Using Peano Curves to Construct Laplacians on Fractals
Molitor, Denali; Ott, Nadia; Strichartz, Robert
2015-12-01
We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.
Directory of Open Access Journals (Sweden)
Jun Zhang
Full Text Available Identification of a small panel of population structure informative markers can reduce genotyping cost and is useful in various applications, such as ancestry inference in association mapping, forensics and evolutionary theory in population genetics. Traditional methods to ascertain ancestral informative markers usually require the prior knowledge of individual ancestry and have difficulty for admixed populations. Recently Principal Components Analysis (PCA has been employed with success to select SNPs which are highly correlated with top significant principal components (PCs without use of individual ancestral information. The approach is also applicable to admixed populations. Here we propose a novel approach based on our recent result on summarizing population structure by graph laplacian eigenfunctions, which differs from PCA in that it is geometric and robust to outliers. Our approach also takes advantage of the priori sparseness of informative markers in the genome. Through simulation of a ring population and the real global population sample HGDP of 650K SNPs genotyped in 940 unrelated individuals, we validate the proposed algorithm at selecting most informative markers, a small fraction of which can recover the similar underlying population structure efficiently. Employing a standard Support Vector Machine (SVM to predict individuals' continental memberships on HGDP dataset of seven continents, we demonstrate that the selected SNPs by our method are more informative but less redundant than those selected by PCA. Our algorithm is a promising tool in genome-wide association studies and population genetics, facilitating the selection of structure informative markers, efficient detection of population substructure and ancestral inference.
The Second Eigenvalue of the p-Laplacian as p Goes to 1
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Enea Parini
2010-01-01
Full Text Available The asymptotic behaviour of the second eigenvalue of the p-Laplacian operator as p goes to 1 is investigated. The limit setting depends only on the geometry of the domain. In the particular case of a planar disc, it is possible to show that the second eigenfunctions are nonradial if p is close enough to 1.
Quadratic Forms and Semiclassical Eigenfunction Hypothesis for Flat Tori
T. Sardari, Naser
2018-03-01
Let Q( X) be any integral primitive positive definite quadratic form in k variables, where {k≥4}, and discriminant D. For any integer n, we give an upper bound on the number of integral solutions of Q( X) = n in terms of n, k, and D. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus {T^d} for {d≥ 5}. This conjecture is motivated by the work of Berry [2,3] on the semiclassical eigenfunction hypothesis.
Eigenvalues of the Laplacian and of the Hecke operators for PSL(2,Z)
International Nuclear Information System (INIS)
Steil, G.
1994-03-01
A new method is described to compute with high accuracy a large number of eigenvalues and eigenfunctions (Maass wave forms) of the Laplacian and of the Hecke operators for the modular group. It relies essentially on the theory of Hecke operators. The results of the computations confirm some important conjectures from number theory, namely Ramanujan-Petersson, Sato-Tate, and the conjecture that the discrete spectrum of the Laplacian be simple. Examples of the numerical data are included as a reference. The algorithm can be generalized to other non-cocompact but cofinite arithmetic groups, like Picard group PSL(2, Z)[i]) and Hecke triangle groups Γ(√2) and Γ(√3). (orig.)
Laplacian embedded regression for scalable manifold regularization.
Chen, Lin; Tsang, Ivor W; Xu, Dong
2012-06-01
Semi-supervised learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical foundations for a large family of SSL algorithms, such as Laplacian support vector machine (LapSVM) and Laplacian regularized least squares (LapRLS). However, most of these algorithms are limited to small scale problems due to the high computational cost of the matrix inversion operation involved in the optimization problem. In this paper, we propose a novel framework called Laplacian embedded regression by introducing an intermediate decision variable into the manifold regularization framework. By using ∈-insensitive loss, we obtain the Laplacian embedded support vector regression (LapESVR) algorithm, which inherits the sparse solution from SVR. Also, we derive Laplacian embedded RLS (LapERLS) corresponding to RLS under the proposed framework. Both LapESVR and LapERLS possess a simpler form of a transformed kernel, which is the summation of the original kernel and a graph kernel that captures the manifold structure. The benefits of the transformed kernel are two-fold: (1) we can deal with the original kernel matrix and the graph Laplacian matrix in the graph kernel separately and (2) if the graph Laplacian matrix is sparse, we only need to perform the inverse operation for a sparse matrix, which is much more efficient when compared with that for a dense one. Inspired by kernel principal component analysis, we further propose to project the introduced decision variable into a subspace spanned by a few eigenvectors of the graph Laplacian matrix in order to better reflect the data manifold, as well as accelerate the calculation of the graph kernel, allowing our methods to efficiently and effectively cope with large scale SSL problems. Extensive experiments on both toy and real
Laplacian eigenmodes for spherical spaces
International Nuclear Information System (INIS)
Lachieze-Rey, M; Caillerie, S
2005-01-01
The possibility that our space is multi-rather than singly-connected has gained renewed interest after the discovery of the low power for the first multipoles of the CMB by WMAP. To test the possibility that our space is a multi-connected spherical space, it is necessary to know the eigenmodes of such spaces. Except for lens and prism space, and to some extent for dodecahedral space, this remains an open problem. Here we derive the eigenmodes of all spherical spaces. For dodecahedral space, the demonstration is much shorter, and the calculation method much simpler than before. We also apply our method to tetrahedric, octahedric and icosahedric spaces. This completes the knowledge of eigenmodes for spherical spaces, and opens the door to new observational tests of the cosmic topology. The vector space V k of the eigenfunctions of the Laplacian on the 3-sphere S 3 , corresponding to the same eigenvalue λ k = -k(k + 2), has dimension (k + 1) 2 . We show that the Wigner functions provide a basis for such a space. Using the properties of the latter, we express the behaviour of a general function of V k under an arbitrary rotation G of SO(4). This offers the possibility of selecting those functions of V k which remain invariant under G. Specifying G to be a generator of the holonomy group of a spherical space X, we give the expression of the vector space V x k of the eigenfunctions of X. We provide a method to calculate the eigenmodes up to an arbitrary order. As an illustration, we give the first modes for the spherical spaces mentioned
Data-driven discovery of Koopman eigenfunctions using deep learning
Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan
2017-11-01
Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems.
Sabeerali, C. T.; Ajayamohan, R. S.; Giannakis, Dimitrios; Majda, Andrew J.
2017-11-01
An improved index for real-time monitoring and forecast verification of monsoon intraseasonal oscillations (MISOs) is introduced using the recently developed nonlinear Laplacian spectral analysis (NLSA) technique. Using NLSA, a hierarchy of Laplace-Beltrami (LB) eigenfunctions are extracted from unfiltered daily rainfall data from the Global Precipitation Climatology Project over the south Asian monsoon region. Two modes representing the full life cycle of the northeastward-propagating boreal summer MISO are identified from the hierarchy of LB eigenfunctions. These modes have a number of advantages over MISO modes extracted via extended empirical orthogonal function analysis including higher memory and predictability, stronger amplitude and higher fractional explained variance over the western Pacific, Western Ghats, and adjoining Arabian Sea regions, and more realistic representation of the regional heat sources over the Indian and Pacific Oceans. Real-time prediction of NLSA-derived MISO indices is demonstrated via extended-range hindcasts based on NCEP Coupled Forecast System version 2 operational output. It is shown that in these hindcasts the NLSA MISO indices remain predictable out to ˜3 weeks.
Symmetries and Laplacians introduction to harmonic analysis, group representations and applications
Gurarie, D
1992-01-01
Designed as an introduction to harmonic analysis and group representations,this book covers a wide range of topics rather than delving deeply into anyparticular one. In the words of H. Weyl ...it is primarily meant forthe humble, who want to learn as new the things set forth therein, rather thanfor the proud and learned who are already familiar with the subject and merelylook for quick and exact information.... The main objective is tointroduce the reader to concepts, ideas, results and techniques that evolvearound symmetry-groups, representations and Laplacians. Morespecifically, the main interest concerns geometrical objects and structures{X}, discrete or continuous, that possess sufficiently large symmetrygroup G, such as regular graphs (Platonic solids), lattices, andsymmetric Riemannian manifolds. All such objects have a natural Laplacian&Dgr;, a linear operator on functions over X, invariant underthe group action. There are many problems associated with Laplacians onX, such as continuous or discrete...
Riesz potential versus fractional Laplacian
Ortigueira, Manuel Duarte; Laleg-Kirati, Taous-Meriem; Machado, José Antó nio Tenreiro
2014-01-01
This paper starts by introducing the Grünwald-Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy-Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.
Riesz potential versus fractional Laplacian
Ortigueira, Manuel Duarte
2014-09-01
This paper starts by introducing the Grünwald-Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy-Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.
Generation of genealogical spin eigenfunctions
International Nuclear Information System (INIS)
Grabenstetter, J.E.; Tseng, T.J.; Grein, F.
1976-01-01
A method is given for generating the Yamanouchi-Kotani genealogical spin eigenfunctions which requires neither storage of eigenfunctions for smaller numbers of electrons, nor summations of large order, nor explicit use of results from the theory of representations of the symmetric group. An explicit formula is given for the coefficients of expansion in terms of spin products
Monte Carlo eigenfunction strategies and uncertainties
International Nuclear Information System (INIS)
Gast, R.C.; Candelore, N.R.
1974-01-01
Comparisons of convergence rates for several possible eigenfunction source strategies led to the selection of the ''straight'' analog of the analytic power method as the source strategy for Monte Carlo eigenfunction calculations. To insure a fair game strategy, the number of histories per iteration increases with increasing iteration number. The estimate of eigenfunction uncertainty is obtained from a modification of a proposal by D. B. MacMillan and involves only estimates of the usual purely statistical component of uncertainty and a serial correlation coefficient of lag one. 14 references. (U.S.)
Super-Laplacians and their symmetries
Energy Technology Data Exchange (ETDEWEB)
Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London, WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,Uppsala, SE-751 20 (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom)
2017-05-22
A super-Laplacian is a set of differential operators in superspace whose highest-dimensional component is given by the spacetime Laplacian. Symmetries of super-Laplacians are given by linear differential operators of arbitrary finite degree and are determined by superconformal Killing tensors. We investigate these in flat superspaces. The differential operators determining the symmetries give rise to algebras which can be identified in many cases with the tensor algebras of the relevant superconformal Lie algebras modulo certain ideals. They have applications to Higher Spin theories.
Super-Laplacians and their symmetries
International Nuclear Information System (INIS)
Howe, P.S.; Lindström, University
2017-01-01
A super-Laplacian is a set of differential operators in superspace whose highest-dimensional component is given by the spacetime Laplacian. Symmetries of super-Laplacians are given by linear differential operators of arbitrary finite degree and are determined by superconformal Killing tensors. We investigate these in flat superspaces. The differential operators determining the symmetries give rise to algebras which can be identified in many cases with the tensor algebras of the relevant superconformal Lie algebras modulo certain ideals. They have applications to Higher Spin theories.
Resolvent kernel for the Kohn Laplacian on Heisenberg groups
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Neur Eddine Askour
2002-07-01
Full Text Available We present a formula that relates the Kohn Laplacian on Heisenberg groups and the magnetic Laplacian. Then we obtain the resolvent kernel for the Kohn Laplacian and find its spectral density. We conclude by obtaining the Green kernel for fractional powers of the Kohn Laplacian.
Successive overrelaxation for laplacian support vector machine.
Qi, Zhiquan; Tian, Yingjie; Shi, Yong
2015-04-01
Semisupervised learning (SSL) problem, which makes use of both a large amount of cheap unlabeled data and a few unlabeled data for training, in the last few years, has attracted amounts of attention in machine learning and data mining. Exploiting the manifold regularization (MR), Belkin et al. proposed a new semisupervised classification algorithm: Laplacian support vector machines (LapSVMs), and have shown the state-of-the-art performance in SSL field. To further improve the LapSVMs, we proposed a fast Laplacian SVM (FLapSVM) solver for classification. Compared with the standard LapSVM, our method has several improved advantages as follows: 1) FLapSVM does not need to deal with the extra matrix and burden the computations related to the variable switching, which make it more suitable for large scale problems; 2) FLapSVM’s dual problem has the same elegant formulation as that of standard SVMs. This means that the kernel trick can be applied directly into the optimization model; and 3) FLapSVM can be effectively solved by successive overrelaxation technology, which converges linearly to a solution and can process very large data sets that need not reside in memory. In practice, combining the strategies of random scheduling of subproblem and two stopping conditions, the computing speed of FLapSVM is rigidly quicker to that of LapSVM and it is a valid alternative to PLapSVM.
Eigenfunctions in chaotic quantum systems
Energy Technology Data Exchange (ETDEWEB)
Baecker, Arnd
2007-07-01
The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)
Eigenfunctions in chaotic quantum systems
International Nuclear Information System (INIS)
Baecker, Arnd
2007-01-01
The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)
Results on Laplacian spectra of graphs with pockets
Directory of Open Access Journals (Sweden)
Sasmita Barik
2018-04-01
Full Text Available Let F , H v be simple connected graphs on n and m + 1 vertices, respectively. Let v be a specified vertex of H v and u 1 , … , u k ∈ F . Then the graph G = G [ F , u 1 , … , u k , H v ] obtained by taking one copy of F and k copies of H v , and then attaching the i th copy of H v to the vertex u i , i = 1 , … , k , at the vertex v of H v (identify u i with the vertex v of the i th copy is called a graph with k pockets. In 2008, Barik raised the question that ‘how far can the Laplacian spectrum of G be described by using the Laplacian spectra of F and H v ?’ and discussed the case when deg ( v = m in H v . In this article, we study the problem for more general cases and describe the Laplacian spectrum. As an application, we construct new nonisomorphic Laplacian cospectral graphs from the known ones. Keywords: Laplacian matrix, Laplacian spectrum, Join, Pockets
Vertical motion and ''scarred'' eigenfunctions in the stadium billiard
International Nuclear Information System (INIS)
Christoffel, K.M.; Brumer, P.
1985-01-01
A subset of pseudoregular eigenfunctions of the classically chaotic stadium billiard is shown to participate strongly in vertically directed motion, supporting the conjectures of McDonald and of Heller regarding periodic orbits and pseudoregular eigenfunctions
Eigenfunction statistics of Wishart Brownian ensembles
International Nuclear Information System (INIS)
Shukla, Pragya
2017-01-01
We theoretically analyze the eigenfunction fluctuation measures for a Hermitian ensemble which appears as an intermediate state of the perturbation of a stationary ensemble by another stationary ensemble of Wishart (Laguerre) type. Similar to the perturbation by a Gaussian stationary ensemble, the measures undergo a diffusive dynamics in terms of the perturbation parameter but the energy-dependence of the fluctuations is different in the two cases. This may have important consequences for the eigenfunction dynamics as well as phase transition studies in many areas of complexity where Brownian ensembles appear. (paper)
Progressive image denoising through hybrid graph Laplacian regularization: a unified framework.
Liu, Xianming; Zhai, Deming; Zhao, Debin; Zhai, Guangtao; Gao, Wen
2014-04-01
Recovering images from corrupted observations is necessary for many real-world applications. In this paper, we propose a unified framework to perform progressive image recovery based on hybrid graph Laplacian regularized regression. We first construct a multiscale representation of the target image by Laplacian pyramid, then progressively recover the degraded image in the scale space from coarse to fine so that the sharp edges and texture can be eventually recovered. On one hand, within each scale, a graph Laplacian regularization model represented by implicit kernel is learned, which simultaneously minimizes the least square error on the measured samples and preserves the geometrical structure of the image data space. In this procedure, the intrinsic manifold structure is explicitly considered using both measured and unmeasured samples, and the nonlocal self-similarity property is utilized as a fruitful resource for abstracting a priori knowledge of the images. On the other hand, between two successive scales, the proposed model is extended to a projected high-dimensional feature space through explicit kernel mapping to describe the interscale correlation, in which the local structure regularity is learned and propagated from coarser to finer scales. In this way, the proposed algorithm gradually recovers more and more image details and edges, which could not been recovered in previous scale. We test our algorithm on one typical image recovery task: impulse noise removal. Experimental results on benchmark test images demonstrate that the proposed method achieves better performance than state-of-the-art algorithms.
Recording of electrohysterogram laplacian potential.
Alberola-Rubio, J; Garcia-Casado, J; Ye-Lin, Y; Prats-Boluda, G; Perales, A
2011-01-01
Preterm birth is the main cause of the neonatal morbidity. Noninvasive recording of uterine myoelectrical activity (electrohysterogram, EHG) could be an alternative to the monitoring of uterine dynamics which are currently based on tocodynamometers (TOCO). The analysis of uterine electromyogram characteristics could help the early diagnosis of preterm birth. Laplacian recordings of other bioelectrical signals have proved to enhance spatial selectivity and to reduce interferences in comparison to monopolar and bipolar surface recordings. The main objective of this paper is to check the feasibility of the noninvasive recording of uterine myoelectrical activity by means of laplacian techniques. Four bipolar EHG signals, discrete laplacian obtained from five monopolar electrodes and the signals picked up by two active concentric-ringed-electrodes were recorded on 5 women with spontaneous or induced labor. Intrauterine pressure (IUP) and TOCO were also simultaneously recorded. To evaluate the uterine contraction detectability of the different noninvasive methods in comparison to IUP the contractions consistency index (CCI) was calculated. Results show that TOCO is less consistent (83%) than most EHG bipolar recording channels (91%, 83%, 87%, and 76%) to detect the uterine contractions identified in IUP. Moreover laplacian EHG signals picked up by ringed-electrodes proved to be as consistent (91%) as the best bipolar recordings in addition to significantly reduce ECG interference.
Semiclassical analysis, Witten Laplacians, and statistical mechanis
Helffer, Bernard
2002-01-01
This important book explains how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin in statistical mechanics. In addition, it compares the Witten Laplacian approach with other techniques, such as the transfer matrix approach and its semiclassical analysis. The author concludes by providing a complete proof of the uniform Log-Sobolev inequality. Contents: Witten Laplacians Approach; Problems in Statistical Mechanics with Discrete Spins; Laplace Integrals and Transfer Operators; S
Dynamical eigenfunction decomposition of turbulent channel flow
Ball, K. S.; Sirovich, L.; Keefe, L. R.
1991-01-01
The results of an analysis of low-Reynolds-number turbulent channel flow based on the Karhunen-Loeve (K-L) expansion are presented. The turbulent flow field is generated by a direct numerical simulation of the Navier-Stokes equations at a Reynolds number Re(tau) = 80 (based on the wall shear velocity and channel half-width). The K-L procedure is then applied to determine the eigenvalues and eigenfunctions for this flow. The random coefficients of the K-L expansion are subsequently found by projecting the numerical flow field onto these eigenfunctions. The resulting expansion captures 90 percent of the turbulent energy with significantly fewer modes than the original trigonometric expansion. The eigenfunctions, which appear either as rolls or shearing motions, possess viscous boundary layers at the walls and are much richer in harmonics than the original basis functions.
Modified Poisson eigenfunctions for electrostatic Bernstein--Greene--Kruskal equilibria
International Nuclear Information System (INIS)
Ling, K.; Abraham-Shrauner, B.
1981-01-01
The stability of an electrostatic Bernstein--Greene--Kruskal equilibrium by Lewis and Symon's general linear stability analysis for spatially inhomogeneous Vlasov equilibria, which employs eigenfunctions and eigenvalues of the equilibrium Liouville operator and the modified Poisson operator, is considered. Analytic expressions for the Liouville eigenfuctions and eigenvalues have already been given; approximate analytic expressions for the dominant eigenfunction and eigenvalue of the modified Poisson operator are given. In the kinetic limit three methods are given: (i) the perturbation method, (ii) the Rayleigh--Ritz method, and (iii) a method based on a Hill's equation. In the fluid limit the Rayleigh--Ritz method is used. The dominant eigenfunction and eigenvalue are then substituted in the dispersion relation and the growth rate calculated. The growth rate agrees very well with previous results found by numerical simulation and by modified Poisson eigenfunctions calculated numerically
Eigenfunction expansion for fractional Brownian motions
International Nuclear Information System (INIS)
Maccone, C.
1981-01-01
The fractional Brownian motions, a class of nonstationary stochastic processes defined as the Riemann-Liouville fractional integral/derivative of the Brownian motion, are studied. It is shown that these processes can be regarded as the output of a suitable linear system of which the input is the white noise. Their autocorrelation is then derived with a study of their standard-deviation curves. Their power spectra are found by resorting to the nonstationary spectral theory. And finally their eigenfunction expansion (Karhunen-Loeve expansion) is obtained: the eigenfunctions are proved to be suitable Bessel functions and the eigenvalues zeros of the Bessel functions. (author)
Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.
Shang, Yilun
2015-01-01
Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.
Stability analysis of the Peregrine solution via squared eigenfunctions
Schober, C. M.; Strawn, M.
2017-10-01
A preliminary numerical investigation involving ensembles of perturbed initial data for the Peregrine soliton (the lowest order rational solution of the nonlinear Schrödinger equation) indicates that it is unstable [16]. In this paper we analytically investigate the linear stability of the Peregrine soliton, appealing to the fact that the Peregrine solution can be viewed as the singular limit of a single mode spatially periodic breathers (SPB). The "squared eigenfunction" connection between the Zakharov-Shabat (Z-S) system and the linearized NLS equation is employed in the stability analysis. Specifically, we determine the eigenfunctions of the Z-S system associated with the Peregrine soliton and construct a family of solutions of the associated linearized NLS (about the Peregrine) in terms of quadratic products of components of the eigenfunctions (i.e., the squared eigenfunction). We find there exist solutions of the linearization that grow exponentially in time, thus showing the Peregrine soliton is linearly unstable.
The Laplacian spectrum of neural networks
de Lange, Siemon C.; de Reus, Marcel A.; van den Heuvel, Martijn P.
2014-01-01
The brain is a complex network of neural interactions, both at the microscopic and macroscopic level. Graph theory is well suited to examine the global network architecture of these neural networks. Many popular graph metrics, however, encode average properties of individual network elements. Complementing these “conventional” graph metrics, the eigenvalue spectrum of the normalized Laplacian describes a network's structure directly at a systems level, without referring to individual nodes or connections. In this paper, the Laplacian spectra of the macroscopic anatomical neuronal networks of the macaque and cat, and the microscopic network of the Caenorhabditis elegans were examined. Consistent with conventional graph metrics, analysis of the Laplacian spectra revealed an integrative community structure in neural brain networks. Extending previous findings of overlap of network attributes across species, similarity of the Laplacian spectra across the cat, macaque and C. elegans neural networks suggests a certain level of consistency in the overall architecture of the anatomical neural networks of these species. Our results further suggest a specific network class for neural networks, distinct from conceptual small-world and scale-free models as well as several empirical networks. PMID:24454286
Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.
Directory of Open Access Journals (Sweden)
Yilun Shang
Full Text Available Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.
Optimized data fusion for K-means Laplacian clustering
Yu, Shi; Liu, Xinhai; Tranchevent, Léon-Charles; Glänzel, Wolfgang; Suykens, Johan A. K.; De Moor, Bart; Moreau, Yves
2011-01-01
Motivation: We propose a novel algorithm to combine multiple kernels and Laplacians for clustering analysis. The new algorithm is formulated on a Rayleigh quotient objective function and is solved as a bi-level alternating minimization procedure. Using the proposed algorithm, the coefficients of kernels and Laplacians can be optimized automatically. Results: Three variants of the algorithm are proposed. The performance is systematically validated on two real-life data fusion applications. The proposed Optimized Kernel Laplacian Clustering (OKLC) algorithms perform significantly better than other methods. Moreover, the coefficients of kernels and Laplacians optimized by OKLC show some correlation with the rank of performance of individual data source. Though in our evaluation the K values are predefined, in practical studies, the optimal cluster number can be consistently estimated from the eigenspectrum of the combined kernel Laplacian matrix. Availability: The MATLAB code of algorithms implemented in this paper is downloadable from http://homes.esat.kuleuven.be/~sistawww/bioi/syu/oklc.html. Contact: shiyu@uchicago.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:20980271
From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport
International Nuclear Information System (INIS)
Ganapol, B.D.
2001-01-01
A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm
Laplacians on discrete and quantum geometries
International Nuclear Information System (INIS)
Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes
2013-01-01
We extend discrete calculus for arbitrary (p-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its combinatorial dual. The precise implementation of geometric volume factors is not unique and, comparing the definition with a circumcentric and a barycentric dual, we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries. (paper)
Eigenfunction statistics on quantum graphs
International Nuclear Information System (INIS)
Gnutzmann, S.; Keating, J.P.; Piotet, F.
2010-01-01
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.
Anderson localization and ballooning eigenfunctions
International Nuclear Information System (INIS)
Dewar, R.L.; Cuthbert, P.
1999-01-01
In solving the ballooning eigenvalue for a low-aspect-ratio stellarator equilibrium it is found that the quasiperiodic behaviour of the equilibrium quantities along a typical magnetic field line can lead to localization of the ballooning eigenfunction (Anderson localization) even in the limit of zero shear. This localization leads to strong field-line dependence of the ballooning eigenvalue, with different branches attaining their maximum growth rates on different field lines. A method is presented of estimating the field-line dependence of various eigenvalue branches by using toroidal and poloidal symmetry operations on the shear-free ballooning equation to generate an approximate set of eigenfunctions. These zero-shear predictions are compared with accurate numerical solutions for the H-1 Heliac and are shown to give a qualitatively correct picture, but finite shear corrections will be needed to give quantitative predictions
International Nuclear Information System (INIS)
Loutsenko, I.; Yermolayeva, O.
2008-06-01
The dynamics of the idealized Laplacian growth (or the Hele-Shaw problem) can be approximated by the Poiselle flow which in appropriate units takes the form of the Darcy law. In this paper we account for the liquid inertia in the Hele-Shaw problem at zero surface tension limit. The Laplace dynamics for the pressure is extended here with one more for the velocity potential for which we call this growth process the Double Laplacian. The application of the conformal mappings technique leads to doubled dynamics for both the conformal map and the complex potential, which is presented in the paper for the radial and the planar growth. We apply the stability analysis and discuss the integrability for the stated problem. (author)
A simple eigenfunction convergence acceleration method for Monte Carlo
International Nuclear Information System (INIS)
Booth, Thomas E.
2011-01-01
Monte Carlo transport codes typically use a power iteration method to obtain the fundamental eigenfunction. The standard convergence rate for the power iteration method is the ratio of the first two eigenvalues, that is, k_2/k_1. Modifications to the power method have accelerated the convergence by explicitly calculating the subdominant eigenfunctions as well as the fundamental. Calculating the subdominant eigenfunctions requires using particles of negative and positive weights and appropriately canceling the negative and positive weight particles. Incorporating both negative weights and a ± weight cancellation requires a significant change to current transport codes. This paper presents an alternative convergence acceleration method that does not require modifying the transport codes to deal with the problems associated with tracking and cancelling particles of ± weights. Instead, only positive weights are used in the acceleration method. (author)
Comparison of bipolar vs. tripolar concentric ring electrode Laplacian estimates.
Besio, W; Aakula, R; Dai, W
2004-01-01
Potentials on the body surface from the heart are of a spatial and temporal function. The 12-lead electrocardiogram (ECG) provides useful global temporal assessment, but it yields limited spatial information due to the smoothing effect caused by the volume conductor. The smoothing complicates identification of multiple simultaneous bioelectrical events. In an attempt to circumvent the smoothing problem, some researchers used a five-point method (FPM) to numerically estimate the analytical solution of the Laplacian with an array of monopolar electrodes. The FPM is generalized to develop a bi-polar concentric ring electrode system. We have developed a new Laplacian ECG sensor, a trielectrode sensor, based on a nine-point method (NPM) numerical approximation of the analytical Laplacian. For a comparison, the NPM, FPM and compact NPM were calculated over a 400 x 400 mesh with 1/400 spacing. Tri and bi-electrode sensors were also simulated and their Laplacian estimates were compared against the analytical Laplacian. We found that tri-electrode sensors have a much-improved accuracy with significantly less relative and maximum errors in estimating the Laplacian operator. Apart from the higher accuracy, our new electrode configuration will allow better localization of the electrical activity of the heart than bi-electrode configurations.
The advantages of the surface Laplacian in brain-computer interface research.
McFarland, Dennis J
2015-09-01
Brain-computer interface (BCI) systems frequently use signal processing methods, such as spatial filtering, to enhance performance. The surface Laplacian can reduce spatial noise and aid in identification of sources. In BCI research, these two functions of the surface Laplacian correspond to prediction accuracy and signal orthogonality. In the present study, an off-line analysis of data from a sensorimotor rhythm-based BCI task dissociated these functions of the surface Laplacian by comparing nearest-neighbor and next-nearest neighbor Laplacian algorithms. The nearest-neighbor Laplacian produced signals that were more orthogonal while the next-nearest Laplacian produced signals that resulted in better accuracy. Both prediction and signal identification are important for BCI research. Better prediction of user's intent produces increased speed and accuracy of communication and control. Signal identification is important for ruling out the possibility of control by artifacts. Identifying the nature of the control signal is relevant both to understanding exactly what is being studied and in terms of usability for individuals with limited motor control. Copyright © 2014 Elsevier B.V. All rights reserved.
Lax-pair operators for squared-sum and squared-difference eigenfunctions
International Nuclear Information System (INIS)
Ichikawa, Yoshihiko; Iino, Kazuhiro.
1984-10-01
Inter-relationship between various representations of the inverse scattering transformation is established by examining eigenfunctions of Lax-pair operators of the sine-Gordon equation and the modified Korteweg-de Vries equation. In particular, it is shown explicitly that there exists Lax-pair operators for the squared-sum and squared-difference eigenfunctions of the Ablowitz-Kaup-Newell-Segur inverse scattering transformation. (author)
Spanning forests and the vector bundle Laplacian
Kenyon, Richard
2011-01-01
The classical matrix-tree theorem relates the determinant of the combinatorial Laplacian on a graph to the number of spanning trees. We generalize this result to Laplacians on one- and two-dimensional vector bundles, giving a combinatorial interpretation of their determinants in terms of so-called cycle rooted spanning forests (CRSFs). We construct natural measures on CRSFs for which the edges form a determinantal process. ¶ This theory gives a natural generalization of the spanning tre...
Quantum Ergodicity and L p Norms of Restrictions of Eigenfunctions
Hezari, Hamid
2018-02-01
We prove an analogue of Sogge's local L p estimates for L p norms of restrictions of eigenfunctions to submanifolds, and use it to show that for quantum ergodic eigenfunctions one can get improvements of the results of Burq-Gérard-Tzvetkov, Hu, and Chen-Sogge. The improvements are logarithmic on negatively curved manifolds (without boundary) and by o(1) for manifolds (with or without boundary) with ergodic geodesic flows. In the case of ergodic billiards with piecewise smooth boundary, we get o(1) improvements on L^∞ estimates of Cauchy data away from a shrinking neighborhood of the corners, and as a result using the methods of Ghosh et al., Jung and Zelditch, Jung and Zelditch, we get that the number of nodal domains of 2-dimensional ergodic billiards tends to infinity as λ \\to ∞. These results work only for a full density subsequence of any given orthonormal basis of eigenfunctions. We also present an extension of the L p estimates of Burq-Gérard-Tzvetkov, Hu, Chen-Sogge for the restrictions of Dirichlet and Neumann eigenfunctions to compact submanifolds of the interior of manifolds with piecewise smooth boundary. This part does not assume ergodicity on the manifolds.
Directory of Open Access Journals (Sweden)
Renato Lemus
2012-11-01
Full Text Available The eigenfunction approach used for discrete symmetries is deduced from the concept of quantum numbers. We show that the irreducible representations (irreps associated with the eigenfunctions are indeed a shorthand notation for the set of eigenvalues of the class operators (character table. The need of a canonical chain of groups to establish a complete set of commuting operators is emphasized. This analysis allows us to establish in natural form the connection between the quantum numbers and the eigenfunction method proposed by J.Q. Chen to obtain symmetry adapted functions. We then proceed to present a friendly version of the eigenfunction method to project functions.
Self-adjointness of the Gaffney Laplacian on Vector Bundles
International Nuclear Information System (INIS)
Bandara, Lashi; Milatovic, Ognjen
2015-01-01
We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator
Self-adjointness of the Gaffney Laplacian on Vector Bundles
Energy Technology Data Exchange (ETDEWEB)
Bandara, Lashi, E-mail: lashi.bandara@chalmers.se [Chalmers University of Technology and University of Gothenburg, Mathematical Sciences (Sweden); Milatovic, Ognjen, E-mail: omilatov@unf.edu [University of North Florida, Department of Mathematics and Statistics (United States)
2015-12-15
We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator.
Logarithmic Laplacian Prior Based Bayesian Inverse Synthetic Aperture Radar Imaging.
Zhang, Shuanghui; Liu, Yongxiang; Li, Xiang; Bi, Guoan
2016-04-28
This paper presents a novel Inverse Synthetic Aperture Radar Imaging (ISAR) algorithm based on a new sparse prior, known as the logarithmic Laplacian prior. The newly proposed logarithmic Laplacian prior has a narrower main lobe with higher tail values than the Laplacian prior, which helps to achieve performance improvement on sparse representation. The logarithmic Laplacian prior is used for ISAR imaging within the Bayesian framework to achieve better focused radar image. In the proposed method of ISAR imaging, the phase errors are jointly estimated based on the minimum entropy criterion to accomplish autofocusing. The maximum a posterior (MAP) estimation and the maximum likelihood estimation (MLE) are utilized to estimate the model parameters to avoid manually tuning process. Additionally, the fast Fourier Transform (FFT) and Hadamard product are used to minimize the required computational efficiency. Experimental results based on both simulated and measured data validate that the proposed algorithm outperforms the traditional sparse ISAR imaging algorithms in terms of resolution improvement and noise suppression.
Logarithmic Laplacian Prior Based Bayesian Inverse Synthetic Aperture Radar Imaging
Directory of Open Access Journals (Sweden)
Shuanghui Zhang
2016-04-01
Full Text Available This paper presents a novel Inverse Synthetic Aperture Radar Imaging (ISAR algorithm based on a new sparse prior, known as the logarithmic Laplacian prior. The newly proposed logarithmic Laplacian prior has a narrower main lobe with higher tail values than the Laplacian prior, which helps to achieve performance improvement on sparse representation. The logarithmic Laplacian prior is used for ISAR imaging within the Bayesian framework to achieve better focused radar image. In the proposed method of ISAR imaging, the phase errors are jointly estimated based on the minimum entropy criterion to accomplish autofocusing. The maximum a posterior (MAP estimation and the maximum likelihood estimation (MLE are utilized to estimate the model parameters to avoid manually tuning process. Additionally, the fast Fourier Transform (FFT and Hadamard product are used to minimize the required computational efficiency. Experimental results based on both simulated and measured data validate that the proposed algorithm outperforms the traditional sparse ISAR imaging algorithms in terms of resolution improvement and noise suppression.
Lax-pair operators for squared eigenfunctions in the inverse scattering transformations
International Nuclear Information System (INIS)
Iino, Kazuhiro; Ichikawa, Yoshihiko.
1982-05-01
Modification of the algorithm of Chen, Lee and Liu enables us to construct alternative Lax-pair operators for the Korteweg-de Vries equation and the modified Korteweg-de Vries equation. These Lax-pair operators stand as the Lax-pair operators for the squared eigenfunction and the sum of squared eigenfunctions of the Ablowitz-Kaup-Newell-Segur inverse scattering transformation for these celebrated nonlinear evolution equations. (author)
Eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide
International Nuclear Information System (INIS)
Derguzov, V.I.
1986-01-01
One proves the existence of the eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide. One gives a normalization of the eigenfunctions of the continuous spectrum relative to an indefinite inner product. One defines the concept of the genus of the multipliers of a Hamiltonian equation, corresponding to the continuous spectrum of the optical waveguide
Eigenfunction expansions and scattering theory in rigged Hilbert spaces
Energy Technology Data Exchange (ETDEWEB)
Gomez-Cubillo, F [Dpt. de Analisis Matematico, Universidad de Valladolid. Facultad de Ciencias, 47011 Valladolid (Spain)], E-mail: fgcubill@am.uva.es
2008-08-15
The work reviews some mathematical aspects of spectral properties, eigenfunction expansions and scattering theory in rigged Hilbert spaces, laying emphasis on Lippmann-Schwinger equations and Schroedinger operators.
Desrosiers, P; Mathieu, P; Desrosiers, Patrick; Lapointe, Luc; Mathieu, Pierre
2003-01-01
We present two constructions of the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement. These eigenfunctions are the superspace extension of the generalized Hermite (or Hi-Jack) polynomials. The conserved quantities of the rational supersymmetric model are first related to their trigonometric relatives through a similarity transformation. This leads to a simple expression for the generalized Hermite superpolynomials as a differential operator acting on the corresponding Jack superpolynomials. The second construction relies on the action of the Hamiltonian on the supermonomial basis. This translates into determinantal expressions for the Hamiltonian's eigenfunctions. As an aside, the maximal superintegrability of the supersymmetric rational Calogero-Moser-Sutherland model is demonstrated.
Improving the accuracy of Laplacian estimation with novel multipolar concentric ring electrodes
Ding, Quan; Besio, Walter G.
2015-01-01
Conventional electroencephalography with disc electrodes has major drawbacks including poor spatial resolution, selectivity and low signal-to-noise ratio that are critically limiting its use. Concentric ring electrodes, consisting of several elements including the central disc and a number of concentric rings, are a promising alternative with potential to improve all of the aforementioned aspects significantly. In our previous work, the tripolar concentric ring electrode was successfully used in a wide range of applications demonstrating its superiority to conventional disc electrode, in particular, in accuracy of Laplacian estimation. This paper takes the next step toward further improving the Laplacian estimation with novel multipolar concentric ring electrodes by completing and validating a general approach to estimation of the Laplacian for an (n + 1)-polar electrode with n rings using the (4n + 1)-point method for n ≥ 2 that allows cancellation of all the truncation terms up to the order of 2n. An explicit formula based on inversion of a square Vandermonde matrix is derived to make computation of multipolar Laplacian more efficient. To confirm the analytic result of the accuracy of Laplacian estimate increasing with the increase of n and to assess the significance of this gain in accuracy for practical applications finite element method model analysis has been performed. Multipolar concentric ring electrode configurations with n ranging from 1 ring (bipolar electrode configuration) to 6 rings (septapolar electrode configuration) were directly compared and obtained results suggest the significance of the increase in Laplacian accuracy caused by increase of n. PMID:26693200
International Nuclear Information System (INIS)
Rabinovich, Vladimir S; Roch, Steffen
2009-01-01
This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z n which are discrete analogs of the Schroedinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of pseudodifference operators (i.e., pseudodifferential operators on the group Z n with analytic symbols), and the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schroedinger operators on Z n , Dirac operators on Z 3 and square root Klein-Gordon operators on Z n .
Jordan blocks and Gamow-Jordan eigenfunctions associated to a double pole of the S-matrix
International Nuclear Information System (INIS)
Hernandez, E.; Mondragon, A.; Jauregui, A.
2002-01-01
An accidental degeneracy of resonances gives rise to a double pole in the scattering matrix, a double zero in the Jost function and a Jordan chain of length two of generalized Gamow-Jordan eigenfunctions of the radial Schrodinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in bound and resonant energy eigenfunctions plus a continuum of scattering wave functions ol complex wave number. In this bi orthonormal basis, any operator f (H r (l) which is a regular function of the Hamiltonian is represented by a complex matrix which is diagonal except for a Jordan block of rank two. The occurrence of a double pole in the Green's function, as well as the non-exponential time evolution of the Gamow-Jordan generalized eigenfunctions are associated to the Jordan block in the complex energy representation. (Author)
The Graph Laplacian and the Dynamics of Complex Networks
Energy Technology Data Exchange (ETDEWEB)
Thulasidasan, Sunil [Los Alamos National Laboratory
2012-06-11
In this talk, we explore the structure of networks from a spectral graph-theoretic perspective by analyzing the properties of the Laplacian matrix associated with the graph induced by a network. We will see how the eigenvalues of the graph Laplacian relate to the underlying network structure and dynamics and provides insight into a phenomenon frequently observed in real world networks - the emergence of collective behavior from purely local interactions seen in the coordinated motion of animals and phase transitions in biological networks, to name a few.
