psi^\\dagger(x_2,t)\\rangle _{+,T}$, in terms of solutions of nonlinear partial differential equations which were introduced in \\cite{kojima:Sl} as a generalization of the nonlinear Schr\\"odinger equations. We generalize the Fredholm minor determinant formulae of ground state correlation functions $\\langle\\psi(x_1)\\psi^\\dagger(x_2)\\rangle _{\\pm,0}$ in \\cite{kojima:K}, to the Fredholm determinant formulae for the time and temperature dependent correlation functions $\\langle\\psi(x_1,0)\\psi^\\dagger(x_2,t)\\rangle _{\\pm,T}$, $t \\in {\\bf R}$, $T \\geq 0$.
Jump-type Hunt processes generated by lower bounded semi-Dirichlet forms
Fukushima, Masatoshi; 10.1214/10-AOP633
2012-01-01
Let $E$ be a locally compact separable metric space and $m$ be a positive Radon measure on it. Given a nonnegative function $k$ defined on $E\\times E$ off the diagonal whose anti-symmetric part is assumed to be less singular than the symmetric part, we construct an associated regular lower bounded semi-Dirichlet form $\\eta$ on $L^2(E;m)$ producing a Hunt process $X^0$ on $E$ whose jump behaviours are governed by $k$. For an arbitrary open subset $D\\subset E$, we also construct a Hunt process $X^{D,0}$ on $D$ in an analogous manner. When $D$ is relatively compact, we show that $X^{D,0}$ is censored in the sense that it admits no killing inside $D$ and killed only when the path approaches to the boundary. When $E$ is a $d$-dimensional Euclidean space and $m$ is the Lebesgue measure, a typical example of $X^0$ is the stable-like process that will be also identified with the solution of a martingale problem up to an $\\eta$-polar set of starting points. Approachability to the boundary $\\partial D$ in finite time o...
Li, Ang; Li, Changyang; Wang, Xiuying; Eberl, Stefan; Feng, Dagan; Fulham, Michael
2016-08-01
Blurred boundaries and heterogeneous intensities make accurate prostate MR image segmentation problematic. To improve prostate MR image segmentation we suggest an approach that includes: (a) an image patch division method to partition the prostate into homogeneous segments for feature extraction; (b) an image feature formulation and classification method, using the relevance vector machine, to provide probabilistic prior knowledge for graph energy construction; (c) a graph energy formulation scheme with Bayesian priors and Dirichlet graph energy and (d) a non-iterative graph energy minimization scheme, based on matrix differentiation, to perform the probabilistic pixel membership optimization. The segmentation output was obtained by assigning pixels with foreground and background labels based on derived membership probabilities. We evaluated our approach on the PROMISE-12 dataset with 50 prostate MR image volumes. Our approach achieved a mean dice similarity coefficient (DSC) of 0.90 ± 0.02, which surpassed the five best prior-based methods in the PROMISE-12 segmentation challenge.
DPNuc: Identifying Nucleosome Positions Based on the Dirichlet Process Mixture Model.
Chen, Huidong; Guan, Jihong; Zhou, Shuigeng
2015-01-01
Nucleosomes and the free linker DNA between them assemble the chromatin. Nucleosome positioning plays an important role in gene transcription regulation, DNA replication and repair, alternative splicing, and so on. With the rapid development of ChIP-seq, it is possible to computationally detect the positions of nucleosomes on chromosomes. However, existing methods cannot provide accurate and detailed information about the detected nucleosomes, especially for the nucleosomes with complex configurations where overlaps and noise exist. Meanwhile, they usually require some prior knowledge of nucleosomes as input, such as the size or the number of the unknown nucleosomes, which may significantly influence the detection results. In this paper, we propose a novel approach DPNuc for identifying nucleosome positions based on the Dirichlet process mixture model. In our method, Markov chain Monte Carlo (MCMC) simulations are employed to determine the mixture model with no need of prior knowledge about nucleosomes. Compared with three existing methods, our approach can provide more detailed information of the detected nucleosomes and can more reasonably reveal the real configurations of the chromosomes; especially, our approach performs better in the complex overlapping situations. By mapping the detected nucleosomes to a synthetic benchmark nucleosome map and two existing benchmark nucleosome maps, it is shown that our approach achieves a better performance in identifying nucleosome positions and gets a higher F-score. Finally, we show that our approach can more reliably detect the size distribution of nucleosomes.
Chen, Yun; Yang, Hui
2016-12-01
In the era of big data, there are increasing interests on clustering variables for the minimization of data redundancy and the maximization of variable relevancy. Existing clustering methods, however, depend on nontrivial assumptions about the data structure. Note that nonlinear interdependence among variables poses significant challenges on the traditional framework of predictive modeling. In the present work, we reformulate the problem of variable clustering from an information theoretic perspective that does not require the assumption of data structure for the identification of nonlinear interdependence among variables. Specifically, we propose the use of mutual information to characterize and measure nonlinear correlation structures among variables. Further, we develop Dirichlet process (DP) models to cluster variables based on the mutual-information measures among variables. Finally, orthonormalized variables in each cluster are integrated with group elastic-net model to improve the performance of predictive modeling. Both simulation and real-world case studies showed that the proposed methodology not only effectively reveals the nonlinear interdependence structures among variables but also outperforms traditional variable clustering algorithms such as hierarchical clustering.
Fan, Wentao; Sallay, Hassen; Bouguila, Nizar
2016-06-09
In this paper, a novel statistical generative model based on hierarchical Pitman-Yor process and generalized Dirichlet distributions (GDs) is presented. The proposed model allows us to perform joint clustering and feature selection thanks to the interesting properties of the GD distribution. We develop an online variational inference algorithm, formulated in terms of the minimization of a Kullback-Leibler divergence, of our resulting model that tackles the problem of learning from high-dimensional examples. This variational Bayes formulation allows simultaneously estimating the parameters, determining the model's complexity, and selecting the appropriate relevant features for the clustering structure. Moreover, the proposed online learning algorithm allows data instances to be processed in a sequential manner, which is critical for large-scale and real-time applications. Experiments conducted using challenging applications, namely, scene recognition and video segmentation, where our approach is viewed as an unsupervised technique for visual learning in high-dimensional spaces, showed that the proposed approach is suitable and promising.