Computation of mode eigenfunctions in graded-index optical fibers by the propagating beam method
International Nuclear Information System (INIS)
Feit, M.D.; Fleck, J.A. Jr.
1980-01-01
The propagating beam method utilizes discrete Fourier transforms for generating configuration-space solutions to optical waveguide problems without reference to modes. The propagating beam method can also give a complete description of the field in terms of modes by a Fourier analysis with respect to axial distance of the computed fields. Earlier work dealt with the accurate determination of mode propagation constants and group delays. In this paper the method is extended to the computation of mode eigenfunctions. The method is efficient, allowing generation of a large number of eigenfunctions from a single propagation run. Computations for parabolic-index profiles show excellent agreement between analytic and numerically generated eigenfunctions
Optimized Laplacian image sharpening algorithm based on graphic processing unit
Ma, Tinghuai; Li, Lu; Ji, Sai; Wang, Xin; Tian, Yuan; Al-Dhelaan, Abdullah; Al-Rodhaan, Mznah
2014-12-01
In classical Laplacian image sharpening, all pixels are processed one by one, which leads to large amount of computation. Traditional Laplacian sharpening processed on CPU is considerably time-consuming especially for those large pictures. In this paper, we propose a parallel implementation of Laplacian sharpening based on Compute Unified Device Architecture (CUDA), which is a computing platform of Graphic Processing Units (GPU), and analyze the impact of picture size on performance and the relationship between the processing time of between data transfer time and parallel computing time. Further, according to different features of different memory, an improved scheme of our method is developed, which exploits shared memory in GPU instead of global memory and further increases the efficiency. Experimental results prove that two novel algorithms outperform traditional consequentially method based on OpenCV in the aspect of computing speed.
Directory of Open Access Journals (Sweden)
Martin Hallnäs
2007-03-01
Full Text Available We review a recent construction of an explicit analytic series representation for symmetric polynomials which up to a groundstate factor are eigenfunctions of Calogero-Sutherland type models. We also indicate a generalisation of this result to polynomials which give the eigenfunctions of so-called 'deformed' Calogero-Sutherland type models.
Liu, Xiang; Makeyev, Oleksandr; Besio, Walter
2011-01-01
We have simulated a four-layer concentric spherical head model. We calculated the spline and tripolar Laplacian estimates and compared them to the analytical Laplacian on the spherical surface. In the simulations we used five different dipole groups and two electrode configurations. The comparison shows that the tripolar Laplacian has higher correlation coefficient to the analytical Laplacian in the electrode configurations tested (19, standard 10/20 locations and 64 electrodes).
A new formulation for the eigenvalue and the eigenfunction in the perturbation theory
International Nuclear Information System (INIS)
Korek, Mahmoud
1999-01-01
Full text.In infrared transitions, the problem of the ro vibrational eigenvalue and eigenfunction of a diatomic molecule is considered. It is shown that, for the transitions vJ↔v'J' the eigenvalues and the eigenfunctions of the two considered states can be expressed respectively in terms of one variable m (transition number), relating these two states, as E vm =Σ i=o e v (i) m i , Ψ vm =Σ i=0 φ v (i) m i and E v'm =Σ i=0 e v' (i) m i , Ψ v'm =Σ i=0 φ v' (i) m i , where m=[J'(J'+1)-J(J+1)]/2, and the coefficients e v (i) , φ v (i) , e v (i) , and φ v (i) , are given by analytical expressions. This m-representation of the eigenvalues and the eigenfunctions is more advantageous for the calculation of many factors in spectroscopy that are given in terms of m as the line intensities, the wave number of a transition, the Herman-Wallis coefficients,...etc. The numerical application to the ground state of the molecule CO shows that the present formulation provides a simple and accurate method for the calculation of the eigenvalues and the eigenfunctions for the two considered states
Laplacian manifold regularization method for fluorescence molecular tomography
He, Xuelei; Wang, Xiaodong; Yi, Huangjian; Chen, Yanrong; Zhang, Xu; Yu, Jingjing; He, Xiaowei
2017-04-01
Sparse regularization methods have been widely used in fluorescence molecular tomography (FMT) for stable three-dimensional reconstruction. Generally, ℓ1-regularization-based methods allow for utilizing the sparsity nature of the target distribution. However, in addition to sparsity, the spatial structure information should be exploited as well. A joint ℓ1 and Laplacian manifold regularization model is proposed to improve the reconstruction performance, and two algorithms (with and without Barzilai-Borwein strategy) are presented to solve the regularization model. Numerical studies and in vivo experiment demonstrate that the proposed Gradient projection-resolved Laplacian manifold regularization method for the joint model performed better than the comparative algorithm for ℓ1 minimization method in both spatial aggregation and location accuracy.
Ground eigenvalue and eigenfunction of a spin-weighted spheroidal wave equation in low frequencies
Institute of Scientific and Technical Information of China (English)
Tang Wen-Lin; Tian Gui-Hua
2011-01-01
Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.
Solving Graph Laplacian Systems Through Recursive Bisections and Two-Grid Preconditioning
Energy Technology Data Exchange (ETDEWEB)
Ponce, Colin [Cornell Univ., Ithaca, NY (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-02-18
We present a parallelizable direct method for computing the solution to graph Laplacian-based linear systems derived from graphs that can be hierarchically bipartitioned with small edge cuts. For a graph of size n with constant-size edge cuts, our method decomposes a graph Laplacian in time O(n log n), and then uses that decomposition to perform a linear solve in time O(n log n). We then use the developed technique to design a preconditioner for graph Laplacians that do not have this property. Finally, we augment this preconditioner with a two-grid method that accounts for much of the preconditioner's weaknesses. We present an analysis of this method, as well as a general theorem for the condition number of a general class of two-grid support graph-based preconditioners. Numerical experiments illustrate the performance of the studied methods.
Marcotte, Christopher D; Grigoriev, Roman O
2016-09-01
This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.
The Method of Subsuper Solutions for Weighted p(r-Laplacian Equation Boundary Value Problems
Directory of Open Access Journals (Sweden)
Zhimei Qiu
2008-10-01
Full Text Available This paper investigates the existence of solutions for weighted p(r-Laplacian ordinary boundary value problems. Our method is based on Leray-Schauder degree. As an application, we give the existence of weak solutions for p(x-Laplacian partial differential equations.
Eigenvalues of the -Laplacian and disconjugacy criteria
Directory of Open Access Journals (Sweden)
Pinasco Juan P
2006-01-01
Full Text Available We derive oscillation and nonoscillation criteria for the one-dimensional -Laplacian in terms of an eigenvalue inequality for a mixed problem. We generalize the results obtained in the linear case by Nehari and Willett, and the proof is based on a Picone-type identity.
Eigenfunction statistics for Anderson model with Hölder continuous ...
Indian Academy of Sciences (India)
We consider random Schrödinger operators on l 2 ( Z d ) with α -Hölder continuous ( 0 < α ≤ 1 ) single site distribution. In localized regime, we study the distribution of eigenfunctions in space and energy simultaneously. In a certain scaling limit, we prove limit points are Poisson.
Analytic families of eigenfunctions on a reductive symmetric space
Ban, E.P. van den; Schlichtkrull, H.
2000-01-01
In harmonic analysis on a reductive symmetric space X an important role is played by families of generalized eigenfunctions for the algebra D (X) of invariant dierential operators. Such families arise for instance as matrix coeÆcients of representations that come in series, such as the (generalized)
Functional brain connectivity is predictable from anatomic network's Laplacian eigen-structure.
Abdelnour, Farras; Dayan, Michael; Devinsky, Orrin; Thesen, Thomas; Raj, Ashish
2018-05-15
How structural connectivity (SC) gives rise to functional connectivity (FC) is not fully understood. Here we mathematically derive a simple relationship between SC measured from diffusion tensor imaging, and FC from resting state fMRI. We establish that SC and FC are related via (structural) Laplacian spectra, whereby FC and SC share eigenvectors and their eigenvalues are exponentially related. This gives, for the first time, a simple and analytical relationship between the graph spectra of structural and functional networks. Laplacian eigenvectors are shown to be good predictors of functional eigenvectors and networks based on independent component analysis of functional time series. A small number of Laplacian eigenmodes are shown to be sufficient to reconstruct FC matrices, serving as basis functions. This approach is fast, and requires no time-consuming simulations. It was tested on two empirical SC/FC datasets, and was found to significantly outperform generative model simulations of coupled neural masses. Copyright © 2018. Published by Elsevier Inc.
Picture change error in quasirelativistic electron/spin density, Laplacian and bond critical points
Bučinský , Luká š; Kucková , Lenka; Malček, Michal; Koží šek, Jozef; Biskupič, Stanislav; Jayatilaka, Dylan; Bü chel, Gabriel E.; Arion, Vladimir B.
2014-01-01
The change of picture of the quasirelativistic Hartree-Fock wave functions is considered for electron/spin densities, the negative Laplacian of electron density and the appropriate bond critical point characteristics from the Quantum Theory of Atoms In Molecules (QTAIM). [OsCl5(Hpz)]- and [RuCl5(NO)]2- transition metal complexes are considered. Both, scalar relativistic and spin-orbit effects have been accounted for using the Infinite Order Two Component (IOTC) Hamiltonian. Picture change error (PCE) correction in the electron and spin densities and the Laplacian of electron density are treated analytically. Generally, PCE is found significant only in the core region of the atoms for the electron/spin density as well as Laplacian.©2014 Elsevier B.V. All rights reserved.
Picture change error in quasirelativistic electron/spin density, Laplacian and bond critical points
Bučinský, Lukáš
2014-06-01
The change of picture of the quasirelativistic Hartree-Fock wave functions is considered for electron/spin densities, the negative Laplacian of electron density and the appropriate bond critical point characteristics from the Quantum Theory of Atoms In Molecules (QTAIM). [OsCl5(Hpz)]- and [RuCl5(NO)]2- transition metal complexes are considered. Both, scalar relativistic and spin-orbit effects have been accounted for using the Infinite Order Two Component (IOTC) Hamiltonian. Picture change error (PCE) correction in the electron and spin densities and the Laplacian of electron density are treated analytically. Generally, PCE is found significant only in the core region of the atoms for the electron/spin density as well as Laplacian.©2014 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Heidbrink, W. W.; Austin, M. E.; Spong, D. A.; Tobias, B. J.; Van Zeeland, M. A.
2013-01-01
Reversed shear Alfvén eigenmodes (RSAEs) usually sweep upward in frequency when the minimum value of the safety factor q min decreases in time. On rare occasions, RSAEs sweep downward prior to the upward sweep. Electron cyclotron emission measurements show that the radial eigenfunction during the downsweeping phase is similar to the eigenfunction of normal, upsweeping RSAEs
International Nuclear Information System (INIS)
Chiang, Yuan-Jen.
1989-01-01
Harmonic maps between manifolds are described as the critical maps of their associated energy functionals. By using Sampson's method [Sam1], the author constructs a Sobolev's chain on a compact V-manifold and obtain Rellich's Theorem (Theorem 3.1), Sobolev's Theorem (Theorem 3.2), the regularity theorem (Theorem 3.3), the property of the eigenspaces for the Laplacian (Theorem 3.5) and the solvability of Laplacian (Theorem 3.6). Then, with these results, he constructs the Green's functions for the Laplacian on a compact V-manifold M in Proposition 4.1; and obtain an orthonormal basis for L 2 (M) formed by the eigenfunctions of the Laplacian corresponding to the eigenvalues in Proposition 4.2. He also estimates the eigenvalues and eigenfunctions of the Laplacian in Theorem 4.3, which is used to construct the heat kernel on a compact V-manifold in Proposition 5.1. Afterwards, he compares the G-invariant heat kernel functions with the G-invariant fundamental solutions of heat equations in the finite V-charts of a compact V-manifold in Theorem 6.1, and then study two integral operators associated to the heat kernel on a compact V-manifold in section 7. With all the preceding results established, in Theorem 8.3 he uses successive approximations to prove the existence of the solutions of parabolic equations on V-manifolds. Finally, he uses Theorem 8.3 to show the existence of harmonic maps from compact V-manifolds into compact Riemannian manifolds in Theorem 9.1 which extends Eells-Sampson's results [E-S
Directory of Open Access Journals (Sweden)
Oleksandr Makeyev
2016-06-01
Full Text Available Noninvasive concentric ring electrodes are a promising alternative to conventional disc electrodes. Currently, the superiority of tripolar concentric ring electrodes over disc electrodes, in particular, in accuracy of Laplacian estimation, has been demonstrated in a range of applications. In our recent work, we have shown that accuracy of Laplacian estimation can be improved with multipolar concentric ring electrodes using a general approach to estimation of the Laplacian for an (n + 1-polar electrode with n rings using the (4n + 1-point method for n ≥ 2. This paper takes the next step toward further improving the Laplacian estimate by proposing novel variable inter-ring distances concentric ring electrodes. Derived using a modified (4n + 1-point method, linearly increasing and decreasing inter-ring distances tripolar (n = 2 and quadripolar (n = 3 electrode configurations are compared to their constant inter-ring distances counterparts. Finite element method modeling and analytic results are consistent and suggest that increasing inter-ring distances electrode configurations may decrease the truncation error resulting in more accurate Laplacian estimates compared to respective constant inter-ring distances configurations. For currently used tripolar electrode configuration, the truncation error may be decreased more than two-fold, while for the quadripolar configuration more than a six-fold decrease is expected.
Makeyev, Oleksandr; Besio, Walter G.
2016-01-01
Noninvasive concentric ring electrodes are a promising alternative to conventional disc electrodes. Currently, the superiority of tripolar concentric ring electrodes over disc electrodes, in particular, in accuracy of Laplacian estimation, has been demonstrated in a range of applications. In our recent work, we have shown that accuracy of Laplacian estimation can be improved with multipolar concentric ring electrodes using a general approach to estimation of the Laplacian for an (n + 1)-polar electrode with n rings using the (4n + 1)-point method for n ≥ 2. This paper takes the next step toward further improving the Laplacian estimate by proposing novel variable inter-ring distances concentric ring electrodes. Derived using a modified (4n + 1)-point method, linearly increasing and decreasing inter-ring distances tripolar (n = 2) and quadripolar (n = 3) electrode configurations are compared to their constant inter-ring distances counterparts. Finite element method modeling and analytic results are consistent and suggest that increasing inter-ring distances electrode configurations may decrease the truncation error resulting in more accurate Laplacian estimates compared to respective constant inter-ring distances configurations. For currently used tripolar electrode configuration, the truncation error may be decreased more than two-fold, while for the quadripolar configuration more than a six-fold decrease is expected. PMID:27294933
The inverse spatial Laplacian of spherically symmetric spacetimes
International Nuclear Information System (INIS)
Fernandes, Karan; Lahiri, Amitabha
2017-01-01
We derive the inverse spatial Laplacian for static, spherically symmetric backgrounds by solving Poisson’s equation for a point source. This is different from the electrostatic Green function, which is defined on the four dimensional static spacetime, while the equation we consider is defined on the spatial hypersurface of such spacetimes. This Green function is relevant in the Hamiltonian dynamics of theories defined on spherically symmetric backgrounds, and closed form expressions for the solutions we find are absent in the literature. We derive an expression in terms of elementary functions for the Schwarzschild spacetime, and comment on the relation of this solution with the known Green function of the spacetime Laplacian operator. We also find an expression for the Green function on the static pure de-Sitter space in terms of hypergeometric functions. We conclude with a discussion of the constraints of the electromagnetic field. (paper)
Quantum and classical eigenfunctions in Calogero and Sutherland systems
International Nuclear Information System (INIS)
Loris, I; Sasaki, R
2004-01-01
An interesting observation was reported by Corrigan-Sasaki that all the frequencies of small oscillations around equilibrium are 'quantized' for Calogero and Sutherland (CS) systems, typical integrable multi-particle dynamics. We present an analytic proof by applying recent results. Explicit forms of 'classical' and quantum eigenfunctions are presented for CS systems based on any root system
Chen, T; Besio, W; Dai, W
2009-01-01
A comparison of the performance of the tripolar and bipolar concentric as well as spline Laplacian electrocardiograms (LECGs) and body surface Laplacian mappings (BSLMs) for localizing and imaging the cardiac electrical activation has been investigated based on computer simulation. In the simulation a simplified eccentric heart-torso sphere-cylinder homogeneous volume conductor model were developed. Multiple dipoles with different orientations were used to simulate the underlying cardiac electrical activities. Results show that the tripolar concentric ring electrodes produce the most accurate LECG and BSLM estimation among the three estimators with the best performance in spatial resolution.
The Geometry of the Semiclassical Wave Front Set for Schrödinger Eigenfunctions on the Torus
Energy Technology Data Exchange (ETDEWEB)
Cardin, Franco, E-mail: cardin@math.unipd.it; Zanelli, Lorenzo, E-mail: lzanelli@math.unipd.it [University of Padova, Department of Mathematics “Tullio Levi Civita” (Italy)
2017-06-15
This paper deals with the phase space analysis for a family of Schrödinger eigenfunctions ψ{sub ℏ} on the flat torus #Mathematical Double-Struck Capital T#{sup n} = (ℝ/2πℤ){sup n} by the semiclassical Wave Front Set. We study those ψ{sub ℏ} such that WF{sub ℏ}(ψ{sub ℏ}) is contained in the graph of the gradient of some viscosity solutions of the Hamilton-Jacobi equation. It turns out that the semiclassical Wave Front Set of such Schrödinger eigenfunctions is stable under viscous perturbations of Mean Field Game kind. These results provide a further viewpoint, and in a wider setting, of the link between the smooth invariant tori of Liouville integrable Hamiltonian systems and the semiclassical localization of Schrödinger eigenfunctions on the torus.
Periodic and subharmonic solutions for second order p-Laplacian ...
Indian Academy of Sciences (India)
Periodic and subharmonic solutions; -Laplacian; difference equations; discrete variational theory. ... Packaging Engineering Institute, Jinan University, Zhuhai 519070, People's Republic of China; College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, People's Republic of China ...
Unbounded planar domains whose second nodal line does not touch the boundary
Czech Academy of Sciences Publication Activity Database
Freitas, P.; Krejčiřík, David
2007-01-01
Roč. 14, č. 1 (2007), s. 107-111 ISSN 1073-2780 R&D Projects: GA MŠk LC06002 Institutional research plan: CEZ:AV0Z10480505 Keywords : Dirichlet Laplacian * eigenfunctions * nodal line Subject RIV: BA - General Mathematics Impact factor: 0.702, year: 2007
Liu, Xiao; Shi, Jun; Zhou, Shichong; Lu, Minhua
2014-01-01
The dimensionality reduction is an important step in ultrasound image based computer-aided diagnosis (CAD) for breast cancer. A newly proposed l2,1 regularized correntropy algorithm for robust feature selection (CRFS) has achieved good performance for noise corrupted data. Therefore, it has the potential to reduce the dimensions of ultrasound image features. However, in clinical practice, the collection of labeled instances is usually expensive and time costing, while it is relatively easy to acquire the unlabeled or undetermined instances. Therefore, the semi-supervised learning is very suitable for clinical CAD. The iterated Laplacian regularization (Iter-LR) is a new regularization method, which has been proved to outperform the traditional graph Laplacian regularization in semi-supervised classification and ranking. In this study, to augment the classification accuracy of the breast ultrasound CAD based on texture feature, we propose an Iter-LR-based semi-supervised CRFS (Iter-LR-CRFS) algorithm, and then apply it to reduce the feature dimensions of ultrasound images for breast CAD. We compared the Iter-LR-CRFS with LR-CRFS, original supervised CRFS, and principal component analysis. The experimental results indicate that the proposed Iter-LR-CRFS significantly outperforms all other algorithms.
Energy Technology Data Exchange (ETDEWEB)
Aarao, J; Bradshaw-Hajek, B H; Miklavcic, S J; Ward, D A, E-mail: Stan.Miklavcic@unisa.edu.a [School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095 (Australia)
2010-05-07
Standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely, if ever, obtainable. In this paper, we propose a solution technique wherein we embed the original domain into one with simple boundaries where the classical eigenfunction solution approach can be used. The solution in the larger domain, when restricted to the original domain, is then the solution of the original boundary value problem. We call this the extended-domain-eigenfunction method. To illustrate the method's strength and scope, we apply it to Laplace's equation on an annular-like domain.
An acceleration system for Laplacian image fusion based on SoC
Gao, Liwen; Zhao, Hongtu; Qu, Xiujie; Wei, Tianbo; Du, Peng
2018-04-01
Based on the analysis of Laplacian image fusion algorithm, this paper proposes a partial pipelining and modular processing architecture, and a SoC based acceleration system is implemented accordingly. Full pipelining method is used for the design of each module, and modules in series form the partial pipelining with unified data formation, which is easy for management and reuse. Integrated with ARM processor, DMA and embedded bare-mental program, this system achieves 4 layers of Laplacian pyramid on the Zynq-7000 board. Experiments show that, with small resources consumption, a couple of 256×256 images can be fused within 1ms, maintaining a fine fusion effect at the same time.
A block structure Laplacian for hyperspectral image data clustering
CSIR Research Space (South Africa)
Lunga, D
2013-12-01
Full Text Available and points to new directions that boost unsupervised pattern classification. In particular, the paper offers design insights on the generation of a well structured graph Laplacian based on an affinity function that induces context-dependence to create compact...
Laser modes as an eigenfunction of an operator equation
International Nuclear Information System (INIS)
Ripper, J.E.; Campos, M.D.; Pudensi, M.A.A.
A new method is proposed of arriving to an approximate solution into mode problems which cannot be treated by the traditional methods. Basically the idea is to treat the laser mode as an eigenfunction of an operator equation so that the mathematical methods developed to treat the wave equations in quantum mechanics can be used as tools to solve the equation. (L.C.) [pt
Directory of Open Access Journals (Sweden)
Akira Ichikawa
2013-02-01
Full Text Available In this study, we developed a compact wireless Laplacian electrode module for electromyograms (EMGs. One of the advantages of the Laplacian electrode configuration is that EMGs obtained with it are expected to be sensitive to the firing of the muscle directly beneath the measurement site. The performance of the developed electrode module was investigated in two human interface applications: character-input interface and detection of finger movement during finger Braille typing. In the former application, the electrode module was combined with an EMG-mouse click converter circuit. In the latter, four electrode modules were used for detection of finger movements during finger Braille typing. Investigation on the character-input interface indicated that characters could be input stably by contraction of (a the masseter, (b trapezius, (c anterior tibialis and (d flexor carpi ulnaris muscles. This wide applicability is desirable when the interface is applied to persons with physical disabilities because the disability differs one to another. The investigation also demonstrated that the electrode module can work properly without any skin preparation. Finger movement detection experiments showed that each finger movement was more clearly detectable when comparing to EMGs recorded with conventional electrodes, suggesting that the Laplacian electrode module is more suitable for detecting the timing of finger movement during typing. This could be because the Laplacian configuration enables us to record EMGs just beneath the electrode. These results demonstrate the advantages of the Laplacian electrode module.
Generation of coherent states of photon-added type via pathway of eigenfunctions
International Nuclear Information System (INIS)
Gorska, K; Penson, K A; Duchamp, G H E
2010-01-01
We obtain and investigate the regular eigenfunctions of simple differential operators x r d r+1 /dx r+1 , r = 1, 2, ..., with the eigenvalues equal to 1. With the help of these eigenfunctions, we construct a non-unitary analogue of a boson displacement operator which will be acting on the vacuum. In this way, we generate collective quantum states of the Fock space which are normalized and equipped with the resolution of unity with the positive weight functions that we obtain explicitly. These states are thus coherent states in the sense of Klauder. They span the truncated Fock space without first r lowest-lying basis states: |0), |1), ..., |r - 1). These states are squeezed, sub-Poissonian in nature and reminiscent of photon-added states in Agarwal and Tara (1991 Phys. Rev. A 43 492).
Rotational Parameters from Vibronic Eigenfunctions of Jahn-Teller Active Molecules
Garner, Scott M.; Miller, Terry A.
2017-06-01
The structure in rotational spectra of many free radical molecules is complicated by Jahn-Teller distortions. Understanding the magnitudes of these distortions is vital to determining the equilibrium geometric structure and details of potential energy surfaces predicted from electronic structure calculations. For example, in the recently studied {\\widetilde{A}^2E^{''} } state of the NO_3 radical, the magnitudes of distortions are yet to be well understood as results from experimental spectroscopic studies of its vibrational and rotational structure disagree with results from electronic structure calculations of the potential energy surface. By fitting either vibrationally resolved spectra or vibronic levels determined by a calculated potential energy surface, we obtain vibronic eigenfunctions for the system as linear combinations of basis functions from products of harmonic oscillators and the degenerate components of the electronic state. Using these vibronic eigenfunctions we are able to predict parameters in the rotational Hamiltonian such as the Watson Jahn-Teller distortion term, h_1, and compare with the results from the analysis of rotational experiments.
The exact Laplacian spectrum for the Dyson hierarchical network.
Agliari, Elena; Tavani, Flavia
2017-01-09
We consider the Dyson hierarchical graph , that is a weighted fully-connected graph, where the pattern of weights is ruled by the parameter σ ∈ (1/2, 1]. Exploiting the deterministic recursivity through which is built, we are able to derive explicitly the whole set of the eigenvalues and the eigenvectors for its Laplacian matrix. Given that the Laplacian operator is intrinsically implied in the analysis of dynamic processes (e.g., random walks) occurring on the graph, as well as in the investigation of the dynamical properties of connected structures themselves (e.g., vibrational structures and relaxation modes), this result allows addressing analytically a large class of problems. In particular, as examples of applications, we study the random walk and the continuous-time quantum walk embedded in , the relaxation times of a polymer whose structure is described by , and the community structure of in terms of modularity measures.
Institute of Scientific and Technical Information of China (English)
Tang Wen-Lin; Tian Gui-Hua
2011-01-01
The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.
Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering
Pelinovsky, Dmitry E.; Sulem, Catherine
A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.
Numerical Aspects of Eigenvalue and Eigenfunction Computations for Chaotic Quantum Systems
Bäcker, A.
Summary: We give an introduction to some of the numerical aspects in quantum chaos. The classical dynamics of two-dimensional area-preserving maps on the torus is illustrated using the standard map and a perturbed cat map. The quantization of area-preserving maps given by their generating function is discussed and for the computation of the eigenvalues a computer program in Python is presented. We illustrate the eigenvalue distribution for two types of perturbed cat maps, one leading to COE and the other to CUE statistics. For the eigenfunctions of quantum maps we study the distribution of the eigenvectors and compare them with the corresponding random matrix distributions. The Husimi representation allows for a direct comparison of the localization of the eigenstates in phase space with the corresponding classical structures. Examples for a perturbed cat map and the standard map with different parameters are shown. Billiard systems and the corresponding quantum billiards are another important class of systems (which are also relevant to applications, for example in mesoscopic physics). We provide a detailed exposition of the boundary integral method, which is one important method to determine the eigenvalues and eigenfunctions of the Helmholtz equation. We discuss several methods to determine the eigenvalues from the Fredholm equation and illustrate them for the stadium billiard. The occurrence of spurious solutions is discussed in detail and illustrated for the circular billiard, the stadium billiard, and the annular sector billiard. We emphasize the role of the normal derivative function to compute the normalization of eigenfunctions, momentum representations or autocorrelation functions in a very efficient and direct way. Some examples for these quantities are given and discussed.
Spectral estimates for Dirichlet Laplacians on perturbed twisted tubes
Czech Academy of Sciences Publication Activity Database
Exner, Pavel; Barseghyan, Diana
2014-01-01
Roč. 8, č. 1 (2014), s. 167-183 ISSN 1846-3886 R&D Projects: GA ČR GAP203/11/0701 Institutional support: RVO:61389005 Keywords : Drichlet Laplacian * twisted tube * discrete spectrum * eigenvalue estimates Subject RIV: BE - Theoretical Physics Impact factor: 0.583, year: 2014
Spectral properties of the massless relativistic quartic oscillator
Durugo, Samuel O.; Lőrinczi, József
2018-03-01
An explicit solution of the spectral problem of the non-local Schrödinger operator obtained as the sum of the square root of the Laplacian and a quartic potential in one dimension is presented. The eigenvalues are obtained as zeroes of special functions related to the fourth order Airy function, and closed formulae for the Fourier transform of the eigenfunctions are derived. These representations allow to derive further spectral properties such as estimates of spectral gaps, heat trace and the asymptotic distribution of eigenvalues, as well as a detailed analysis of the eigenfunctions. A subtle spectral effect is observed which manifests in an exponentially tight approximation of the spectrum by the zeroes of the dominating term in the Fourier representation of the eigenfunctions and its derivative.
Classical limit for quantum mechanical energy eigenfunctions
International Nuclear Information System (INIS)
Sen, D.; Sengupta, S.
2004-01-01
The classical limit problem is discussed for the quantum mechanical energy eigenfunctions using the Wentzel-Kramers-Brillouin approximation, free from the problem at the classical turning points. A proper perspective of the whole issue is sought to appreciate the significance of the discussion. It is observed that for bound states in arbitrary potential, appropriate limiting condition is definable in terms of a dimensionless classical limit parameter leading smoothly to all observable classical results. Most important results are the emergence of classical phase space, keeping the observable distribution functions non-zero only within the so-called classical region at the limit point and resolution of some well-known paradoxes. (author)
Deep learning the quantum phase transitions in random two-dimensional electron systems
International Nuclear Information System (INIS)
Ohtsuki, Tomoki; Ohtsuki, Tomi
2016-01-01
Random electron systems show rich phases such as Anderson insulator, diffusive metal, quantum Hall and quantum anomalous Hall insulators, Weyl semimetal, as well as strong/weak topological insulators. Eigenfunctions of each matter phase have specific features, but owing to the random nature of systems, determining the matter phase from eigenfunctions is difficult. Here, we propose the deep learning algorithm to capture the features of eigenfunctions. Localization-delocalization transition, as well as disordered Chern insulator-Anderson insulator transition, is discussed. (author)
A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ Lie-Group Shooting Method
Directory of Open Access Journals (Sweden)
Chein-Shan Liu
2013-01-01
Full Text Available The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP. In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,ℝ. Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can iteratively solve the missing left boundary conditions, which are determined by matching the right boundary conditions through a finer tuning of r∈[0,1]. The present SL(3,ℝ Lie-group shooting method is easily implemented and is efficient to tackle the multiple solutions of the third-order p-Laplacian. When the missing left boundary values can be determined accurately, we can apply the fourth-order Runge-Kutta (RK4 method to obtain a quite accurate numerical solution of the p-Laplacian.
Note on the nodal line of the p-Laplacian
Directory of Open Access Journals (Sweden)
Abdel R. El Amrouss
2006-09-01
Full Text Available In this paper, we prove that the length of the nodal line of the eigenfunctions associated to the second eigenvalue of the problem $$ -Delta_p u = lambda ho (x |u|^{p-2}u quad hbox{in } Omega $$ with the Dirichlet conditions is not bounded uniformly with respect to the weight.
A graph-Laplacian-based feature extraction algorithm for neural spike sorting.
Ghanbari, Yasser; Spence, Larry; Papamichalis, Panos
2009-01-01
Analysis of extracellular neural spike recordings is highly dependent upon the accuracy of neural waveform classification, commonly referred to as spike sorting. Feature extraction is an important stage of this process because it can limit the quality of clustering which is performed in the feature space. This paper proposes a new feature extraction method (which we call Graph Laplacian Features, GLF) based on minimizing the graph Laplacian and maximizing the weighted variance. The algorithm is compared with Principal Components Analysis (PCA, the most commonly-used feature extraction method) using simulated neural data. The results show that the proposed algorithm produces more compact and well-separated clusters compared to PCA. As an added benefit, tentative cluster centers are output which can be used to initialize a subsequent clustering stage.
International Nuclear Information System (INIS)
Kravtsov, V.E.; Yudson, V.I.
2011-01-01
Highlights: → Statistics of normalized eigenfunctions in one-dimensional Anderson localization at E = 0 is studied. → Moments of inverse participation ratio are calculated. → Equation for generating function is derived at E = 0. → An exact solution for generating function at E = 0 is obtained. → Relation of the generating function to the phase distribution function is established. - Abstract: The one-dimensional (1d) Anderson model (AM), i.e. a tight-binding chain with random uncorrelated on-site energies, has statistical anomalies at any rational point f=(2a)/(λ E ) , where a is the lattice constant and λ E is the de Broglie wavelength. We develop a regular approach to anomalous statistics of normalized eigenfunctions ψ(r) at such commensurability points. The approach is based on an exact integral transfer-matrix equation for a generating function Φ r (u, φ) (u and φ have a meaning of the squared amplitude and phase of eigenfunctions, r is the position of the observation point). This generating function can be used to compute local statistics of eigenfunctions of 1d AM at any disorder and to address the problem of higher-order anomalies at f=p/q with q > 2. The descender of the generating function P r (φ)≡Φ r (u=0,φ) is shown to be the distribution function of phase which determines the Lyapunov exponent and the local density of states. In the leading order in the small disorder we derived a second-order partial differential equation for the r-independent ('zero-mode') component Φ(u, φ) at the E = 0 (f=1/2 ) anomaly. This equation is nonseparable in variables u and φ. Yet, we show that due to a hidden symmetry, it is integrable and we construct an exact solution for Φ(u, φ) explicitly in quadratures. Using this solution we computed moments I m = N 2m > (m ≥ 1) for a chain of the length N → ∞ and found an essential difference between their m-behavior in the center-of-band anomaly and for energies outside this anomaly. Outside the
Kayser, Jürgen; Tenke, Craig E.
2015-01-01
Despite the recognition that the surface Laplacian may counteract adverse effects of volume conduction and recording reference for surface potential data, electrophysiology as a discipline has been reluctant to embrace this approach for data analysis. The reasons for such hesitation are manifold but often involve unfamiliarity with the nature of the underlying transformation, as well as intimidation by a perceived mathematical complexity, and concerns of signal loss, dense electrode array requirements, or susceptibility to noise. We revisit the pitfalls arising from volume conduction and the mandated arbitrary choice of EEG reference, describe the basic principle of the surface Laplacian transform in an intuitive fashion, and exemplify the differences between common reference schemes (nose, linked mastoids, average) and the surface Laplacian for frequently-measured EEG spectra (theta, alpha) and standard event-related potential (ERP) components, such as N1 or P3. We specifically review common reservations against the universal use of the surface Laplacian, which can be effectively addressed by employing spherical spline interpolations with an appropriate selection of the spline flexibility parameter and regularization constant. We argue from a pragmatic perspective that not only are these reservations unfounded but that the continued predominant use of surface potentials poses a considerable impediment on the progress of EEG and ERP research. PMID:25920962
International Nuclear Information System (INIS)
Cloninger, Alexander; Czaja, Wojciech; Doster, Timothy
2017-01-01
As the popularity of non-linear manifold learning techniques such as kernel PCA and Laplacian Eigenmaps grows, vast improvements have been seen in many areas of data processing, including heterogeneous data fusion and integration. One problem with the non-linear techniques, however, is the lack of an easily calculable pre-image. Existence of such pre-image would allow visualization of the fused data not only in the embedded space, but also in the original data space. The ability to make such comparisons can be crucial for data analysts and other subject matter experts who are the end users of novel mathematical algorithms. In this paper, we propose a pre-image algorithm for Laplacian Eigenmaps. Our method offers major improvements over existing techniques, which allow us to address the problem of noisy inputs and the issue of how to calculate the pre-image of a point outside the convex hull of training samples; both of which have been overlooked in previous studies in this field. We conclude by showing that our pre-image algorithm, combined with feature space rotations, allows us to recover occluded pixels of an imaging modality based off knowledge of that image measured by heterogeneous modalities. We demonstrate this data recovery on heterogeneous hyperspectral (HS) cameras, as well as by recovering LIDAR measurements from HS data. (paper)
Cloninger, Alexander; Czaja, Wojciech; Doster, Timothy
2017-07-01
As the popularity of non-linear manifold learning techniques such as kernel PCA and Laplacian Eigenmaps grows, vast improvements have been seen in many areas of data processing, including heterogeneous data fusion and integration. One problem with the non-linear techniques, however, is the lack of an easily calculable pre-image. Existence of such pre-image would allow visualization of the fused data not only in the embedded space, but also in the original data space. The ability to make such comparisons can be crucial for data analysts and other subject matter experts who are the end users of novel mathematical algorithms. In this paper, we propose a pre-image algorithm for Laplacian Eigenmaps. Our method offers major improvements over existing techniques, which allow us to address the problem of noisy inputs and the issue of how to calculate the pre-image of a point outside the convex hull of training samples; both of which have been overlooked in previous studies in this field. We conclude by showing that our pre-image algorithm, combined with feature space rotations, allows us to recover occluded pixels of an imaging modality based off knowledge of that image measured by heterogeneous modalities. We demonstrate this data recovery on heterogeneous hyperspectral (HS) cameras, as well as by recovering LIDAR measurements from HS data.
On the solvability of Dirichlet problem for the weighted p-Laplacian
Directory of Open Access Journals (Sweden)
Ewa Szlachtowska
2012-01-01
Full Text Available The paper investigates the existence and uniqueness of weak solutions for a non-linear boundary value problem involving the weighted \\(p\\-Laplacian. Our approach is based on variational principles and representation properties of the associated spaces.
Potential theory, path integrals and the Laplacian of the indicator
R.-J. Lange (Rutger-Jan)
2012-01-01
markdownabstractThis paper links the field of potential theory — i.e. the Dirichlet and Neumann problems for the heat and Laplace equation — to that of the Feynman path integral, by postulating the some seemingly ill-defined potential. The Laplacian of the indicator can be interpreted using the
A Variance Minimization Criterion to Feature Selection Using Laplacian Regularization.
He, Xiaofei; Ji, Ming; Zhang, Chiyuan; Bao, Hujun
2011-10-01
In many information processing tasks, one is often confronted with very high-dimensional data. Feature selection techniques are designed to find the meaningful feature subset of the original features which can facilitate clustering, classification, and retrieval. In this paper, we consider the feature selection problem in unsupervised learning scenarios, which is particularly difficult due to the absence of class labels that would guide the search for relevant information. Based on Laplacian regularized least squares, which finds a smooth function on the data manifold and minimizes the empirical loss, we propose two novel feature selection algorithms which aim to minimize the expected prediction error of the regularized regression model. Specifically, we select those features such that the size of the parameter covariance matrix of the regularized regression model is minimized. Motivated from experimental design, we use trace and determinant operators to measure the size of the covariance matrix. Efficient computational schemes are also introduced to solve the corresponding optimization problems. Extensive experimental results over various real-life data sets have demonstrated the superiority of the proposed algorithms.
Vidal, Franck; Burle, Boris; Spieser, Laure; Carbonnell, Laurence; Meckler, Cédric; Casini, Laurence; Hasbroucq, Thierry
2015-09-01
Electroencephalography (EEG) is a very popular technique for investigating brain functions and/or mental processes. To this aim, EEG activities must be interpreted in terms of brain and/or mental processes. EEG signals being a direct manifestation of neuronal activity it is often assumed that such interpretations are quite obvious or, at least, straightforward. However, they often rely on (explicit or even implicit) assumptions regarding the structures supposed to generate the EEG activities of interest. For these assumptions to be used appropriately, reliable links between EEG activities and the underlying brain structures must be established. Because of volume conduction effects and the mixture of activities they induce, these links are difficult to establish with scalp potential recordings. We present different examples showing how the Laplacian transformation, acting as an efficient source separation method, allowed to establish more reliable links between EEG activities and brain generators and, ultimately, with mental operations. The nature of those links depends on the depth of inferences that can vary from weak to strong. Along this continuum, we show that 1) while the effects of experimental manipulation can appear widely distributed with scalp potentials, Laplacian transformation allows to reveal several generators contributing (in different manners) to these modulations, 2) amplitude variations within the same set of generators can generate spurious differences in scalp potential topographies, often interpreted as reflecting different source configurations. In such a case, Laplacian transformation provides much more similar topographies, evidencing the same generator(s) set, and 3) using the LRP as an index of response activation most often produces ambiguous results, Laplacian-transformed response-locked ERPs obtained over motor areas allow resolving these ambiguities. Copyright © 2015 Elsevier B.V. All rights reserved.
Bardhan, Jaydeep P; Knepley, Matthew G; Brune, Peter
2015-01-01
In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.
Uniqueness of non-linear ground states for fractional Laplacians in R
DEFF Research Database (Denmark)
Frank, Rupert L.; Lenzmann, Enno
2013-01-01
We prove uniqueness of ground state solutions Q = Q(|x|) ≥ 0 of the non-linear equation (−Δ)sQ+Q−Qα+1=0inR,where 0 fractional Laplacian in one dimension. In particular, we answer affirmatively an open question...... recently raised by Kenig–Martel–Robbiano and we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for s=12 and α = 1 in [5] for the Benjamin–Ono equation. As a technical key result in this paper, we show that the associated linearized operator L...... + = (−Δ) s +1−(α+1)Q α is non-degenerate; i.e., its kernel satisfies ker L + = span{Q′}. This result about L + proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for non-linear dispersive PDEs with fractional Laplacians, such as the generalized...
Kayser, Jürgen; Tenke, Craig E
2015-09-01
Despite the recognition that the surface Laplacian may counteract adverse effects of volume conduction and recording reference for surface potential data, electrophysiology as a discipline has been reluctant to embrace this approach for data analysis. The reasons for such hesitation are manifold but often involve unfamiliarity with the nature of the underlying transformation, as well as intimidation by a perceived mathematical complexity, and concerns of signal loss, dense electrode array requirements, or susceptibility to noise. We revisit the pitfalls arising from volume conduction and the mandated arbitrary choice of EEG reference, describe the basic principle of the surface Laplacian transform in an intuitive fashion, and exemplify the differences between common reference schemes (nose, linked mastoids, average) and the surface Laplacian for frequently-measured EEG spectra (theta, alpha) and standard event-related potential (ERP) components, such as N1 or P3. We specifically review common reservations against the universal use of the surface Laplacian, which can be effectively addressed by employing spherical spline interpolations with an appropriate selection of the spline flexibility parameter and regularization constant. We argue from a pragmatic perspective that not only are these reservations unfounded but that the continued predominant use of surface potentials poses a considerable impediment on the progress of EEG and ERP research. Copyright © 2015 Elsevier B.V. All rights reserved.
Existence of Three Positive Solutions to Some p-Laplacian Boundary Value Problems
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Moulay Rchid Sidi Ammi
2013-01-01
Full Text Available We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some p-Laplacian boundary value problems on time scales.
Laplacian eigenvectors of graphs Perron-Frobenius and Faber-Krahn type theorems
Biyikoğu, Türker; Stadler, Peter F
2007-01-01
Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) "Geometric" properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors. The volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology.
A note on 'Oriental magic mirrors and the Laplacian image'
International Nuclear Information System (INIS)
Riesz, Ferenc
2006-01-01
Berry has shown (2006 Eur. J. Phys. 27 109-18) that the image of an oriental magic mirror (an essentially flat mirror with small surface relief) is the Laplacian of the surface relief for low-curvature features. In this note, an alternative derivation is presented and the physical meaning of the used approximations is explained. (note)
An eigenfunction method for reconstruction of large-scale and high-contrast objects.
Waag, Robert C; Lin, Feng; Varslot, Trond K; Astheimer, Jeffrey P
2007-07-01
A multiple-frequency inverse scattering method that uses eigenfunctions of a scattering operator is extended to image large-scale and high-contrast objects. The extension uses an estimate of the scattering object to form the difference between the scattering by the object and the scattering by the estimate of the object. The scattering potential defined by this difference is expanded in a basis of products of acoustic fields. These fields are defined by eigenfunctions of the scattering operator associated with the estimate. In the case of scattering objects for which the estimate is radial, symmetries in the expressions used to reconstruct the scattering potential greatly reduce the amount of computation. The range of parameters over which the reconstruction method works well is illustrated using calculated scattering by different objects. The method is applied to experimental data from a 48-mm diameter scattering object with tissue-like properties. The image reconstructed from measurements has, relative to a conventional B-scan formed using a low f-number at the same center frequency, significantly higher resolution and less speckle, implying that small, high-contrast structures can be demonstrated clearly using the extended method.
Bardhan, Jaydeep P.; Knepley, Matthew G.; Brune, Peter
2015-01-01
In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online. PMID:26273581
On Consensus of Star-Composed Networks with an Application of Laplacian Spectrum
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Da Huang
2017-01-01
Full Text Available In this paper, we mainly study the performance of star-composed networks which can achieve consensus. Specifically, we investigate the convergence speed and robustness of the consensus of the networks, which can be measured by the smallest nonzero eigenvalue λ2 of the Laplacian matrix and the H2 norm of the graph, respectively. In particular, we introduce the notion of the corona of two graphs to construct star-composed networks and apply the Laplacian spectrum to discuss the convergence speed and robustness for the communication network. Finally, the performances of the star-composed networks have been compared, and we find that the network in which the centers construct a balanced complete bipartite graph has the most advantages of performance. Our research would provide a new insight into the combination between the field of consensus study and the theory of graph spectra.
Manifest rotation symmetric expressions for angular momentum eigenfunctions
International Nuclear Information System (INIS)
Eeg, J.O.; Wroldsen, J.
1983-01-01
Manifest rotation symmetric expressions for eigenfunctions for spin s, orbital angular momentum l and total angular momentum j = l+s, .... , /l-s/ in terms of (2j+1) x (2s+1) multipole transition matrices (MTM) is given. These matrices, which are irreducible tensor matrices, have an algebra together with ordinary spin matrices for spin s and spin j. Explicit expressions for MTM's and their algebra are given for angular momenta <-3. By means of some examples it is shown that within this formalism angular integrations in central field problems will be simplified considerably. Thus the formalism turns out to be very useful for instance for calculations within the MIT-bag and also within spin-spin interactions in atomic physics. (Auth.)
Czech Academy of Sciences Publication Activity Database
Exner, Pavel; Barseghyan, Diana
2013-01-01
Roč. 3, č. 4 (2013), s. 465-484 ISSN 1664-039X R&D Projects: GA ČR GAP203/11/0701 Institutional support: RVO:61389005 Keywords : Dirichlet Laplacian * cusp-shaped region * Lieb-Thirring inequalities * bending and twisting Subject RIV: BE - Theoretical Physics
On Two Functionals Connected to the Laplacian in a Class of ...
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 115; Issue 1. On Two Functionals Connected to the Laplacian in a Class of Doubly Connected Domains in Space-Forms. M H C Anisa A R Aithal. Volume 115 Issue 1 February ... M H C Anisa1 A R Aithal1. Department of Mathematics, University of Mumbai, ...
Spherical Dunkl-monogenics and a factorization of the Dunkl-Laplacian
International Nuclear Information System (INIS)
Fei Minggang; Cerejeiras, Paula; Kaehler, Uwe
2010-01-01
In this paper, we consider and study a factorization of the Dunkl-Laplacian in terms of spherical coordinates. This allows for the construction of a direct sum decomposition of spherical Dunkl-harmonics. By explicit representation in spherical coordinates of Dunkl-harmonics, one obtains explicit projection operators from Dunkl-harmonics to inner (resp. outer) Dunkl-monogenics. Concrete examples of spherical Dunkl-monogenics will be given at the end.
Second-order periodic problem with Phi-Laplacian and impulses
Czech Academy of Sciences Publication Activity Database
Rachůnková, I.; Tvrdý, Milan
2005-01-01
Roč. 63, 5-7/Sp.Is/ (2005), e257-e266 ISSN 0362-546X. [Invited Talks from the Fourth World Congress of Nonlinear Analysts (WCNA 2004). Orlando , 30.7.2004-7.8.2004] R&D Projects: GA ČR(CZ) GA201/04/1077 Institutional research plan: CEZ:AV0Z1019905 Keywords : Laplacian * impulses * lower/upper functions Subject RIV: BA - General Mathematics Impact factor: 0.519, year: 2005 www.elsevier.com/locate/na
One-dimensional unstable eigenfunction and manifold computations in delay differential equations
International Nuclear Information System (INIS)
Green, Kirk; Krauskopf, Bernd; Engelborghs, Koen
2004-01-01
In this paper we present a new numerical technique for computing the unstable eigenfunctions of a saddle periodic orbit in a delay differential equation. This is used to obtain the necessary starting data for an established algorithm for computing one-dimensional (1D) unstable manifolds of an associated saddle fixed point of a suitable Poincare map. To illustrate our method, we investigate an intermittent transition to chaos in a delay system describing a semiconductor laser subject to phase-conjugate feedback
On the number of negative eigenvalues of the Laplacian on a metric graph
International Nuclear Information System (INIS)
Behrndt, Jussi; Luger, Annemarie
2010-01-01
The number of negative eigenvalues of self-adjoint Laplacians on metric graphs is calculated in terms of the boundary conditions and the underlying geometric structure. This extends and complements earlier results by Kostrykin and Schrader (2006 Contemp. Math. 415 201-25).
On the number of negative eigenvalues of the Laplacian on a metric graph
Energy Technology Data Exchange (ETDEWEB)
Behrndt, Jussi [Institut fuer Mathematik, MA 6-4, Technische Universitaet Berlin, Strasse des 17. Juni 136, 10623 Berlin (Germany); Luger, Annemarie, E-mail: behrndt@math.tu-berlin.d, E-mail: luger@maths.lth.s [Center for Mathematical Sciences, Lund Institute of Technology/Lund University, Box 118, SE-221 00 Lund (Sweden)
2010-11-26
The number of negative eigenvalues of self-adjoint Laplacians on metric graphs is calculated in terms of the boundary conditions and the underlying geometric structure. This extends and complements earlier results by Kostrykin and Schrader (2006 Contemp. Math. 415 201-25).
Zou, Hai-Long; Yu, Zu-Guo; Anh, Vo; Ma, Yuan-Lin
2018-05-01
In recent years, researchers have proposed several methods to transform time series (such as those of fractional Brownian motion) into complex networks. In this paper, we construct horizontal visibility networks (HVNs) based on the -stable Lévy motion. We aim to study the relations of multifractal and Laplacian spectrum of transformed networks on the parameters and of the -stable Lévy motion. First, we employ the sandbox algorithm to compute the mass exponents and multifractal spectrum to investigate the multifractality of these HVNs. Then we perform least squares fits to find possible relations of the average fractal dimension , the average information dimension and the average correlation dimension against using several methods of model selection. We also investigate possible dependence relations of eigenvalues and energy on , calculated from the Laplacian and normalized Laplacian operators of the constructed HVNs. All of these constructions and estimates will help us to evaluate the validity and usefulness of the mappings between time series and networks, especially between time series of -stable Lévy motions and HVNs.
The critical slab problem for pure-triplet anisotropic scattering by singular eigenfunction method
Energy Technology Data Exchange (ETDEWEB)
Tuereci, R.G. [Kirikkale Univ. (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministery of Education, Ankara (Turkey). General Directorate of Secondary Education
2017-12-15
The infinite medium Green function can be written by using the jump condition, found Case's eigenfunctions. Thus, any reactor theory problem which is inplane geometry such the criticality problem as can be investigated by using the proper boundary conditions and suggested flux definitions. By using the criticality equation the critical thicknesses can be calculated as numerically. The selected numerical results can be tabulated.
Ahmedov, Anvarjon; Materneh, Ehab; Zainuddin, Hishamuddin
2017-09-01
The relevance of waves in quantum mechanics naturally implies that the decomposition of arbitrary wave packets in terms of monochromatic waves plays an important role in applications of the theory. When eigenfunction expansions does not converge, then the expansions of the functions with certain smoothness should be considered. Such functions gained prominence primarily through their application in quantum mechanics. In this work we study the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_p^α ({T^N}), related to the self-adjoint extension of the Laplace operator in torus TN . The sufficient conditions for summability is obtained using the modified Poisson formula. Isomorphism properties of the elliptic differential operators is applied in order to obtain estimation for the Fourier series of the functions from the classes of Liouville L_p^α .
Class of nonsingular exact solutions for Laplacian pattern formation
International Nuclear Information System (INIS)
Mineev-Weinstein, M.B.; Dawson, S.P.
1994-01-01
We present a class of exact solutions for the so-called Laplacian growth equation describing the zero-surface-tension limit of a variety of two-dimensional pattern formation problems. These solutions are free of finite-time singularities (cusps) for quite general initial conditions. They reproduce various features of viscous fingering observed in experiments and numerical simulations with surface tension, such as existence of stagnation points, screening, tip splitting, and coarsening. In certain cases the asymptotic interface consists of N separated moving Saffman-Taylor fingers
Xin, Yun; Liu, Hongmin; Cheng, Zhibo
2018-01-01
In this paper, we consider a kind of p -Laplacian neutral Rayleigh equation with singularity of attractive type, [Formula: see text] By applications of an extension of Mawhin's continuation theorem, sufficient conditions for the existence of periodic solution are established.
Construction of six-quark states from parity eigenfunctions for n-n processes
International Nuclear Information System (INIS)
Stancu, F.; Wilets, L.
1987-01-01
The work presented is to classify and construct six-quark states as totally antisymmetric states of six fermions, each described by orbital, spin, isospin, and color degrees of freedom. A classification scheme is proposed based on parity eigenfunctions. The single-particle hamiltonian is assumed to be reflectionally and axially symmetric and can be obtained, for example, from constrained Hartree-Fock or solition mean field theories. The ultimate aim is to study N-N processes in the context of the (relativistic) soliton bag model
DEFF Research Database (Denmark)
Fournais, Søren; Hoffmann-Ostenhof, Maria; Hoffmann-Ostenhof, Thomas
2008-01-01
We review recent results by the authors on the regularity of molecular eigenfunctions ψ and their corresponding one-electron densities ρ, as well as of the spherically averaged one-electron atomic density ρ. Furthermore, we prove an exponentially decreasing lower bound for ρ in the case when...
Directory of Open Access Journals (Sweden)
Bin Qin
2014-04-01
Full Text Available By using the genus properties, we establish some criteria for the second-order p(t-Laplacian system $$ \\frac{d}{dt}\\big(|\\dot{u}(t|^{p(t-2}\\dot{u}(t\\big-a(t|u(t|^{p(t-2}u(t +\
Group theoretic reduction of Laplacian dynamical problems on fractal lattices
International Nuclear Information System (INIS)
Schwalm, W.A.; Schwalm, M.K.; Giona, M.
1997-01-01
Discrete forms of the Schroedinger equation, the diffusion equation, the linearized Landau-Ginzburg equation, and discrete models for vibrations and spin dynamics belong to a class of Laplacian-based finite difference models. Real-space renormalization of such models on finitely ramified regular fractals is known to give exact recursion relations. It is shown that these recursions commute with Lie groups representing continuous symmetries of the discrete models. Each such symmetry reduces the order of the renormalization recursions by one, resulting in a system of recursions with one fewer variable. Group trajectories are obtained from inverse images of fixed and invariant sets of the recursions. A subset of the Laplacian finite difference models can be mapped by change of boundary conditions and time dependence to a diffusion problem with closed boundaries. In such cases conservation of mass simplifies the group flow and obtaining the groups becomes easier. To illustrate this, the renormalization recursions for Green functions on four standard examples are decoupled. The examples are (1) the linear chain, (2) an anisotropic version of Dhar close-quote s 3-simplex, similar to a model dealt with by Hood and Southern, (3) the fourfold coordinated Sierpiacute nski lattice of Rammal and of Domany et al., and (4) a form of the Vicsek lattice. Prospects for applying the group theoretic method to more general dynamical systems are discussed. copyright 1997 The American Physical Society
International Nuclear Information System (INIS)
Gurbanovich, N.S.; Zelenskaya, I.N.
1976-01-01
The solution for eigenfunction and eigenvalue for effective Hamiltonians anti Hsub(p) in two-particle channels corresponding to division of four particles into groups (3.1) and (2.2) is very essential in the four-body problem as applied to nuclear reactions. The interaction of anti√sub(p) in each channel may be written in the form of an integral operator which takes account of the structure of a target nucleus or of an incident particle and satisfying the integral equation. While assuming the two-particle potentials to be central, it is possible to expand the effective interactions anti√sub(p) in partial waves and write the radial equation for anti Hsub(p). In the approximation on a mass shell the radial equations for the eigenfunctions of Hsub(p) are reduced to an algebraic equations system. The coefficients of the latter are expressed through the Fourier images for products of wave functions of bound clusters and the two-particle central potential which are localized in a momentum space
Quadrilateral mesh fitting that preserves sharp features based on multi-normals for Laplacian energy
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Yusuke Imai
2014-04-01
Full Text Available Because the cost of performance testing using actual products is expensive, manufacturers use lower-cost computer-aided design simulations for this function. In this paper, we propose using hexahedral meshes, which are more accurate than tetrahedral meshes, for finite element analysis. We propose automatic hexahedral mesh generation with sharp features to precisely represent the corresponding features of a target shape. Our hexahedral mesh is generated using a voxel-based algorithm. In our previous works, we fit the surface of the voxels to the target surface using Laplacian energy minimization. We used normal vectors in the fitting to preserve sharp features. However, this method could not represent concave sharp features precisely. In this proposal, we improve our previous Laplacian energy minimization by adding a term that depends on multi-normal vectors instead of using normal vectors. Furthermore, we accentuate a convex/concave surface subset to represent concave sharp features.
Analyzing self-similar and fractal properties of the C. elegans neural network.
Directory of Open Access Journals (Sweden)
Tyler M Reese
Full Text Available The brain is one of the most studied and highly complex systems in the biological world. While much research has concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons. A better understanding of the structural connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron "giant component" of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been "rewired" to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs.
Phase space eigenfunctions of multidimensional quadratic Hamiltonians
International Nuclear Information System (INIS)
Dodonov, V.V.; Man'ko, V.I.
1986-01-01
We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)
The Solution of a Velocity-Dependent Slowing-Down Problem Using Case's Eigenfunction Expansion
Energy Technology Data Exchange (ETDEWEB)
Claesson, A
1964-11-15
The slowing-down of neutrons in a hydrogenous moderator is calculated assuming a plane source of monoenergetic neutrons. The scattering is regarded as spherically symmetric, but it is shown that a generalization to anisotropy is possible. The cross-section is assumed to be constant. The virgin neutrons are separated out, and it follows that the distribution of the remaining neutrons can be obtained by using an expansion in the eigenfunctions given by Case for the velocity-independent problem.
Directory of Open Access Journals (Sweden)
Ureña Antonio J
2002-01-01
Full Text Available A generalization of the well-known Hartman–Nagumo inequality to the case of the vector ordinary -Laplacian and classical degree theory provide existence results for some associated nonlinear boundary value problems.
Study on a kind of ϕ-Laplacian Liénard equation with attractive and repulsive singularities.
Xin, Yun; Cheng, Zhibo
2017-01-01
In this paper, by application of the Manasevich-Mawhin continuation theorem, we investigate the existence of a positive periodic solution for a kind of ϕ -Laplacian singular Liénard equation with attractive and repulsive singularities.
Vibration modes of 3n-gaskets and other fractals
Energy Technology Data Exchange (ETDEWEB)
Bajorin, N; Chen, T; Dagan, A; Emmons, C; Hussein, M; Khalil, M; Mody, P; Steinhurst, B; Teplyaev, A [Department of Mathematics, University of Connecticut, Storrs CT 06269 (United States)
2008-01-11
We rigorously study eigenvalues and eigenfunctions (vibration modes) on the class of self-similar symmetric finitely ramified fractals, which include the Sierpinski gasket and other 3n-gaskets. We consider the classical Laplacian on fractals which generalizes the usual one-dimensional second derivative, is the generator of the self-similar diffusion process, and has possible applications as the quantum Hamiltonian. We develop a theoretical matrix analysis, including analysis of singularities, which allows us to compute eigenvalues, eigenfunctions and their multiplicities exactly. We support our theoretical analysis by symbolic and numerical computations. Our analysis, in particular, allows the computation of the spectral zeta function on fractals and the limiting distribution of eigenvalues (i.e., integrated density of states). We consider such examples as the level-3 Sierpinski gasket, a fractal 3-tree, and the diamond fractal.
Directory of Open Access Journals (Sweden)
Ling-Yun Dai
2017-01-01
Full Text Available Differential expression plays an important role in cancer diagnosis and classification. In recent years, many methods have been used to identify differentially expressed genes. However, the recognition rate and reliability of gene selection still need to be improved. In this paper, a novel constrained method named robust nonnegative matrix factorization via joint graph Laplacian and discriminative information (GLD-RNMF is proposed for identifying differentially expressed genes, in which manifold learning and the discriminative label information are incorporated into the traditional nonnegative matrix factorization model to train the objective matrix. Specifically, L2,1-norm minimization is enforced on both the error function and the regularization term which is robust to outliers and noise in gene data. Furthermore, the multiplicative update rules and the details of convergence proof are shown for the new model. The experimental results on two publicly available cancer datasets demonstrate that GLD-RNMF is an effective method for identifying differentially expressed genes.
Factorization of the Laplacian and families of elementary particles
International Nuclear Information System (INIS)
Keller, J.
1994-01-01
It is shown that multi-vector Clifford algebra allows a series of factorizations of the Laplacian operator and associated Dirac-like equations, this set of related equations generates 3 families of elementary particles with the experimentally observed lepton and quark content for each family and the experimentally observed electroweak color interactions and other related properties. In contrast to the usual approach to the standard model the properties for the different fields of the model are consequences of the relative properties of the equations, among themselves and in relation to space-time, and therefore, they do not need to be postulates of the theory. 11 refs
Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals
Steinhurst, Benjamin; Teplyaev, Alexander
2012-01-01
We show that if a Barlow-Evans Markov process on a vermiculated space is symmetric, then one can study the spectral properties of the corresponding Laplacian using projective limits. For some examples, such as the Laakso spaces and a Spierpinski P\\^ate \\`a Choux, one can develop a complete spectral theory, including the eigenfunction expansions that are analogous to Fourier series. Also, one can construct connected fractal spaces isospectral to the fractal strings of Lapidus and van Frankenhu...
International Nuclear Information System (INIS)
Hong, Ser Gi; Lee, Deokjung
2015-01-01
A highly accurate S 4 eigenfunction-based nodal method has been developed to solve multi-group discrete ordinate neutral particle transport problems with a linearly anisotropic scattering in slab geometry. The new method solves the even-parity form of discrete ordinates transport equation with an arbitrary S N order angular quadrature using two sub-cell balance equations and the S 4 eigenfunctions of within-group transport equation. The four eigenfunctions from S 4 approximation have been chosen as basis functions for the spatial expansion of the angular flux in each mesh. The constant and cubic polynomial approximations are adopted for the scattering source terms from other energy groups and fission source. A nodal method using the conventional polynomial expansion and the sub-cell balances was also developed to be used for demonstrating the high accuracy of the new methods. Using the new methods, a multi-group eigenvalue problem has been solved as well as fixed source problems. The numerical test results of one-group problem show that the new method has third-order accuracy as mesh size is finely refined and it has much higher accuracies for large meshes than the diamond differencing method and the nodal method using sub-cell balances and polynomial expansion of angular flux. For multi-group problems including eigenvalue problem, it was demonstrated that the new method using the cubic polynomial approximation of the sources could produce very accurate solutions even with large mesh sizes. (author)
Symbol Error Rate of MPSK over EGK Channels Perturbed by a Dominant Additive Laplacian Noise
Souri, Hamza; Alouini, Mohamed-Slim
2015-01-01
The Laplacian noise has received much attention during the recent years since it affects many communication systems. We consider in this paper the probability of error of an M-ary phase shift keying (PSK) constellation operating over a generalized fading channel in presence of a dominant additive Laplacian noise. In this context, the decision regions of the receiver are determined using the maximum likelihood and the minimum distance detectors. Once the decision regions are extracted, the resulting symbol error rate expressions are computed and averaged over an Extended Generalized-K fading distribution. Generic closed form expressions of the conditional and the average probability of error are obtained in terms of the Fox’s H function. Simplifications for some special cases of fading are presented and the resulting formulas end up being often expressed in terms of well known elementary functions. Finally, the mathematical formalism is validated using some selected analytical-based numerical results as well as Monte- Carlo simulation-based results.
Symbol Error Rate of MPSK over EGK Channels Perturbed by a Dominant Additive Laplacian Noise
Souri, Hamza
2015-06-01
The Laplacian noise has received much attention during the recent years since it affects many communication systems. We consider in this paper the probability of error of an M-ary phase shift keying (PSK) constellation operating over a generalized fading channel in presence of a dominant additive Laplacian noise. In this context, the decision regions of the receiver are determined using the maximum likelihood and the minimum distance detectors. Once the decision regions are extracted, the resulting symbol error rate expressions are computed and averaged over an Extended Generalized-K fading distribution. Generic closed form expressions of the conditional and the average probability of error are obtained in terms of the Fox’s H function. Simplifications for some special cases of fading are presented and the resulting formulas end up being often expressed in terms of well known elementary functions. Finally, the mathematical formalism is validated using some selected analytical-based numerical results as well as Monte- Carlo simulation-based results.
The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators
Ahmedov, Anvarjon
2018-03-01
In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral
Solvability of fractional multi-point boundary-value problems with p-Laplacian operator at resonance
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Tengfei Shen
2014-02-01
Full Text Available In this article, we consider the multi-point boundary-value problem for nonlinear fractional differential equations with $p$-Laplacian operator: $$\\displaylines{ D_{0^+}^\\beta \\varphi_p (D_{0^+}^\\alpha u(t = f(t,u(t,D_{0^+}^{\\alpha - 2} u(t,D_{0^+}^{\\alpha - 1} u(t, D_{0^+}^\\alpha u(t,\\quad t \\in (0,1, \\cr u(0 = u'(0=D_{0^+}^\\alpha u(0 = 0,\\quad D_{0^+}^{\\alpha - 1} u(1 = \\sum_{i = 1}^m {\\sigma_i D_{0^+}^{\\alpha - 1} u(\\eta_i } , }$$ where $2 < \\alpha \\le 3$, $0 < \\beta \\le 1$, $3 < \\alpha + \\beta \\le 4$, $\\sum_{i = 1}^m {\\sigma_i } = 1$, $D_{0^+}^\\alpha$ is the standard Riemann-Liouville fractional derivative. $\\varphi_{p}(s=|s|^{p-2}s$ is p-Laplacians operator. The existence of solutions for above fractional boundary value problem is obtained by using the extension of Mawhin's continuation theorem due to Ge, which enrich konwn results. An example is given to illustrate the main result.
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Liu Yang
2007-10-01
Full Text Available By using coincidence degree theory of Mawhin, existence results for some higher order resonance multipoint boundary value problems with one dimensional p-Laplacian operator are obtained.
International Nuclear Information System (INIS)
Pathak, R.K.; Chandra, A.K.; Bhattacharyya, K.
1994-01-01
Eigenfunctions of the quantum mechanical particle-in-a-box problem are shown to lead to a new trigonometric expansion scheme with good convergence properties. This hitherto unexplored expansion strategy is found to be quite efficient in variational calculations and as an alternative to the Fourier series. Demonstrative computations involve a few one-dimensional models of confining potentials for bound states and pulses of various shapes in signal analysis. ((orig.))
Directory of Open Access Journals (Sweden)
Wen-Zhen Gong
2012-01-01
Full Text Available By using minimax methods in critical point theory, a new existence theorem of infinitely many periodic solutions is obtained for a class of second-order p-Laplacian systems with impulsive effects. Our result generalizes many known works in the literature.
Directory of Open Access Journals (Sweden)
Li Wang
2016-12-01
Full Text Available In this article, we show the existence of infinitely many solutions for the fractional p-Laplacian equations of Schrodinger-Kirchhoff type equation $$ M([u]_{s, p}^p (-\\Delta _p^s u+V(x|u|^{p-2}u= \\alpha |u|^{ p_s^{*}-2 }u+\\beta k(x|u|^{q-2}u \\quad x\\in \\mathbb{R}^N, $$ where $(-\\Delta ^s_p$ is the fractional p-Laplacian operator, $[u]_{s,p}$ is the Gagliardo p-seminorm, $0 sp$, $1
Distortion Correction in Fetal EPI Using Non-Rigid Registration With a Laplacian Constraint.
Kuklisova-Murgasova, Maria; Lockwood Estrin, Georgia; Nunes, Rita G; Malik, Shaihan J; Rutherford, Mary A; Rueckert, Daniel; Hajnal, Joseph V
2018-01-01
Geometric distortion induced by the main B0 field disrupts the consistency of fetal echo planar imaging (EPI) data, on which diffusion and functional magnetic resonance imaging is based. In this paper, we present a novel data-driven method for simultaneous motion and distortion correction of fetal EPI. A motion-corrected and reconstructed T2 weighted single shot fast spin echo (ssFSE) volume is used as a model of undistorted fetal brain anatomy. Our algorithm interleaves two registration steps: estimation of fetal motion parameters by aligning EPI slices to the model; and deformable registration of EPI slices to slices simulated from the undistorted model to estimate the distortion field. The deformable registration is regularized by a physically inspired Laplacian constraint, to model distortion induced by a source-free background B0 field. Our experiments show that distortion correction significantly improves consistency of reconstructed EPI volumes with ssFSE volumes. In addition, the estimated distortion fields are consistent with fields calculated from acquired field maps, and the Laplacian constraint is essential for estimation of plausible distortion fields. The EPI volumes reconstructed from different scans of the same subject were more consistent when the proposed method was used in comparison with EPI volumes reconstructed from data distortion corrected using a separately acquired B0 field map.
International Nuclear Information System (INIS)
Hoogenboom, J.E.
1981-01-01
An adjoint Monte Carlo technique is described for the solution of neutron transport problems. The optimum biasing function for a zero-variance collision estimator is derived. The optimum treatment of an analog of a non-velocity thermal group has also been derived. The method is extended to multiplying systems, especially for eigenfunction problems to enable the estimate of averages over the unknown fundamental neutron flux distribution. A versatile computer code, FOCUS, has been written, based on the described theory. Numerical examples are given for a shielding problem and a critical assembly, illustrating the performance of the FOCUS code. 19 refs
Directory of Open Access Journals (Sweden)
Khaleghi Moghadam Mohsen
2017-08-01
Full Text Available Triple solutions are obtained for a discrete problem involving a nonlinearly perturbed one-dimensional p(k-Laplacian operator and satisfying Dirichlet boundary conditions. The methods for existence rely on a Ricceri-local minimum theorem for differentiable functionals. Several examples are included to illustrate the main results.
Selberg zeta functions and transfer operators an experimental approach to singular perturbations
Fraczek, Markus Szymon
2017-01-01
This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations. Areas in which the theory has not yet been sufficiently developed, such as the spectral theory of transfer operators or the singular perturbation theory of hyperbolic Laplacians, will profit from the numerical experiments discussed in this book. Detailed descriptions of numerical approaches to the spectra and eigenfunctions of transfer operators and to computations of Selberg zeta functions will be of value to researchers active in analysis, while those researchers focusing more on numerical aspects will benefit from discussions of the analytic theory, in particular those concerning the transfer operator method and the spectral theory of hyperbolic spac...
The eigenfunction method and the mass operator in intense-field quantum electrodynamics
International Nuclear Information System (INIS)
Ritus, V.I.
1987-01-01
A method is given for calculating radiation effects in constant intense-field quantum electrodynamics; this method is based on the use of the eigenfunctions of the mass operator and diagonalization of the latter. A compact expression is found for the eigenvalue of the mass operator of the electron in a random constant field together with the corresponding elastic scattering amplitude. The anomalous electric moment that arises in the field with a pseudoscalar EH not equal to O is found and investigated in detail together with the anomalous magnetic moment in the electrical field that approaches the double Schwinger value with an increase in the field together with the mass shift and the rate of decay of the ground state of the electron in the electrical field
Directory of Open Access Journals (Sweden)
K.R. Prasad
2015-11-01
Full Text Available In this paper, we establish the existence of at least three positive solutions for a system of (p,q-Laplacian fractional order two-point boundary value problems by applying five functionals fixed point theorem under suitable conditions on a cone in a Banach space.
Energy Technology Data Exchange (ETDEWEB)
Feng, Wenqiang, E-mail: wfeng1@vols.utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States); Salgado, Abner J., E-mail: asalgad1@utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States); Wang, Cheng, E-mail: cwang1@umassd.edu [Department of Mathematics, The University of Massachusetts, North Dartmouth, MA 02747 (United States); Wise, Steven M., E-mail: swise1@utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States)
2017-04-01
We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems – including thin film epitaxy with slope selection and the square phase field crystal model – are carried out to verify the efficiency of the scheme.
Makeyev, Oleksandr; Lee, Colin; Besio, Walter G
2017-07-01
Tripolar concentric ring electrodes are showing great promise in a range of applications including braincomputer interface and seizure onset detection due to their superiority to conventional disc electrodes, in particular, in accuracy of surface Laplacian estimation. Recently, we proposed a general approach to estimation of the Laplacian for an (n + 1)-polar electrode with n rings using the (4n + 1)-point method for n ≥ 2 that allows cancellation of all the truncation terms up to the order of 2n. This approach has been used to introduce novel multipolar and variable inter-ring distances concentric ring electrode configurations verified using finite element method. The obtained results suggest their potential to improve Laplacian estimation compared to currently used constant interring distances tripolar concentric ring electrodes. One of the main limitations of the proposed (4n + 1)-point method is that the radius of the central disc and the widths of the concentric rings are not included and therefore cannot be optimized. This study incorporates these two parameters by representing the central disc and both concentric rings as clusters of points with specific radius and widths respectively as opposed to the currently used single point and concentric circles. A proof of concept Laplacian estimate is derived for a tripolar concentric ring electrode with non-negligible radius of the central disc and non-negligible widths of the concentric rings clearly demonstrating how both of these parameters can be incorporated into the (4n + 1)-point method.
The spectrum of hyperbolic surfaces
Bergeron, Nicolas
2016-01-01
This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithmetic hyperbolic surfaces”, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss. The fruit of several graduate level courses at Orsay...
Learning theory of distributed spectral algorithms
International Nuclear Information System (INIS)
Guo, Zheng-Chu; Lin, Shao-Bo; Zhou, Ding-Xuan
2017-01-01
Spectral algorithms have been widely used and studied in learning theory and inverse problems. This paper is concerned with distributed spectral algorithms, for handling big data, based on a divide-and-conquer approach. We present a learning theory for these distributed kernel-based learning algorithms in a regression framework including nice error bounds and optimal minimax learning rates achieved by means of a novel integral operator approach and a second order decomposition of inverse operators. Our quantitative estimates are given in terms of regularity of the regression function, effective dimension of the reproducing kernel Hilbert space, and qualification of the filter function of the spectral algorithm. They do not need any eigenfunction or noise conditions and are better than the existing results even for the classical family of spectral algorithms. (paper)
Directory of Open Access Journals (Sweden)
Jufang Wang
2013-01-01
Full Text Available We establish the existence of triple positive solutions of an m-point boundary value problem for the nonlinear singular second-order differential equations of mixed type with a p-Laplacian operator by Leggett-William fixed point theorem. At last, we give an example to demonstrate the use of the main result of this paper. The conclusions in this paper essentially extend and improve the known results.
Existence of standing waves for Schrodinger equations involving the fractional Laplacian
Directory of Open Access Journals (Sweden)
Everaldo S. de Medeiros
2017-03-01
Full Text Available We study a class of fractional Schrodinger equations of the form $$ \\varepsilon^{2\\alpha}(-\\Delta^\\alpha u+ V(xu = f(x,u \\quad\\text{in } \\mathbb{R}^N, $$ where $\\varepsilon$ is a positive parameter, $0 < \\alpha < 1$, $2\\alpha < N$, $(-\\Delta^\\alpha$ is the fractional Laplacian, $V:\\mathbb{R}^{N}\\to \\mathbb{R}$ is a potential which may be bounded or unbounded and the nonlinearity $f:\\mathbb{R}^{N}\\times \\mathbb{R}\\to \\mathbb{R}$ is superlinear and behaves like $|u|^{p-2}u$ at infinity for some $2
International Nuclear Information System (INIS)
Fernandez Nunez, J.; Garcia Fuertes, W.; Perelomov, A.M.
2003-01-01
We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra D 4 in terms of a set of Weyl-invariant variables, namely, the characters of the fundamental representations of the Lie algebra. This parametrization allows us to solve for the energy eigenfunctions of the theory and to study properties of the system of orthogonal polynomials associated with them such as recurrence relations and generating functions
Directory of Open Access Journals (Sweden)
Svatoslav Stanêk
2008-03-01
Full Text Available The paper presents an existence principle for solving a large class of nonlocal regular discrete boundary value problems with the ÃÂ†-Laplacian. Applications of the existence principle to singular discrete problems are given.
Overt foot movement detection in one single Laplacian EEG derivation.
Solis-Escalante, Teodoro; Müller-Putz, Gernot; Pfurtscheller, Gert
2008-10-30
In this work one single Laplacian derivation and a full description of band power values in a broad frequency band are used to detect brisk foot movement execution in the ongoing EEG. Two support vector machines (SVM) are trained to detect the event-related desynchronization (ERD) during motor execution and the following beta rebound (event-related synchronization, ERS) independently. Their performance is measured through the simulation of an asynchronous brain switch. ERS (true positive rate=0.74+/-0.21) after motor execution is shown to be more stable than ERD (true positive rate=0.21+/-0.12). A novel combination of ERD and post-movement ERS is introduced. The SVM outputs are combined with a product rule to merge ERD and ERS detection. For this novel approach the average information transfer rate obtained was 11.19+/-3.61bits/min.
Directory of Open Access Journals (Sweden)
Qiying Wei
2009-01-01
Full Text Available By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an -point singular -Laplacian dynamic equation on time scales with the sign changing nonlinearity. These results are new even for the corresponding differential (=ℝ and difference equations (=ℤ, as well as in general time scales setting. As an application, an example is given to illustrate the results.
International Nuclear Information System (INIS)
Zhidkov, P.E.
1996-01-01
First, the eigenvalue problem on the segment [0,1] for the Sturm-Liouville operator with a potential depending on the spectral parameter with the zero Dirichlet boundary conditions is considered. For this problem, under some hypotheses on the potential, it is proved that the necessary and sufficient condition for an arbitrary system of eigenfunctions, possessing a unique function with n roots in the interval (0,1) for an arbitrary non-negative integer number n, being complete in the space L 2 (0,1) is the linear independence of the functions from this system in the space L 2 (0,1). Then, this result is applied to the investigation of an eigenvalue problem for a nonlinear operator on the Sturm-Liouville type. For this problem, the completeness of the system of its eigenfunctions in the space L 2 (0,1) is proved. (author). 12 refs
Directory of Open Access Journals (Sweden)
Shihuang Hong
2009-01-01
Full Text Available We present sufficient conditions for the existence of at least twin or triple positive solutions of a nonlinear four-point singular boundary value problem with a p-Laplacian dynamic equation on a time scale. Our results are obtained via some new multiple fixed point theorems.