Dirichlet Casimir Energy for a Scalar Field in a Sphere: An Alternative Method
Valuyan, M A
2009-01-01
In this paper we compute the leading order of the Casimir energy for a free massless scalar field confined in a sphere in three spatial dimensions, with the Dirichlet boundary condition. When one tabulates all of the reported values of the Casimir energies for two closed geometries, cubical and spherical, in different space-time dimensions and with different boundary conditions, one observes a complicated pattern of signs. This pattern shows that the Casimir energy depends crucially on the details of the geometry, the number of the spatial dimensions, and the boundary conditions. The dependence of the \\emph{sign} of the Casimir energy on the details of the geometry, for a fixed spatial dimensions and boundary conditions has been a surprise to us and this is our main motivation for doing the calculations presented in this paper. Moreover, all of the calculations for spherical geometries include the use of numerical methods combined with intricate analytic continuations to handle many different sorts of diverge...
THE VALUE DISTRIBUTION OF RANDOM DIRICHLET SERIES ON THE RIGHT HALF PLANE(Ⅱ)
Institute of Scientific and Technical Information of China (English)
田范基; 任耀峰
2003-01-01
Kahane has studiedthe value distribution ofthe Gauss-Taylor series∑anXnzn,∞where{Xn}is a complex Gauss sequence and∑|an|2=∞.Inthis paper,by trans forming the right half plane into the unit disc and setting up some important inequalities,the value distribution of the Dirichlet series∑Xne- nS is studied where{Xn}is a sequence of some non-degenerate independent random variable satisfying conditions:EXn=0;∞E|Xn|2=+∞;An∈N,Xn or ReXn or ImXn of bounded density.There exists α＞0 such that An:α2E|Xn|2≤E2|Xn|＜+∞(the classic Gauss and Steinhaus random variables are special cases of such random variables).The important results are obtainedthat every point on the line Res=0 is a Picard point of the series withoutfinite exceptional value a.s..
Chen, Yun; Yang, Hui
2016-12-14
In the era of big data, there are increasing interests on clustering variables for the minimization of data redundancy and the maximization of variable relevancy. Existing clustering methods, however, depend on nontrivial assumptions about the data structure. Note that nonlinear interdependence among variables poses significant challenges on the traditional framework of predictive modeling. In the present work, we reformulate the problem of variable clustering from an information theoretic perspective that does not require the assumption of data structure for the identification of nonlinear interdependence among variables. Specifically, we propose the use of mutual information to characterize and measure nonlinear correlation structures among variables. Further, we develop Dirichlet process (DP) models to cluster variables based on the mutual-information measures among variables. Finally, orthonormalized variables in each cluster are integrated with group elastic-net model to improve the performance of predictive modeling. Both simulation and real-world case studies showed that the proposed methodology not only effectively reveals the nonlinear interdependence structures among variables but also outperforms traditional variable clustering algorithms such as hierarchical clustering.
A Dirichlet Process Mixture Based Name Origin Clustering and Alignment Model for Transliteration
Directory of Open Access Journals (Sweden)
Chunyue Zhang
2015-01-01
Full Text Available In machine transliteration, it is common that the transliterated names in the target language come from multiple language origins. A conventional maximum likelihood based single model can not deal with this issue very well and often suffers from overfitting. In this paper, we exploit a coupled Dirichlet process mixture model (cDPMM to address overfitting and names multiorigin cluster issues simultaneously in the transliteration sequence alignment step over the name pairs. After the alignment step, the cDPMM clusters name pairs into many groups according to their origin information automatically. In the decoding step, in order to use the learned origin information sufficiently, we use a cluster combination method (CCM to build clustering-specific transliteration models by combining small clusters into large ones based on the perplexities of name language and transliteration model, which makes sure each origin cluster has enough data for training a transliteration model. On the three different Western-Chinese multiorigin names corpora, the cDPMM outperforms two state-of-the-art baseline models in terms of both the top-1 accuracy and mean F-score, and furthermore the CCM significantly improves the cDPMM.
Directory of Open Access Journals (Sweden)
Maryam Asnaashari
2015-01-01
Full Text Available In this study, in order to introduce natural antioxidative vegetable oil in food industry, the kolkhoung hull oil and kernel oil were extracted. To evaluate their antioxidant efficiency, gas chromatography analysis of the composition of kolkhoung hull and kernel oil fatty acids and high–performance liquid chromatography analysis of tocopherols were done. Also, the oxidative stability of the oil was considered based on the peroxide value and anisidine value during heating at 100, 110 and 120 °C. Gas chromatography analysis showed that oleic acid was the major fatty acid of both types of oil (hull and kernel and based on a low content of saturated fatty acids, high content of monounsaturated fatty acids, and the ratio of ω-6 and ω-3 polyunsaturated fatty acids, they were nutritionally well-balanced. Moreover, both hull and kernel oil showed high oxidative stability during heating, which can be attributed to high content of tocotrienols. Based on the results, kolkhoung hull oil acted slightly better than its kernel oil. However, both of them can be added to oxidation–sensitive oils to improve their shelf life.
A Kernel Approach to Multi-Task Learning with Task-Specific Kernels
Institute of Scientific and Technical Information of China (English)
Wei Wu; Hang Li; Yun-Hua Hu; Rong Jin
2012-01-01
Several kernel-based methods for multi-task learning have been proposed,which leverage relations among tasks as regularization to enhance the overall learning accuracies.These methods assume that the tasks share the same kernel,which could limit their applications because in practice different tasks may need different kernels.The main challenge of introducing multiple kernels into multiple tasks is that models from different reproducing kernel Hilbert spaces (RKHSs) are not comparable,making it difficult to exploit relations among tasks.This paper addresses the challenge by formalizing the problem in the square integrable space (SIS).Specially,it proposes a kernel-based method which makes use of a regularization term defined in SIS to represent task relations.We prove a new representer theorem for the proposed approach in SIS.We further derive a practical method for solving the learning problem and conduct consistency analysis of the method.We discuss the relationship between our method and an existing method.We also give an SVM (support vector machine)-based implementation of our method for multi-label classification.Experiments on an artificial example and two real-world datasets show that the proposed method performs better than the existing method.