Assessment of Schrodinger Eigenmaps for target detection
Dorado Munoz, Leidy P.; Messinger, David W.; Czaja, Wojtek
2014-06-01
Non-linear dimensionality reduction methods have been widely applied to hyperspectral imagery due to its structure as the information can be represented in a lower dimension without losing information, and because the non-linear methods preserve the local geometry of the data while the dimension is reduced. One of these methods is Laplacian Eigenmaps (LE), which assumes that the data lies on a low dimensional manifold embedded in a high dimensional space. LE builds a nearest neighbor graph, computes its Laplacian and performs the eigendecomposition of the Laplacian. These eigenfunctions constitute a basis for the lower dimensional space in which the geometry of the manifold is preserved. In addition to the reduction problem, LE has been widely used in tasks such as segmentation, clustering, and classification. In this regard, a new Schrodinger Eigenmaps (SE) method was developed and presented as a semi-supervised classification scheme in order to improve the classification performance and take advantage of the labeled data. SE is an algorithm built upon LE, where the former Laplacian operator is replaced by the Schrodinger operator. The Schrodinger operator includes a potential term V, that, taking advantage of the additional information such as labeled data, allows clustering of similar points. In this paper, we explore the idea of using SE in target detection. In this way, we present a framework where the potential term V is defined as a barrier potential: a diagonal matrix encoding the spatial position of the target, and the detection performance is evaluated by using different targets and different hyperspectral scenes.
Image denoising via adaptive eigenvectors of graph Laplacian
Chen, Ying; Tang, Yibin; Xu, Ning; Zhou, Lin; Zhao, Li
2016-07-01
An image denoising method via adaptive eigenvectors of graph Laplacian (EGL) is proposed. Unlike the trivial parameter setting of the used eigenvectors in the traditional EGL method, in our method, the eigenvectors are adaptively selected in the whole denoising procedure. In detail, a rough image is first built with the eigenvectors from the noisy image, where the eigenvectors are selected by using the deviation estimation of the clean image. Subsequently, a guided image is effectively restored with a weighted average of the noisy and rough images. In this operation, the average coefficient is adaptively obtained to set the deviation of the guided image to approximately that of the clean image. Finally, the denoised image is achieved by a group-sparse model with the pattern from the guided image, where the eigenvectors are chosen in the error control of the noise deviation. Moreover, a modified group orthogonal matching pursuit algorithm is developed to efficiently solve the above group sparse model. The experiments show that our method not only improves the practicality of the EGL methods with the dependence reduction of the parameter setting, but also can outperform some well-developed denoising methods, especially for noise with large deviations.
Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite Interval
Ruyun Ma; Chunjie Xie; Abubaker Ahmed
2013-01-01
We use the quadrature method to show the existence and multiplicity of positive solutions of the boundary value problems involving one-dimensional $p$ -Laplacian ${\\left({u}^{\\prime }\\left(t\\right){|}^{p-2}{u}^{\\prime }\\left(t\\right)\\right)}^{\\prime }+\\lambda f\\left(u\\left(t\\right)\\right)=0$ , $t\\in \\left(0,1\\right)$ , $u\\left(0\\right)=u\\left(1\\right)=0$ , where $p\\in \\left(1,2\\right]$ , $\\lambda \\in \\left(0,\\mathrm{\\infty }\\right)$ is a parameter, $f\\in {C}^{1}\\left(\\left[0,r\\right),\\l...
Tripolar Laplacian electrocardiogram and moment of activation isochronal mapping.
Besio, W; Chen, T
2007-05-01
The electrocardiogram (ECG) provides useful global temporal assessment of the cardiac activity, but has limited spatial capabilities. The Laplacian electrocardiogram (LECG), an improvement over the ECG, provides high spatiotemporal distributed information about cardiac electrical activation. We designed and developed LECG tripolar concentric ring electrode active sensors based on the finite element algorithm 'nine-point method' (NPM). The active sensors were used in an array of 6 by 12 (72) locations to record bipolar and tripolar LECG from the body surface over the anterolateral chest. Compared to bipolar LECG, tripolar LECG showed significantly higher spatial selectivity which may be helpful in inferring information about cardiac activations detected on the body surface. In this study the moment of activation (MOA), an indicator of a depolarization wave passing below the active sensors, was used to surmise possible timing information of the cardiac electrical activation below the active sensors' recording sites. The MOA on the body surface was used to generate isochronal maps that may some day be used by clinicians in diagnosing arrhythmias and assessing the efficacy of therapies.
International Nuclear Information System (INIS)
Lafore, P.
1965-01-01
The object of the present work is to draw up a basic set of orthogonal eigenfunctions; resolution of the one-velocity integral-differential Boltzmann equation; this in the case of a spherical geometry system. (author) [fr
International Nuclear Information System (INIS)
Bolte, J.
1992-08-01
The Selberg trace formula for automorphic forms of weight m ε- Z, on bordered Riemann surfaces is developed. The trace formula is formulated for arbitrary Fuchsian groups of the first kind which include hyperbolic, elliptic and parabolic conjugacy classes. In the case of compact bordered Riemann surfaces we can explicitly evaluate determinants of Maass-Laplacians for both Dirichlet and Neumann boundary-conditions, respectively. Some implications for the open bosonic string theory are mentioned. (orig.)
DEFF Research Database (Denmark)
Gimperlein, Heiko; Grubb, Gerd
2014-01-01
The purpose of this article is to establish upper and lower estimates for the integral kernel of the semigroup exp(−t P) associated to a classical, strongly elliptic pseudodifferential operator P of positive order on a closed manifold. The Poissonian bounds generalize those obtained for perturbat......The purpose of this article is to establish upper and lower estimates for the integral kernel of the semigroup exp(−t P) associated to a classical, strongly elliptic pseudodifferential operator P of positive order on a closed manifold. The Poissonian bounds generalize those obtained...... for perturbations of fractional powers of the Laplacian. In the selfadjoint case, extensions to t∈C+ are studied. In particular, our results apply to the Dirichlet-to-Neumann semigroup....
Chen, Zigang; Li, Lixiang; Peng, Haipeng; Liu, Yuhong; Yang, Yixian
2018-04-01
Community mining for complex social networks with link and attribute information plays an important role according to different application needs. In this paper, based on our proposed general non-negative matrix factorization (GNMF) algorithm without dimension matching constraints in our previous work, we propose the joint GNMF with graph Laplacian (LJGNMF) to implement community mining of complex social networks with link and attribute information according to different application needs. Theoretical derivation result shows that the proposed LJGNMF is fully compatible with previous methods of integrating traditional NMF and symmetric NMF. In addition, experimental results show that the proposed LJGNMF can meet the needs of different community minings by adjusting its parameters, and the effect is better than traditional NMF in the community vertices attributes entropy.
Conformal invariant powers of the Laplacian, Fefferman-Graham ambient metric and Ricci gauging
International Nuclear Information System (INIS)
Manvelyan, Ruben; Mkrtchyan, Karapet; Mkrtchyan, Ruben
2007-01-01
The hierarchy of conformally invariant kth powers of the Laplacian acting on a scalar field with scaling dimensions Δ (k) =k-d/2, k=1,2,3, as obtained in the recent work [R. Manvelyan, D.H. Tchrakian, Phys. Lett. B 644 (2007) 370, (hep-th/0611077)] is rederived using the Fefferman-Graham (d+2)-dimensional ambient space approach. The corresponding mysterious 'holographic' structure of these operators is clarified. We explore also the (d+2)-dimensional ambient space origin of the Ricci gauging procedure proposed by A. Iorio, L. O'Raifeartaigh, I. Sachs and C. Wiesendanger as another method of constructing the Weyl invariant Lagrangians. The corresponding gauged ambient metric, Fefferman-Graham expansion and extended Penrose-Brown-Henneaux transformations are proposed and analyzed
Soury, Hamza
2015-01-07
This work considers the symbol error rate of M-ary phase shift keying (MPSK) constellations over extended Generalized-K fading with Laplacian noise and using a minimum distance detector. A generic closed form expression of the conditional and the average probability of error is obtained and simplified in terms of the Fox’s H function. More simplifications to well known functions for some special cases of fading are also presented. Finally, the mathematical formalism is validated with some numerical results examples done by computer based simulations [1].
Soury, Hamza; Alouini, Mohamed-Slim
2015-01-01
This work considers the symbol error rate of M-ary phase shift keying (MPSK) constellations over extended Generalized-K fading with Laplacian noise and using a minimum distance detector. A generic closed form expression of the conditional and the average probability of error is obtained and simplified in terms of the Fox’s H function. More simplifications to well known functions for some special cases of fading are also presented. Finally, the mathematical formalism is validated with some numerical results examples done by computer based simulations [1].
L1-norm locally linear representation regularization multi-source adaptation learning.
Tao, Jianwen; Wen, Shiting; Hu, Wenjun
2015-09-01
In most supervised domain adaptation learning (DAL) tasks, one has access only to a small number of labeled examples from target domain. Therefore the success of supervised DAL in this "small sample" regime needs the effective utilization of the large amounts of unlabeled data to extract information that is useful for generalization. Toward this end, we here use the geometric intuition of manifold assumption to extend the established frameworks in existing model-based DAL methods for function learning by incorporating additional information about the target geometric structure of the marginal distribution. We would like to ensure that the solution is smooth with respect to both the ambient space and the target marginal distribution. In doing this, we propose a novel L1-norm locally linear representation regularization multi-source adaptation learning framework which exploits the geometry of the probability distribution, which has two techniques. Firstly, an L1-norm locally linear representation method is presented for robust graph construction by replacing the L2-norm reconstruction measure in LLE with L1-norm one, which is termed as L1-LLR for short. Secondly, considering the robust graph regularization, we replace traditional graph Laplacian regularization with our new L1-LLR graph Laplacian regularization and therefore construct new graph-based semi-supervised learning framework with multi-source adaptation constraint, which is coined as L1-MSAL method. Moreover, to deal with the nonlinear learning problem, we also generalize the L1-MSAL method by mapping the input data points from the input space to a high-dimensional reproducing kernel Hilbert space (RKHS) via a nonlinear mapping. Promising experimental results have been obtained on several real-world datasets such as face, visual video and object. Copyright © 2015 Elsevier Ltd. All rights reserved.
On a Volume Constrained for the First Eigenvalue of the P-Laplacian Operator
International Nuclear Information System (INIS)
Ly, Idrissa
2009-10-01
In this paper, we are interested in a shape optimization problem which consists in minimizing the functional that associates to an open set the first eigenvalue for p-Laplacian operator with homogeneous boundary condition. The minimum is taken among all open subsets with prescribed measure of a given bounded domain. We study an existence result for the associate variational problem. Our technique consists in enlarging the class of admissible functions to the whole space W 0 1,p (D), penalizing those functions whose level sets have a measure which is less than those required. In fact, we study the minimizers of a family of penalized functionals J λ , λ > 0 showing they are Hoelder continuous. And we prove that such functions minimize the initial problem provided the penalization parameter λ is large enough. (author)
Soury, Hamza
2014-06-01
This paper considers the symbol error rate of M-ary phase shift keying (MPSK) constellations over extended Generalized-K fading with Laplacian noise and using a minimum distance detector. A generic closed form expression of the conditional and the average probability of error is obtained and simplified in terms of the Fox\\'s H function. More simplifications to well known functions for some special cases of fading are also presented. Finally, the mathematical formalism is validated with some numerical results examples done by computer based simulations. © 2014 IEEE.
Soury, Hamza; Alouini, Mohamed-Slim
2014-01-01
This paper considers the symbol error rate of M-ary phase shift keying (MPSK) constellations over extended Generalized-K fading with Laplacian noise and using a minimum distance detector. A generic closed form expression of the conditional and the average probability of error is obtained and simplified in terms of the Fox's H function. More simplifications to well known functions for some special cases of fading are also presented. Finally, the mathematical formalism is validated with some numerical results examples done by computer based simulations. © 2014 IEEE.
Statistical distribution of components of energy eigenfunctions: from nearly-integrable to chaotic
International Nuclear Information System (INIS)
Wang, Jiaozi; Wang, Wen-ge
2016-01-01
We study the statistical distribution of components in the non-perturbative parts of energy eigenfunctions (EFs), in which main bodies of the EFs lie. Our numerical simulations in five models show that deviation of the distribution from the prediction of random matrix theory (RMT) is useful in characterizing the process from nearly-integrable to chaotic, in a way somewhat similar to the nearest-level-spacing distribution. But, the statistics of EFs reveals some more properties, as described below. (i) In the process of approaching quantum chaos, the distribution of components shows a delay feature compared with the nearest-level-spacing distribution in most of the models studied. (ii) In the quantum chaotic regime, the distribution of components always shows small but notable deviation from the prediction of RMT in models possessing classical counterparts, while, the deviation can be almost negligible in models not possessing classical counterparts. (iii) In models whose Hamiltonian matrices possess a clear band structure, tails of EFs show statistical behaviors obviously different from those in the main bodies, while, the difference is smaller for Hamiltonian matrices without a clear band structure.
A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian
Quaas, Alexander; Xia, Aliang
2016-08-01
We establish a Liouville type theorem for the fractional Lane-Emden system: {(-Δ)αu=vqin RN,(-Δ)αv=upin RN, where α \\in (0,1) , N>2α and p, q are positive real numbers and in an appropriate new range. To prove our result we will use the local realization of fractional Laplacian, which can be constructed as a Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre (2007 Commun. PDE 32 1245-60). Our proof is based on a monotonicity argument for suitable transformed functions and the method of moving planes in a half infinite cylinder ({IR}× S+N , where S+N is the half unit sphere in {{{R}}N+1} ) based on maximum principles which are obtained by barrier functions and a coupling argument using a fractional Sobolev trace inequality.
Morphology of Laplacian growth processes and statistics of equivalent many-body systems
International Nuclear Information System (INIS)
Blumenfeld, R.
1994-01-01
The authors proposes a theory for the nonlinear evolution of two dimensional interfaces in Laplacian fields. The growing region is conformally mapped onto the unit disk, generating an equivalent many-body system whose dynamics and statistics are studied. The process is shown to be Hamiltonian, with the Hamiltonian being the imaginary part of the complex electrostatic potential. Surface effects are introduced through the Hamiltonian as an external field. An extension to a continuous density of particles is presented. The results are used to study the morphology of the interface using statistical mechanics for the many-body system. The distribution of the curvature and the moments of the growth probability along the interface are calculated exactly from the distribution of the particles. In the dilute limit, the distribution of the curvature is shown to develop algebraic tails, which may, for the first time, explain the origin of fractality in diffusion controlled processes
Automatic Seizure Detection in Rats Using Laplacian EEG and Verification with Human Seizure Signals
Feltane, Amal; Boudreaux-Bartels, G. Faye; Besio, Walter
2012-01-01
Automated detection of seizures is still a challenging problem. This study presents an approach to detect seizure segments in Laplacian electroencephalography (tEEG) recorded from rats using the tripolar concentric ring electrode (TCRE) configuration. Three features, namely, median absolute deviation, approximate entropy, and maximum singular value were calculated and used as inputs into two different classifiers: support vector machines and adaptive boosting. The relative performance of the extracted features on TCRE tEEG was examined. Results are obtained with an overall accuracy between 84.81 and 96.51%. In addition to using TCRE tEEG data, the seizure detection algorithm was also applied to the recorded EEG signals from Andrzejak et al. database to show the efficiency of the proposed method for seizure detection. PMID:23073989
On the Nodal Lines of Eisenstein Series on Schottky Surfaces
Jakobson, Dmitry; Naud, Frédéric
2017-04-01
On convex co-compact hyperbolic surfaces {X=Γ backslash H2}, we investigate the behavior of nodal curves of real valued Eisenstein series {F_λ(z,ξ)}, where {λ} is the spectral parameter, {ξ} the direction at infinity. Eisenstein series are (non-{L^2}) eigenfunctions of the Laplacian {Δ_X} satisfying {Δ_X F_λ=(1/4+λ^2)F_λ}. As {λ} goes to infinity (the high energy limit), we show that, for generic {ξ}, the number of intersections of nodal lines with any compact segment of geodesic grows like {λ}, up to multiplicative constants. Applications to the number of nodal domains inside the convex core of the surface are then derived.
Inflationary perturbations in anisotropic, shear-free universes
International Nuclear Information System (INIS)
Pereira, Thiago S.; Carneiro, Saulo; Marugan, Guillermo A. Mena
2012-01-01
In this work, the linear and gauge-invariant theory of cosmological perturbations in a class of anisotropic and shear-free spacetimes is developed. After constructing an explicit set of complete eigenfunctions in terms of which perturbations can be expanded, we identify the effective degrees of freedom during a generic slow-roll inflationary phase. These correspond to the anisotropic equivalent of the standard Mukhanov-Sasaki variables. The associated equations of motion present a remarkable resemblance to those found in perturbed Friedmann-Robertson-Walker spacetimes with curvature, apart from the spectrum of the Laplacian, which exhibits the characteristic frequencies of the underlying geometry. In particular, it is found that the perturbations cannot develop arbitrarily large super-Hubble modes
The Path Resistance Method for Bounding the Smallest Nontrivial Eigenvalue of a Laplacian
Guattery, Stephen; Leighton, Tom; Miller, Gary L.
1997-01-01
We introduce the path resistance method for lower bounds on the smallest nontrivial eigenvalue of the Laplacian matrix of a graph. The method is based on viewing the graph in terms of electrical circuits; it uses clique embeddings to produce lower bounds on lambda(sub 2) and star embeddings to produce lower bounds on the smallest Rayleigh quotient when there is a zero Dirichlet boundary condition. The method assigns priorities to the paths in the embedding; we show that, for an unweighted tree T, using uniform priorities for a clique embedding produces a lower bound on lambda(sub 2) that is off by at most an 0(log diameter(T)) factor. We show that the best bounds this method can produce for clique embeddings are the same as for a related method that uses clique embeddings and edge lengths to produce bounds.
International Nuclear Information System (INIS)
Kurihara, Kenichi
1997-11-01
Plasma current density distribution is one of the most important controlled variables to determine plasma performance of energy confinement and stability in a tokamak. However, its reproduction by using magnetic measurements solely is recognized to yield an ill-posed problem. A method to presume the formulas giving profiles of plasma pressure and current has been adopted to regularize the ill-posedness, and hence it has been reported the current density distribution can be reproduced as a solution of Grad-Shafranov equation within a certain accuracy. In order to investigate its strict reproducibility from magnetic measurements in this inverse problem, a new method of 'bounded-eigenfunction expansion' is introduced, and it was found that the reproducibility directly corresponds to the independence of a series of the special function. The results from various investigations in an aspect of applied mathematics concerning this inverse problem are presented in detail. (author)
Directory of Open Access Journals (Sweden)
Wei Han
2008-01-01
Full Text Available Several existence theorems of twin positive solutions are established for a nonlinear m-point boundary value problem of third-order p-Laplacian dynamic equations on time scales by using a fixed point theorem. We present two theorems and four corollaries which generalize the results of related literature. As an application, an example to demonstrate our results is given. The obtained conditions are different from some known results.
Learning-based 3D surface optimization from medical image reconstruction
Wei, Mingqiang; Wang, Jun; Guo, Xianglin; Wu, Huisi; Xie, Haoran; Wang, Fu Lee; Qin, Jing
2018-04-01
Mesh optimization has been studied from the graphical point of view: It often focuses on 3D surfaces obtained by optical and laser scanners. This is despite the fact that isosurfaced meshes of medical image reconstruction suffer from both staircases and noise: Isotropic filters lead to shape distortion, while anisotropic ones maintain pseudo-features. We present a data-driven method for automatically removing these medical artifacts while not introducing additional ones. We consider mesh optimization as a combination of vertex filtering and facet filtering in two stages: Offline training and runtime optimization. In specific, we first detect staircases based on the scanning direction of CT/MRI scanners, and design a staircase-sensitive Laplacian filter (vertex-based) to remove them; and then design a unilateral filtered facet normal descriptor (uFND) for measuring the geometry features around each facet of a given mesh, and learn the regression functions from a set of medical meshes and their high-resolution reference counterparts for mapping the uFNDs to the facet normals of the reference meshes (facet-based). At runtime, we first perform staircase-sensitive Laplacian filter on an input MC (Marching Cubes) mesh, and then filter the mesh facet normal field using the learned regression functions, and finally deform it to match the new normal field for obtaining a compact approximation of the high-resolution reference model. Tests show that our algorithm achieves higher quality results than previous approaches regarding surface smoothness and surface accuracy.
Directory of Open Access Journals (Sweden)
Sukjung Hwang
2015-11-01
Full Text Available Here we generalize quasilinear parabolic p-Laplacian type equations to obtain the prototype equation $$ u_t - \\hbox{div} \\Big(\\frac{g(|Du|}{|Du|} Du\\Big = 0, $$ where g is a nonnegative, increasing, and continuous function trapped in between two power functions $|Du|^{g_0 -1}$ and $|Du|^{g_1 -1}$ with $1
Eigenfunction method and mass operator in the quantum electrodynamics of a constant field
International Nuclear Information System (INIS)
Ritus, V.I.
1978-01-01
A method is presented for the calculation of radiative effects in the quantum electrodynamics of an intense constant field. It is based on the application of the mass operator eigenfunctions and on diagonalization of the operator. A compact expression for the proper value of the electron mass operator in an arbitrary constant field and the corresponding elastic scattering amplitude are found. The imaginary part of the amplitude determines the decay rate of various states of the electron in the field; the real part contains the mass shift and the anomalous magnetic and electric moments as functions of the field and electron momentum. THe anomalous electric moment which arises in a field with a pseudoscalar EH not equal to 0 and the anomalous magnetic moment in an electric field which tends to the double Schwinger value with increase of the field strength are found and investigated in detail as are the mass shift and decay rate of the ground state of an electron in an electric field. In a weak field the mass shift contains the linear with respect to the field modulus classical term which characterizes the effect of acceleration on the structure of electron
Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields
International Nuclear Information System (INIS)
Han, Tiancheng; Qiu, Cheng-Wei
2016-01-01
The full control of single or even multiple physical fields has attracted intensive research attention in the past decade, thanks to the development of metamaterials and transformation optics. Significant progress has been made in vector fields (e.g., optics, electromagnetics, and acoustics), leading to a host of strikingly functional metamaterials, such as invisibility cloaks, illusion devices, concentrators, and rotators. However, metamaterials in vector fields, designed through coordinate transformation of Maxwell’s equations, usually require extreme parameters and impose challenges on the actual realization. In this context, metamaterials in scalar fields (e.g., thermal and dc fields), which are mostly governed by the Laplace equation, lead to more plausible and facile implementations, since there are native insulators and excellent conductors (serving as two extreme cases). This paper therefore is particularly dedicated to reviewing the most recent advances in Laplacian metamaterials in manipulating thermal (both transient and steady states) and dc fields, separately and (or) simultaneously. We focus on the theory, design, and realization of thermal/dc functional metamaterials that can be used to control heat flux and electric current at will. We also provide an outlook toward the challenges and future directions in this fascinating area. (review)
Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields
Han, Tiancheng; Qiu, Cheng-Wei
2016-04-01
The full control of single or even multiple physical fields has attracted intensive research attention in the past decade, thanks to the development of metamaterials and transformation optics. Significant progress has been made in vector fields (e.g., optics, electromagnetics, and acoustics), leading to a host of strikingly functional metamaterials, such as invisibility cloaks, illusion devices, concentrators, and rotators. However, metamaterials in vector fields, designed through coordinate transformation of Maxwell’s equations, usually require extreme parameters and impose challenges on the actual realization. In this context, metamaterials in scalar fields (e.g., thermal and dc fields), which are mostly governed by the Laplace equation, lead to more plausible and facile implementations, since there are native insulators and excellent conductors (serving as two extreme cases). This paper therefore is particularly dedicated to reviewing the most recent advances in Laplacian metamaterials in manipulating thermal (both transient and steady states) and dc fields, separately and (or) simultaneously. We focus on the theory, design, and realization of thermal/dc functional metamaterials that can be used to control heat flux and electric current at will. We also provide an outlook toward the challenges and future directions in this fascinating area.
Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD
International Nuclear Information System (INIS)
Morningstar, C.; Lenkner, D.; Wong, C.H.; Bulava, J.; Foley, J.; Juge, K.J.; Peardon, M.
2011-08-01
A new method of stochastically estimating the low-lying effects of quark propagation is proposed which allows accurate determinations of temporal correlations of single-hadron and multi-hadron operators in lattice QCD. The method is well suited for calculations in large volumes. Contributions involving quark propagation connecting hadron sink operators at the same final time can be handled in a straightforward manner, even for a large number of final time slices. The method exploits Laplacian Heaviside (LapH) smearing. Z N noise is introduced in a novel way, and variance reduction is achieved using judiciously-chosen noise dilution projectors. The method is tested using isoscalar mesons in the scalar, pseudoscalar, and vector channels, and using the two-pion system of total isospin I=0,1,2 on large anisotropic 24 3 x 128 lattices with spatial spacing a s ∝0.12 fm and temporal spacing a t ∝0.034 fm for pion masses m π ∼ 390 and 240 MeV. (orig.)
Self-dual form of Ruijsenaars–Schneider models and ILW equation with discrete Laplacian
Directory of Open Access Journals (Sweden)
A. Zabrodin
2018-02-01
Full Text Available We discuss a self-dual form or the Bäcklund transformations for the continuous (in time variable glN Ruijsenaars–Schneider model. It is based on the first order equations in N+M complex variables which include N positions of particles and M dual variables. The latter satisfy equations of motion of the glM Ruijsenaars–Schneider model. In the elliptic case it holds M=N while for the rational and trigonometric models M is not necessarily equal to N. Our consideration is similar to the previously obtained results for the Calogero–Moser models which are recovered in the non-relativistic limit. We also show that the self-dual description of the Ruijsenaars–Schneider models can be derived from complexified intermediate long wave equation with discrete Laplacian by means of the simple pole ansatz likewise the Calogero–Moser models arise from ordinary intermediate long wave and Benjamin–Ono equations.
Automated spike sorting algorithm based on Laplacian eigenmaps and k-means clustering.
Chah, E; Hok, V; Della-Chiesa, A; Miller, J J H; O'Mara, S M; Reilly, R B
2011-02-01
This study presents a new automatic spike sorting method based on feature extraction by Laplacian eigenmaps combined with k-means clustering. The performance of the proposed method was compared against previously reported algorithms such as principal component analysis (PCA) and amplitude-based feature extraction. Two types of classifier (namely k-means and classification expectation-maximization) were incorporated within the spike sorting algorithms, in order to find a suitable classifier for the feature sets. Simulated data sets and in-vivo tetrode multichannel recordings were employed to assess the performance of the spike sorting algorithms. The results show that the proposed algorithm yields significantly improved performance with mean sorting accuracy of 73% and sorting error of 10% compared to PCA which combined with k-means had a sorting accuracy of 58% and sorting error of 10%.A correction was made to this article on 22 February 2011. The spacing of the title was amended on the abstract page. No changes were made to the article PDF and the print version was unaffected.
Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.
2017-12-01
We analyze a Markovian random walk strategy on undirected regular networks involving power matrix functions of the type L\\frac{α{2}} where L indicates a ‘simple’ Laplacian matrix. We refer to such walks as ‘fractional random walks’ with admissible interval 0walk. From these analytical results we establish a generalization of Polya’s recurrence theorem for fractional random walks on d-dimensional infinite lattices: The fractional random walk is transient for dimensions d > α (recurrent for d≤slantα ) of the lattice. As a consequence, for 0walk is transient for all lattice dimensions d=1, 2, .. and in the range 1≤slantα walk is transient only for lattice dimensions d≥slant 3 . The generalization of Polya’s recurrence theorem remains valid for the class of random walks with Lévy flight asymptotics for long-range steps. We also analyze the mean first passage probabilities, mean residence times, mean first passage times and global mean first passage times (Kemeny constant) for the fractional random walk. For an infinite 1D lattice (infinite ring) we obtain for the transient regime 0walk is generated by the non-diagonality of the fractional Laplacian matrix with Lévy-type heavy tailed inverse power law decay for the probability of long-range moves. This non-local and asymptotic behavior of the fractional random walk introduces small-world properties with the emergence of Lévy flights on large (infinite) lattices.
Directory of Open Access Journals (Sweden)
George N. Galanis
2005-10-01
Full Text Available In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem$$ -[phi _{p}(u']'=q(tf(t,u(t,quad 0
Robust Visual Knowledge Transfer via Extreme Learning Machine Based Domain Adaptation.
Zhang, Lei; Zhang, David
2016-08-10
We address the problem of visual knowledge adaptation by leveraging labeled patterns from source domain and a very limited number of labeled instances in target domain to learn a robust classifier for visual categorization. This paper proposes a new extreme learning machine based cross-domain network learning framework, that is called Extreme Learning Machine (ELM) based Domain Adaptation (EDA). It allows us to learn a category transformation and an ELM classifier with random projection by minimizing the -norm of the network output weights and the learning error simultaneously. The unlabeled target data, as useful knowledge, is also integrated as a fidelity term to guarantee the stability during cross domain learning. It minimizes the matching error between the learned classifier and a base classifier, such that many existing classifiers can be readily incorporated as base classifiers. The network output weights cannot only be analytically determined, but also transferrable. Additionally, a manifold regularization with Laplacian graph is incorporated, such that it is beneficial to semi-supervised learning. Extensively, we also propose a model of multiple views, referred as MvEDA. Experiments on benchmark visual datasets for video event recognition and object recognition, demonstrate that our EDA methods outperform existing cross-domain learning methods.
Zheng, Jinde; Pan, Haiyang; Yang, Shubao; Cheng, Junsheng
2018-01-01
Multiscale permutation entropy (MPE) is a recently proposed nonlinear dynamic method for measuring the randomness and detecting the nonlinear dynamic change of time series and can be used effectively to extract the nonlinear dynamic fault feature from vibration signals of rolling bearing. To solve the drawback of coarse graining process in MPE, an improved MPE method called generalized composite multiscale permutation entropy (GCMPE) was proposed in this paper. Also the influence of parameters on GCMPE and its comparison with the MPE are studied by analyzing simulation data. GCMPE was applied to the fault feature extraction from vibration signal of rolling bearing and then based on the GCMPE, Laplacian score for feature selection and the Particle swarm optimization based support vector machine, a new fault diagnosis method for rolling bearing was put forward in this paper. Finally, the proposed method was applied to analyze the experimental data of rolling bearing. The analysis results show that the proposed method can effectively realize the fault diagnosis of rolling bearing and has a higher fault recognition rate than the existing methods.
Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Morningstar, C.; Lenkner, D.; Wong, C.H. [Pittsburgh Univ., PA (United States). Dept. of Physics; Bulava, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Foley, J. [Utah Univ., Salt Lake City, UT (United States). Dept. of Physics and Astronomy; Juge, K.J. [University of the Pacific, Stockton, CA (United States). Dept. of Physics; Peardon, M. [Trinity College, Dublin (Ireland). School of Mathematics
2011-08-15
A new method of stochastically estimating the low-lying effects of quark propagation is proposed which allows accurate determinations of temporal correlations of single-hadron and multi-hadron operators in lattice QCD. The method is well suited for calculations in large volumes. Contributions involving quark propagation connecting hadron sink operators at the same final time can be handled in a straightforward manner, even for a large number of final time slices. The method exploits Laplacian Heaviside (LapH) smearing. Z{sub N} noise is introduced in a novel way, and variance reduction is achieved using judiciously-chosen noise dilution projectors. The method is tested using isoscalar mesons in the scalar, pseudoscalar, and vector channels, and using the two-pion system of total isospin I=0,1,2 on large anisotropic 24{sup 3} x 128 lattices with spatial spacing a{sub s} {proportional_to}0.12 fm and temporal spacing a{sub t} {proportional_to}0.034 fm for pion masses m{sub {pi}} {approx} 390 and 240 MeV. (orig.)
Directory of Open Access Journals (Sweden)
Yves Biollay
1979-01-01
Full Text Available We show in this paper that the sequence {max|uk|}, where the uk are the eigenfunctions of the problem Δu+λu=0 in D⊂Rn and u=0 on ∂D, is not bounded generally if one imposes the norm ∫Du2p(xdx=1, p=(1,2,3,…. The same holds with the norm ∫D|gradu|2pdx=1 when n>4p−1. On the other hand, if D⊂R2, resp. R3 the norm ∫D|gradu|2dx=1 implies max|uk|→k→∞0, resp. max|uk|=0(1.
International Nuclear Information System (INIS)
Prati, M.C.
1986-01-01
The eigenfunctions psub(nm)sup(μ) (z, z-bar), n,m are elements of N, μ is an element of (-1/3, + infinity), z is an element of C, of two differential operators, which for some particular values of μ are the generators of the algebra of invariant differential operators on symmetric spaces, having A 2 as a restricted root system, are studied. The group-theoretic interpretation and the explicit form of these functions as polynomials of z , z-bar are given in the following cases: when μ = 0, 1 for every n, m belonging to N; when m = 0, for every n belonging to N and when μ is an element of (-1/3, +infinity). Furthermore, all solutions psub(nm)sup(μ) (z, z-bar) for every μ belonging to (-1/3, +infinity) and n + m <= 5 are explicitly written. This research has applications in quantum mechanics and in quantum field theory
Salman, Yehonatan
2017-09-01
The aim of this paper is to introduce a new inversion procedure for recovering functions, defined on R2 , from the spherical mean transform, which integrates functions on a prescribed family Λ of circles, where Λ consists of circles whose centers belong to a given ellipse E on the plane. The method presented here follows the same procedure which was used by Norton (J Acoust Soc Am 67:1266-1273, 1980) for recovering functions in case where Λ consists of circles with centers on a circle. However, at some point we will have to modify the method in [24] by using expansion in elliptical coordinates, rather than spherical coordinates, in order to solve the more generalized elliptical case. We will rely on a recent result obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the eigenfunction expansion of the Bessel function in elliptical coordinates.
Energy Technology Data Exchange (ETDEWEB)
Tanguy, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1957-07-01
In this report are described and interpreted some experiments, carried out in the pile G1 during a period of shut-down, which have made it possible to measure the variation of the material Laplacian of the lattice with the radius of the uranium bar. The variation of the reactivity of the pile is measured when an increasing number of fuel elements are progressively replaced in the central region by fuel elements of greater diameter; it is shown that, starting from measurements based on less than ten per cent of the total number of elements, the variation of reactivity corresponding to the replacement of all the elements can be determined; it is then easy to deduce the variations of the Laplacian. Results: the variations of the Laplacian with the uranium rod diameter are 0 (d. 26 mm), +0.065 {+-} 0.004 m{sup -2} (d. 28 mm) and +0.080 {+-} 0.008 m{sup -2} (d. 32 mm). (author) [French] Dans ce rapport sont decrites et interpretees des experiences realisees sur la pile G1 'froide', experiences qui ont permis de mesurer la variation du Laplacien matiere du reseau avec le rayon du barreau d'uranium. On mesure la variation de reactivite de la pile lorsqu'on remplace progressivement dans la region centrale un nombre croissant de cartouches par des cartouches de plus gros diametre; on montre qu'a partir de mesures portant sur moins de dix pour cent du nombre total de cartouches, on peut determiner la variation de reactivite qui correspondrait au remplacement de toutes les cartouches; il est facile d'en deduire les variations du Laplacien. Resultats: les variations du Laplacien en fonction du diametre du barreau d'uranium sont: 0 (d. 26 mm), +0.065 {+-} 0.004 m{sup -2} (d. 28 mm) and +0.080 {+-} 0.008 m{sup -2} (d. 32 mm). (auteur)
Valizade Hasanloei, Mohammad Amin; Sheikhpour, Razieh; Sarram, Mehdi Agha; Sheikhpour, Elnaz; Sharifi, Hamdollah
2018-02-01
Quantitative structure-activity relationship (QSAR) is an effective computational technique for drug design that relates the chemical structures of compounds to their biological activities. Feature selection is an important step in QSAR based drug design to select the most relevant descriptors. One of the most popular feature selection methods for classification problems is Fisher score which aim is to minimize the within-class distance and maximize the between-class distance. In this study, the properties of Fisher criterion were extended for QSAR models to define the new distance metrics based on the continuous activity values of compounds with known activities. Then, a semi-supervised feature selection method was proposed based on the combination of Fisher and Laplacian criteria which exploits both compounds with known and unknown activities to select the relevant descriptors. To demonstrate the efficiency of the proposed semi-supervised feature selection method in selecting the relevant descriptors, we applied the method and other feature selection methods on three QSAR data sets such as serine/threonine-protein kinase PLK3 inhibitors, ROCK inhibitors and phenol compounds. The results demonstrated that the QSAR models built on the selected descriptors by the proposed semi-supervised method have better performance than other models. This indicates the efficiency of the proposed method in selecting the relevant descriptors using the compounds with known and unknown activities. The results of this study showed that the compounds with known and unknown activities can be helpful to improve the performance of the combined Fisher and Laplacian based feature selection methods.
International Nuclear Information System (INIS)
Gorbachev, D V; Ivanov, V I
2015-01-01
Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles
Energy decay for wave equations of phi-Laplacian type with weakly nonlinear dissipation
Directory of Open Access Journals (Sweden)
Aissa Guesmia
2008-08-01
Full Text Available In this paper, first we prove the existence of global solutions in Sobolev spaces for the initial boundary value problem of the wave equation of $phi$-Laplacian with a general dissipation of the form $$ (|u'|^{l-2}u''-Delta_{phi}u+sigma(t g(u'=0 quadext{in } Omegaimes mathbb{R}_+ , $$ where $Delta_{phi}=sum_{i=1}^n partial_{x_i}igl(phi (|partial_{x_i}|^2partial_{x_i}igr$. Then we prove general stability estimates using multiplier method and general weighted integral inequalities proved by the second author in [18]. Without imposing any growth condition at the origin on $g$ and $phi$, we show that the energy of the system is bounded above by a quantity, depending on $phi$, $sigma$ and $g$, which tends to zero (as time approaches infinity. These estimates allows us to consider large class of functions $g$ and $phi$ with general growth at the origin. We give some examples to illustrate how to derive from our general estimates the polynomial, exponential or logarithmic decay. The results of this paper improve and generalize many existing results in the literature, and generate some interesting open problems.
Automatic arrival time detection for earthquakes based on Modified Laplacian of Gaussian filter
Saad, Omar M.; Shalaby, Ahmed; Samy, Lotfy; Sayed, Mohammed S.
2018-04-01
Precise identification of onset time for an earthquake is imperative in the right figuring of earthquake's location and different parameters that are utilized for building seismic catalogues. P-wave arrival detection of weak events or micro-earthquakes cannot be precisely determined due to background noise. In this paper, we propose a novel approach based on Modified Laplacian of Gaussian (MLoG) filter to detect the onset time even in the presence of very weak signal-to-noise ratios (SNRs). The proposed algorithm utilizes a denoising-filter algorithm to smooth the background noise. In the proposed algorithm, we employ the MLoG mask to filter the seismic data. Afterward, we apply a Dual-threshold comparator to detect the onset time of the event. The results show that the proposed algorithm can detect the onset time for micro-earthquakes accurately, with SNR of -12 dB. The proposed algorithm achieves an onset time picking accuracy of 93% with a standard deviation error of 0.10 s for 407 field seismic waveforms. Also, we compare the results with short and long time average algorithm (STA/LTA) and the Akaike Information Criterion (AIC), and the proposed algorithm outperforms them.
Analytic functionals on the sphere
Morimoto, Mitsuo
1998-01-01
This book treats spherical harmonic expansion of real analytic functions and hyperfunctions on the sphere. Because a one-dimensional sphere is a circle, the simplest example of the theory is that of Fourier series of periodic functions. The author first introduces a system of complex neighborhoods of the sphere by means of the Lie norm. He then studies holomorphic functions and analytic functionals on the complex sphere. In the one-dimensional case, this corresponds to the study of holomorphic functions and analytic functionals on the annular set in the complex plane, relying on the Laurent series expansion. In this volume, it is shown that the same idea still works in a higher-dimensional sphere. The Fourier-Borel transformation of analytic functionals on the sphere is also examined; the eigenfunction of the Laplacian can be studied in this way.