Kernel based orthogonalization for change detection in hyperspectral images
DEFF Research Database (Denmark)
Nielsen, Allan Aasbjerg
Kernel versions of principal component analysis (PCA) and minimum noise fraction (MNF) analysis are applied to change detection in hyperspectral image (HyMap) data. The kernel versions are based on so-called Q-mode analysis in which the data enter into the analysis via inner products in the Gram...... the kernel function and then performing a linear analysis in that space. An example shows the successful application of (kernel PCA and) kernel MNF analysis to change detection in HyMap data covering a small agricultural area near Lake Waging-Taching, Bavaria, in Southern Germany. In the change detection...
Geodesic exponential kernels: When Curvature and Linearity Conflict
DEFF Research Database (Denmark)
Feragen, Aase; Lauze, François; Hauberg, Søren
2015-01-01
We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian...... Laplacian kernel can be generalized while retaining positive definiteness. This implies that geodesic Laplacian kernels can be generalized to some curved spaces, including spheres and hyperbolic spaces. Our theoretical results are verified empirically....
The pre-image problem in kernel methods.
Kwok, James Tin-yau; Tsang, Ivor Wai-hung
2004-11-01
In this paper, we address the problem of finding the pre-image of a feature vector in the feature space induced by a kernel. This is of central importance in some kernel applications, such as on using kernel principal component analysis (PCA) for image denoising. Unlike the traditional method which relies on nonlinear optimization, our proposed method directly finds the location of the pre-image based on distance constraints in the feature space. It is noniterative, involves only linear algebra and does not suffer from numerical instability or local minimum problems. Evaluations on performing kernel PCA and kernel clustering on the USPS data set show much improved performance.
Generalization Performance of Regularized Ranking With Multiscale Kernels.
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.
Selection and properties of alternative forming fluids for TRISO fuel kernel production
Energy Technology Data Exchange (ETDEWEB)
Baker, M. P. [Colorado School of Mines, Golden, CO (United States); King, J. C. [Colorado School of Mines, Golden, CO (United States); Gorman, B. P. [Colorado School of Mines, Golden, CO (United States); Marshall, Doug W. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2013-01-01
Current Very High Temperature Reactor (VHTR) designs incorporate TRi-structural ISOtropic (TRISO) fuel, which consists of a spherical fissile fuel kernel surrounded by layers of pyrolytic carbon and silicon carbide. An internal sol-gel process forms the fuel kernel using wet chemistry to produce uranium oxyhydroxide gel spheres by dropping a cold precursor solution into a hot column of trichloroethylene (TCE). Over time, gelation byproducts inhibit complete gelation, and the TCE must be purified or discarded. The resulting TCE waste stream contains both radioactive and hazardous materials and is thus considered a mixed hazardous waste. Changing the forming fluid to a non-hazardous alternative could greatly improve the economics of TRISO fuel kernel production. Selection criteria for a replacement forming fluid narrowed a list of ~10,800 chemicals to yield ten potential replacement forming fluids: 1-bromododecane, 1- bromotetradecane, 1-bromoundecane, 1-chlorooctadecane, 1-chlorotetradecane, 1-iododecane, 1-iodododecane, 1-iodohexadecane, 1-iodooctadecane, and squalane. The density, viscosity, and surface tension for each potential replacement forming fluid were measured as a function of temperature between 25 °C and 80 °C. Calculated settling velocities and heat transfer rates give an overall column height approximation. 1-bromotetradecane, 1-chlorooctadecane, and 1-iodododecane show the greatest promise as replacements, and future tests will verify their ability to form satisfactory fuel kernels.
Selection and properties of alternative forming fluids for TRISO fuel kernel production
Baker, M. P.; King, J. C.; Gorman, B. P.; Marshall, D. W.
2013-01-01
Current Very High Temperature Reactor (VHTR) designs incorporate TRi-structural ISOtropic (TRISO) fuel, which consists of a spherical fissile fuel kernel surrounded by layers of pyrolytic carbon and silicon carbide. An internal sol-gel process forms the fuel kernel using wet chemistry to produce uranium oxyhydroxide gel spheres by dropping a cold precursor solution into a hot column of trichloroethylene (TCE). Over time, gelation byproducts inhibit complete gelation, and the TCE must be purified or discarded. The resulting TCE waste stream contains both radioactive and hazardous materials and is thus considered a mixed hazardous waste. Changing the forming fluid to a non-hazardous alternative could greatly improve the economics of TRISO fuel kernel production. Selection criteria for a replacement forming fluid narrowed a list of ˜10,800 chemicals to yield ten potential replacement forming fluids: 1-bromododecane, 1-bromotetradecane, 1-bromoundecane, 1-chlorooctadecane, 1-chlorotetradecane, 1-iododecane, 1-iodododecane, 1-iodohexadecane, 1-iodooctadecane, and squalane. The density, viscosity, and surface tension for each potential replacement forming fluid were measured as a function of temperature between 25 °C and 80 °C. Calculated settling velocities and heat transfer rates give an overall column height approximation. 1-bromotetradecane, 1-chlorooctadecane, and 1-iodododecane show the greatest promise as replacements, and future tests will verify their ability to form satisfactory fuel kernels.
UO{sub 2} Kernel Preparation by M-EG Process and Its Irradiation Test
Energy Technology Data Exchange (ETDEWEB)
Jeong, K. C.; Eom, S. H.; Kim, Y. K.; Yeo, S. H.; Kim, Y. M.; Kim, B. G.; Cho, M. S. [KAERI, Daejeon (Korea, Republic of)
2016-05-15
Kernels of KAERI TRISO fuels are prepared in the following steps: (1) preparation of a raw material solution(UN solution) by UO{sub 3} (or U{sub 3}O{sub 8}) powder dissolution in the concentrated HNO{sub 3}; (2) broth preparation and physical property control by mixing UN, THFA, PVA, and H{sub 2}O; (3) preparation of spherical liquid gel droplets and dried-ADU gels in sequence through a reaction between uranyl ions and ammonia ions in a gelation column; (4) ageing, washing, and drying processes of ADU gel using AWD equipment; (5) UO{sub 3} calcination by thermal decomposition of driedADU gel in the air; (6) fabrication of UO{sub 2} kernel by reducing the UO{sub 3} and sintering in the H{sub 2}. In this study, improved KAERI processes for UO{sub 2} kernel preparation were presented. ADU gel washing procedure in AWD processes and the heating mode in sintering process were modified and the internal structures of UO{sub 2} kernels are presented as a result.