Energy Technology Data Exchange (ETDEWEB)
Soliman, A; Safigholi, H [Sunnybrook Research Institute, Toronto, ON (Canada); Sunnybrook Health Sciences Center, Toronto, ON (Canada); Nosrati, R [Sunnybrook Health Sciences Center, Toronto, ON (Canada); Ryerson University, Toronto, ON (Canada); Owrangi, A; Morton, G [Sunnybrook Health Sciences Center, Toronto, ON (Canada); University of Toronto, Toronto, ON (Canada); Song, W [Sunnybrook Research Institute, Toronto, ON (Canada); Sunnybrook Health Sciences Center, Toronto, ON (Canada); Ryerson University, Toronto, ON (Canada); University of Toronto, Toronto, ON (Canada)
2016-06-15
Purpose: To propose a new method that provides a positive contrast visualization of the prostate brachytherapy seeds using the phase information from MR images. Additionally, the feasibility of using the processed phase information to distinguish seeds from calcifications is explored. Methods: A gel phantom was constructed using 2% agar dissolved in 1 L of distilled water. Contrast agents were added to adjust the relaxation times. Four iodine-125 (Eckert & Ziegler SML86999) dummy seeds were placed at different orientations with respect to the main magnetic field (B0). Calcifications were obtained from a sheep femur cortical bone due to its close similarity to human bone tissue composition. Five samples of calcifications were shaped into different dimensions with lengths ranging between 1.2 – 6.1 mm.MR imaging was performed on a 3T Philips Achieva using an 8-channel head coil. Eight images were acquired at eight echo-times using a multi-gradient echo sequence. Spatial resolution was 0.7 × 0.7 × 2 mm, TR/TE/dTE = 20.0/2.3/2.3 ms and BW = 541 Hz/pixel. Complex images were acquired and fed into a two-step processing pipeline: the first includes phase unwrapping and background phase removal using Laplacian operator (Wei et al. 2013). The second step applies a specific phase mask on the resulting tissue phase from the first step to provide the desired positive contrast of the seeds and to, potentially, differentiate them from the calcifications. Results: The phase-processing was performed in less than 30 seconds. The proposed method has successfully resulted in a positive contrast of the brachytherapy seeds. Additionally, the final processed phase image showed difference between the appearance of seeds and calcifications. However, the shape of the seeds was slightly distorted compared to the original dimensions. Conclusion: It is feasible to provide a positive contrast of the seeds from MR images using Laplacian operator-based phase processing.
Energy Technology Data Exchange (ETDEWEB)
Samin, Adib; Lahti, Erik; Zhang, Jinsuo, E-mail: zhang.3558@osu.edu [Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19" t" h Avenue, Columbus, Ohio 43210 (United States)
2015-08-15
Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.
International Nuclear Information System (INIS)
th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Samin, Adib; th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Lahti, Erik; th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Zhang, Jinsuo
2015-01-01
Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes
Detection of anomaly in human retina using Laplacian Eigenmaps and vectorized matched filtering
Yacoubou Djima, Karamatou A.; Simonelli, Lucia D.; Cunningham, Denise; Czaja, Wojciech
2015-03-01
We present a novel method for automated anomaly detection on auto fluorescent data provided by the National Institute of Health (NIH). This is motivated by the need for new tools to improve the capability of diagnosing macular degeneration in its early stages, track the progression over time, and test the effectiveness of new treatment methods. In previous work, macular anomalies have been detected automatically through multiscale analysis procedures such as wavelet analysis or dimensionality reduction algorithms followed by a classification algorithm, e.g., Support Vector Machine. The method that we propose is a Vectorized Matched Filtering (VMF) algorithm combined with Laplacian Eigenmaps (LE), a nonlinear dimensionality reduction algorithm with locality preserving properties. By applying LE, we are able to represent the data in the form of eigenimages, some of which accentuate the visibility of anomalies. We pick significant eigenimages and proceed with the VMF algorithm that classifies anomalies across all of these eigenimages simultaneously. To evaluate our performance, we compare our method to two other schemes: a matched filtering algorithm based on anomaly detection on single images and a combination of PCA and VMF. LE combined with VMF algorithm performs best, yielding a high rate of accurate anomaly detection. This shows the advantage of using a nonlinear approach to represent the data and the effectiveness of VMF, which operates on the images as a data cube rather than individual images.
Directory of Open Access Journals (Sweden)
Yongzhi Liao
2013-01-01
Full Text Available By applying the method of coincidence degree, some criteria are established for the existence of antiperiodic solutions for a generalized high-order (p,q-Laplacian neutral differential system with delays (φp((x(t-cx(t-τ(k(m-k=F(t,xθ0(t,xθ1(t′,…,xθk(t(k,yϑ0(t,yϑ1(t′,…,yϑl(t(l, (φq((y(t-dy(t-σ(l(n-l=G(t,yμ0(t,yμ1(t′,…,yμl(t(l,xν0(t,xν1(t′,…,xνk(t(k in the critical case |c|=|d|=1. The results of this paper are completely new. Finally, an example is employed to illustrate our results.
Dynamic isoperimetry and the geometry of Lagrangian coherent structures
International Nuclear Information System (INIS)
Froyland, Gary
2015-01-01
The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. We propose a novel, direct geometric method to identify subsets of phase space that remain strongly coherent over a finite time duration. This new method is based on a dynamic extension of classical (static) isoperimetric problems; the latter are concerned with identifying submanifolds with the smallest boundary size relative to their volume.The present work introduces dynamic isoperimetric problems; the study of sets with small boundary size relative to volume as they are evolved by a general dynamical system. We formulate and prove dynamic versions of the fundamental (static) isoperimetric (in)equalities; a dynamic Federer–Fleming theorem and a dynamic Cheeger inequality. We introduce a new dynamic Laplace operator and describe a computational method to identify coherent sets based on eigenfunctions of the dynamic Laplacian.Our results include formal mathematical statements concerning geometric properties of finite-time coherent sets, whose boundaries can be regarded as Lagrangian coherent structures. The computational advantages of our new approach are a well-separated spectrum for the dynamic Laplacian, and flexibility in appropriate numerical approximation methods. Finally, we demonstrate that the dynamic Laplace operator can be realised as a zero-diffusion limit of a newly advanced probabilistic transfer operator method [9] for finding coherent sets, which is based on small diffusion. Thus, the present approach sits naturally alongside the probabilistic approach [9], and adds a formal geometric interpretation. (paper)
Lu, Shen; Xia, Yong; Cai, Tom Weidong; Feng, David Dagan
2015-01-01
Dementia, Alzheimer's disease (AD) in particular is a global problem and big threat to the aging population. An image based computer-aided dementia diagnosis method is needed to providing doctors help during medical image examination. Many machine learning based dementia classification methods using medical imaging have been proposed and most of them achieve accurate results. However, most of these methods make use of supervised learning requiring fully labeled image dataset, which usually is not practical in real clinical environment. Using large amount of unlabeled images can improve the dementia classification performance. In this study we propose a new semi-supervised dementia classification method based on random manifold learning with affinity regularization. Three groups of spatial features are extracted from positron emission tomography (PET) images to construct an unsupervised random forest which is then used to regularize the manifold learning objective function. The proposed method, stat-of-the-art Laplacian support vector machine (LapSVM) and supervised SVM are applied to classify AD and normal controls (NC). The experiment results show that learning with unlabeled images indeed improves the classification performance. And our method outperforms LapSVM on the same dataset.
Czech Academy of Sciences Publication Activity Database
Drábek, P.; Namlyeyeva, Yu.; Nečasová, Šárka
2010-01-01
Roč. 140, č. 3 (2010), s. 573-596 ISSN 0308-2105 R&D Projects: GA ČR GA201/05/0005; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : perforated domains * homogenization Subject RIV: BA - General Mathematics Impact factor: 0.669, year: 2010 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7782353&fileId=S0308210507001035
Feature selection and multi-kernel learning for sparse representation on a manifold
Wang, Jim Jing-Yan
2014-03-01
Sparse representation has been widely studied as a part-based data representation method and applied in many scientific and engineering fields, such as bioinformatics and medical imaging. It seeks to represent a data sample as a sparse linear combination of some basic items in a dictionary. Gao etal. (2013) recently proposed Laplacian sparse coding by regularizing the sparse codes with an affinity graph. However, due to the noisy features and nonlinear distribution of the data samples, the affinity graph constructed directly from the original feature space is not necessarily a reliable reflection of the intrinsic manifold of the data samples. To overcome this problem, we integrate feature selection and multiple kernel learning into the sparse coding on the manifold. To this end, unified objectives are defined for feature selection, multiple kernel learning, sparse coding, and graph regularization. By optimizing the objective functions iteratively, we develop novel data representation algorithms with feature selection and multiple kernel learning respectively. Experimental results on two challenging tasks, N-linked glycosylation prediction and mammogram retrieval, demonstrate that the proposed algorithms outperform the traditional sparse coding methods. © 2013 Elsevier Ltd.
Feature selection and multi-kernel learning for sparse representation on a manifold.
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
2014-03-01
Sparse representation has been widely studied as a part-based data representation method and applied in many scientific and engineering fields, such as bioinformatics and medical imaging. It seeks to represent a data sample as a sparse linear combination of some basic items in a dictionary. Gao et al. (2013) recently proposed Laplacian sparse coding by regularizing the sparse codes with an affinity graph. However, due to the noisy features and nonlinear distribution of the data samples, the affinity graph constructed directly from the original feature space is not necessarily a reliable reflection of the intrinsic manifold of the data samples. To overcome this problem, we integrate feature selection and multiple kernel learning into the sparse coding on the manifold. To this end, unified objectives are defined for feature selection, multiple kernel learning, sparse coding, and graph regularization. By optimizing the objective functions iteratively, we develop novel data representation algorithms with feature selection and multiple kernel learning respectively. Experimental results on two challenging tasks, N-linked glycosylation prediction and mammogram retrieval, demonstrate that the proposed algorithms outperform the traditional sparse coding methods. Copyright © 2013 Elsevier Ltd. All rights reserved.
Riemannian geometry during the second half of the twentieth century
Berger, Marcel
1999-01-01
In the last fifty years of the twentieth century Riemannian geometry has exploded with activity. Berger marks the start of this period with Rauch's pioneering paper of 1951, which contains the first real pinching theorem and an amazing leap in the depth of the connection between geometry and topology. Since then, the field has become so rich that it is almost impossible for the uninitiated to find their way through it. Textbooks on the subject invariably must choose a particular approach, thus narrowing the path. In this book, Berger provides a truly remarkable survey of the main developments in Riemannian geometry in the last fifty years, focusing his main attention on the following five areas: Curvature and topology; the construction of and the classification of space forms; distinguished metrics, especially Einstein metrics; eigenvalues and eigenfunctions of the Laplacian; the study of periodic geodesics and the geodesic flow. Other topics are treated in less detail in a separate section. Berger's survey p...
Large-scale parameter extraction in electrocardiology models through Born approximation
He, Yuan
2012-12-04
One of the main objectives in electrocardiology is to extract physical properties of cardiac tissues from measured information on electrical activity of the heart. Mathematically, this is an inverse problem for reconstructing coefficients in electrocardiology models from partial knowledge of the solutions of the models. In this work, we consider such parameter extraction problems for two well-studied electrocardiology models: the bidomain model and the FitzHugh-Nagumo model. We propose a systematic reconstruction method based on the Born approximation of the original nonlinear inverse problem. We describe a two-step procedure that allows us to reconstruct not only perturbations of the unknowns, but also the backgrounds around which the linearization is performed. We show some numerical simulations under various conditions to demonstrate the performance of our method. We also introduce a parameterization strategy using eigenfunctions of the Laplacian operator to reduce the number of unknowns in the parameter extraction problem. © 2013 IOP Publishing Ltd.
Junwei Ma; Han Yuan; Sunderam, Sridhar; Besio, Walter; Lei Ding
2017-07-01
Neural activity inside the human brain generate electrical signals that can be detected on the scalp. Electroencephalograph (EEG) is one of the most widely utilized techniques helping physicians and researchers to diagnose and understand various brain diseases. Due to its nature, EEG signals have very high temporal resolution but poor spatial resolution. To achieve higher spatial resolution, a novel tri-polar concentric ring electrode (TCRE) has been developed to directly measure Surface Laplacian (SL). The objective of the present study is to accurately calculate SL for TCRE based on a realistic geometry head model. A locally dense mesh was proposed to represent the head surface, where the local dense parts were to match the small structural components in TCRE. Other areas without dense mesh were used for the purpose of reducing computational load. We conducted computer simulations to evaluate the performance of the proposed mesh and evaluated possible numerical errors as compared with a low-density model. Finally, with achieved accuracy, we presented the computed forward lead field of SL for TCRE for the first time in a realistic geometry head model and demonstrated that it has better spatial resolution than computed SL from classic EEG recordings.
Manifold regularized matrix completion for multi-label learning with ADMM.
Liu, Bin; Li, Yingming; Xu, Zenglin
2018-05-01
Multi-label learning is a common machine learning problem arising from numerous real-world applications in diverse fields, e.g, natural language processing, bioinformatics, information retrieval and so on. Among various multi-label learning methods, the matrix completion approach has been regarded as a promising approach to transductive multi-label learning. By constructing a joint matrix comprising the feature matrix and the label matrix, the missing labels of test samples are regarded as missing values of the joint matrix. With the low-rank assumption of the constructed joint matrix, the missing labels can be recovered by minimizing its rank. Despite its success, most matrix completion based approaches ignore the smoothness assumption of unlabeled data, i.e., neighboring instances should also share a similar set of labels. Thus they may under exploit the intrinsic structures of data. In addition, the matrix completion problem can be less efficient. To this end, we propose to efficiently solve the multi-label learning problem as an enhanced matrix completion model with manifold regularization, where the graph Laplacian is used to ensure the label smoothness over it. To speed up the convergence of our model, we develop an efficient iterative algorithm, which solves the resulted nuclear norm minimization problem with the alternating direction method of multipliers (ADMM). Experiments on both synthetic and real-world data have shown the promising results of the proposed approach. Copyright © 2018 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Werby, M.F.; Broadhead, M.K.; Strayer, M.R.; Bottcher, C.
1992-01-01
The Helmholtz-Poincarf Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWECs. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can be obtained in matrix form by expanding all relevant terms in partial wave expansions, including a bi-orthogonal expansion of the Green's function. However some freedom in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways so long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermitian operator. The methodology will be explained in detail and examples will be presented
Completing sparse and disconnected protein-protein network by deep learning.
Huang, Lei; Liao, Li; Wu, Cathy H
2018-03-22
Protein-protein interaction (PPI) prediction remains a central task in systems biology to achieve a better and holistic understanding of cellular and intracellular processes. Recently, an increasing number of computational methods have shifted from pair-wise prediction to network level prediction. Many of the existing network level methods predict PPIs under the assumption that the training network should be connected. However, this assumption greatly affects the prediction power and limits the application area because the current golden standard PPI networks are usually very sparse and disconnected. Therefore, how to effectively predict PPIs based on a training network that is sparse and disconnected remains a challenge. In this work, we developed a novel PPI prediction method based on deep learning neural network and regularized Laplacian kernel. We use a neural network with an autoencoder-like architecture to implicitly simulate the evolutionary processes of a PPI network. Neurons of the output layer correspond to proteins and are labeled with values (1 for interaction and 0 for otherwise) from the adjacency matrix of a sparse disconnected training PPI network. Unlike autoencoder, neurons at the input layer are given all zero input, reflecting an assumption of no a priori knowledge about PPIs, and hidden layers of smaller sizes mimic ancient interactome at different times during evolution. After the training step, an evolved PPI network whose rows are outputs of the neural network can be obtained. We then predict PPIs by applying the regularized Laplacian kernel to the transition matrix that is built upon the evolved PPI network. The results from cross-validation experiments show that the PPI prediction accuracies for yeast data and human data measured as AUC are increased by up to 8.4 and 14.9% respectively, as compared to the baseline. Moreover, the evolved PPI network can also help us leverage complementary information from the disconnected training network
International Nuclear Information System (INIS)
Brito, P E de; Nazareno, H N
2007-01-01
In the present work we treat the problem of a particle in a uniform magnetic field along the symmetric gauge, so chosen since the wavefunctions present the required cylindrical symmetry. It is our understanding that by means of this work we can make a contribution to the teaching of the present subject, as well as encourage students to use computer algebra systems in solving problems of quantum mechanics. We obtained the degeneracy of the spectrum of eigenvalues in a very clear way. Through the use of a computer algebra system we show graphs of the probability density associated with different eigenvalues as well as compare such functions for some degenerate states, which helps us to visualize the physics of the problem. We also present a semiclassical model which gives a physical insight regarding the paradoxical fact that eigenfunctions associated with opposite angular momenta and different energy eigenvalues have the same probability density. Finally, by solving the time-dependent Schroedinger equation we obtain the time evolution of a wave packet that at time zero was considered to be localized in a definite region of the lattice. The centroid of such a packet performs an orbit similar to that obtained in the classical treatment of a particle in a magnetic field
Jirapatnakul, Artit C; Fotin, Sergei V; Reeves, Anthony P; Biancardi, Alberto M; Yankelevitz, David F; Henschke, Claudia I
2009-01-01
Estimation of nodule location and size is an important pre-processing step in some nodule segmentation algorithms to determine the size and location of the region of interest. Ideally, such estimation methods will consistently find the same nodule location regardless of where the the seed point (provided either manually or by a nodule detection algorithm) is placed relative to the "true" center of the nodule, and the size should be a reasonable estimate of the true nodule size. We developed a method that estimates nodule location and size using multi-scale Laplacian of Gaussian (LoG) filtering. Nodule candidates near a given seed point are found by searching for blob-like regions with high filter response. The candidates are then pruned according to filter response and location, and the remaining candidates are sorted by size and the largest candidate selected. This method was compared to a previously published template-based method. The methods were evaluated on the basis of stability of the estimated nodule location to changes in the initial seed point and how well the size estimates agreed with volumes determined by a semi-automated nodule segmentation method. The LoG method exhibited better stability to changes in the seed point, with 93% of nodules having the same estimated location even when the seed point was altered, compared to only 52% of nodules for the template-based method. Both methods also showed good agreement with sizes determined by a nodule segmentation method, with an average relative size difference of 5% and -5% for the LoG and template-based methods respectively.
Boyd, John P.; Amore, Paolo; Fernández, Francisco M.
2018-03-01
A "bent waveguide" in the sense used here is a small perturbation of a two-dimensional rectangular strip which is infinitely long in the down-channel direction and has a finite, constant width in the cross-channel coordinate. The goal is to calculate the smallest ("ground state") eigenvalue of the stationary Schrödinger equation which here is a two-dimensional Helmholtz equation, ψxx +ψyy + Eψ = 0 where E is the eigenvalue and homogeneous Dirichlet boundary conditions are imposed on the walls of the waveguide. Perturbation theory gives a good description when the "bending strength" parameter ɛ is small as described in our previous article (Amore et al., 2017) and other works cited therein. However, such series are asymptotic, and it is often impractical to calculate more than a handful of terms. It is therefore useful to develop numerical methods for the perturbed strip to cover intermediate ɛ where the perturbation series may be inaccurate and also to check the pertubation expansion when ɛ is small. The perturbation-induced change-in-eigenvalue, δ ≡ E(ɛ) - E(0) , is O(ɛ2) . We show that the computation becomes very challenging as ɛ → 0 because (i) the ground state eigenfunction varies on both O(1) and O(1 / ɛ) length scales and (ii) high accuracy is needed to compute several correct digits in δ, which is itself small compared to the eigenvalue E. The multiple length scales are not geographically separate, but rather are inextricably commingled in the neighborhood of the boundary deformation. We show that coordinate mapping and immersed boundary strategies both reduce the computational domain to the uniform strip, allowing application of pseudospectral methods on tensor product grids with tensor product basis functions. We compared different basis sets; Chebyshev polynomials are best in the cross-channel direction. However, sine functions generate rather accurate analytical approximations with just a single basis function. In the down
Chen, Jing; Tang, Yuan Yan; Chen, C L Philip; Fang, Bin; Lin, Yuewei; Shang, Zhaowei
2014-12-01
Protein subcellular location prediction aims to predict the location where a protein resides within a cell using computational methods. Considering the main limitations of the existing methods, we propose a hierarchical multi-label learning model FHML for both single-location proteins and multi-location proteins. The latent concepts are extracted through feature space decomposition and label space decomposition under the nonnegative data factorization framework. The extracted latent concepts are used as the codebook to indirectly connect the protein features to their annotations. We construct dual fuzzy hypergraphs to capture the intrinsic high-order relations embedded in not only feature space, but also label space. Finally, the subcellular location annotation information is propagated from the labeled proteins to the unlabeled proteins by performing dual fuzzy hypergraph Laplacian regularization. The experimental results on the six protein benchmark datasets demonstrate the superiority of our proposed method by comparing it with the state-of-the-art methods, and illustrate the benefit of exploiting both feature correlations and label correlations.
Feature selection and multi-kernel learning for sparse representation on a manifold
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
2014-01-01
combination of some basic items in a dictionary. Gao etal. (2013) recently proposed Laplacian sparse coding by regularizing the sparse codes with an affinity graph. However, due to the noisy features and nonlinear distribution of the data samples, the affinity
Lestari, A. W.; Rustam, Z.
2017-07-01
In the last decade, breast cancer has become the focus of world attention as this disease is one of the primary leading cause of death for women. Therefore, it is necessary to have the correct precautions and treatment. In previous studies, Fuzzy Kennel K-Medoid algorithm has been used for multi-class data. This paper proposes an algorithm to classify the high dimensional data of breast cancer using Fuzzy Possibilistic C-means (FPCM) and a new method based on clustering analysis using Normed Kernel Function-Based Fuzzy Possibilistic C-Means (NKFPCM). The objective of this paper is to obtain the best accuracy in classification of breast cancer data. In order to improve the accuracy of the two methods, the features candidates are evaluated using feature selection, where Laplacian Score is used. The results show the comparison accuracy and running time of FPCM and NKFPCM with and without feature selection.
Crystal structure representations for machine learning models of formation energies
Energy Technology Data Exchange (ETDEWEB)
Faber, Felix [Department of Chemistry, Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, University of Basel Switzerland; Lindmaa, Alexander [Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping Sweden; von Lilienfeld, O. Anatole [Department of Chemistry, Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, University of Basel Switzerland; Argonne Leadership Computing Facility, Argonne National Laboratory, 9700 S. Cass Avenue Lemont Illinois 60439; Armiento, Rickard [Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping Sweden
2015-04-20
We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a Coulomb matrix representation of the molecule. We consider three ways to generalize such representations to periodic systems: (i) a matrix where each element is related to the Ewald sum of the electrostatic interaction between two different atoms in the unit cell repeated over the lattice; (ii) an extended Coulomb-like matrix that takes into account a number of neighboring unit cells; and (iii) an ansatz that mimics the periodicity and the basic features of the elements in the Ewald sum matrix using a sine function of the crystal coordinates of the atoms. The representations are compared for a Laplacian kernel with Manhattan norm, trained to reproduce formation energies using a dataset of 3938 crystal structures obtained from the Materials Project. For training sets consisting of 3000 crystals, the generalization error in predicting formation energies of new structures corresponds to (i) 0.49, (ii) 0.64, and (iii) 0.37eV/atom for the respective representations.
Dictionary Pair Learning on Grassmann Manifolds for Image Denoising.
Zeng, Xianhua; Bian, Wei; Liu, Wei; Shen, Jialie; Tao, Dacheng
2015-11-01
Image denoising is a fundamental problem in computer vision and image processing that holds considerable practical importance for real-world applications. The traditional patch-based and sparse coding-driven image denoising methods convert 2D image patches into 1D vectors for further processing. Thus, these methods inevitably break down the inherent 2D geometric structure of natural images. To overcome this limitation pertaining to the previous image denoising methods, we propose a 2D image denoising model, namely, the dictionary pair learning (DPL) model, and we design a corresponding algorithm called the DPL on the Grassmann-manifold (DPLG) algorithm. The DPLG algorithm first learns an initial dictionary pair (i.e., the left and right dictionaries) by employing a subspace partition technique on the Grassmann manifold, wherein the refined dictionary pair is obtained through a sub-dictionary pair merging. The DPLG obtains a sparse representation by encoding each image patch only with the selected sub-dictionary pair. The non-zero elements of the sparse representation are further smoothed by the graph Laplacian operator to remove the noise. Consequently, the DPLG algorithm not only preserves the inherent 2D geometric structure of natural images but also performs manifold smoothing in the 2D sparse coding space. We demonstrate that the DPLG algorithm also improves the structural SIMilarity values of the perceptual visual quality for denoised images using the experimental evaluations on the benchmark images and Berkeley segmentation data sets. Moreover, the DPLG also produces the competitive peak signal-to-noise ratio values from popular image denoising algorithms.
Manifold regularized multitask feature learning for multimodality disease classification.
Jie, Biao; Zhang, Daoqiang; Cheng, Bo; Shen, Dinggang
2015-02-01
Multimodality based methods have shown great advantages in classification of Alzheimer's disease (AD) and its prodromal stage, that is, mild cognitive impairment (MCI). Recently, multitask feature selection methods are typically used for joint selection of common features across multiple modalities. However, one disadvantage of existing multimodality based methods is that they ignore the useful data distribution information in each modality, which is essential for subsequent classification. Accordingly, in this paper we propose a manifold regularized multitask feature learning method to preserve both the intrinsic relatedness among multiple modalities of data and the data distribution information in each modality. Specifically, we denote the feature learning on each modality as a single task, and use group-sparsity regularizer to capture the intrinsic relatedness among multiple tasks (i.e., modalities) and jointly select the common features from multiple tasks. Furthermore, we introduce a new manifold-based Laplacian regularizer to preserve the data distribution information from each task. Finally, we use the multikernel support vector machine method to fuse multimodality data for eventual classification. Conversely, we also extend our method to the semisupervised setting, where only partial data are labeled. We evaluate our method using the baseline magnetic resonance imaging (MRI), fluorodeoxyglucose positron emission tomography (FDG-PET), and cerebrospinal fluid (CSF) data of subjects from AD neuroimaging initiative database. The experimental results demonstrate that our proposed method can not only achieve improved classification performance, but also help to discover the disease-related brain regions useful for disease diagnosis. © 2014 Wiley Periodicals, Inc.
Summing up D-instantons in N=2 supergravity
International Nuclear Information System (INIS)
Ketov, Sergei V.
2003-01-01
The non-perturbative quantum geometry of the universal hypermultiplet (UH) is investigated in N=2 supergravity. The UH low-energy effective action is given by the four-dimensional quaternionic non-linear sigma-model having an U(1)xU(1) isometry. The UH metric is governed by the single real pre-potential that is an eigenfunction of the Laplacian in the hyperbolic plane. We calculate the classical pre-potential corresponding to the standard (Ferrara-Sabharwal) metric of the UH arising in the Calabi-Yau compactification of type-II superstrings. The non-perturbative quaternionic metric, describing the D-instanton contributions to the UH geometry, is found by requiring the SL(2,Z) modular invariance of the UH pre-potential. The pre-potential found is unique, while it coincides with the D-instanton function of Green and Gutperle, given by the order-3/2 Eisenstein series. As a by-product, we prove cluster decomposition of D-instantons in curved spacetime. The non-perturbative UH pre-potential interpolates between the perturbative (large CY volume) region and the superconformal (Landau-Ginzburg) region in the UH moduli space. We also calculate a non-perturbative scalar potential in the hyper-Kaehler limit, when an abelian isometry of the UH metric is gauged in the presence of D-instantons
Summing up D-instantons in N=2 supergravity
Energy Technology Data Exchange (ETDEWEB)
Ketov, Sergei V. E-mail: ketov@phys.metro-u.ac.jp
2003-01-20
The non-perturbative quantum geometry of the universal hypermultiplet (UH) is investigated in N=2 supergravity. The UH low-energy effective action is given by the four-dimensional quaternionic non-linear sigma-model having an U(1)xU(1) isometry. The UH metric is governed by the single real pre-potential that is an eigenfunction of the Laplacian in the hyperbolic plane. We calculate the classical pre-potential corresponding to the standard (Ferrara-Sabharwal) metric of the UH arising in the Calabi-Yau compactification of type-II superstrings. The non-perturbative quaternionic metric, describing the D-instanton contributions to the UH geometry, is found by requiring the SL(2,Z) modular invariance of the UH pre-potential. The pre-potential found is unique, while it coincides with the D-instanton function of Green and Gutperle, given by the order-3/2 Eisenstein series. As a by-product, we prove cluster decomposition of D-instantons in curved spacetime. The non-perturbative UH pre-potential interpolates between the perturbative (large CY volume) region and the superconformal (Landau-Ginzburg) region in the UH moduli space. We also calculate a non-perturbative scalar potential in the hyper-Kaehler limit, when an abelian isometry of the UH metric is gauged in the presence of D-instantons.
Energy Technology Data Exchange (ETDEWEB)
Milewski, J., E-mail: jsmilew@wp.pl [Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań (Poland); Lulek, B., E-mail: barlulek@amu.edu.pl [East European State Higher School, ul. Tymona Terleckiego 6, 37-700 Przemyśl (Poland); Lulek, T., E-mail: tadlulek@prz.edu.pl [Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań (Poland); East European State Higher School, ul. Tymona Terleckiego 6, 37-700 Przemyśl (Poland); Łabuz, M., E-mail: labuz@univ.rzeszow.pl [University of Rzeszow, Institute of Physics, Rejtana 16a, 35-959 Rzeszów (Poland); Stagraczyński, R., E-mail: rstag@prz.edu.pl [Rzeszow University of Technology, The Faculty of Mathematics and Applied Physics, Powstańców Warszawy 6, 35-959 Rzeszów (Poland)
2014-02-01
The exact Bethe eigenfunctions for the heptagonal ring within the isotropic XXX model exhibit a doubly degenerated energy level in the three-deviation sector at the centre of the Brillouin zone. We demonstrate an explicit construction of these eigenfunctions by use of algebraic Bethe Ansatz, and point out a relation of degeneracy to parity conservation, applied to the configuration of strings for these eigenfunctions. Namely, the internal structure of the eigenfunctions (the 2-string and the 1-string, with opposite quasimomenta) admits generation of two mutually orthogonal eigenfunctions due to the fact that the strings which differ by their length are distinguishable objects.
Kinjo, Ken; Uchibe, Eiji; Doya, Kenji
2013-01-01
Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunction problem in a continuous state using the knowledge of the system dynamics and the action, state, and terminal cost functions. In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in which the dynamics of the body and the environment have to be learned from experience. We first perform a simulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynamics model on the derived the action policy. The result shows that a crude linear approximation of the non-linear dynamics can still allow solution of the task, despite with a higher total cost. We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robot platform. The state is given by the position and the size of a battery in its camera view and two neck joint angles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servo controller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state cost functions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics model performed equivalently with the optimal linear quadratic regulator (LQR). In the non-quadratic task, the LMDP controller with a linear dynamics model showed the best performance. The results demonstrate the usefulness of the LMDP framework in real robot control even when simple linear models are used for dynamics learning.
OpenMP Parallelization and Optimization of Graph-based Machine Learning Algorithms
2016-05-01
Understanding Application Data Movement Characteristics using Intel VTune Amplifier and Software Development Emulator tools, Intel Xeon Phi User Group...sured by a summation of the weights along the graph cut) for this problem. This is equivalent to assigning a scalar or vector value ui to each i th data...graph Laplacian [9]. By projecting all vectors onto this sub-eigenspace, the iteration step reduces to a simple coefficient update. 2.2 Semi-supervised
Gene selection for microarray data classification via subspace learning and manifold regularization.
Tang, Chang; Cao, Lijuan; Zheng, Xiao; Wang, Minhui
2017-12-19
With the rapid development of DNA microarray technology, large amount of genomic data has been generated. Classification of these microarray data is a challenge task since gene expression data are often with thousands of genes but a small number of samples. In this paper, an effective gene selection method is proposed to select the best subset of genes for microarray data with the irrelevant and redundant genes removed. Compared with original data, the selected gene subset can benefit the classification task. We formulate the gene selection task as a manifold regularized subspace learning problem. In detail, a projection matrix is used to project the original high dimensional microarray data into a lower dimensional subspace, with the constraint that the original genes can be well represented by the selected genes. Meanwhile, the local manifold structure of original data is preserved by a Laplacian graph regularization term on the low-dimensional data space. The projection matrix can serve as an importance indicator of different genes. An iterative update algorithm is developed for solving the problem. Experimental results on six publicly available microarray datasets and one clinical dataset demonstrate that the proposed method performs better when compared with other state-of-the-art methods in terms of microarray data classification. Graphical Abstract The graphical abstract of this work.
Bapat, Ravindra B
2014-01-01
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...
Possible world based consistency learning model for clustering and classifying uncertain data.
Liu, Han; Zhang, Xianchao; Zhang, Xiaotong
2018-06-01
Possible world has shown to be effective for handling various types of data uncertainty in uncertain data management. However, few uncertain data clustering and classification algorithms are proposed based on possible world. Moreover, existing possible world based algorithms suffer from the following issues: (1) they deal with each possible world independently and ignore the consistency principle across different possible worlds; (2) they require the extra post-processing procedure to obtain the final result, which causes that the effectiveness highly relies on the post-processing method and the efficiency is also not very good. In this paper, we propose a novel possible world based consistency learning model for uncertain data, which can be extended both for clustering and classifying uncertain data. This model utilizes the consistency principle to learn a consensus affinity matrix for uncertain data, which can make full use of the information across different possible worlds and then improve the clustering and classification performance. Meanwhile, this model imposes a new rank constraint on the Laplacian matrix of the consensus affinity matrix, thereby ensuring that the number of connected components in the consensus affinity matrix is exactly equal to the number of classes. This also means that the clustering and classification results can be directly obtained without any post-processing procedure. Furthermore, for the clustering and classification tasks, we respectively derive the efficient optimization methods to solve the proposed model. Experimental results on real benchmark datasets and real world uncertain datasets show that the proposed model outperforms the state-of-the-art uncertain data clustering and classification algorithms in effectiveness and performs competitively in efficiency. Copyright © 2018 Elsevier Ltd. All rights reserved.
Handbook of mathematical techniques for wavestructure interactions
Linton, CM
2001-01-01
INTRODUCTIONThe Water-Wave ProblemThe Linearised EquationsInteraction of a Wave with a StructureReciprocity RelationsEnergy of the Fluid MotionEIGENFUNCTION EXPANSIONSIntroductionConstruction of Vertical EigenfunctionTwo-Dimensional ProblemsThree-Dimensional ProblemsMatched Eigenfunction ExpansionsMULTIPOLE EXPANSIONSIntroductionIsolated ObstaclesMultiple BodiesINTEGRAL EQUATIONSSource DistributionGreen's TheoremThin ObstaclesInterior ProblemsFree-Surface ProblemsNumerical Evaluation of Green's functions
Separating variables in two-way diffusion equations
International Nuclear Information System (INIS)
Fisch, N.J.; Kruskal, M.D.
1979-10-01
It is shown that solutions to a class of diffusion equations of the two-way type may be found by a method akin to separation of variables. The difficulty with such equations is that the boundary data must be specified partly as initial and partly as final conditions. In contrast to the one-way diffusion equation, where the solution separates only into decaying eigenfunctions, the two-way equations separate into both decaying and growing eigenfunctions. Criteria are set forth for the existence of linear eigenfunctions, which may not be found directly by separating variables. A speculation with interesting ramifications is that the growing and decaying eigenfunctions are separately complete in an appropriate half of the problem domain
Multiview Hessian regularization for image annotation.
Liu, Weifeng; Tao, Dacheng
2013-07-01
The rapid development of computer hardware and Internet technology makes large scale data dependent models computationally tractable, and opens a bright avenue for annotating images through innovative machine learning algorithms. Semisupervised learning (SSL) therefore received intensive attention in recent years and was successfully deployed in image annotation. One representative work in SSL is Laplacian regularization (LR), which smoothes the conditional distribution for classification along the manifold encoded in the graph Laplacian, however, it is observed that LR biases the classification function toward a constant function that possibly results in poor generalization. In addition, LR is developed to handle uniformly distributed data (or single-view data), although instances or objects, such as images and videos, are usually represented by multiview features, such as color, shape, and texture. In this paper, we present multiview Hessian regularization (mHR) to address the above two problems in LR-based image annotation. In particular, mHR optimally combines multiple HR, each of which is obtained from a particular view of instances, and steers the classification function that varies linearly along the data manifold. We apply mHR to kernel least squares and support vector machines as two examples for image annotation. Extensive experiments on the PASCAL VOC'07 dataset validate the effectiveness of mHR by comparing it with baseline algorithms, including LR and HR.
Adaptively Learning an Importance Function Using Transport Constrained Monte Carlo
International Nuclear Information System (INIS)
Booth, T.E.
1998-01-01
It is well known that a Monte Carlo estimate can be obtained with zero-variance if an exact importance function for the estimate is known. There are many ways that one might iteratively seek to obtain an ever more exact importance function. This paper describes a method that has obtained ever more exact importance functions that empirically produce an error that is dropping exponentially with computer time. The method described herein constrains the importance function to satisfy the (adjoint) Boltzmann transport equation. This constraint is provided by using the known form of the solution, usually referred to as the Case eigenfunction solution
Stochastic Levy Divergence and Maxwell's Equations
Directory of Open Access Journals (Sweden)
B. O. Volkov
2015-01-01
Full Text Available One of the main reasons for interest in the Levy Laplacian and its analogues such as Levy d'Alembertian is a connection of these operators with gauge fields. The theorem proved by Accardi, Gibillisco and Volovich stated that a connection in a bundle over a Euclidean space or over a Minkowski space is a solution of the Yang-Mills equations if and only if the corresponding parallel transport to the connection is a solution of the Laplace equation for the Levy Laplacian or of the d'Alembert equation for the Levy d'Alembertian respectively (see [5, 6]. There are two approaches to define Levy type operators, both of which date back to the original works of Levy [7]. The first is that the Levy Laplacian (or Levy d'Alembertian is defined as an integral functional generated by a special form of the second derivative. This approach is used in the works [5, 6], as well as in the paper [8] of Leandre and Volovich, where stochastic Levy-Laplacian is discussed. Another approach to the Levy Laplacian is defining it as the Cesaro mean of second order derivatives along the family of vectors, which is an orthonormal basis in the Hilbert space. This definition of the Levy Laplacian is used for the description of solutions of the Yang-Mills equations in the paper [10].The present work shows that the definitions of the Levy Laplacian and the Levy d'Alembertian based on Cesaro averaging of the second order directional derivatives can be transferred to the stochastic case. In the article the values of these operators on a stochastic parallel transport associated with a connection (vector potential are found. In this case, unlike the deterministic case and the stochastic case of Levy Laplacian from [8], these values are not equal to zero if the vector potential corresponding to the stochastic parallel transport is a solution of the Maxwell's equations. As a result, two approaches to definition of the Levy Laplacian in the stochastic case give different operators. This
Direct extraction of boundaries from computed tomography scans
International Nuclear Information System (INIS)
Thirion, J.P.
1994-01-01
This paper presents a method, based on the Filtered Backprojection technique (FBP), to extract directly the boundaries of X-ray images, without previous image reconstruction. The authors preprocess the raw data in order to compute directly the reconstructed values of the gradient or of the Laplacian at any location in the plane (defined with real coordinates). The reconstructed value of the gradient and of the Laplacian correspond to the exact mathematical definition of the differentials of the image. For noisy data, the authors propose also to use an extension of existing FBP techniques, adapted to the computation of the gradient and of the Laplacian. Finally, the authors show how to use the corresponding operators to perform the segmentation of a slice, without image reconstruction. Images of the reconstructed gradient, Laplacian, and segmented objects are presented
A Spectral Algorithm for Envelope Reduction of Sparse Matrices
Barnard, Stephen T.; Pothen, Alex; Simon, Horst D.
1993-01-01
The problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorithm for computing an envelope-reducing reordering is obtained by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. This Laplacian eigenvector solves a continuous relaxation of a discrete problem related to envelope minimization called the minimum 2-sum problem. The permutation vector computed by the spectral algorithm is a closest permutation vector to the specified Laplacian eigenvector. Numerical results show that the new reordering algorithm usually computes smaller envelope sizes than those obtained from the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK reverse Cuthill-McKee (RCM), in some cases reducing the envelope by more than a factor of two.
Decoupling of the leading contribution in the discrete BFKL analysis of high-precision HERA data
Energy Technology Data Exchange (ETDEWEB)
Kowalski, H. [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany); Lipatov, L.N. [St. Petersburg State University, St. Petersburg (Russian Federation); Petersburg Nuclear Physics Institute, Gatchina (Russian Federation); Ross, D.A. [University of Southampton, School of Physics and Astronomy, Southampton (United Kingdom); Schulz, O. [Max Planck Institute for Physics, Munich (Germany)
2017-11-15
We analyse, in NLO, the physical properties of the discrete eigenvalue solution for the BFKL equation. We show that a set of eigenfunctions with positive eigenvalues, ω, together with a small contribution from a continuum of eigenfunctions with negative ω, provide an excellent description of high-precision HERA F{sub 2} data in the region, x < 0.001, Q{sup 2} > 6 GeV{sup 2}. The phases of the eigenfunctions can be obtained from a simple parametrisation of the pomeron spectrum, which has a natural motivation within BFKL. The data analysis shows that the first eigenfunction decouples completely or almost completely from the proton. This suggests that there exists an additional ground state, which is naturally saturated and may have the properties of the soft pomeron. (orig.)
Accidental degeneracy of resonances
International Nuclear Information System (INIS)
Hernandez, E.; Mondragon, A.; Jauregui, A.
2001-01-01
Full text: It will be shown that a degeneracy of resonances is associated with a second rank pole in the scattering matrix and a Jordan cycle of generalized eigenfunctions of the radial Schrodinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in complex resonance energy eigenfunctions. In this orthonormal basis, the Hamiltonian is represented by a non-diagonal complex matrix with a Jordan block of rank two. Some general properties of the degeneracy of resonances will be exhibited and discussed in an explicit example of degeneracy of resonant states and double poles in the scattering matrix of a double barrier potential. The cross section, scattering wave functions and Jordan-Gamow eigenfunctions are computed at degeneracy and their properties as functions of the control parameters of the system are discussed. (Author)
Completeness in quantum mechanics and the Weyl-Titchmarsh-Kodaira theorem
Energy Technology Data Exchange (ETDEWEB)
Palma, G [Departamento de Fisica, Universidad de Santiago de Chile, Casilla 307, Santiago 2 (Chile); Prado, H; Reyes, E G, E-mail: guillermo.palma@usach.c, E-mail: humberto.prado@usach.c, E-mail: ereyes@fermat.usach.c [Departamento de Matematica y Ciencia de la Computacion, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago (Chile)
2010-06-25
We discuss the completeness of (generalized) eigenfunctions in quantum mechanics using the classical theory developed by Weyl, Titchmarsh, and Kodaira. As applications, we rigorously prove the completeness of generalized eigenfunctions for the step and well potentials.
A regularized, model-based approach to phase-based conductivity mapping using MRI.
Ropella, Kathleen M; Noll, Douglas C
2017-11-01
To develop a novel regularized, model-based approach to phase-based conductivity mapping that uses structural information to improve the accuracy of conductivity maps. The inverse of the three-dimensional Laplacian operator is used to model the relationship between measured phase maps and the object conductivity in a penalized weighted least-squares optimization problem. Spatial masks based on structural information are incorporated into the problem to preserve data near boundaries. The proposed Inverse Laplacian method was compared against a restricted Gaussian filter in simulation, phantom, and human experiments. The Inverse Laplacian method resulted in lower reconstruction bias and error due to noise in simulations than the Gaussian filter. The Inverse Laplacian method also produced conductivity maps closer to the measured values in a phantom and with reduced noise in the human brain, as compared to the Gaussian filter. The Inverse Laplacian method calculates conductivity maps with less noise and more accurate values near boundaries. Improving the accuracy of conductivity maps is integral for advancing the applications of conductivity mapping. Magn Reson Med 78:2011-2021, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
Enhanced manifold regularization for semi-supervised classification.
Gan, Haitao; Luo, Zhizeng; Fan, Yingle; Sang, Nong
2016-06-01
Manifold regularization (MR) has become one of the most widely used approaches in the semi-supervised learning field. It has shown superiority by exploiting the local manifold structure of both labeled and unlabeled data. The manifold structure is modeled by constructing a Laplacian graph and then incorporated in learning through a smoothness regularization term. Hence the labels of labeled and unlabeled data vary smoothly along the geodesics on the manifold. However, MR has ignored the discriminative ability of the labeled and unlabeled data. To address the problem, we propose an enhanced MR framework for semi-supervised classification in which the local discriminative information of the labeled and unlabeled data is explicitly exploited. To make full use of labeled data, we firstly employ a semi-supervised clustering method to discover the underlying data space structure of the whole dataset. Then we construct a local discrimination graph to model the discriminative information of labeled and unlabeled data according to the discovered intrinsic structure. Therefore, the data points that may be from different clusters, though similar on the manifold, are enforced far away from each other. Finally, the discrimination graph is incorporated into the MR framework. In particular, we utilize semi-supervised fuzzy c-means and Laplacian regularized Kernel minimum squared error for semi-supervised clustering and classification, respectively. Experimental results on several benchmark datasets and face recognition demonstrate the effectiveness of our proposed method.
The eigenvalue problem for a singular quasilinear elliptic equation
Directory of Open Access Journals (Sweden)
Benjin Xuan
2004-02-01
Full Text Available We show that many results about the eigenvalues and eigenfunctions of a quasilinear elliptic equation in the non-singular case can be extended to the singular case. Among these results, we have the first eigenvalue is associated to a $C^{1,alpha}(Omega$ eigenfunction which is positive and unique (up to a multiplicative constant, that is, the first eigenvalue is simple. Moreover the first eigenvalue is isolated and is the unique positive eigenvalue associated to a non-negative eigenfunction. We also prove some variational properties of the second eigenvalue.
Analyticity of the density of electronic wavefunctions
DEFF Research Database (Denmark)
Fournais, Søren; Hoffmann-Ostenhof, Maria; Hoffmann-Ostenhof, Thomas
2004-01-01
We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in R^3 away from the nuclei.......We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in R^3 away from the nuclei....
Spectrum of the multigroup neutron transport operator for bounded spatial domains
International Nuclear Information System (INIS)
Larsen, E.W.
1979-01-01
The spectrum of the multigroup neutron transport operator A is studied for bounded spatial regions D which consist of a finite number of material subregions. Our main results provide simple conditions on the material cross sections which guarantee that (1) A possesses eigenvalues in the finite plane; (2) A possesses a ''leading'' eigenvalue lambda 0 which is real, not less than the real part of any other eigenvalue, and to which there corresponds at least one nonnegative eigenfunction psi/sub lambda/0; and (3) A possesses a ''dominant'' eigenvalue lambda 0 which is real, simple, greater than the real part of any other eigenvalue, and whose eigenfunction psi/sub lambda/0 satisfies psi/sub lambda/0> or =0 and ∫psi/sub lambda/0d 2 Ω>0. We give examples to illustrate the results and to show that a leading eigenvalue need not be simple, nor its eigenfunction(s) positive
High-performance dynamic quantum clustering on graphics processors
Energy Technology Data Exchange (ETDEWEB)
Wittek, Peter, E-mail: peterwittek@acm.org [Swedish School of Library and Information Science, University of Boras, Boras (Sweden)
2013-01-15
Clustering methods in machine learning may benefit from borrowing metaphors from physics. Dynamic quantum clustering associates a Gaussian wave packet with the multidimensional data points and regards them as eigenfunctions of the Schroedinger equation. The clustering structure emerges by letting the system evolve and the visual nature of the algorithm has been shown to be useful in a range of applications. Furthermore, the method only uses matrix operations, which readily lend themselves to parallelization. In this paper, we develop an implementation on graphics hardware and investigate how this approach can accelerate the computations. We achieve a speedup of up to two magnitudes over a multicore CPU implementation, which proves that quantum-like methods and acceleration by graphics processing units have a great relevance to machine learning.
Alberola-Rubio, J; Prats-Boluda, G; Ye-Lin, Y; Valero, J; Perales, A; Garcia-Casado, J
2013-12-01
Non-invasive recording of uterine myoelectric activity (electrohysterogram, EHG) could provide an alternative to monitoring uterine dynamics by systems based on tocodynamometers (TOCO). Laplacian recording of bioelectric signals has been shown to give better spatial resolution and less interference than mono- and bipolar surface recordings. The aim of this work was to study the signal quality obtained from monopolar, bipolar and Laplacian techniques in EHG recordings, as well as to assess their ability to detect uterine contractions. Twenty-two recording sessions were carried out on singleton pregnant women during the active phase of labour. In each session the following simultaneous recordings were obtained: internal uterine pressure (IUP), external tension of abdominal wall (TOCO) and EHG signals (5 monopolar and 4 bipolar recordings, 1 discrete approximation to the Laplacian of the potential and 2 estimates of the Laplacian from two active annular electrodes). The results obtained show that EHG is able to detect a higher number of uterine contractions than TOCO. Laplacian recordings give improved signal quality over monopolar and bipolar techniques, reduce maternal cardiac interference and improve the signal-to-noise ratio. The optimal position for recording EHG was found to be the uterine median axis and the lower centre-right umbilical zone. Copyright © 2013 IPEM. Published by Elsevier Ltd. All rights reserved.
Hofstadter's butterfly in a two-dimensional lattice consisting of two sublattices
International Nuclear Information System (INIS)
Vugalter, G A; Pastukhov, A S
2004-01-01
Harper's equations for simple and complex two-dimensional lattices subject to a magnetic field have been derived in the tight-binding approximation. In our derivation we do not neglect the influence of the magnetic field on the electron eigenfunctions and eigenvalues in isolated atoms. Using a variational procedure for finding eigenfunctions and eigenvalues, we have self-consistently obtained Hofstadter's butterflies. Even for a simple square lattice Hofstadter's butterfly differs from the butterfly obtained in the case in which the influence of the magnetic field on the electron eigenvalues and eigenfunctions in isolated atoms is not taken into account
Spectral Results on Some Hamiltonian Properties of Graphs
Directory of Open Access Journals (Sweden)
Rao Li
2014-10-01
Full Text Available Using Lotker’s interlacing theorem on the Laplacian eigenvalues of a graph in [5] and Wang and Belardo’s interlacing theorem on the signless Laplacian eigenvalues of a graph in [6], we in this note obtain spectral conditions for some Hamiltonian properties of graphs
On the Curvature and Heat Flow on Hamiltonian Systems
Directory of Open Access Journals (Sweden)
Ohta Shin-ichi
2014-01-01
Full Text Available We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.
Modeling of MAI in UWB System Using MGGD
Ahmed, Qasim Zeeshan
2014-01-06
Multivariate generalized Gaussian density (MGGD) is used to approximate the multiple access interference (MAI) and additive white Gaussian noise in pulse-based ultrawide bandwidth (UWB) system. The MGGD probability density function (pdf) is shown to be a better approximation of a UWB system as compared to Gaussian, Laplacian and Gaussian-Laplacian mixture (GLM). The similarity between the simulated and the approximated pdf is measured with the help of modified Kullback-Leibler distance (KLD). It is also shown that MGGD has the smallest KLD as compared to Gaussian, Laplacian and GLM densities. Finally, a receiver based on the principles of minimum bit error rate is designed for the MGGD pdf.
A new approach to the BFKL mechanism. Application to high-precision HERA data
International Nuclear Information System (INIS)
Kowalski, H.; Lipatov, L.N.; Ross, D.A.
2017-07-01
We analyse here in NLO the physical properties of the discrete eigenvalue solution for the BFKL equation. We show that a set of positive ω eigenfunctions together with a small contribution from a continuum of negative ω's provide an excellent description of high-precision HERA F_2 data in the region, x 6 GeV"2. The phases of the eigenfunctions can be obtained from a simple parametrisation of the pomeron spectrum, which has a natural motivation within BFKL. The data analysis shows that the first eigenfunction decouples or nearly decouples from the proton. This suggests that there exist an additional ground state, which has no nodes.
Hofstadter's butterfly in a two-dimensional lattice consisting of two sublattices
Energy Technology Data Exchange (ETDEWEB)
Vugalter, G A; Pastukhov, A S [Department of Physics, Nizhny Novgorod State University, 23 Gagarin Avenue, Nizhny Novgorod 603950 (Russian Federation)
2004-06-04
Harper's equations for simple and complex two-dimensional lattices subject to a magnetic field have been derived in the tight-binding approximation. In our derivation we do not neglect the influence of the magnetic field on the electron eigenfunctions and eigenvalues in isolated atoms. Using a variational procedure for finding eigenfunctions and eigenvalues, we have self-consistently obtained Hofstadter's butterflies. Even for a simple square lattice Hofstadter's butterfly differs from the butterfly obtained in the case in which the influence of the magnetic field on the electron eigenvalues and eigenfunctions in isolated atoms is not taken into account.
Discretisation Schemes for Level Sets of Planar Gaussian Fields
Beliaev, D.; Muirhead, S.
2018-01-01
Smooth random Gaussian functions play an important role in mathematical physics, a main example being the random plane wave model conjectured by Berry to give a universal description of high-energy eigenfunctions of the Laplacian on generic compact manifolds. Our work is motivated by questions about the geometry of such random functions, in particular relating to the structure of their nodal and level sets. We study four discretisation schemes that extract information about level sets of planar Gaussian fields. Each scheme recovers information up to a different level of precision, and each requires a maximum mesh-size in order to be valid with high probability. The first two schemes are generalisations and enhancements of similar schemes that have appeared in the literature (Beffara and Gayet in Publ Math IHES, 2017. https://doi.org/10.1007/s10240-017-0093-0; Mischaikow and Wanner in Ann Appl Probab 17:980-1018, 2007); these give complete topological information about the level sets on either a local or global scale. As an application, we improve the results in Beffara and Gayet (2017) on Russo-Seymour-Welsh estimates for the nodal set of positively-correlated planar Gaussian fields. The third and fourth schemes are, to the best of our knowledge, completely new. The third scheme is specific to the nodal set of the random plane wave, and provides global topological information about the nodal set up to `visible ambiguities'. The fourth scheme gives a way to approximate the mean number of excursion domains of planar Gaussian fields.
Strong diamagnetism for general domains and applications
DEFF Research Database (Denmark)
Fournais, Søren; Helffer, Bernard
2007-01-01
We consider the Neumann Laplacian with constant magnetic field on a regular domain. Let $B$ be the strength of the magnetic field, and let $\\lambda_1(B)$ be the first eigenvalue of the magnetic Neumann Laplacian on the domain. It is proved that $B \\mapsto \\lambda_1(B)$ is monotone increasing for ...
International Nuclear Information System (INIS)
Debnath, S.; Maji, Smarajit; Meyur, Sanjib
2014-01-01
We have obtained exact solution of the effective mass Schrödinger equation for the generalised Hylleraas potential. The exact bound state energy eigenvalues and corresponding eigenfunctions are presented. The bound state eigenfunctions are obtained in terms of the hypergeometric functions. Results are also given for the special case of potential parameter.
Quantum algorithms for topological and geometric analysis of data
Lloyd, Seth; Garnerone, Silvano; Zanardi, Paolo
2016-01-01
Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying topological features and for determining how such features persist as the data is viewed at different scales. Here we present quantum machine learning algorithms for calculating Betti numbers—the numbers of connected components, holes and voids—in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speed-up over the best currently known classical algorithms for topological data analysis. PMID:26806491
High-performance dynamic quantum clustering on graphics processors
International Nuclear Information System (INIS)
Wittek, Peter
2013-01-01
Clustering methods in machine learning may benefit from borrowing metaphors from physics. Dynamic quantum clustering associates a Gaussian wave packet with the multidimensional data points and regards them as eigenfunctions of the Schrödinger equation. The clustering structure emerges by letting the system evolve and the visual nature of the algorithm has been shown to be useful in a range of applications. Furthermore, the method only uses matrix operations, which readily lend themselves to parallelization. In this paper, we develop an implementation on graphics hardware and investigate how this approach can accelerate the computations. We achieve a speedup of up to two magnitudes over a multicore CPU implementation, which proves that quantum-like methods and acceleration by graphics processing units have a great relevance to machine learning.
A new approach to the BFKL mechanism. Application to high-precision HERA data
Energy Technology Data Exchange (ETDEWEB)
Kowalski, H. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Lipatov, L.N. [Sankt-Peterburgskij Univ., St. Petersburg (Russian Federation); Petersburg Nuclear Physics Institute, Gatchina (Russian Federation); Ross, D.A. [Southampton Univ. (United Kingdom). School of Physics and Astronomy; Schulz, O. [Max Planck Institute for Physics, Munich (Germany)
2017-07-15
We analyse here in NLO the physical properties of the discrete eigenvalue solution for the BFKL equation. We show that a set of positive ω eigenfunctions together with a small contribution from a continuum of negative ω's provide an excellent description of high-precision HERA F{sub 2} data in the region, x < 0.001, Q{sup 2} > 6 GeV{sup 2}. The phases of the eigenfunctions can be obtained from a simple parametrisation of the pomeron spectrum, which has a natural motivation within BFKL. The data analysis shows that the first eigenfunction decouples or nearly decouples from the proton. This suggests that there exist an additional ground state, which has no nodes.
A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems
Directory of Open Access Journals (Sweden)
Muhammed I. Syam
2017-11-01
Full Text Available This article is devoted to both theoretical and numerical studies of eigenvalues of regular fractional $2\\alpha $-order Sturm-Liouville problem where $\\frac{1}{2}< \\alpha \\leq 1$. In this paper, we implement the reproducing kernel method RKM to approximate the eigenvalues. To find the eigenvalues, we force the approximate solution produced by the RKM satisfy the boundary condition at $x=1$. The fractional derivative is described in the Caputo sense. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the eigenfunctions of the proposed problem. Uniformly convergence of the approximate eigenfunctions produced by the RKM to the exact eigenfunctions is proven.
An extended Harry Dym hierarchy
International Nuclear Information System (INIS)
Ma Wenxiu
2010-01-01
An extended Harry Dym hierarchy is constructed by using eigenfunctions and adjoint eigenfunctions of the spectral problems of the Harry Dym hierarchy associated with the pseudo-differential operator L = u∂ + u 0 + u 1 ∂ -1 + .... The corresponding Lax presentation possesses a self-consistent source involving squared eigenfunctions. The resulting extended Harry Dym hierarchy is reduced to the Harry Dym hierarchy with self-consistent sources under the n-reduction, L n = (L n ) ≥2 , and the k-constrained Harry Dym hierarchy under the k-constraint, L k = (L k ) ≥2 + Σ N i=1 q i ∂ -1 r i ∂ 2 . A few particular examples are computed, together with their Lax pairs.
The q-deformed analogue of the Onsager algebra: Beyond the Bethe ansatz approach
International Nuclear Information System (INIS)
Baseilhac, Pascal
2006-01-01
The spectral properties of operators formed from generators of the q-Onsager non-Abelian infinite-dimensional algebra are investigated. Using a suitable functional representation, all eigenfunctions are shown to obey a second-order q-difference equation (or its degenerate discrete version). In the algebraic sector associated with polynomial eigenfunctions (or their discrete analogues), Bethe equations naturally appear. Beyond this sector, where the Bethe ansatz approach is not applicable in related massive quantum integrable models, the eigenfunctions are also described. The spin-half XXZ open spin chain with general integrable boundary conditions is reconsidered in light of this approach: all the eigenstates are constructed. In the algebraic sector which corresponds to special relations among the parameters, known results are recovered
Indian Academy of Sciences (India)
gen bonding interactions, it is now well established that ... molecules.11 The results of this work were found to be .... (Y is acceptor atom). Table 2 presents electron den- sity values ρ(r) and Laplacian of electron density values. Table 2. Electron densities (ρ(r)) and the Laplacian (∇2ρ(r)) values at the intermolecular BCP for ...
Three-body Coulomb systems using generalized angular-momentum S states
Whitten, R. C.; Sims, J. S.
1974-01-01
An expansion of the three-body Coulomb potential in generalized angular-momentum eigenfunctions developed earlier by one of the authors is used to compute energy eigenvalues and eigenfunctions of bound S states of three-body Coulomb systems. The results for He, H(-), e(-)e(+)e(-), and pmu(-)p are compared with the results of other computational approaches.
On spectral resolutions of differential vector-operators
International Nuclear Information System (INIS)
Ashurov, R.R.; Sokolov, M.S.
2004-04-01
We show that spectral resolutions of differential vector-operators may be represented as a specific direct sum integral operator with a kernel written in terms of generalized vector-operator eigenfunctions. Then we prove that a generalized eigenfunction measurable with respect to the spectral parameter may be decomposed using a set of analytical defining systems of coordinate operators. (author)
Explicit formulae for the generalized Hermite polynomials in superspace
International Nuclear Information System (INIS)
Desrosiers, Patrick; Lapointe, Luc; Mathieu, Pierre
2004-01-01
We provide explicit formulae for the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement, i.e., the generalized Hermite (or Hi-Jack) polynomials in superspace. The construction relies on the triangular action of the Hamiltonian on the supermonomial basis. This translates into determinantal expressions for the Hamiltonian's eigenfunctions
Energy Technology Data Exchange (ETDEWEB)
Tuereci, R. Goekhan [Kirikkale Univ. (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School
2017-11-15
One speed, time independent and homogeneous medium neutron transport equation is solved with the anisotropic scattering which includes both the linearly and the quadratically anisotropic scattering kernel. Having written Case's eigenfunctions and the orthogonality relations among of these eigenfunctions, slab albedo problem is investigated as numerically by using Modified F{sub N} method. Selected numerical results are presented in tables.
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. Copyright © 2015 Elsevier B.V. All rights reserved.
The self-similar field and its application to a diffusion problem
International Nuclear Information System (INIS)
Michelitsch, Thomas M
2011-01-01
We introduce a continuum approach which accounts for self-similarity as a symmetry property of an infinite medium. A self-similar Laplacian operator is introduced which is the source of self-similar continuous fields. In this way ‘self-similar symmetry’ appears in an analogous manner as transverse isotropy or cubic symmetry of a medium. As a consequence of the self-similarity the Laplacian is a non-local fractional operator obtained as the continuum limit of the discrete self-similar Laplacian introduced recently by Michelitsch et al (2009 Phys. Rev. E 80 011135). The dispersion relation of the Laplacian and its Green’s function is deduced in closed forms. As a physical application of the approach we analyze a self-similar diffusion problem. The statistical distributions, which constitute the solutions of this problem, turn out to be Lévi-stable distributions with infinite variances characterizing the statistics of one-dimensional Lévi flights. The self-similar continuum approach introduced in this paper has the potential to be applied on a variety of scale invariant and fractal problems in physics such as in continuum mechanics, electrodynamics and in other fields. (paper)
Ohtsuki, Tomi; Ohtsuki, Tomoki
2017-04-01
Three-dimensional random electron systems undergo quantum phase transitions and show rich phase diagrams. Examples of the phases are the band gap insulator, Anderson insulator, strong and weak topological insulators, Weyl semimetal, and diffusive metal. As in the previous paper on two-dimensional quantum phase transitions [J. Phys. Soc. Jpn. 85, 123706 (2016)], we use an image recognition algorithm based on a multilayered convolutional neural network to identify which phase the eigenfunction belongs to. The Anderson model for localization-delocalization transition, the Wilson-Dirac model for topological insulators, and the layered Chern insulator model for Weyl semimetal are studied. The situation where the standard transfer matrix approach is not applicable is also treated by this method.
A general framework for regularized, similarity-based image restoration.
Kheradmand, Amin; Milanfar, Peyman
2014-12-01
Any image can be represented as a function defined on a weighted graph, in which the underlying structure of the image is encoded in kernel similarity and associated Laplacian matrices. In this paper, we develop an iterative graph-based framework for image restoration based on a new definition of the normalized graph Laplacian. We propose a cost function, which consists of a new data fidelity term and regularization term derived from the specific definition of the normalized graph Laplacian. The normalizing coefficients used in the definition of the Laplacian and associated regularization term are obtained using fast symmetry preserving matrix balancing. This results in some desired spectral properties for the normalized Laplacian such as being symmetric, positive semidefinite, and returning zero vector when applied to a constant image. Our algorithm comprises of outer and inner iterations, where in each outer iteration, the similarity weights are recomputed using the previous estimate and the updated objective function is minimized using inner conjugate gradient iterations. This procedure improves the performance of the algorithm for image deblurring, where we do not have access to a good initial estimate of the underlying image. In addition, the specific form of the cost function allows us to render the spectral analysis for the solutions of the corresponding linear equations. In addition, the proposed approach is general in the sense that we have shown its effectiveness for different restoration problems, including deblurring, denoising, and sharpening. Experimental results verify the effectiveness of the proposed algorithm on both synthetic and real examples.
Cross-Modality 2D-3D Face Recognition via Multiview Smooth Discriminant Analysis Based on ELM
Directory of Open Access Journals (Sweden)
Yi Jin
2014-01-01
Full Text Available In recent years, 3D face recognition has attracted increasing attention from worldwide researchers. Rather than homogeneous face data, more and more applications require flexible input face data nowadays. In this paper, we propose a new approach for cross-modality 2D-3D face recognition (FR, which is called Multiview Smooth Discriminant Analysis (MSDA based on Extreme Learning Machines (ELM. Adding the Laplacian penalty constrain for the multiview feature learning, the proposed MSDA is first proposed to extract the cross-modality 2D-3D face features. The MSDA aims at finding a multiview learning based common discriminative feature space and it can then fully utilize the underlying relationship of features from different views. To speed up the learning phase of the classifier, the recent popular algorithm named Extreme Learning Machine (ELM is adopted to train the single hidden layer feedforward neural networks (SLFNs. To evaluate the effectiveness of our proposed FR framework, experimental results on a benchmark face recognition dataset are presented. Simulations show that our new proposed method generally outperforms several recent approaches with a fast training speed.
Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.
Sun, Shiliang; Xie, Xijiong
2016-09-01
Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.
Level density approach to perturbation theory and inverse-energy-weighted sum-rules
International Nuclear Information System (INIS)
Halemane, T.R.
1983-01-01
The terms in the familiar Rayleigh-Schroedinger perturbation series involve eigenvalues and eigenfunctions of the unperturbed operator. A level density formalism, that does not involve computation of eigenvalues and eigenfunctions, is given here for the perturbation series. In the CLT (central limit theorem) limit the expressions take very simple linear forms. The evaluation is in terms of moments and traces of operators and operator products. 3 references
Zeta functions and regularized determinants related to the Selberg trace formula
DEFF Research Database (Denmark)
Momeni, Arash; Venkov, Alexei
determinants of one dimensional Schroedinger operator for harmonic oscillator. We decompose the determinant of the automorphic Laplacian into a product of the determinants where each factor is a determinant representation of a zeta function related to Selberg's trace formula. Then we derive an identity...... connecting the determinants of the automorphic Laplacians on different Riemannian surfaces related to the arithmetical groups. Finally, by using the Jacquet-Langlands correspondence we connect the determinant of the automorphic Laplacian for the unit group of quaternions to the product of the determinants......For a general Fuchsian group of the first kind with an arbitrary unitary representation we define the zeta functions related to the contributions of the identity, hyperbolic, elliptic and parabolic conjugacy classes in Selberg's trace formula. We present Selberg's zeta function in terms...
International Nuclear Information System (INIS)
Bulut, S.; Guelecyuez, M.C.; Kaskas, A.; Tezcan, C.
2007-01-01
H N and singular eigenfunction methods are used to determine the neutron distribution everywhere in a source-free half space with zero incident flux for a linearly anisotropic scattering kernel. The singular eigenfunction expansion of the method of elementary solutions is used. The orthogonality relations of the discrete and continuous eigenfunctions for linearly anisotropic scattering provides the determination of the expansion coefficients. Different expansions of the exit distribution are used: the expansion in powers of μ, the expansion in terms of Legendre polynomials and the expansion in powers of 1/(1+μ). The results are compared to each other. In the second part of our work, the transport equation and the infinite medium Green function are used. The numerical results of the extrapolation length obtained for the different expansions is discussed. (orig.)
DCTNet and PCANet for acoustic signal feature extraction
Xian, Yin; Thompson, Andrew; Sun, Xiaobai; Nowacek, Douglas; Nolte, Loren
2016-01-01
We introduce the use of DCTNet, an efficient approximation and alternative to PCANet, for acoustic signal classification. In PCANet, the eigenfunctions of the local sample covariance matrix (PCA) are used as filterbanks for convolution and feature extraction. When the eigenfunctions are well approximated by the Discrete Cosine Transform (DCT) functions, each layer of of PCANet and DCTNet is essentially a time-frequency representation. We relate DCTNet to spectral feature representation method...
Nonlinear dimensionality reduction methods for synthetic biology biobricks' visualization.
Yang, Jiaoyun; Wang, Haipeng; Ding, Huitong; An, Ning; Alterovitz, Gil
2017-01-19
Visualizing data by dimensionality reduction is an important strategy in Bioinformatics, which could help to discover hidden data properties and detect data quality issues, e.g. data noise, inappropriately labeled data, etc. As crowdsourcing-based synthetic biology databases face similar data quality issues, we propose to visualize biobricks to tackle them. However, existing dimensionality reduction methods could not be directly applied on biobricks datasets. Hereby, we use normalized edit distance to enhance dimensionality reduction methods, including Isomap and Laplacian Eigenmaps. By extracting biobricks from synthetic biology database Registry of Standard Biological Parts, six combinations of various types of biobricks are tested. The visualization graphs illustrate discriminated biobricks and inappropriately labeled biobricks. Clustering algorithm K-means is adopted to quantify the reduction results. The average clustering accuracy for Isomap and Laplacian Eigenmaps are 0.857 and 0.844, respectively. Besides, Laplacian Eigenmaps is 5 times faster than Isomap, and its visualization graph is more concentrated to discriminate biobricks. By combining normalized edit distance with Isomap and Laplacian Eigenmaps, synthetic biology biobircks are successfully visualized in two dimensional space. Various types of biobricks could be discriminated and inappropriately labeled biobricks could be determined, which could help to assess crowdsourcing-based synthetic biology databases' quality, and make biobricks selection.
Dynamics-based centrality for directed networks.
Masuda, Naoki; Kori, Hiroshi
2010-11-01
Determining the relative importance of nodes in directed networks is important in, for example, ranking websites, publications, and sports teams, and for understanding signal flows in systems biology. A prevailing centrality measure in this respect is the PageRank. In this work, we focus on another class of centrality derived from the Laplacian of the network. We extend the Laplacian-based centrality, which has mainly been applied to strongly connected networks, to the case of general directed networks such that we can quantitatively compare arbitrary nodes. Toward this end, we adopt the idea used in the PageRank to introduce global connectivity between all the pairs of nodes with a certain strength. Numerical simulations are carried out on some networks. We also offer interpretations of the Laplacian-based centrality for general directed networks in terms of various dynamical and structural properties of networks. Importantly, the Laplacian-based centrality defined as the stationary density of the continuous-time random walk with random jumps is shown to be equivalent to the absorption probability of the random walk with sinks at each node but without random jumps. Similarly, the proposed centrality represents the importance of nodes in dynamics on the original network supplied with sinks but not with random jumps.
DEFF Research Database (Denmark)
Lauridsen, Karen M.; Lauridsen, Ole
Ole Lauridsen, Aarhus School of Business and Social Sciences, Aarhus University, Denmark Karen M. Lauridsen, Aarhus School of Business and Social Sciences, Aarhus University, Denmark Learning Styles in Higher Education – Learning How to Learn Applying learning styles (LS) in higher education...... by Constructivist learning theory and current basic knowledge of how the brain learns. The LS concept will thus be placed in a broader learning theoretical context as a strong learning and teaching tool. Participants will be offered the opportunity to have their own LS preferences established before...... teaching leads to positive results and enhanced student learning. However, learning styles should not only be considered a didactic matter for the teacher, but also a tool for the individual students to improve their learning capabilities – not least in contexts where information is not necessarily...
Learning target masks in infrared linescan imagery
Fechner, Thomas; Rockinger, Oliver; Vogler, Axel; Knappe, Peter
1997-04-01
In this paper we propose a neural network based method for the automatic detection of ground targets in airborne infrared linescan imagery. Instead of using a dedicated feature extraction stage followed by a classification procedure, we propose the following three step scheme: In the first step of the recognition process, the input image is decomposed into its pyramid representation, thus obtaining a multiresolution signal representation. At the lowest three levels of the Laplacian pyramid a neural network filter of moderate size is trained to indicate the target location. The last step consists of a fusion process of the several neural network filters to obtain the final result. To perform this fusion we use a belief network to combine the various filter outputs in a statistical meaningful way. In addition, the belief network allows the integration of further knowledge about the image domain. By applying this multiresolution recognition scheme, we obtain a nearly scale- and rotational invariant target recognition with a significantly decreased false alarm rate compared with a single resolution target recognition scheme.
A new approach to obtaining the roots of the dispersion equation for slab geometry multiplying media
International Nuclear Information System (INIS)
Silva, Davi J.M.; Barros, Ricardo C.; Alves Filho, Hermes
2013-01-01
In this work we describe an alternative approach for obtaining the roots of the dispersion equation. For the mathematical model, we used the slab-geometry neutron transport equation in the discrete ordinates (S N ), formulation, considering isotropic scattering and monoenergetic model. The basic idea is to find a basis for the kernel of the S N differential operator, whose elements are exponential eigenfunctions corresponding to distinct eigenvalues which are the roots of the dispersion equation. That strategy yields a gain in programming computational codes, including the strategy used to obtain the purely imaginary eigenvalues and their associated complex eigenfunctions, that appear in the spectral analysis of the S N equations in multiplying media. These eigenvalues and corresponding eigenfunctions are used to obtain the parameters of the auxiliary equations of the spectral nodal methods, e.g., the spectral diamond (SD) auxiliary equation. (author)
Active feedback stabilization of axisymmetric modes in highly elongated tokamak plasmas
International Nuclear Information System (INIS)
Ward, D.J.; Hofmann, F.
1993-07-01
Active feedback stabilization of the vertical instability is studied for highly elongated tokamak plasmas (1≤κ≤3), and evaluated in particular for the TCV configuration. It is shown that the feedback can strongly affect the form of the eigenfunction for these highly elongated equilibria, and this can have detrimental effects on the ability of the feedback system to properly detect and stabilize the plasma. A calculation of the vertical displacement that uses poloidal flux measurements, poloidal magnetic field measurements, and corrections for the vessel eddy currents and active feedback currents was found to be effective even in the cases with the worst deformations of the eigenfunction. We also examine how these deformations affect differently shaped equilibria, and it is seen that the magnitude of the deformation of the eigenfunction is strongly function of the plasma elongation. (author) 15 figs., 13 refs
Determinantal spanning forests on planar graphs
Kenyon, Richard
2017-01-01
We generalize the uniform spanning tree to construct a family of determinantal measures on essential spanning forests on periodic planar graphs in which every component tree is bi-infinite. Like the uniform spanning tree, these measures arise naturally from the laplacian on the graph. More generally these results hold for the "massive" laplacian determinant which counts rooted spanning forests with weight $M$ per finite component. These measures typically have a form of conformal invariance, ...
Multiplicative formulation of quantum mechanics
International Nuclear Information System (INIS)
Voros, A.; Leboeuf, P.
1991-01-01
A general semi-classical description for the eigenfunctions of the multidimensional Schroedinger operator cannot be based on the WKB method which is incompatible with classically ergodic behavior. An alternative, more general multiplicative parametrization of quantum wave functions is suggested, whereby the semi-classical behavior of eigenfunctions can be traced in the presence of classical ergodicity, in the form of diffusive patterns of phase-space zeros in the quantum wave functions. (author) 24 refs.; 4 figs
Advanced Variance Reduction for Global k-Eigenvalue Simulations in MCNP
Energy Technology Data Exchange (ETDEWEB)
Edward W. Larsen
2008-06-01
The "criticality" or k-eigenvalue of a nuclear system determines whether the system is critical (k=1), or the extent to which it is subcritical (k<1) or supercritical (k>1). Calculations of k are frequently performed at nuclear facilities to determine the criticality of nuclear reactor cores, spent nuclear fuel storage casks, and other fissile systems. These calculations can be expensive, and current Monte Carlo methods have certain well-known deficiencies. In this project, we have developed and tested a new "functional Monte Carlo" (FMC) method that overcomes several of these deficiencies. The current state-of-the-art Monte Carlo k-eigenvalue method estimates the fission source for a sequence of fission generations (cycles), during each of which M particles per cycle are processed. After a series of "inactive" cycles during which the fission source "converges," a series of "active" cycles are performed. For each active cycle, the eigenvalue and eigenfunction are estimated; after N >> 1 active cycles are performed, the results are averaged to obtain estimates of the eigenvalue and eigenfunction and their standard deviations. This method has several disadvantages: (i) the estimate of k depends on the number M of particles per cycle, (iii) for optically thick systems, the eigenfunction estimate may not converge due to undersampling of the fission source, and (iii) since the fission source in any cycle depends on the estimated fission source from the previous cycle (the fission sources in different cycles are correlated), the estimated variance in k is smaller than the real variance. For an acceptably large number M of particles per cycle, the estimate of k is nearly independent of M; this essentially takes care of item (i). Item (ii) can be addressed by taking M sufficiently large, but for optically thick systems a sufficiently large M can easily be unrealistic. Item (iii) cannot be accounted for by taking M or N sufficiently large; it is an inherent deficiency due
Weiss, Helen; Weiss, Martin
1988-01-01
The article reviews theories of learning (e.g., stimulus-response, trial and error, operant conditioning, cognitive), considers the role of motivation, and summarizes nine research-supported rules of effective learning. Suggestions are applied to teaching learning strategies to learning-disabled students. (DB)
Discriminative sparse coding on multi-manifolds
Wang, J.J.-Y.; Bensmail, H.; Yao, N.; Gao, Xin
2013-01-01
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.
Discriminative sparse coding on multi-manifolds
Wang, J.J.-Y.
2013-09-26
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.
Ruzhansky, Michael; Suragan, Durvudkhan
2015-01-01
We propose the analogues of boundary layer potentials for the sub-Laplacian on homogeneous Carnot groups/stratified Lie groups and prove continuity results for them. In particular, we show continuity of the single layer potential and establish the Plemelj type jump relations for the double layer potential. We prove sub-Laplacian adapted versions of the Stokes theorem as well as of Green's first and second formulae on homogeneous Carnot groups. Several applications to boundary value problems a...
Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups
Ruzhansky, Michael; Suragan, Durvudkhan
2017-01-01
We propose the analogues of boundary layer potentials for the sub-Laplacian on homogeneous Carnot groups/stratified Lie groups and prove continuity results for them. In particular, we show continuity of the single layer potential and establish the Plemelj type jump relations for the double layer potential. We prove sub-Laplacian adapted versions of the Stokes theorem as well as of Green's first and second formulae on homogeneous Carnot groups. Several applications to boundary value problems a...
Ultrawide Bandwidth Receiver Based on a Multivariate Generalized Gaussian Distribution
Ahmed, Qasim Zeeshan
2015-04-01
Multivariate generalized Gaussian density (MGGD) is used to approximate the multiple access interference (MAI) and additive white Gaussian noise in pulse-based ultrawide bandwidth (UWB) system. The MGGD probability density function (pdf) is shown to be a better approximation of a UWB system as compared to multivariate Gaussian, multivariate Laplacian and multivariate Gaussian-Laplacian mixture (GLM). The similarity between the simulated and the approximated pdf is measured with the help of modified Kullback-Leibler distance (KLD). It is also shown that MGGD has the smallest KLD as compared to Gaussian, Laplacian and GLM densities. A receiver based on the principles of minimum bit error rate is designed for the MGGD pdf. As the requirement is stringent, the adaptive implementation of the receiver is also carried out in this paper. Training sequence of the desired user is the only requirement when implementing the detector adaptively. © 2002-2012 IEEE.