Kernel Methods for Machine Learning with Life Science Applications
DEFF Research Database (Denmark)
Abrahamsen, Trine Julie
Kernel methods refer to a family of widely used nonlinear algorithms for machine learning tasks like classification, regression, and feature extraction. By exploiting the so-called kernel trick straightforward extensions of classical linear algorithms are enabled as long as the data only appear...... models to kernel learning, and means for restoring the generalizability in both kernel Principal Component Analysis and the Support Vector Machine are proposed. Viability is proved on a wide range of benchmark machine learning data sets....... as innerproducts in the model formulation. This dissertation presents research on improving the performance of standard kernel methods like kernel Principal Component Analysis and the Support Vector Machine. Moreover, the goal of the thesis has been two-fold. The first part focuses on the use of kernel Principal...
Efficient $\\chi ^{2}$ Kernel Linearization via Random Feature Maps.
Yuan, Xiao-Tong; Wang, Zhenzhen; Deng, Jiankang; Liu, Qingshan
2016-11-01
Explicit feature mapping is an appealing way to linearize additive kernels, such as χ(2) kernel for training large-scale support vector machines (SVMs). Although accurate in approximation, feature mapping could pose computational challenges in high-dimensional settings as it expands the original features to a higher dimensional space. To handle this issue in the context of χ(2) kernel SVMs learning, we introduce a simple yet efficient method to approximately linearize χ(2) kernel through random feature maps. The main idea is to use sparse random projection to reduce the dimensionality of feature maps while preserving their approximation capability to the original kernel. We provide approximation error bound for the proposed method. Furthermore, we extend our method to χ(2) multiple kernel SVMs learning. Extensive experiments on large-scale image classification tasks confirm that the proposed approach is able to significantly speed up the training process of the χ(2) kernel SVMs at almost no cost of testing accuracy.
Multiple Kernel Learning in Fisher Discriminant Analysis for Face Recognition
Directory of Open Access Journals (Sweden)
Xiao-Zhang Liu
2013-02-01
Full Text Available Recent applications and developments based on support vector machines (SVMs have shown that using multiple kernels instead of a single one can enhance classifier performance. However, there are few reports on performance of the kernel‐based Fisher discriminant analysis (kernel‐based FDA method with multiple kernels. This paper proposes a multiple kernel construction method for kernel‐based FDA. The constructed kernel is a linear combination of several base kernels with a constraint on their weights. By maximizing the margin maximization criterion (MMC, we present an iterative scheme for weight optimization. The experiments on the FERET and CMU PIE face databases show that, our multiple kernel Fisher discriminant analysis (MKFD achieves high recognition performance, compared with single‐kernel‐based FDA. The experiments also show that the constructed kernel relaxes parameter selection for kernel‐based FDA to some extent.
A Novel Framework for Learning Geometry-Aware Kernels.
Pan, Binbin; Chen, Wen-Sheng; Xu, Chen; Chen, Bo
2016-05-01
The data from real world usually have nonlinear geometric structure, which are often assumed to lie on or close to a low-dimensional manifold in a high-dimensional space. How to detect this nonlinear geometric structure of the data is important for the learning algorithms. Recently, there has been a surge of interest in utilizing kernels to exploit the manifold structure of the data. Such kernels are called geometry-aware kernels and are widely used in the machine learning algorithms. The performance of these algorithms critically relies on the choice of the geometry-aware kernels. Intuitively, a good geometry-aware kernel should utilize additional information other than the geometric information. In many applications, it is required to compute the out-of-sample data directly. However, most of the geometry-aware kernel methods are restricted to the available data given beforehand, with no straightforward extension for out-of-sample data. In this paper, we propose a framework for more general geometry-aware kernel learning. The proposed framework integrates multiple sources of information and enables us to develop flexible and effective kernel matrices. Then, we theoretically show how the learned kernel matrices are extended to the corresponding kernel functions, in which the out-of-sample data can be computed directly. Under our framework, a novel family of geometry-aware kernels is developed. Especially, some existing geometry-aware kernels can be viewed as instances of our framework. The performance of the kernels is evaluated on dimensionality reduction, classification, and clustering tasks. The empirical results show that our kernels significantly improve the performance.
Kernel Density Estimation, Kernel Methods, and Fast Learning in Large Data Sets.
Wang, Shitong; Wang, Jun; Chung, Fu-lai
2014-01-01
Kernel methods such as the standard support vector machine and support vector regression trainings take O(N(3)) time and O(N(2)) space complexities in their naïve implementations, where N is the training set size. It is thus computationally infeasible in applying them to large data sets, and a replacement of the naive method for finding the quadratic programming (QP) solutions is highly desirable. By observing that many kernel methods can be linked up with kernel density estimate (KDE) which can be efficiently implemented by some approximation techniques, a new learning method called fast KDE (FastKDE) is proposed to scale up kernel methods. It is based on establishing a connection between KDE and the QP problems formulated for kernel methods using an entropy-based integrated-squared-error criterion. As a result, FastKDE approximation methods can be applied to solve these QP problems. In this paper, the latest advance in fast data reduction via KDE is exploited. With just a simple sampling strategy, the resulted FastKDE method can be used to scale up various kernel methods with a theoretical guarantee that their performance does not degrade a lot. It has a time complexity of O(m(3)) where m is the number of the data points sampled from the training set. Experiments on different benchmarking data sets demonstrate that the proposed method has comparable performance with the state-of-art method and it is effective for a wide range of kernel methods to achieve fast learning in large data sets.
Controllability of the Heat Equation with a Control Acting on a Measurable Set
Institute of Scientific and Technical Information of China (English)
Hang YU
2012-01-01
The paper deals with the controllability of a heat equation.It is well-known that the heat equation yt - △y =uxE in (0,T) × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T ＞ 0 and any open nonempty subset E of Ω.In this note,the author studies the case that E is an arbitrary measurable set with positive measure.