International Nuclear Information System (INIS)
Zhikov, Vasilii V; Pastukhova, Svetlana E
2008-01-01
Elliptic equations of p(x)-Laplacian type are investigated. There is a well-known logarithmic condition on the modulus of continuity of the nonlinearity exponent p(x), which ensures that a Laplacian with variable order of nonlinearity inherits many properties of the usual p-Laplacian of constant order. One of these is the so-called improved integrability of the gradient of the solution. It is proved in this paper that this property holds also under a slightly more general condition on the exponent p(x), although then the improvement of integrability is logarithmic rather than power-like. The method put forward is based on a new generalization of Gehring's lemma, which relies upon the reverse Hoelder inequality 'with increased support and exponent on the right-hand side'. A counterexample is constructed that reveals the extent to which the condition on the modulus of continuity obtained is sharp. Bibliography: 28 titles.
Choi, Woojae; Jacobs, Ronald L.
2011-01-01
While workplace learning includes formal and informal learning, the relationship between the two has been overlooked, because they have been viewed as separate entities. This study investigated the effects of formal learning, personal learning orientation, and supportive learning environment on informal learning among 203 middle managers in Korean…
The SU(1, 1) Perelomov number coherent states and the non-degenerate parametric amplifier
Energy Technology Data Exchange (ETDEWEB)
Ojeda-Guillén, D., E-mail: dojedag@ipn.mx; Granados, V. D. [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, C.P. 07738 México D. F. (Mexico); Mota, R. D. [Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacán, C.P. 04430, México D. F. (Mexico)
2014-04-15
We construct the Perelomov number coherent states for an arbitrary su(1, 1) group operation and study some of their properties. We introduce three operators which act on Perelomov number coherent states and close the su(1, 1) Lie algebra. By using the tilting transformation we apply our results to obtain the energy spectrum and eigenfunctions of the non-degenerate parametric amplifier. We show that these eigenfunctions are the Perelomov number coherent states of the two-dimensional harmonic oscillator.
Ground state representation of the infinite one-dimensional Heisenberg ferromagnet. Pt. 2
International Nuclear Information System (INIS)
Babbitt, D.; Thomas, L.
1977-01-01
In its ground state representation, the infinite, spin 1/2 Heisenberg chain provides a model for spin wave scattering, which entails many features of the quantum mechanical N-body problem. Here, we give a complete eigenfunction expansion for the Hamiltonian of the chain in this representation, for all numbers of spin waves. Our results resolve the questions of completeness and orthogonality of the eigenfunctions given by Bethe for finite chains, in the infinite volume limit. (orig.) [de
International Nuclear Information System (INIS)
Hagedorn, G.A.
1979-01-01
We investigate elastic and inelastic (2 cluster)→(2 cluster)scattering for classes of two, three, and four body Schroedinger operators H=H 0 +ΣVij. Formulas are derived for those generalized eigenfunctions of H which correspond asymptotically in the past to two freely moving clusters. With these eigenfunctions, we establish a formula for the (2 cluster)→(2 cluster) T-matrix and prove the convergence of a Born series for the T-matrix at high energy. (orig.) [de
The Theory of Quantized Fields. III
Schwinger, J.
1953-05-01
In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.
Spin eigen-states of Dirac equation for quasi-two-dimensional electrons
Energy Technology Data Exchange (ETDEWEB)
Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)
2015-10-15
Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.
Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.
Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong
2015-11-01
The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.
Possibility of modifying the growth trajectory in Raeini Cashmere goat.
Ghiasi, Heydar; Mokhtari, M S
2018-03-27
The objective of this study was to investigate the possibility of modifying the growth trajectory in Raeini Cashmere goat breed. In total, 13,193 records on live body weight collected from 4788 Raeini Cashmere goats were used. According to Akanke's information criterion (AIC), the sing-trait random regression model included fourth-order Legendre polynomial for direct and maternal genetic effect; maternal and individual permanent environmental effect was the best model for estimating (co)variance components. The matrices of eigenvectors for (co)variances between random regression coefficients of direct additive genetic were used to calculate eigenfunctions, and different eigenvector indices were also constructed. The obtained results showed that the first eigenvalue explained 79.90% of total genetic variance. Therefore, changing the body weights applying the first eigenfunction will be obtained rapidly. Selection based on the first eigenvector will cause favorable positive genetic gains for all body weight considered from birth to 12 months of age. For modifying the growth trajectory in Raeini Cashmere goat, the selection should be based on the second eigenfunction. The second eigenvalue accounted for 14.41% of total genetic variance for body weights that is low in comparison with genetic variance explained by the first eigenvalue. The complex patterns of genetic change in growth trajectory observed under the third and fourth eigenfunction and low amount of genetic variance explained by the third and fourth eigenvalues.
On a non-self adjoint eigenfunction expansion
Directory of Open Access Journals (Sweden)
D. Naylor
1984-01-01
Full Text Available This paper develops a formula of inversion for an integral transform similar to that associated with the names of Kontorovich and Lebedev. The kernel involves the Hankel function Hu(1(kr, in which r varies over a truncated infinite interval a≤r0 and the parameter k is complex. This kind of transform is useful in the investigation of functions that satisfy the Helmholtz equation and the condition of radiation.
Application of eigenfunction orthogonalities to vibration problems
CSIR Research Space (South Africa)
Fedotov, I
2009-07-01
Full Text Available The modelling of vibration problems is of great importance in engineering. A popular method of analysing such problems is the variational method. The simplest vibration model is represented using the example of a long rod. Two kinds...
Eigenfunctions of quadratic hamiltonians in Wigner representation
International Nuclear Information System (INIS)
Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.
1984-01-01
Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail
Scattering theory for Riemannian Laplacians
DEFF Research Database (Denmark)
Ito, Kenichi; Skibsted, Erik
In this paper we introduce a notion of scattering theory for the Laplace-Beltrami operator on non-compact, connected and complete Riemannian manifolds. A principal condition is given by a certain positive lower bound of the second fundamental form of angular submanifolds at infinity. Another...... condition is certain bounds of derivatives up to order one of the trace of this quantity. These conditions are shown to be optimal for existence and completeness of a wave operator. Our theory does not involve prescribed asymptotic behaviour of the metric at infinity (like asymptotic Euclidean or hyperbolic...
Energy Technology Data Exchange (ETDEWEB)
Tuereci, R.G. [Kirikkale Univ., Kirikkale (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School
2017-05-15
One speed, time independent and homogeneous medium neutron transport equation can be solved with the anisotropic scattering which includes both the linear anisotropic and the quadratic anisotropic scattering properties. Having solved Case's eigenfunctions and the orthogonality relations among these eigenfunctions, some neutron transport problems such as albedo problem can be calculated as numerically by using numerical or semi-analytic methods. In this study the half-space albedo problem is investigated by using the modified F{sub N} method.
The Schroedinger equation as a singular perturbation problem
International Nuclear Information System (INIS)
Jager, E.M. de; Kuepper, T.
1978-01-01
Comparisons are made of the eigenvalues and the corresponding eigenfunctions of the eigenvalue problem connected with the one dimensional Schroedinger equation in Hilbert space. The difference of the eigenvalues is estimated by applying Weyl's monotonicity principle and the minimum maximum principle. The difference of the eigenfunctions is estimated in L 2 norm and in maximum norm obtained by using simple tools from operator theory in Hilbert spaces. An application concerning perturbations of the Planck ideal linear oscillator is given. (author)
Readiness of Adults to Learn Using E-Learning, M-Learning and T-Learning Technologies
Vilkonis, Rytis; Bakanoviene, Tatjana; Turskiene, Sigita
2013-01-01
The article presents results of the empirical research revealing readiness of adults to participate in the lifelong learning process using e-learning, m-learning and t-learning technologies. The research has been carried out in the framework of the international project eBig3 aiming at development a new distance learning platform blending virtual…
EXCEPTIONAL POINTS IN OPEN AND PT-SYMMETRIC SYSTEMS
Directory of Open Access Journals (Sweden)
Hichem Eleuch
2014-04-01
Full Text Available Exceptional points (EPs determine the dynamics of open quantum systems and cause also PT symmetry breaking in PT symmetric systems. From a mathematical point of view, this is caused by the fact that the phases of the wavefunctions (eigenfunctions of a non-Hermitian Hamiltonian relative to one another are not rigid when an EP is approached. The system is therefore able to align with the environment to which it is coupled and, consequently, rigorous changes of the system properties may occur. We compare analytically as well as numerically the eigenvalues and eigenfunctions of a 2 × 2 matrix that is characteristic either of open quantum systems at high level density or of PT symmetric optical lattices. In both cases, the results show clearly the influence of the environment on the system in the neighborhood of EPs. Although the systems are very different from one another, the eigenvalues and eigenfunctions indicate the same characteristic features.
International Nuclear Information System (INIS)
Ward, D.J.; Jardin, S.C.
1991-09-01
The effects of plasma deformability on the feedback stabilization of axisymmetric modes of tokamak plasmas are studied. It is seen that plasmas with strongly shaped cross sections have unstable motion different from a rigid shift. Furthermore, the placement of passive conductors is shown to modify the non-rigid components of the eigenfunction in a way that reduces the stabilizing eddy currents in these conductors. Passive feedback results using several equilibria of varying shape are presented. The eigenfunction is also modified under the effects of active feedback. This deformation is seen to depend strongly on the position of the flux loops which are used to determine plasma vertical position for the active feedback system. The variations of these non-rigid components of the eigenfunction always serve to reduce the stabilizing effect of the active feedback system by reducing the measurable poloidal flux at the flux-loop locations. Active feedback results are presented for the PBX-M tokamak configuration. (author) 19 figs., 2 tabs., 30 refs
Independent component analysis of edge information for face recognition
Karande, Kailash Jagannath
2013-01-01
The book presents research work on face recognition using edge information as features for face recognition with ICA algorithms. The independent components are extracted from edge information. These independent components are used with classifiers to match the facial images for recognition purpose. In their study, authors have explored Canny and LOG edge detectors as standard edge detection methods. Oriented Laplacian of Gaussian (OLOG) method is explored to extract the edge information with different orientations of Laplacian pyramid. Multiscale wavelet model for edge detection is also propos
From learning objects to learning activities
DEFF Research Database (Denmark)
Dalsgaard, Christian
2005-01-01
This paper discusses and questions the current metadata standards for learning objects from a pedagogical point of view. From a social constructivist approach, the paper discusses how learning objects can support problem based, self-governed learning activities. In order to support this approach......, it is argued that it is necessary to focus on learning activities rather than on learning objects. Further, it is argued that descriptions of learning objectives and learning activities should be separated from learning objects. The paper presents a new conception of learning objects which supports problem...... based, self-governed activities. Further, a new way of thinking pedagogy into learning objects is introduced. It is argued that a lack of pedagogical thinking in learning objects is not solved through pedagogical metadata. Instead, the paper suggests the concept of references as an alternative...
Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials
Horozov, Emil
2016-05-01
We construct new families of vector orthogonal polynomials that have the property to be eigenfunctions of some differential operator. They are extensions of the Hermite and Laguerre polynomial systems. A third family, whose first member has been found by Y. Ben Cheikh and K. Douak is also constructed. The ideas behind our approach lie in the studies of bispectral operators. We exploit automorphisms of associative algebras which transform elementary vector orthogonal polynomial systems which are eigenfunctions of a differential operator into other systems of this type.
(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
Klimyk, A U; Patera, J
2007-01-01
We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found
Can machine learning explain human learning?
Vahdat, M.; Oneto, L.; Anguita, D.; Funk, M.; Rauterberg, G.W.M.
2016-01-01
Learning Analytics (LA) has a major interest in exploring and understanding the learning process of humans and, for this purpose, benefits from both Cognitive Science, which studies how humans learn, and Machine Learning, which studies how algorithms learn from data. Usually, Machine Learning is
E-Learning 2.0: Learning Redefined
Kumar, Rupesh
2009-01-01
The conventional e-learning approach emphasizes a learning system more than a learning environment. While traditional e-learning systems continue to be significant, there is a new set of services emerging, embracing the philosophy of Web 2.0. Known as e-learning 2.0, it aims to create a personalized learning environment. E-learning 2.0 combines the use of discrete but complementary tools and web services to support the creation of ad-hoc learning communities. This paper discusses the influenc...
The Future of Learning: From eLearning to mLearning.
Keegan, Desmond
The future of electronic learning was explored in an analysis that viewed the provision of learning at a distance as a continuum and traced the evolution from distance learning to electronic learning to mobile learning in Europe and elsewhere. Special attention was paid to the following topics: (1) the impact of the industrial revolution, the…
Directory of Open Access Journals (Sweden)
Ya-huei Wang
2017-08-01
Full Text Available This study attempted to test whether the use of computer-assisted language learning (CALL and innovative collaborative learning could be more effective than the use of traditional collaborative learning in improving students’ English proficiencies. A true experimental design was used in the study. Four randomly-assigned groups participated in the study: a traditional collaborative learning group (TCLG, 34 students, an innovative collaborative learning group (ICLG, 31 students, a CALL traditional collaborative learning group (CALLTCLG, 32 students, and a CALL innovative collaborative learning group (CALLICLG, 31 students. TOEIC (Test of English for International Communication listening, reading, speaking, and writing pre-test and post-test assessments were given to all students at an interval of sixteen weeks. Multivariate analysis of covariance (MANCOVA, multivariate analysis of variance (MANOVA, and analysis of variance (ANOVA were used to analyze the data. The results revealed that students who used CALL had significantly better learning performance than those who did not. Students in innovative collaborative learning had significantly better learning performances than those in traditional collaborative learning. Additionally, students using CALL innovative collaborative learning had better learning performances than those in CALL collaborative learning, those in innovative collaborative learning, and those in traditional collaborative learning.
Guided discovery learning in geometry learning
Khasanah, V. N.; Usodo, B.; Subanti, S.
2018-03-01
Geometry is a part of the mathematics that must be learned in school. The purpose of this research was to determine the effect of Guided Discovery Learning (GDL) toward geometry learning achievement. This research had conducted at junior high school in Sukoharjo on academic years 2016/2017. Data collection was done based on student’s work test and documentation. Hypothesis testing used two ways analysis of variance (ANOVA) with unequal cells. The results of this research that GDL gave positive effect towards mathematics learning achievement. GDL gave better mathematics learning achievement than direct learning. There was no difference of mathematics learning achievement between male and female. There was no an interaction between sex differences and learning models toward student’s mathematics learning achievement. GDL can be used to improve students’ mathematics learning achievement in geometry.
Learning scikit-learn machine learning in Python
Garreta, Raúl
2013-01-01
The book adopts a tutorial-based approach to introduce the user to Scikit-learn.If you are a programmer who wants to explore machine learning and data-based methods to build intelligent applications and enhance your programming skills, this the book for you. No previous experience with machine-learning algorithms is required.
International Nuclear Information System (INIS)
Soler, Roberto; Terradas, Jaume; Oliver, Ramón; Goossens, Marcel
2013-01-01
Magnetohydrodynamic (MHD) waves are ubiquitously observed in the solar atmosphere. Kink waves are a type of transverse MHD waves in magnetic flux tubes that are damped due to resonant absorption. The theoretical study of kink MHD waves in solar flux tubes is usually based on the simplification that the transverse variation of density is confined to a nonuniform layer much thinner than the radius of the tube, i.e., the so-called thin boundary approximation. Here, we develop a general analytic method to compute the dispersion relation and the eigenfunctions of ideal MHD waves in pressureless flux tubes with transversely nonuniform layers of arbitrary thickness. Results for kink waves are produced and compared with fully numerical resistive MHD eigenvalue computations in the limit of small resistivity. We find that the frequency and resonant damping rate are the same in both ideal and resistive cases. The actual results for thick nonuniform layers deviate from the behavior predicted in the thin boundary approximation and strongly depend on the shape of the nonuniform layer. The eigenfunctions in ideal MHD are very different from those in resistive MHD. The ideal eigenfunctions display a global character regardless of the thickness of the nonuniform layer, while the resistive eigenfunctions are localized around the resonance and are indistinguishable from those of ordinary resistive Alfvén modes. Consequently, the spatial distribution of wave energy in the ideal and resistive cases is dramatically different. This poses a fundamental theoretical problem with clear observational consequences
SEARCH FOR GLOBAL f-MODES AND p-MODES IN THE {sup 8}B NEUTRINO FLUX
Energy Technology Data Exchange (ETDEWEB)
Lopes, Ilídio, E-mail: ilidio.lopes@ist.utl.pt, E-mail: ilopes@uevora.pt [Centro Multidisciplinar de Astrofísica, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Departamento de Física, Escola de Ciências e Tecnologia, Universidade de Évora, Colégio Luis António Verney, 7002-554 Évora (Portugal)
2013-11-01
The impact of global acoustic modes on the {sup 8}B neutrino flux time series is computed for the first time. It is shown that the time fluctuations of the {sup 8}B neutrino flux depend on the amplitude of acoustic eigenfunctions in the region where the {sup 8}B neutrino flux is produced: modes with low n (or order) that have eigenfunctions with a relatively large amplitude in the Sun's core strongly affect the neutrino flux; conversely, modes with high n that have eigenfunctions with a minimal amplitude in the Sun's core have a very small impact on the neutrino flux. It was found that the global modes with a larger impact on the {sup 8}B neutrino flux have a frequency of oscillation in the interval 250 μHz to 500 μHz (or a period in the interval 30 minutes to 70 minutes), such as the f-modes (n = 0) for the low degrees, radial modes of order n ≤ 3, and the dipole mode of order n = 1. Their corresponding neutrino eigenfunctions are very sensitive to the solar inner core and are unaffected by the variability of the external layers of the solar surface. If time variability of neutrinos is observed for these modes, it will lead to new ways of improving the sound speed profile inversion in the central region of the Sun.
Learning to learn in the European Reference Framework for lifelong learning
Pirrie, Anne; Thoutenhoofd, Ernst D.
2013-01-01
This article explores the construction of learning to learn that is implicit in the document Key Competences for Lifelong LearningEuropean Reference Framework and related education policy from the European Commission. The authors argue that the hallmark of learning to learn is the development of a
Harnack's Inequality for Degenerate and Singular Parabolic Equations
DiBenedetto, Emmanuele; Vespri, Vincenzo
2012-01-01
Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete. It seemed therefore timely to trace a comprehensive
The driving mechanism of roAp stars
Energy Technology Data Exchange (ETDEWEB)
Dupret, M-A [Observatoire de Paris, LESIA, CNRS UMR 8109, 5 place J. Janssen, 92195 Meudon (France); Theado, S; Noels, A [Institut d' Astrophysique et Geophysique, Universite de Liege (Belgium)], E-mail: MA.dupret@obspm.fr
2008-10-15
We analyse in detail the driving mechanism of roAp stars and present the theoretical instability strip predicted by our models with solar metallicity. A particular attention is given to the interpretation of the role played by the different eigenfunctions in the stabilization of the modes at the red edge of the instability strip. The gradient of temperature in the H{sub I} opacity bump appears to play a major role in this context. We also consider the particular and complex role played by the shape of the eigenfunctions (location of the nodes, ...)
Solving the Schroedinger equation using the finite difference time domain method
International Nuclear Information System (INIS)
Sudiarta, I Wayan; Geldart, D J Wallace
2007-01-01
In this paper, we solve the Schroedinger equation using the finite difference time domain (FDTD) method to determine energies and eigenfunctions. In order to apply the FDTD method, the Schroedinger equation is first transformed into a diffusion equation by the imaginary time transformation. The resulting time-domain diffusion equation is then solved numerically by the FDTD method. The theory and an algorithm are provided for the procedure. Numerical results are given for illustrative examples in one, two and three dimensions. It is shown that the FDTD method accurately determines eigenfunctions and energies of these systems
Band theory of metals the elements
Altmann, Simon L
1970-01-01
Band Theory of Metals: The Elements focuses on the band theory of solids. The book first discusses revision of quantum mechanics. Topics include Heisenberg's uncertainty principle, normalization, stationary states, wave and group velocities, mean values, and variational method. The text takes a look at the free-electron theory of metals, including heat capacities, density of states, Fermi energy, core and metal electrons, and eigenfunctions in three dimensions. The book also reviews the effects of crystal fields in one dimension. The eigenfunctions of the translations; symmetry operations of t
Spectral transform and orthogonality relations for the Kadomtsev-Petviashvili I equation
Energy Technology Data Exchange (ETDEWEB)
Boiti, M; Leon, J J.P.; Pempinelli, F [Montpellier-2 Univ., 34 (France). Lab. de Physique Mathematique
1989-10-30
We define a new spectral transform r(k,l) of the potential u in the time dependent Schroedinger equation (associated to the KPI equation). Orthogonality relations for the sectionally holomorphic eigenfunctions of the Schroedinger equation are used to express the spectral transform f(k,l) previously introduced by Manakov and Fokas and Ablowitz in terms of r(k,l). The main advantage of the new spectral transform r(k,l) is that its definition does not require to introduce an additional nonanalytic eigenfunction N. Characterization equations for r(k,l) are also obtained. (orig.).
Application of the Asymptotic Taylor Expansion Method to Bistable Potentials
Directory of Open Access Journals (Sweden)
Okan Ozer
2013-01-01
Full Text Available A recent method called asymptotic Taylor expansion (ATEM is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.
The driving mechanism of roAp stars
International Nuclear Information System (INIS)
Dupret, M-A; Theado, S; Noels, A
2008-01-01
We analyse in detail the driving mechanism of roAp stars and present the theoretical instability strip predicted by our models with solar metallicity. A particular attention is given to the interpretation of the role played by the different eigenfunctions in the stabilization of the modes at the red edge of the instability strip. The gradient of temperature in the H I opacity bump appears to play a major role in this context. We also consider the particular and complex role played by the shape of the eigenfunctions (location of the nodes, ...).
Symmetry-adapted basis sets automatic generation for problems in chemistry and physics
Avery, John Scales; Avery, James Emil
2012-01-01
In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This gives rise to eigenvalue problems of which some solutions may be very difficult to find. For example, the problem of finding eigenfunctions and eigenvalues for the Hamiltonian of a many-particle system is usually so difficult that it requires approximate methods, the most common of which is expansion of the eigenfunctions in terms of basis functions that obey the boundary conditions of the problem. The computational effort needed
Spectral transform and orthogonality relations for the Kadomtsev-Petviashvili I equation
International Nuclear Information System (INIS)
Boiti, M.; Leon, J.J.P.; Pempinelli, F.
1989-01-01
We define a new spectral transform r(k,l) of the potential u in the time dependent Schroedinger equation (associated to the KPI equation). Orthogonality relations for the sectionally holomorphic eigenfunctions of the Schroedinger equation are used to express the spectral transform f(k,l) previously introduced by Manakov and Fokas and Ablowitz in terms of r(k,l). The main advantage of the new spectral transform r(k,l) is that its definition does not require to introduce an additional nonanalytic eigenfunction N. Characterization equations for r(k,l) are also obtained. (orig.)
Deep Learning in Open Source Learning Streams
DEFF Research Database (Denmark)
Kjærgaard, Thomas
2016-01-01
This chapter presents research on deep learning in a digital learning environment and raises the question if digital instructional designs can catalyze deeper learning than traditional classroom teaching. As a theoretical point of departure the notion of ‘situated learning’ is utilized...... and contrasted to the notion of functionalistic learning in a digital context. The mechanism that enables deep learning in this context is ‘The Open Source Learning Stream’. ‘The Open Source Learning Stream’ is the notion of sharing ‘learning instances’ in a digital space (discussion board, Facebook group......, unistructural, multistructural or relational learning. The research concludes that ‘The Open Source Learning Stream’ can catalyze deep learning and that there are four types of ‘Open Source Learning streams’; individual/ asynchronous, individual/synchronous, shared/asynchronous and shared...
Active Learning Through Discussion in E-Learning
Daru Wahyuningsih
2016-01-01
Active learning is generally made by a lecturer in learning face to face. In the face to face learning, lecturer can implement a variety of teaching methods to make students actively involved in learning. This is different from learning that is actuating in e-learning. The main characteristic of e-learning is learning that can take place anytime and anywhere. Special strategies are needed so that lecturer can make students play an active role in the course of e-learning. Research in order to ...
Deepening Learning through Learning-by-Inventing
Apiola, Mikko; Tedre, Matti
2013-01-01
It has been shown that deep approaches to learning, intrinsic motivation, and self-regulated learning have strong positive effects on learning. How those pedagogical theories can be integrated in computing curricula is, however, still lacking empirically grounded analyses. This study integrated, in a robotics-based programming class, a method of learning-by-inventing, and studied its qualitative effects on students’ learning through 144 interviews. Five findings were related with learning the...
Intentional Learning Vs Incidental Learning
Shahbaz Ahmed
2017-01-01
This study is conducted to demonstrate the knowledge of intentional learning and incidental learning. Hypothesis of this experiment is intentional learning is better than incidental learning, participants were demonstrated and were asked to learn the 10 non sense syllables in a specific sequence from the colored cards in the end they were asked to recall the background color of each card instead of non-sense syllables. Independent variables of the experiment are the colored cards containing n...
基于流形学习的社会化媒体网络数据分类%Networked data classification in social media based on manifold learning
Institute of Scientific and Technical Information of China (English)
史仍浩; 陈秀真; 李生红
2013-01-01
Social media provided massive, large-scale heterogeneous networked data. Classification in networked data is a new problem that needed to be solved. Based on latent social dimension model,this paper proposed using Laplacian eigenmaps from manifold learning to extract social dimensions . Experiments show that it is superior to original modularity maximization social dimension model in performance metrics like exact match ratio, micro average and macro average. The algorithm can capture implicit user relations better and analysis Web user behavior better.%社会化媒体提供了海量的、大尺度的异质网络数据,如何对网络数据进行分类是一个亟待解决的新问题.基于潜在社会维模型,提出利用流形学习中的拉普拉斯特征映射算法进行社会维抽取.实验表明,在精确匹配率、微平均、宏平均等性能指标上,均优于基于模块度最大化的原有社会维模型.该算法能更好地获取用户的隐性联系,从而更好地分析网络用户行为.
Clustering by reordering of similarity and Laplacian matrices: Application to galaxy clusters
Mahmoud, E.; Shoukry, A.; Takey, A.
2018-04-01
Similarity metrics, kernels and similarity-based algorithms have gained much attention due to their increasing applications in information retrieval, data mining, pattern recognition and machine learning. Similarity Graphs are often adopted as the underlying representation of similarity matrices and are at the origin of known clustering algorithms such as spectral clustering. Similarity matrices offer the advantage of working in object-object (two-dimensional) space where visualization of clusters similarities is available instead of object-features (multi-dimensional) space. In this paper, sparse ɛ-similarity graphs are constructed and decomposed into strong components using appropriate methods such as Dulmage-Mendelsohn permutation (DMperm) and/or Reverse Cuthill-McKee (RCM) algorithms. The obtained strong components correspond to groups (clusters) in the input (feature) space. Parameter ɛi is estimated locally, at each data point i from a corresponding narrow range of the number of nearest neighbors. Although more advanced clustering techniques are available, our method has the advantages of simplicity, better complexity and direct visualization of the clusters similarities in a two-dimensional space. Also, no prior information about the number of clusters is needed. We conducted our experiments on two and three dimensional, low and high-sized synthetic datasets as well as on an astronomical real-dataset. The results are verified graphically and analyzed using gap statistics over a range of neighbors to verify the robustness of the algorithm and the stability of the results. Combining the proposed algorithm with gap statistics provides a promising tool for solving clustering problems. An astronomical application is conducted for confirming the existence of 45 galaxy clusters around the X-ray positions of galaxy clusters in the redshift range [0.1..0.8]. We re-estimate the photometric redshifts of the identified galaxy clusters and obtain acceptable values
Does peer learning or higher levels of e-learning improve learning abilities?
DEFF Research Database (Denmark)
Worm, Bjarne Skjødt; Jensen, Kenneth
2013-01-01
The fast development of e-learning and social forums demands us to update our understanding of e-learning and peer learning. We aimed to investigate if higher, pre-defined levels of e-learning or social interaction in web forums improved students' learning ability....
On two energy-like invariants of line graphs and related graph operations
Directory of Open Access Journals (Sweden)
Xiaodan Chen
2016-02-01
Full Text Available Abstract For a simple graph G of order n, let μ 1 ≥ μ 2 ≥ ⋯ ≥ μ n = 0 $\\mu_{1}\\geq\\mu_{2}\\geq\\cdots\\geq\\mu_{n}=0$ be its Laplacian eigenvalues, and let q 1 ≥ q 2 ≥ ⋯ ≥ q n ≥ 0 $q_{1}\\geq q_{2}\\geq\\cdots\\geq q_{n}\\geq0$ be its signless Laplacian eigenvalues. The Laplacian-energy-like invariant and incidence energy of G are defined as, respectively, LEL ( G = ∑ i = 1 n − 1 μ i and IE ( G = ∑ i = 1 n q i . $$\\mathit{LEL}(G=\\sum_{i=1}^{n-1}\\sqrt{ \\mu_{i}} \\quad\\mbox{and}\\quad \\mathit {IE}(G=\\sum_{i=1}^{n} \\sqrt{q_{i}}. $$ In this paper, we present some new upper and lower bounds on LEL and IE of line graph, subdivision graph, para-line graph and total graph of a regular graph, some of which improve previously known results. The main tools we use here are the Cauchy-Schwarz inequality and the Ozeki inequality.
International Nuclear Information System (INIS)
DeVries, Nicole A.; Gassman, Esther E.; Kallemeyn, Nicole A.; Shivanna, Kiran H.; Magnotta, Vincent A.; Grosland, Nicole M.
2008-01-01
To examine the validity of manually defined bony regions of interest from computed tomography (CT) scans. Segmentation measurements were performed on the coronal reformatted CT images of the three phalanx bones of the index finger from five cadaveric specimens. Two smoothing algorithms (image-based and Laplacian surface-based) were evaluated to determine their ability to represent accurately the anatomic surface. The resulting surfaces were compared with laser surface scans of the corresponding cadaveric specimen. The average relative overlap between two tracers was 0.91 for all bones. The overall mean difference between the manual unsmoothed surface and the laser surface scan was 0.20 mm. Both image-based and Laplacian surface-based smoothing were compared; the overall mean difference for image-based smoothing was 0.21 mm and 0.20 mm for Laplacian smoothing. This study showed that manual segmentation of high-contrast, coronal, reformatted, CT datasets can accurately represent the true surface geometry of bones. Additionally, smoothing techniques did not significantly alter the surface representations. This validation technique should be extended to other bones, image segmentation and spatial filtering techniques. (orig.)
Energy Technology Data Exchange (ETDEWEB)
DeVries, Nicole A.; Gassman, Esther E.; Kallemeyn, Nicole A. [The University of Iowa, Department of Biomedical Engineering, Center for Computer Aided Design, Iowa City, IA (United States); Shivanna, Kiran H. [The University of Iowa, Center for Computer Aided Design, Iowa City, IA (United States); Magnotta, Vincent A. [The University of Iowa, Department of Biomedical Engineering, Department of Radiology, Center for Computer Aided Design, Iowa City, IA (United States); Grosland, Nicole M. [The University of Iowa, Department of Biomedical Engineering, Department of Orthopaedics and Rehabilitation, Center for Computer Aided Design, Iowa City, IA (United States)
2008-01-15
To examine the validity of manually defined bony regions of interest from computed tomography (CT) scans. Segmentation measurements were performed on the coronal reformatted CT images of the three phalanx bones of the index finger from five cadaveric specimens. Two smoothing algorithms (image-based and Laplacian surface-based) were evaluated to determine their ability to represent accurately the anatomic surface. The resulting surfaces were compared with laser surface scans of the corresponding cadaveric specimen. The average relative overlap between two tracers was 0.91 for all bones. The overall mean difference between the manual unsmoothed surface and the laser surface scan was 0.20 mm. Both image-based and Laplacian surface-based smoothing were compared; the overall mean difference for image-based smoothing was 0.21 mm and 0.20 mm for Laplacian smoothing. This study showed that manual segmentation of high-contrast, coronal, reformatted, CT datasets can accurately represent the true surface geometry of bones. Additionally, smoothing techniques did not significantly alter the surface representations. This validation technique should be extended to other bones, image segmentation and spatial filtering techniques. (orig.)
Learning, Learning Organisations and the Global Enterprise
Manikutty, Sankaran
2009-01-01
The steadily increasing degree of globalisation of enterprises implies development of many skills, among which the skills to learn are among the most important. Learning takes place at the individual level, but collective learning and organisational learning are also important. Learning styles of individuals are different and learning styles are…
Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model
Pont, Federico M.; Osenda, Omar; Serra, Pablo
2018-05-01
The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heun’s confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Rényi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Rényi entropy and entanglement spectrum for the whole parameter space.
Choi, Beomkyu
2016-01-01
The purpose of this study was to examine the relationships between learners' learning strategies and learning satisfaction in an asynchronous online learning environment. In an attempt to shed some light on how people learn in an online learning environment, one hundred and sixteen graduate students who were taking online learning courses…
Learning Theories In Instructional Multimedia For English Learning
Farani, Rizki
2016-01-01
Learning theory is the concept of human learning. This concept is one of the important components in instructional for learning, especially English learning. English subject becomes one of important subjects for students but learning English needs specific strategy since it is not our vernacular. Considering human learning process in English learning is expected to increase students' motivation to understand English better. Nowadays, the application of learning theories in English learning ha...
Blended Learning as Transformational Institutional Learning
VanDerLinden, Kim
2014-01-01
This chapter reviews institutional approaches to blended learning and the ways in which institutions support faculty in the intentional redesign of courses to produce optimal learning. The chapter positions blended learning as a strategic opportunity to engage in organizational learning.
Organizational learning viewed from a social learning perspective
DEFF Research Database (Denmark)
Elkjær, Bente; Brandi, Ulrik
2011-01-01
This chapter reviews the literature on organizational learning through the lens of a social learning perspective. We start with an individual learning perspective, before moving on to a social learning perspective with a particular focus upon pragmatism. The literature review covers the following...... four issues: the content of learning, the process of learning, the relation between individual and organization, and the concept of organization. An important separator between individual and social learning perspectives is the different emphasis on learning as acquisition of skills and knowledge......, versus learning as encompassing development of identities and socialization to organizational work and life. A pragmatist social learning perspective emphasizes both learning as acquisition through experience and inquiry, and learning as development of identities and socialization through individuals...
Discovery learning with SAVI approach in geometry learning
Sahara, R.; Mardiyana; Saputro, D. R. S.
2018-05-01
Geometry is one branch of mathematics that an important role in learning mathematics in the schools. This research aims to find out about Discovery Learning with SAVI approach to achievement of learning geometry. This research was conducted at Junior High School in Surakarta city. Research data were obtained through test and questionnaire. Furthermore, the data was analyzed by using two-way Anova. The results showed that Discovery Learning with SAVI approach gives a positive influence on mathematics learning achievement. Discovery Learning with SAVI approach provides better mathematics learning outcomes than direct learning. In addition, students with high self-efficacy categories have better mathematics learning achievement than those with moderate and low self-efficacy categories, while student with moderate self-efficacy categories are better mathematics learning achievers than students with low self-efficacy categories. There is an interaction between Discovery Learning with SAVI approach and self-efficacy toward student's mathematics learning achievement. Therefore, Discovery Learning with SAVI approach can improve mathematics learning achievement.
Learning Design Development for Blended Learning
DEFF Research Database (Denmark)
Hansen, Janne Saltoft
Learning design development for blended learning We started implementing Blackboard at Aarhus University in 2013. At the Health Faculty Blackboard replaced AULA which was a LMS with functionality for file distribution and only a vague focus on learning tools. Most teachers therefore had...... no experiences with blended leaning and technology supported out-of-class activities. At the pedagogical unit at the Health faculty we wanted to follow the Blackboard implementation with pedagogical tools for learning design to evolve the pedagogical use of the system. We needed to make development of blended...... learning courses easier for the teachers and also ensure quality in the courses. This poster describes the process from development of the learning design to implementation of the learning design at the faculty: 1. How to place demands on a learning design-model and how to develop and use such a model. 2...
E-learning and blended learning in orthodontic education
Directory of Open Access Journals (Sweden)
Avinash Kumar
2017-01-01
Full Text Available The purpose of this article is to evaluate how effective and efficient e-learning and blended learning is when compared with traditional face-to-face learning in orthodontic education. This article also provides a comparison between face-to-face learning, e-learning, and blended learning. An open PubMed literature search was done from 1980 to 2015, and a total of 23 relevant key articles were reviewed. Information emerging from studies in orthodontic education has indicated that e-learning classes are at least as good as and/or better than face-to-face classroom learning. Till date, only one study stated that the face-to-face conventional learning is better than e-learning. Two studies stated that blended approach using both traditional face-to-face learning and e-learning is the best method. In one study, the advantages of e-learning observed in the theoretical fields of orthodontics were not achieved in learning practical procedures for manual skills. Few studies found improvements in the efficiency of learning with e-learning program. Studies performed through questionnaires showed that student's attitude and acceptance toward the use of e-learning was positive and favorable; however, blended learning was always rated high. Future research should be based on experiences of both faculty and student on a large scale for implementation of e-learning and blended learning in academic institutions. There is also need to provide professional development for faculty who will be teaching both in the physical and virtual environments.
Learning style, judgements of learning, and learning of verbal and visual information.
Knoll, Abby R; Otani, Hajime; Skeel, Reid L; Van Horn, K Roger
2017-08-01
The concept of learning style is immensely popular despite the lack of evidence showing that learning style influences performance. This study tested the hypothesis that the popularity of learning style is maintained because it is associated with subjective aspects of learning, such as judgements of learning (JOLs). Preference for verbal and visual information was assessed using the revised Verbalizer-Visualizer Questionnaire (VVQ). Then, participants studied a list of word pairs and a list of picture pairs, making JOLs (immediate, delayed, and global) while studying each list. Learning was tested by cued recall. The results showed that higher VVQ verbalizer scores were associated with higher immediate JOLs for words, and higher VVQ visualizer scores were associated with higher immediate JOLs for pictures. There was no association between VVQ scores and recall or JOL accuracy. As predicted, learning style was associated with subjective aspects of learning but not objective aspects of learning. © 2016 The British Psychological Society.
Consensus of second-order multi-agent dynamic systems with quantized data
Energy Technology Data Exchange (ETDEWEB)
Guan, Zhi-Hong, E-mail: zhguan@mail.hust.edu.cn [Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074 (China); Meng, Cheng [Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074 (China); Liao, Rui-Quan [Petroleum Engineering College,Yangtze University, Jingzhou, 420400 (China); Zhang, Ding-Xue, E-mail: zdx7773@163.com [Petroleum Engineering College,Yangtze University, Jingzhou, 420400 (China)
2012-01-09
The consensus problem of second-order multi-agent systems with quantized link is investigated in this Letter. Some conditions are derived for the quantized consensus of the second-order multi-agent systems by the stability theory. Moreover, a result characterizing the relationship between the eigenvalues of the Laplacians matrix and the quantized consensus is obtained. Examples are given to illustrate the theoretical analysis. -- Highlights: ► A second-order multi-agent model with quantized data is proposed. ► Two sufficient and necessary conditions are obtained. ► The relationship between the eigenvalues of the Laplacians matrix and the quantized consensus is discovered.
Siu Loon Hoe
2007-01-01
Organisational learning has over the years been subject of much study by scholars and managers. In the process, the organisational learning concept has been linked to many other knowledge concepts such as individual learning, learning organisation, and knowledge management. This paper draws from existing literature in organisational behaviour, human resource management, marketing, and information management, to further develop the conceptual links between organisational learning and these kno...