Fourth-Order Deferred Correction Scheme for Solving Heat Conduction Problem
Directory of Open Access Journals (Sweden)
D. Yambangwai
2013-01-01
Full Text Available A deferred correction method is utilized to increase the order of spatial accuracy of the Crank-Nicolson scheme for the numerical solution of the one-dimensional heat equation. The fourth-order methods proposed are the easier development and can be solved by using Thomas algorithms. The stability analysis and numerical experiments have been limited to one-dimensional heat-conducting problems with Dirichlet boundary conditions and initial data.
Wilson Dslash Kernel From Lattice QCD Optimization
Energy Technology Data Exchange (ETDEWEB)
Joo, Balint [Jefferson Lab, Newport News, VA; Smelyanskiy, Mikhail [Parallel Computing Lab, Intel Corporation, California, USA; Kalamkar, Dhiraj D. [Parallel Computing Lab, Intel Corporation, India; Vaidyanathan, Karthikeyan [Parallel Computing Lab, Intel Corporation, India
2015-07-01
Lattice Quantum Chromodynamics (LQCD) is a numerical technique used for calculations in Theoretical Nuclear and High Energy Physics. LQCD is traditionally one of the first applications ported to many new high performance computing architectures and indeed LQCD practitioners have been known to design and build custom LQCD computers. Lattice QCD kernels are frequently used as benchmarks (e.g. 168.wupwise in the SPEC suite) and are generally well understood, and as such are ideal to illustrate several optimization techniques. In this chapter we will detail our work in optimizing the Wilson-Dslash kernels for Intel Xeon Phi, however, as we will show the technique gives excellent performance on regular Xeon Architecture as well.
Learning Potential Energy Landscapes using Graph Kernels
Ferré, G; Barros, K
2016-01-01
Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab-initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. We show on a standard benchmark that our Graph Approximated Energy (GRAPE) method is competitive with state of the art kernel m...
Viability Kernel for Ecosystem Management Models
Anaya, Eladio Ocana; Oliveros--Ramos, Ricardo; Tam, Jorge
2009-01-01
We consider sustainable management issues formulated within the framework of control theory. The problem is one of controlling a discrete--time dynamical system (e.g. population model) in the presence of state and control constraints, representing conflicting economic and ecological issues for instance. The viability kernel is known to play a basic role for the analysis of such problems and the design of viable control feedbacks, but its computation is not an easy task in general. We study the viability of nonlinear generic ecosystem models under preservation and production constraints. Under simple conditions on the growth rates at the boundary constraints, we provide an explicit description of the viability kernel. A numerical illustration is given for the hake--anchovy couple in the Peruvian upwelling ecosystem.
A kernel version of spatial factor analysis
DEFF Research Database (Denmark)
Nielsen, Allan Aasbjerg
2009-01-01
of PCA and related techniques. An interesting dilemma in reduction of dimensionality of data is the desire to obtain simplicity for better understanding, visualization and interpretation of the data on the one hand, and the desire to retain sufficient detail for adequate representation on the other hand......Based on work by Pearson in 1901, Hotelling in 1933 introduced principal component analysis (PCA). PCA is often used for general feature generation and linear orthogonalization or compression by dimensionality reduction of correlated multivariate data, see Jolliffe for a comprehensive description...... 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...
Quark-hadron duality: pinched kernel approch
Dominguez, C A; Schilcher, K; Spiesberger, H
2016-01-01
Hadronic spectral functions measured by the ALEPH collaboration in the vector and axial-vector channels are used to study potential quark-hadron duality violations (DV). This is done entirely in the framework of pinched kernel finite energy sum rules (FESR), i.e. in a model independent fashion. The kinematical range of the ALEPH data is effectively extended up to $s = 10\\; {\\mbox{GeV}^2}$ by using an appropriate kernel, and assuming that in this region the spectral functions are given by perturbative QCD. Support for this assumption is obtained by using $e^+ e^-$ annihilation data in the vector channel. Results in both channels show a good saturation of the pinched FESR, without further need of explicit models of DV.
Analog Forecasting with Dynamics-Adapted Kernels
Zhao, Zhizhen
2014-01-01
Analog forecasting is a non-parametric 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 state-space reconstruction for dynamical systems and kernel methods developed in harmonic analysis and machine learning. The first improvement is to augment the dimension of the initial data using Takens' delay-coordinate maps to recover information in the initial data lost through partial observations. Then, instead of using Euclidean distances between the states, weighted ensembles of analogs are constructed according to similarity kernels in delay-coordinate space, featuring an explicit dependence on the dynamical vector field generating the data. The eigenvalues and eigenfunctions ...
Eighth-Order Compact Finite Difference Scheme for 1D Heat Conduction Equation
Directory of Open Access Journals (Sweden)
Asma Yosaf
2016-01-01
Full Text Available The purpose of this paper is to develop a high-order compact finite difference method for solving one-dimensional (1D heat conduction equation with Dirichlet and Neumann boundary conditions, respectively. A parameter is used for the direct implementation of Dirichlet and Neumann boundary conditions. The introduced parameter adjusts the position of the neighboring nodes very next to the boundary. In the case of Dirichlet boundary condition, we developed eighth-order compact finite difference method for the entire domain and fourth-order accurate proposal is presented for the Neumann boundary conditions. In the case of Dirichlet boundary conditions, the introduced parameter behaves like a free parameter and could take any value from its defined domain but for the Neumann boundary condition we obtained a particular value of the parameter. In both proposed compact finite difference methods, the order of accuracy is the same for all nodes. The time discretization is performed by using Crank-Nicholson finite difference method. The unconditional convergence of the proposed methods is presented. Finally, a set of 1D heat conduction equations is solved to show the validity and accuracy of our proposed methods.
Searching and Indexing Genomic Databases via Kernelization
Directory of Open Access Journals (Sweden)
Travis eGagie
2015-02-01
Full Text Available The rapid advance of DNA sequencing technologies has yielded databases of thousands of genomes. To search and index these databases effectively, it is important that we take advantage of the similarity between those genomes. Several authors have recently suggested searching or indexing only one reference genome and the parts of the other genomes where they differ. In this paper we survey the twenty-year history of this idea and discuss its relation to kernelization in parameterized complexity.
Kernel based subspace projection of hyperspectral images
DEFF Research Database (Denmark)
Larsen, Rasmus; Nielsen, Allan Aasbjerg; Arngren, Morten
In hyperspectral image analysis an exploratory approach to analyse the image data is to conduct subspace projections. As linear projections often fail to capture the underlying structure of the data, we present kernel based subspace projections of PCA and Maximum Autocorrelation Factors (MAF). Th......). The MAF projection exploits the fact that interesting phenomena in images typically exhibit spatial autocorrelation. The analysis is based on nearinfrared hyperspectral images of maize grains demonstrating the superiority of the kernelbased MAF method....
Wheat kernel dimensions: how do they contribute to kernel weight at an individual QTL level?
Indian Academy of Sciences (India)
Fa Cui; Anming Ding; Jun Li; Chunhua Zhao; Xingfeng Li; Deshun Feng; Xiuqin Wang; Lin Wang; Jurong Gao; Honggang Wang
2011-12-01
Kernel dimensions (KD) contribute greatly to thousand-kernel weight (TKW) in wheat. In the present study, quantitative trait loci (QTL) for TKW, kernel length (KL), kernel width (KW) and kernel diameter ratio (KDR) were detected by both conditional and unconditional QTL mapping methods. Two related F8:9 recombinant inbred line (RIL) populations, comprising 485 and 229 lines, respectively, were used in this study, and the trait phenotypes were evaluated in four environments. Unconditional QTL mapping analysis detected 77 additive QTL for four traits in two populations. Of these, 24 QTL were verified in at least three trials, and five of them were major QTL, thus being of great value for marker assisted selection in breeding programmes. Conditional QTL mapping analysis, compared with unconditional QTL mapping analysis, resulted in reduction in the number of QTL for TKW due to the elimination of TKW variations caused by its conditional traits; based on which we first dissected genetic control system involved in the synthetic process between TKW and KD at an individual QTL level. Results indicated that, at the QTL level, KW had the strongest influence on TKW, followed by KL, and KDR had the lowest level contribution to TKW. In addition, the present study proved that it is not all-inclusive to determine genetic relationships of a pairwise QTL for two related/causal traits based on whether they were co-located. Thus, conditional QTL mapping method should be used to evaluate possible genetic relationships of two related/causal traits.
Absolute Orientation Based on Distance Kernel Functions
Directory of Open Access Journals (Sweden)
Yanbiao Sun
2016-03-01
Full Text Available The classical absolute orientation method is capable of transforming tie points (TPs from a local coordinate system to a global (geodetic coordinate system. The method is based only on a unique set of similarity transformation parameters estimated by minimizing the total difference between all ground control points (GCPs and the fitted points. Nevertheless, it often yields a transformation with poor accuracy, especially in large-scale study cases. To address this problem, this study proposes a novel absolute orientation method based on distance kernel functions, in which various sets of similarity transformation parameters instead of only one set are calculated. When estimating the similarity transformation parameters for TPs using the iterative solution of a non-linear least squares problem, we assigned larger weighting matrices for the GCPs for which the distances from the point are short. The weighting matrices can be evaluated using the distance kernel function as a function of the distances between the GCPs and the TPs. Furthermore, we used the exponential function and the Gaussian function to describe distance kernel functions in this study. To validate and verify the proposed method, six synthetic and two real datasets were tested. The accuracy was significantly improved by the proposed method when compared to the classical method, although a higher computational complexity is experienced.
Physicochemical Properties of Palm Kernel Oil
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Amira P. Olaniyi
2014-09-01
Full Text Available Physicochemical analyses were carried out on palm kernel oil (Adin and the following results were obtained: Saponification value; 280.5±56.1 mgKOH/g, acid value; 2.7±0.3 mg KOH/g, Free Fatty Acid (FFA; 1.35±0.15 KOH/g, ester value; 277.8±56.4 mgKOH/g, peroxide value; 14.3±0.8 mEq/kg; iodine value; 15.86±4.02 mgKOH/g, Specific Gravity (S.G value; 0.904, refractive index; 1.412 and inorganic materials; 1.05%. Its odour and colour were heavy burnt smell and burnt brown, respectively. These values were compared with those obtained for groundnut and coconut oils. It was found that the physico-chemical properties of palm kernel oil are comparable to those of groundnut and coconut oils except for the peroxide value (i.e., 14.3±0.8 mEq which was not detectable in groundnut and coconut oils. Also the odour of both groundnut and coconut oils were pleasant while that of the palm kernel oil was not as pleasant (i.e., heavy burnt smell.
Convolution kernels for multi-wavelength imaging
Boucaud, Alexandre; Abergel, Alain; Orieux, François; Dole, Hervé; Hadj-Youcef, Mohamed Amine
2016-01-01
Astrophysical images issued from different instruments and/or spectral bands often require to be processed together, either for fitting or comparison purposes. However each image is affected by an instrumental response, also known as PSF, that depends on the characteristics of the instrument as well as the wavelength and the observing strategy. Given the knowledge of the PSF in each band, a straightforward way of processing images is to homogenise them all to a target PSF using convolution kernels, so that they appear as if they had been acquired by the same instrument. We propose an algorithm that generates such PSF-matching kernels, based on Wiener filtering with a tunable regularisation parameter. This method ensures all anisotropic features in the PSFs to be taken into account. We compare our method to existing procedures using measured Herschel/PACS and SPIRE PSFs and simulated JWST/MIRI PSFs. Significant gains up to two orders of magnitude are obtained with respect to the use of kernels computed assumin...
A Fast Reduced Kernel Extreme Learning Machine.
Deng, Wan-Yu; Ong, Yew-Soon; Zheng, Qing-Hua
2016-04-01
In this paper, we present a fast and accurate kernel-based supervised algorithm referred to as the Reduced Kernel Extreme Learning Machine (RKELM). In contrast to the work on Support Vector Machine (SVM) or Least Square SVM (LS-SVM), which identifies the support vectors or weight vectors iteratively, the proposed RKELM randomly selects a subset of the available data samples as support vectors (or mapping samples). By avoiding the iterative steps of SVM, significant cost savings in the training process can be readily attained, especially on Big datasets. RKELM is established based on the rigorous proof of universal learning involving reduced kernel-based SLFN. In particular, we prove that RKELM can approximate any nonlinear functions accurately under the condition of support vectors sufficiency. Experimental results on a wide variety of real world small instance size and large instance size applications in the context of binary classification, multi-class problem and regression are then reported to show that RKELM can perform at competitive level of generalized performance as the SVM/LS-SVM at only a fraction of the computational effort incurred.
Kernel methods for phenotyping complex plant architecture.
Kawamura, Koji; Hibrand-Saint Oyant, Laurence; Foucher, Fabrice; Thouroude, Tatiana; Loustau, Sébastien
2014-02-07
The Quantitative Trait Loci (QTL) mapping of plant architecture is a critical step for understanding the genetic determinism of plant architecture. Previous studies adopted simple measurements, such as plant-height, stem-diameter and branching-intensity for QTL mapping of plant architecture. Many of these quantitative traits were generally correlated to each other, which give rise to statistical problem in the detection of QTL. We aim to test the applicability of kernel methods to phenotyping inflorescence architecture and its QTL mapping. We first test Kernel Principal Component Analysis (KPCA) and Support Vector Machines (SVM) over an artificial dataset of simulated inflorescences with different types of flower distribution, which is coded as a sequence of flower-number per node along a shoot. The ability of discriminating the different inflorescence types by SVM and KPCA is illustrated. We then apply the KPCA representation to the real dataset of rose inflorescence shoots (n=1460) obtained from a 98 F1 hybrid mapping population. We find kernel principal components with high heritability (>0.7), and the QTL analysis identifies a new QTL, which was not detected by a trait-by-trait analysis of simple architectural measurements. The main tools developed in this paper could be use to tackle the general problem of QTL mapping of complex (sequences, 3D structure, graphs) phenotypic traits.
Laguerre Kernels –Based SVM for Image Classification
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Ashraf Afifi
2014-01-01
Full Text Available Support vector machines (SVMs have been promising methods for classification and regression analysis because of their solid mathematical foundations which convey several salient properties that other methods hardly provide. However the performance of SVMs is very sensitive to how the kernel function is selected, the challenge is to choose the kernel function for accurate data classification. In this paper, we introduce a set of new kernel functions derived from the generalized Laguerre polynomials. The proposed kernels could improve the classification accuracy of SVMs for both linear and nonlinear data sets. The proposed kernel functions satisfy Mercer’s condition and orthogonally properties which are important and useful in some applications when the support vector number is needed as in feature selection. The performance of the generalized Laguerre kernels is evaluated in comparison with the existing kernels. It was found that the choice of the kernel function, and the values of the parameters for that kernel are critical for a given amount of data. The proposed kernels give good classification accuracy in nearly all the data sets, especially those of high dimensions.
Identification of Fusarium damaged wheat kernels using image analysis
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Ondřej Jirsa
2011-01-01
Full Text Available Visual evaluation of kernels damaged by Fusarium spp. pathogens is labour intensive and due to a subjective approach, it can lead to inconsistencies. Digital imaging technology combined with appropriate statistical methods can provide much faster and more accurate evaluation of the visually scabby kernels proportion. The aim of the present study was to develop a discrimination model to identify wheat kernels infected by Fusarium spp. using digital image analysis and statistical methods. Winter wheat kernels from field experiments were evaluated visually as healthy or damaged. Deoxynivalenol (DON content was determined in individual kernels using an ELISA method. Images of individual kernels were produced using a digital camera on dark background. Colour and shape descriptors were obtained by image analysis from the area representing the kernel. Healthy and damaged kernels differed significantly in DON content and kernel weight. Various combinations of individual shape and colour descriptors were examined during the development of the model using linear discriminant analysis. In addition to basic descriptors of the RGB colour model (red, green, blue, very good classification was also obtained using hue from the HSL colour model (hue, saturation, luminance. The accuracy of classification using the developed discrimination model based on RGBH descriptors was 85 %. The shape descriptors themselves were not specific enough to distinguish individual kernels.
Implementing Kernel Methods Incrementally by Incremental Nonlinear Projection Trick.
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.
Image quality of mixed convolution kernel in thoracic computed tomography.
Neubauer, Jakob; Spira, Eva Maria; Strube, Juliane; Langer, Mathias; Voss, Christian; Kotter, Elmar
2016-11-01
The mixed convolution kernel alters his properties geographically according to the depicted organ structure, especially for the lung. Therefore, we compared the image quality of the mixed convolution kernel to standard soft and hard kernel reconstructions for different organ structures in thoracic computed tomography (CT) images.Our Ethics Committee approved this prospective study. In total, 31 patients who underwent contrast-enhanced thoracic CT studies were included after informed consent. Axial reconstructions were performed with hard, soft, and mixed convolution kernel. Three independent and blinded observers rated the image quality according to the European Guidelines for Quality Criteria of Thoracic CT for 13 organ structures. The observers rated the depiction of the structures in all reconstructions on a 5-point Likert scale. Statistical analysis was performed with the Friedman Test and post hoc analysis with the Wilcoxon rank-sum test.Compared to the soft convolution kernel, the mixed convolution kernel was rated with a higher image quality for lung parenchyma, segmental bronchi, and the border between the pleura and the thoracic wall (P kernel, the mixed convolution kernel was rated with a higher image quality for aorta, anterior mediastinal structures, paratracheal soft tissue, hilar lymph nodes, esophagus, pleuromediastinal border, large and medium sized pulmonary vessels and abdomen (P kernel cannot fully substitute the standard CT reconstructions. Hard and soft convolution kernel reconstructions still seem to be mandatory for thoracic CT.
A Kernel-free Boundary Integral Method for Elliptic Boundary Value Problems ⋆
Ying, Wenjun; Henriquez, Craig S.
2013-01-01
This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green's functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GM-RES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong. PMID:23519600
Distributional asymptotic expansions of spectral functions and of the associated Green kernels
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R. Estrada
1999-03-01
Full Text Available Asymptotic expansions of Green functions and spectral densities associated with partial differential operators are widely applied in quantum field theory and elsewhere. The mathematical properties of these expansions can be clarified and more precisely determined by means of tools from distribution theory and summability theory. (These are the same, insofar as recently the classic Cesaro--Riesz theory of summability of series and integrals has been given a distributional interpretation. When applied to the spectral analysis of Green functions (which are then to be expanded as series in a parameter, usually the time,these methods show: (1 The ``local'' or ``global'' dependence of the expansion coefficients on the background geometry, etc., is determined by the regularity of the asymptotic expansion of the integrand at the origin (in ``frequency space''; this marks the difference between a heat kernel and a Wightman two-point function, for instance. (2 The behavior of the integrand at infinity determines whether the expansion of the Green function is genuinely asymptotic in the literal, pointwise sense, or is merely valid in a distributional (Cesaro-averaged sense; this is the difference between the heat kernel and the Schrodinger kernel. (3 The high-frequency expansion of the spectral density itself is local in a distributional sense (but not pointwise. These observations make rigorous sense out of calculations in the physics literature that are sometimes dismissed as merely formal.
Reimer, Ashton S.; Cheviakov, Alexei F.
2013-03-01
A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.
CHARACTERIZATION OF BIO-OIL FROM PALM KERNEL SHELL PYROLYSIS
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R. Ahmad
2014-12-01
Full Text Available Pyrolysis of palm kernel shell in a fixed-bed reactor was studied in this paper. The objectives were to investigate the effect of pyrolysis temperature and particle size on the products yield and to characterize the bio-oil product. In order to get the optimum pyrolysis parameters on bio-oil yield, temperatures of 350, 400, 450, 500 and 550 °C and particle sizes of 212–300 µm, 300–600 µm, 600µm–1.18 mm and 1.18–2.36 mm under a heating rate of 50 °C min-1 were investigated. The maximum bio-oil yield was 38.40% at 450 °C with a heating rate of 50 °C min-1 and a nitrogen sweep gas flow rate of 50 ml min-1. The bio-oil products were analysed by Fourier transform infra-red spectroscopy (FTIR and gas chromatography–mass spectroscopy (GCMS. The FTIR analysis showed that the bio-oil was dominated by oxygenated species. The phenol, phenol, 2-methoxy- and furfural that were identified by GCMS analysis are highly suitable for extraction from the bio-oil as value-added chemicals. The highly oxygenated oils need to be upgraded in order to be used in other applications such as transportation fuels.
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Muzhir Shaban Al-Ani
2011-05-01
Full Text Available Detecting faces across multiple views is more challenging than in a frontal view. To address this problem,an efficient approach is presented in this paper using a kernel machine based approach for learning suchnonlinear mappings to provide effective view-based representation for multi-view face detection. In thispaper Kernel Principal Component Analysis (KPCA is used to project data into the view-subspaces thencomputed as view-based features. Multi-view face detection is performed by classifying each input imageinto face or non-face class, by using a two class Kernel Support Vector Classifier (KSVC. Experimentalresults demonstrate successful face detection over a wide range of facial variation in color, illuminationconditions, position, scale, orientation, 3D pose, and expression in images from several photo collections.
Lee, Yi-Hsuan; von Davier, Alina A.
2008-01-01
The kernel equating method (von Davier, Holland, & Thayer, 2004) is based on a flexible family of equipercentile-like equating functions that use a Gaussian kernel to continuize the discrete score distributions. While the classical equipercentile, or percentile-rank, equating method carries out the continuization step by linear interpolation,…
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Michael S. Milgram
2013-01-01
Full Text Available Contour integral representations of Riemann's Zeta function and Dirichlet's Eta (alternating Zeta function are presented and investigated. These representations flow naturally from methods developed in the 1800s, but somehow they do not appear in the standard reference summaries, textbooks, or literature. Using these representations as a basis, alternate derivations of known series and integral representations for the Zeta and Eta function are obtained on a unified basis that differs from the textbook approach, and results are developed that appear to be new.
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Zhiren Jin
2008-02-01
Full Text Available We prove growth rate estimates and existence of solutions to Dirichlet problems for prescribed mean curvature equation on unbounded domains inside the complement of a cone or a parabola like region in $mathbb{R}^n$ ($ngeq 2$. The existence results are proved using a modified Perron's method by which a subsolution is a solution to the minimal surface equation, while the role played by a supersolution is replaced by estimates on the uniform $C^{0}$ bounds on the liftings of subfunctions on compact sets.
März, Thomas
2010-01-01
Here we study the Dirichlet problem for first order linear and quasi-linear hyperbolic PDEs on a simply connected bounded domain of $\\R^2$, where the domain has an interior outflow set and a mere inflow boundary. By means of a Lyapunov function we show the existence of a unique solution in the space of functions of bounded variation and its continuous dependence on all the data of the linear problem. Finally, we conclude the existence of a solution to the quasi-linear case by utilizing the Schauder fixed point theorem. This type of problems considered here appears in applications such as transport based image inpainting.
The Compactness of Toeplitz Operators on Dirichlet Spaces%Dirchlet空间上ToePlitz算子的紧性
Institute of Scientific and Technical Information of China (English)
曹广福; 朱渌涛
2001-01-01
本文给出了Dirichlet空间上Toelpitz算子为紧算子的充要条件.并证明具有C1-符号的Toeplitz算子为紧算子当且仅当它为零算子，当且仅当符号的边值为零.%In the present paper, an iff condition on the compactness of Toeplitz operators on Dirichlet spaces is obtained, in addition, it is proved that a Toeplitz operator with C1- symbol is compact if and only if it equals zero if and only if the boundary value of its symbol equals zero.
Hyponormality of Toeplitz Operators on the Dirichlet Space%Dirichlet空间上Toeplitz算子的亚正规性
Institute of Scientific and Technical Information of China (English)
陈丽琼; 徐辉明
2012-01-01
In this paper, we study tile hyponormality of Toeplitz operators on the Dirich- let space of the unit disk, and give some necessary and sufficient conditions for the hy- ponormality of Toeplitz operators with a class of continuous symbols on Dirichlet space.%讨论单位圆盘中Dirichlet空间上Toeplitz算子的性质，给出了Dirichiet空间上以一类连续函数为符号的Toeplitz算子满足亚正规性的充分必要条件．