Spectrum and Collapse of a Particle in a Nonlocal Field of Centrifugal Type
Pupyshev, V V
2004-01-01
The investigated problem is the one-dimensional Schrödinger equation with the zero boundary conditions at the ends of the segment $[0,\\pi/2]$, and the interaction equal to the product of the potential proportional to squared secant of the argument and the sum of the unity and integral operators. For this problem the dependence of the spectrum of real eigenvalues and the corresponding eigenfunctions on the real potential parameter is analyzed qualitatively and numerically. For analysis the Fourier- and spline-approximations of the searched eigenfunction are proposed and applied. Special attention is paid to the particle collapse.
Comment on "Calculations for the one-dimensional soft Coulomb problem and the hard Coulomb limit".
Carrillo-Bernal, M A; Núñez-Yépez, H N; Salas-Brito, A L; Solis, Didier A
2015-02-01
In the referred paper, the authors use a numerical method for solving ordinary differential equations and a softened Coulomb potential -1/√[x(2)+β(2)] to study the one-dimensional Coulomb problem by approaching the parameter β to zero. We note that even though their numerical findings in the soft potential scenario are correct, their conclusions do not extend to the one-dimensional Coulomb problem (β=0). Their claims regarding the possible existence of an even ground state with energy -∞ with a Dirac-δ eigenfunction and of well-defined parity eigenfunctions in the one-dimensional hydrogen atom are questioned.
A new approach to the Schrödinger equation with rational potentials
Dong, Ming-de; Chu, Jue-Hui
1984-04-01
A new analytic theory is established for the Schrödinger equation with a rational potential, including a complete classification of the regular eigenfunctions into three different types, an exact method of obtaining wavefunctions, an explicit formulation of the spectral equation (3 x 3 determinant) etc. All representations are exhibited in a unifying way via function-theoretic methods and therefore given in explicit form, in contrast to the prevailing discussion appealing to perturbation or variation methods or continued-fraction techniques. The irregular eigenfunctions at infinity can be obtained analogously and will be discussed separately as another solvable case for singular potentials.
Destabilization of drift waves due to nonuniform density gradient
International Nuclear Information System (INIS)
Hirose, A.; Ishihara, O.
1985-01-01
It is shown that the conventional mode differential equation for low frequency electrostatic waves in a tokamak does not contain full ion dynamics. Both electrons and ions contribute to the ballooning term, which is subject to finite ion Larmor radius effects. Also, both fluid ion approximation and kinetic ion model yield the same correction. Reexamined are the density gradient universal mode and ion temperature gradient instability employing the lowest order Pearlstein-Berk type radial eigenfunctions. No unstable, bounded, energy outgoing eigenfunctions have been found. In particular, a large ion temperature gradient (eta/sub i/) tends to further stabilize the temperature gradient driven mode
Analytic solution of boundary-value problems for nonstationary model kinetic equations
International Nuclear Information System (INIS)
Latyshev, A.V.; Yushkanov, A.A.
1993-01-01
A theory for constructing the solutions of boundary-value problems for non-stationary model kinetic equations is constructed. This theory was incorrectly presented equation, separation of the variables is used, this leading to a characteristic equation. Eigenfunctions are found in the space of generalized functions, and the eigenvalue spectrum is investigated. An existence and uniqueness theorem for the expansion of the Laplace transform of the solution with respect to the eigenfunctions is proved. The proof is constructive and gives explicit expressions for the expansion coefficients. An application to the Rayleigh problem is obtained, and the corresponding result of Cercignani is corrected
Quantum influence of topological defects in Goedel-type space-times
Energy Technology Data Exchange (ETDEWEB)
Carvalho, Josevi [Universidade Federal de Campina Grande, Unidade Academica de Tecnologia de Alimentos, Centro de Ciencias e Tecnologia Agroalimentar, Pombal, PB (Brazil); Carvalho, M.; Alexandre, M. de [Universidade Federal de Alagoas, Instituto de Fisica, Maceio, AL (Brazil); Furtado, Claudio [Universidade Federal da Paraiba, Cidade Universitaria, Departamento de Fisica, CCEN, Joao Pessoa, PB (Brazil)
2014-06-15
In this contribution, some solutions of the Klein-Gordon equation in Goedel-type metrics with an embedded cosmic string are considered. The quantum dynamics of a scalar particle in three spaces whose metrics are described by different classes of Goedel solutions, with a cosmic string passing through the spaces, is found. The energy levels and eigenfunctions of the Klein-Gordon operator are obtained. We show that these eigenvalues and eigenfunctions depend on the parameter characterizing the presence of a cosmic string in the space-time. We note that the presence of topological defects breaks the degeneracy of energy levels. (orig.)
Mouri, Kousuke; Uosaki, Noriko; Ogata, Hiroaki
2018-01-01
Seamless learning has been recognized as an effective learning approach across various dimensions including formal and informal learning contexts, individual and social learning, and physical world and cyberspace. With the emergence of seamless learning, the majority of the current research focuses on realizing a seamless learning environment at…
Schüpfer, G; Gfrörer, R; Schleppers, A
2007-10-01
In only a few contexts is the need for substantial learning more pronounced than in health care. For a health care provider, the ability to learn is essential in a changing environment. Although individual humans are programmed to learn naturally, organisations are not. Learning that is limited to individual professions and traditional approaches to continuing medical education is not sufficient to bring about substantial changes in the learning capacity of an institution. Also, organisational learning is an important issue for anaesthesia departments. Future success of an organisation often depends on new capabilities and competencies. Organisational learning is the capacity or processes within an organisation to maintain or improve performance based on experience. Learning is seen as a system-level phenomenon as it stays in the organisation regardless of the players involved. Experience from other industries shows that learning strategies tend to focus on single loop learning, with relatively little double loop learning and virtually no meta-learning or non-learning. The emphasis on team delivery of health care reinforces the need for team learning. Learning organisations make learning an intrinsic part of their organisations and are a place where people continually learn how to learn together. Organisational learning practice can help to improve existing skills and competencies and to change outdated assumptions, procedures and structures. So far, learning theory has been ignored in medicine, due to a wide variety of complex political, economic, social, organisational culture and medical factors that prevent innovation and resist change. The organisational culture is central to every stage of the learning process. Learning organisations move beyond simple employee training into organisational problem solving, innovation and learning. Therefore, teamwork and leadership are necessary. Successful organisations change the competencies of individuals, the systems
Beyond blended learning! Undiscovered potentials for e-learning in organizational learning
DEFF Research Database (Denmark)
Bang, Jørgen; Dalsgaard, Christian; Kjær, Arne
2007-01-01
The basic question raised in this article is: Is pure e-learning able to support learning in organizations better today than 4-5 years ago? Based on two case studies on blended learning courses for company training, the article discusses whether use of new Web 2.0 and social software tools may help...... overcome previous limitations of e-learning....
Miatun, A.; Muntazhimah
2018-01-01
The aim of this research was to determine the effect of learning models on mathematics achievement viewed from student’s self-regulated learning. The learning model compared were discovery learning and problem-based learning. The population was all students at the grade VIII of Junior High School in Boyolali regency. The samples were students of SMPN 4 Boyolali, SMPN 6 Boyolali, and SMPN 4 Mojosongo. The instruments used were mathematics achievement tests and self-regulated learning questionnaire. The data were analyzed using unbalanced two-ways Anova. The conclusion was as follows: (1) discovery learning gives better achievement than problem-based learning. (2) Achievement of students who have high self-regulated learning was better than students who have medium and low self-regulated learning. (3) For discovery learning, achievement of students who have high self-regulated learning was better than students who have medium and low self-regulated learning. For problem-based learning, students who have high and medium self-regulated learning have the same achievement. (4) For students who have high self-regulated learning, discovery learning gives better achievement than problem-based learning. Students who have medium and low self-regulated learning, both learning models give the same achievement.
Effects of Cooperative E-Learning on Learning Outcomes
Yeh, Shang-Pao; Fu, Hsin-Wei
2014-01-01
This study aims to discuss the effects of E-Learning and cooperative learning on learning outcomes. E-Learning covers the dimensions of Interpersonal communication, abundant resources, Dynamic instruction, and Learning community; and, cooperative learning contains three dimensions of Cooperative motive, Social interaction, and Cognition…
Hodson, Derek
2014-01-01
This opinion piece paper urges teachers and teacher educators to draw careful distinctions among four basic learning goals: learning science, learning about science, doing science and learning to address socio-scientific issues. In elaboration, the author urges that careful attention is paid to the selection of teaching/learning methods that…
Still to Learn from Vicarious Learning
Mayes, J. T.
2015-01-01
The term "vicarious learning" was introduced in the 1960s by Bandura, who demonstrated how learning can occur through observing the behaviour of others. Such social learning is effective without the need for the observer to experience feedback directly. More than twenty years later a series of studies on vicarious learning was undertaken…
Tile-Based Semisupervised Classification of Large-Scale VHR Remote Sensing Images
Directory of Open Access Journals (Sweden)
Haikel Alhichri
2018-01-01
Full Text Available This paper deals with the problem of the classification of large-scale very high-resolution (VHR remote sensing (RS images in a semisupervised scenario, where we have a limited training set (less than ten training samples per class. Typical pixel-based classification methods are unfeasible for large-scale VHR images. Thus, as a practical and efficient solution, we propose to subdivide the large image into a grid of tiles and then classify the tiles instead of classifying pixels. Our proposed method uses the power of a pretrained convolutional neural network (CNN to first extract descriptive features from each tile. Next, a neural network classifier (composed of 2 fully connected layers is trained in a semisupervised fashion and used to classify all remaining tiles in the image. This basically presents a coarse classification of the image, which is sufficient for many RS application. The second contribution deals with the employment of the semisupervised learning to improve the classification accuracy. We present a novel semisupervised approach which exploits both the spectral and spatial relationships embedded in the remaining unlabelled tiles. In particular, we embed a spectral graph Laplacian in the hidden layer of the neural network. In addition, we apply regularization of the output labels using a spatial graph Laplacian and the random Walker algorithm. Experimental results obtained by testing the method on two large-scale images acquired by the IKONOS2 sensor reveal promising capabilities of this method in terms of classification accuracy even with less than ten training samples per class.
From Learning Object to Learning Cell: A Resource Organization Model for Ubiquitous Learning
Yu, Shengquan; Yang, Xianmin; Cheng, Gang; Wang, Minjuan
2015-01-01
This paper presents a new model for organizing learning resources: Learning Cell. This model is open, evolving, cohesive, social, and context-aware. By introducing a time dimension into the organization of learning resources, Learning Cell supports the dynamic evolution of learning resources while they are being used. In addition, by introducing a…
Learning Companion Systems, Social Learning Systems, and the Global Social Learning Club.
Chan, Tak-Wai
1996-01-01
Describes the development of learning companion systems and their contributions to the class of social learning systems that integrate artificial intelligence agents and use machine learning to tutor and interact with students. Outlines initial social learning projects, their programming languages, and weakness. Future improvements will include…
Wahyu Utami, Niken; Aziz Saefudin, Abdul
2018-01-01
This study aims to determine: 1) differences in students taking independent learning by using e-learning and the students who attend the learning by using the print instructional materials ; 2) differences in the creativity of students who follow learning with e-learning and the students who attend the learning by using the print instructional materials ; 3) differences in learning independence and creativity of students attend learning with e-learning and the students who attend lessons using printed teaching materials in the subject of Mathematics Instructional Media Development. This study was a quasi-experimental research design using only posttest control design. The study population was all students who take courses in Learning Mathematics Media Development, Academic Year 2014/2015 100 students and used a random sample (random sampling) is 60 students. To test the hypothesis used multivariate analysis of variance or multivariable analysis of variance (MANOVA) of the track. The results of this study indicate that 1) There is a difference in student learning independence following study using the e-learning and the students who attend lessons using printed teaching materials in the lecture PMPM ( F = 4.177, p = 0.046 0.05) ; No difference learning independence and creativity of students attend learning by using e-learning and the students who attend the learning using printed teaching materials in the lecture PMPM (F = 2.452, p = 0.095 > 0.05). Based on these studies suggested that the learning using e -learning can be used to develop student creativity, while learning to use e -learning and teaching materials can be printed to use to develop students’ independence.
Eigenfunctions in disordered systems near the mobility edge
International Nuclear Information System (INIS)
Brezini, A.
1982-08-01
A model is proposed to calculate the average probability and the average size of the localization domain for an electron being localized at a given site in a Cayley tree lattice. The numerical results are presented in the limit of weak disorder in the case of Cauchy distribution for site energies. Attention is paid to the states near the mobility edge in the localized regime. Particularly, features exhibited in the linear chain case are observed for the first time for higher dimensions. (author)
e-Learning for Lifelong Learning in Denmark
DEFF Research Database (Denmark)
Buhl, Mie; Andreasen, Lars Birch
2010-01-01
The chapter on 'e-Learning for Lifelong Learning in Denmark' is part of an international White Paper, focusing on educational systems, describing status and characteristics and highlighting specific cases of e-learning and of lifelong learning....
Is mobile learning a substitute for electronic learning?
Sitthiworachart, Jirarat; Joy, Mike
2008-01-01
Mobile learning is widely regarded as the next generation of learning technologies, and refers to the use of mobile devices in education to enhance learning activities. The increasing use of mobile devices has encouraged research into the capabilities of mobile learning systems. Many questions arise about mobile learning, such as whether mobile learning can be a substitute for electronic learning, what the potential benefits and problems of utilizing mobile devices in education are, and what ...
Learning how to learn: Meta-learning strategies for the challenges of learning pharmacology.
Alton, Suzanne
2016-03-01
Nursing students have difficulty with pharmacology courses because of the complicated nomenclature and the difficulty of applying drug information to actual patient care. As part of a new pharmacology course being created, meta-learning strategies designed to diminish the difficulties of learning this difficult content were part of the course pedagogy. Strategies were demonstrated, reviewed in class, and implemented through homework assignments. The setting was an Academic Health Center's School of Nursing in the southern United States. Participants were third-year nursing students in an undergraduate nursing program. Surveys of students' opinions of learning gains were conducted at the end of the course over several semesters. In addition, pharmacology scores on a standardized exit exam were compared prior to implementing the course and after. Students reported learning dry material more easily, having greater confidence, and finding substantial value in the learning strategies. Students indicated the most helpful strategies, in descending order, as follows: making charts to compare and contrast drugs and drug classes, writing out drug flash cards, making or reviewing creative projects, prioritizing information, making or using visual study aids, and using time and repetition to space learning. Implementation of the new course improved pharmacology scores on a standardized exit exam from 67.0% to 74.3%. Overall response to learning strategies was positive, and the increase in the pharmacology standardized exit exam scores demonstrated the effectiveness of this instructional approach. Copyright © 2016 Elsevier Ltd. All rights reserved.
Jeong, Hyeonjeong; Sugiura, Motoaki; Sassa, Yuko; Wakusawa, Keisuke; Horie, Kaoru; Sato, Shigeru; Kawashima, Ryuta
2010-04-01
Second language (L2) acquisition necessitates learning and retrieving new words in different modes. In this study, we attempted to investigate the cortical representation of an L2 vocabulary acquired in different learning modes and in cross-modal transfer between learning and retrieval. Healthy participants learned new L2 words either by written translations (text-based learning) or in real-life situations (situation-based learning). Brain activity was then measured during subsequent retrieval of these words. The right supramarginal gyrus and left middle frontal gyrus were involved in situation-based learning and text-based learning, respectively, whereas the left inferior frontal gyrus was activated when learners used L2 knowledge in a mode different from the learning mode. Our findings indicate that the brain regions that mediate L2 memory differ according to how L2 words are learned and used. Copyright 2009 Elsevier Inc. All rights reserved.
Di Mitri, Daniele; Scheffel, Maren; Drachsler, Hendrik; Börner, Dirk; Ternier, Stefaan; Specht, Marcus
2017-01-01
The Learning Pulse study aims to explore whether physiological data such as heart rate and step count correlate with learning activity data and whether they are good predictors for learning success during self-regulated learning. To verify this hypothesis an experiment was set up involving eight
Use of blended learning in workplace learning
DEFF Research Database (Denmark)
Georgsen, Marianne; Løvstad, Charlotte Vange
2014-01-01
-based teaching materials. This paper presents the experiences of this particular project, and goes on to discuss the following points: • The blended learning design – use of IT for teaching, learning and communication • Digital learning materials – principals of design and use • Work place learning and learning......In 2014, a new system has been put in place for the inspection and approval of social welfare institutions in Denmark. In as little as 10 weeks, 330 new employees in five regional centres participated in an introductory course, designed as work place learning with extensive use of e-learning and IT...... from work – the interplay between experiences of the learner and the curriculum of the program •The approach taken to customising the e-learning design to the needs and demands of a particular case....
Directory of Open Access Journals (Sweden)
Asep Saefullah
2017-05-01
Full Text Available This study aimed to determine correlation between learning independence attitudes and student’s learning achievement. Type of this research is a correlation study to detect the connection of learning independence attitude’s variance in relation to learning achievement variance. This study used an attitude scale to measure the student’s learning independence attitude and objective multiple-choice questions to measure the student’s learning achievement. The results showed that there is a positive correlation (unidirectional and significant betweenthe learning independence attitude and learning achievement. This means that the better student’s learning independence attitude, it will be the better students learning achievement. The attitude of learning independence contributed to 40.96% of students learning achievement.
Learning Opportunities for Group Learning
Gil, Alfonso J.; Mataveli, Mara
2017-01-01
Purpose: This paper aims to analyse the impact of organizational learning culture and learning facilitators in group learning. Design/methodology/approach: This study was conducted using a survey method applied to a statistically representative sample of employees from Rioja wine companies in Spain. A model was tested using a structural equation…
Learning outcomes between Socioscientific Issues-Based Learning and Conventional Learning Activities
Piyaluk Wongsri; Prasart Nuangchalerm
2010-01-01
Problem statement: Socioscientific issues-based learning activity is essential for scientific reasoning skills and it could be used for analyzing problems be applied to each situation for more successful and suitable. The purposes of this research aimed to compare learning achievement, analytical thinking and moral reasoning of seventh grade students who were organized between socioscientific issues-based learning and conventional learning activities. Approach: The samples used in research we...
DEFF Research Database (Denmark)
Milligan, Sandra; Ringtved, Ulla Lunde
This paper outlines one way of understanding what it is about learning in MOOCs that is so distinctive, and explores the implications for the design of MOOCs. It draws on an ongoing research study into the nature of learning in MOOCs at the University of Melbourne.......This paper outlines one way of understanding what it is about learning in MOOCs that is so distinctive, and explores the implications for the design of MOOCs. It draws on an ongoing research study into the nature of learning in MOOCs at the University of Melbourne....
DEFF Research Database (Denmark)
Dau, Susanne
2016-01-01
Blended Learning has been implemented, evaluated and researched for the last decades within different educational areas and levels. Blended learning has been coupled with different epistemological understandings and learning theories, but the fundamental character and dimensions of learning...... in blended learning are still insufficient. Moreover, blended learning is a misleading concept described as learning, despite the fact that it fundamentally is an instructional and didactic approach (Oliver & Trigwell, 2005) addressing the learning environment (Inglis, Palipoana, Trenhom & Ward, 2011......) instead of the learning processes behind. Much of the existing research within the field seems to miss this perspective. The consequence is a lack of acknowledgement of the driven forces behind the context and the instructional design limiting the knowledge foundation of learning in blended learning. Thus...
Yamada, Masanori; Goda, Yoshiko; Matsuda, Takeshi; Kato, Hiroshi; Miyagawa, Hiroyuki
2015-01-01
This research aims to investigate the relationship among the awareness of self-regulated learning (SRL), procrastination, and learning behaviors in blended learning environment. One hundred seventy nine freshmen participated in this research, conducted in the blended learning style class using learning management system. Data collection was…
"Minesweeper" and spectrum of discrete Laplacians
German, Oleg; Lakshtanov, Evgeny
2008-01-01
The paper is devoted to a problem inspired by the "Minesweeper" computer game. It is shown that certain configurations of open cells guarantee the existence and the uniqueness of solution. Mathematically the problem is reduced to some spectral properties of discrete differential operators. It is shown how the uniqueness can be used to create a new game which preserves the spirit of "Minesweeper" but does not require a computer.
Learning Effectiveness of a Strategic Learning Course
Burchard, Melinda S.; Swerdzewski, Peter
2009-01-01
The effectiveness of a postsecondary strategic learning course for improving metacognitive awareness and regulation was evaluated through systematic program assessment. The course emphasized students' awareness of personal learning through the study of learning theory and through practical application of specific learning strategies. Students…
Learning to Learn Together with CSCL Tools
Schwarz, Baruch B.; de Groot, Reuma; Mavrikis, Manolis; Dragon, Toby
2015-01-01
In this paper, we identify "Learning to Learn Together" (L2L2) as a new and important educational goal. Our view of L2L2 is a substantial extension of "Learning to Learn" (L2L): L2L2 consists of learning to collaborate to successfully face L2L challenges. It is inseparable from L2L, as it emerges when individuals face problems…
Learning after acquired brain injury. Learning the hard way
Boosman, H.
2015-01-01
Background: When the brain has suffered damage, the learning process can be considerably disturbed. Brain damage can influence what is learned, but also how learning takes place. What patients can learn can be viewed in terms of ‘learning ability’ and how patients learn in terms of ‘learning style’.
International Nuclear Information System (INIS)
Sunaguchi, Naoki; Yuasa, Tetsuya; Gupta, Rajiv; Ando, Masami
2015-01-01
The main focus of this paper is reconstruction of tomographic phase-contrast image from a set of projections. We propose an efficient reconstruction algorithm for differential phase-contrast computed tomography that can considerably reduce the number of projections required for reconstruction. The key result underlying this research is a projection theorem that states that the second derivative of the projection set is linearly related to the Laplacian of the tomographic image. The proposed algorithm first reconstructs the Laplacian image of the phase-shift distribution from the second-derivative of the projections using total variation regularization. The second step is to obtain the phase-shift distribution by solving a Poisson equation whose source is the Laplacian image previously reconstructed under the Dirichlet condition. We demonstrate the efficacy of this algorithm using both synthetically generated simulation data and projection data acquired experimentally at a synchrotron. The experimental phase data were acquired from a human coronary artery specimen using dark-field-imaging optics pioneered by our group. Our results demonstrate that the proposed algorithm can reduce the number of projections to approximately 33% as compared with the conventional filtered backprojection method, without any detrimental effect on the image quality
Spectral methods for the detection of network community structure: a comparative analysis
International Nuclear Information System (INIS)
Shen, Hua-Wei; Cheng, Xue-Qi
2010-01-01
Spectral analysis has been successfully applied to the detection of community structure of networks, respectively being based on the adjacency matrix, the standard Laplacian matrix, the normalized Laplacian matrix, the modularity matrix, the correlation matrix and several other variants of these matrices. However, the comparison between these spectral methods is less reported. More importantly, it is still unclear which matrix is more appropriate for the detection of community structure. This paper answers the question by evaluating the effectiveness of these five matrices against benchmark networks with heterogeneous distributions of node degree and community size. Test results demonstrate that the normalized Laplacian matrix and the correlation matrix significantly outperform the other three matrices at identifying the community structure of networks. This indicates that it is crucial to take into account the heterogeneous distribution of node degree when using spectral analysis for the detection of community structure. In addition, to our surprise, the modularity matrix exhibits very similar performance to the adjacency matrix, which indicates that the modularity matrix does not gain benefits from using the configuration model as a reference network with the consideration of the node degree heterogeneity
Li, Wei
2017-05-01
This paper considers the designated convergence rate (DCR) (or the designated convergence margin) problems of consensus or flocking of coupled double-integrator agents. The DCR problems are more valuable for systems design than just convergence or stability conditions. The system setting in this paper is general, i.e., the velocity coupling and position coupling (VCPC) between agents, respectively, are set to be general and nonequal (up to rescaling), together with distinct damping and stiffness gains for the VCPC, respectively. This paper has two primary contributions on consensus: 1) further necessary and sufficient conditions are established to guarantee the DCR problems of the system, which have enriched the previous results and 2) the patterns of the convergence rate contours for the DCR are characterized, in terms of the damping and stiffness gains, which are closely related to the characteristics of the spectra of the two Laplacian matrices of the VCPC. Additionally, this paper has a contribution on matrix theory, i.e., the sufficient conditions for the simultaneous upper-triangularization of two independent Laplacian matrices, particularly from an easily verifiable topological perspective on the corresponding digraphs of these Laplacian matrices.
International Nuclear Information System (INIS)
Michel, Eric; Hernandez, Daniel; Cho, Min Hyoung; Lee, Soo Yeol
2014-01-01
Purpose: To validate the use of adaptive nonlinear filters in reconstructing conductivity and permittivity images from the noisy B 1 + maps in electrical properties tomography (EPT). Methods: In EPT, electrical property images are computed by taking Laplacian of the B 1 + maps. To mitigate the noise amplification in computing the Laplacian, the authors applied adaptive nonlinear denoising filters to the measured complex B 1 + maps. After the denoising process, they computed the Laplacian by central differences. They performed EPT experiments on phantoms and a human brain at 3 T along with corresponding EPT simulations on finite-difference time-domain models. They evaluated the EPT images comparing them with the ones obtained by previous EPT reconstruction methods. Results: In both the EPT simulations and experiments, the nonlinear filtering greatly improved the EPT image quality when evaluated in terms of the mean and standard deviation of the electrical property values at the regions of interest. The proposed method also improved the overall similarity between the reconstructed conductivity images and the true shapes of the conductivity distribution. Conclusions: The nonlinear denoising enabled us to obtain better-quality EPT images of the phantoms and the human brain at 3 T
Ma, Yuanyuan; Hu, Xiaohua; He, Tingting; Jiang, Xingpeng
2016-12-01
Nonnegative matrix factorization (NMF) has received considerable attention due to its interpretation of observed samples as combinations of different components, and has been successfully used as a clustering method. As an extension of NMF, Symmetric NMF (SNMF) inherits the advantages of NMF. Unlike NMF, however, SNMF takes a nonnegative similarity matrix as an input, and two lower rank nonnegative matrices (H, H T ) are computed as an output to approximate the original similarity matrix. Laplacian regularization has improved the clustering performance of NMF and SNMF. However, Laplacian regularization (LR), as a classic manifold regularization method, suffers some problems because of its weak extrapolating ability. In this paper, we propose a novel variant of SNMF, called Hessian regularization based symmetric nonnegative matrix factorization (HSNMF), for this purpose. In contrast to Laplacian regularization, Hessian regularization fits the data perfectly and extrapolates nicely to unseen data. We conduct extensive experiments on several datasets including text data, gene expression data and HMP (Human Microbiome Project) data. The results show that the proposed method outperforms other methods, which suggests the potential application of HSNMF in biological data clustering. Copyright Â© 2016. Published by Elsevier Inc.
Squires, David R.
2014-01-01
The aim of this paper is to examine the potential and effectiveness of m-learning in the field of Education and Learning domains. The purpose of this research is to illustrate how mobile technology can and is affecting novel change in instruction, from m-learning and the link to adaptive learning, to the uninitiated learner and capacities of…
When does social learning become cultural learning?
Heyes, Cecilia
2017-03-01
Developmental research on selective social learning, or 'social learning strategies', is currently a rich source of information about when children copy behaviour, and who they prefer to copy. It also has the potential to tell us when and how human social learning becomes cultural learning; i.e. mediated by psychological mechanisms that are specialized, genetically or culturally, to promote cultural inheritance. However, this review article argues that, to realize its potential, research on the development of selective social learning needs more clearly to distinguish functional from mechanistic explanation; to achieve integration with research on attention and learning in adult humans and 'dumb' animals; and to recognize that psychological mechanisms can be specialized, not only by genetic evolution, but also by associative learning and cultural evolution. © 2015 John Wiley & Sons Ltd.
Machine Learning for Neuroimaging with Scikit-Learn
Directory of Open Access Journals (Sweden)
Alexandre eAbraham
2014-02-01
Full Text Available Statistical machine learning methods are increasingly used for neuroimaging data analysis. Their main virtue is their ability to model high-dimensional datasets, e.g. multivariate analysis of activation images or resting-state time series. Supervised learning is typically used in decoding or encoding settings to relate brain images to behavioral or clinical observations, while unsupervised learning can uncover hidden structures in sets of images (e.g. resting state functional MRI or find sub-populations in large cohorts. By considering different functional neuroimaging applications, we illustrate how scikit-learn, a Python machine learning library, can be used to perform some key analysis steps. Scikit-learn contains a very large set of statistical learning algorithms, both supervised and unsupervised, and its application to neuroimaging data provides a versatile tool to study the brain.
Machine learning for neuroimaging with scikit-learn.
Abraham, Alexandre; Pedregosa, Fabian; Eickenberg, Michael; Gervais, Philippe; Mueller, Andreas; Kossaifi, Jean; Gramfort, Alexandre; Thirion, Bertrand; Varoquaux, Gaël
2014-01-01
Statistical machine learning methods are increasingly used for neuroimaging data analysis. Their main virtue is their ability to model high-dimensional datasets, e.g., multivariate analysis of activation images or resting-state time series. Supervised learning is typically used in decoding or encoding settings to relate brain images to behavioral or clinical observations, while unsupervised learning can uncover hidden structures in sets of images (e.g., resting state functional MRI) or find sub-populations in large cohorts. By considering different functional neuroimaging applications, we illustrate how scikit-learn, a Python machine learning library, can be used to perform some key analysis steps. Scikit-learn contains a very large set of statistical learning algorithms, both supervised and unsupervised, and its application to neuroimaging data provides a versatile tool to study the brain.
Inertial modes of rigidly rotating neutron stars in Cowling approximation
International Nuclear Information System (INIS)
Kastaun, Wolfgang
2008-01-01
In this article, we investigate inertial modes of rigidly rotating neutron stars, i.e. modes for which the Coriolis force is dominant. This is done using the assumption of a fixed spacetime (Cowling approximation). We present frequencies and eigenfunctions for a sequence of stars with a polytropic equation of state, covering a broad range of rotation rates. The modes were obtained with a nonlinear general relativistic hydrodynamic evolution code. We further show that the eigenequations for the oscillation modes can be written in a particularly simple form for the case of arbitrary fast but rigid rotation. Using these equations, we investigate some general characteristics of inertial modes, which are then compared to the numerically obtained eigenfunctions. In particular, we derive a rough analytical estimate for the frequency as a function of the number of nodes of the eigenfunction, and find that a similar empirical relation matches the numerical results with unexpected accuracy. We investigate the slow rotation limit of the eigenequations, obtaining two different sets of equations describing pressure and inertial modes. For the numerical computations we only considered axisymmetric modes, while the analytic part also covers nonaxisymmetric modes. The eigenfunctions suggest that the classification of inertial modes by the quantum numbers of the leading term of a spherical harmonic decomposition is artificial in the sense that the largest term is not strongly dominant, even in the slow rotation limit. The reason for the different structure of pressure and inertial modes is that the Coriolis force remains important in the slow rotation limit only for inertial modes. Accordingly, the scalar eigenequation we obtain in that limit is spherically symmetric for pressure modes, but not for inertial modes
Social software: E-learning beyond learning management systems
DEFF Research Database (Denmark)
Dalsgaard, Christian
2006-01-01
The article argues that it is necessary to move e-learning beyond learning management systems and engage students in an active use of the web as a resource for their self-governed, problem-based and collaborative activities. The purpose of the article is to discuss the potential of social software...... to move e-learning beyond learning management systems. An approach to use of social software in support of a social constructivist approach to e-learning is presented, and it is argued that learning management systems do not support a social constructivist approach which emphasizes self-governed learning...... activities of students. The article suggests a limitation of the use of learning management systems to cover only administrative issues. Further, it is argued that students' self-governed learning processes are supported by providing students with personal tools and engaging them in different kinds of social...
Hybrid e-learning tool TransLearning
Meij, van der Marjoleine G.; Kupper, Frank; Beers, P.J.; Broerse, Jacqueline E.W.
2016-01-01
E-learning and storytelling approaches can support informal vicarious learning within geographically widely distributed multi-stakeholder collaboration networks. This case study evaluates hybrid e-learning and video-storytelling approach ‘TransLearning’ by investigation into how its storytelling
Energy Technology Data Exchange (ETDEWEB)
Shin, Jae Goo; Park, Soo Jin [Daegu Health College, Daegu (Korea, Republic of); Kim, Yon Min [Dept. of Radiotechnology, Wonkwang Health Science University, Iksan (Korea, Republic of)
2016-12-15
The purpose of this was to study and analyze smart learning the self directed learning, self efficacy, learning satisfaction about department of radiology in a college. For this study total students 102 in 3 classes were surveyed at the end of semester. The research data was analyzed using SPSS also self directed learning ,self learning efficacy, learning satisfaction analyzed t-test, ANOVA and Pearson's correlation coefficient results were followings. First, Men is more higher than women in a self learning efficacy, self directed learning, learning satisfaction. Second, in a learning satisfaction smart learning ever heard in a first time group more satisfaction. Third, during the smart learning classes a students appeared a positive response. As a results, learning satisfaction will increase a learning when learners need a ability of self control planning and learning motivation by themselves in voluntarily and actively. Suggest to change a paradigm in a radiology classes so we have to improve a teaching skills this solution recommend is two way communication. In conclusion, smart learning applied for classes of college is meaningful as a new teaching, which can be change gradually learning satisfaction by teaching methods.
International Nuclear Information System (INIS)
Shin, Jae Goo; Park, Soo Jin; Kim, Yon Min
2016-01-01
The purpose of this was to study and analyze smart learning the self directed learning, self efficacy, learning satisfaction about department of radiology in a college. For this study total students 102 in 3 classes were surveyed at the end of semester. The research data was analyzed using SPSS also self directed learning ,self learning efficacy, learning satisfaction analyzed t-test, ANOVA and Pearson's correlation coefficient results were followings. First, Men is more higher than women in a self learning efficacy, self directed learning, learning satisfaction. Second, in a learning satisfaction smart learning ever heard in a first time group more satisfaction. Third, during the smart learning classes a students appeared a positive response. As a results, learning satisfaction will increase a learning when learners need a ability of self control planning and learning motivation by themselves in voluntarily and actively. Suggest to change a paradigm in a radiology classes so we have to improve a teaching skills this solution recommend is two way communication. In conclusion, smart learning applied for classes of college is meaningful as a new teaching, which can be change gradually learning satisfaction by teaching methods
Social Media and Seamless Learning: Lessons Learned
Panke, Stefanie; Kohls, Christian; Gaiser, Birgit
2017-01-01
The paper discusses best practice approaches and metrics for evaluation that support seamless learning with social media. We draw upon the theoretical frameworks of social learning theory, transfer learning (bricolage), and educational design patterns to elaborate upon different ideas for ways in which social media can support seamless learning.…
Mastering machine learning with scikit-learn
Hackeling, Gavin
2014-01-01
If you are a software developer who wants to learn how machine learning models work and how to apply them effectively, this book is for you. Familiarity with machine learning fundamentals and Python will be helpful, but is not essential.
A low dimensional dynamical system for the wall layer
Aubry, N.; Keefe, L. R.
1987-01-01
Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.
Chung, Moo K.; Kim, Seung-Goo; Schaefer, Stacey M.; van Reekum, Carien M.; Peschke-Schmitz, Lara; Sutterer, Matthew J.; Davidson, Richard J.
2014-03-01
The sparse regression framework has been widely used in medical image processing and analysis. However, it has been rarely used in anatomical studies. We present a sparse shape modeling framework using the Laplace- Beltrami (LB) eigenfunctions of the underlying shape and show its improvement of statistical power. Tradition- ally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes as a form of Fourier descriptors. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we present a LB-based method to filter out only the significant eigenfunctions by imposing a sparse penalty. For dense anatomical data such as deformation fields on a surface mesh, the sparse regression behaves like a smoothing process, which will reduce the error of incorrectly detecting false negatives. Hence the statistical power improves. The sparse shape model is then applied in investigating the influence of age on amygdala and hippocampus shapes in the normal population. The advantage of the LB sparse framework is demonstrated by showing the increased statistical power.
Mixed-mode loading of the structural elements with defect
Directory of Open Access Journals (Sweden)
Larisa V. Stepanova
2015-06-01
Full Text Available In the article the problem of determining the stress-strain state near the mixed-mode crack tip in a power-law material under plane stress conditions is considered. The eigenfunction method is used for the mixed-mode crack tip problem. It is shown that the eigenfunction expansion method results in the nonlinear eigenvalue problem. The numeric solution of the nonlinear eigenvalue problem formulated is obtained. The power of the distance from the crack tip is the eigenvalue of the nonlinear eigenvalue problem considered whereas the angular distributions of the stress components are the eigenfunctions. The new eigenvalues different from the eigenvalues of the Hutchinson–Rice–Rosengren are found. It is shown that the new asymptotic solution can be interpreted as the self-similar intermediate asymptotics of the stress field in the vicinity of the crack tip at distances which are very small compared to the crack length or the size of the specimen and at distances which are large compared to the length of the completely damaged zone. The developed method allows us to construct the geometry of the completely damaged zone in vicinity of the crack tip.
Expressive body movement responses to music are coherent, consistent, and low dimensional.
Amelynck, Denis; Maes, Pieter-Jan; Martens, Jean Pierre; Leman, Marc
2014-12-01
Embodied music cognition stresses the role of the human body as mediator for the encoding and decoding of musical expression. In this paper, we set up a low dimensional functional model that accounts for 70% of the variability in the expressive body movement responses to music. With the functional principal component analysis, we modeled individual body movements as a linear combination of a group average and a number of eigenfunctions. The group average and the eigenfunctions are common to all subjects and make up what we call the commonalities. An individual performance is then characterized by a set of scores (the individualities), one score per eigenfunction. The model is based on experimental data which finds high levels of coherence/consistency between participants when grouped according to musical education. This shows an ontogenetic effect. Participants without formal musical education focus on the torso for the expression of basic musical structure (tempo). Musically trained participants decode additional structural elements in the music and focus on body parts having more degrees of freedom (such as the hands). Our results confirm earlier studies that different body parts move differently along with the music.
Quantum mechanics on Laakso spaces
Kauffman, Christopher J.; Kesler, Robert M.; Parshall, Amanda G.; Stamey, Evelyn A.; Steinhurst, Benjamin A.
2012-04-01
We first review the spectrum of the Laplacian operator on a general Laakso space before considering modified Hamiltonians for the infinite square well, parabola, and Coulomb potentials. Additionally, we compute the spectrum for the Laplacian and its multiplicities when certain regions of a Laakso space are compressed or stretched and calculate the Casimir force experienced by two uncharged conducting plates by imposing physically relevant boundary conditions and then analytically regularizing the resulting zeta function. Lastly, we derive a general formula for the spectral zeta function and its derivative for Laakso spaces with strict self-similar structure before listing explicit spectral values for some special cases
Linking Action Learning and Inter-Organisational Learning: The Learning Journey Approach
Schumacher, Thomas
2015-01-01
The article presents and illustrates the learning journey (LJ)--a new management development approach to inter-organisational learning based on observation, reflection and problem-solving. The LJ involves managers from different organisations and applies key concepts of action learning and systemic organisational development. Made up of…
Learning Networks, Networked Learning
Sloep, Peter; Berlanga, Adriana
2010-01-01
Sloep, P. B., & Berlanga, A. J. (2011). Learning Networks, Networked Learning [Redes de Aprendizaje, Aprendizaje en Red]. Comunicar, XIX(37), 55-63. Retrieved from http://dx.doi.org/10.3916/C37-2011-02-05
Quantum nodal points as fingerprints of classical chaos
International Nuclear Information System (INIS)
Leboeuf, P.; Voros, A.
1992-08-01
Semiclassical analysis of the individual eigenfunctions in a quantum system is presented, especially when the classical dynamics is chaotic and the quantum bound states are considered. Quantum maps have emerged as ideal dynamical models for basic studies, with their ability to exhibit classical chaos within a single degree of freedom. On the other hand, phase space techniques have become recognized as extremely powerful for describing quantum states. It is argued that representations of eigenfunctions are essential for semiclassical analysis. An explicit realization of that program in one degree is overviewed, in which the crucial ingredient is a phase-space parametrization of 1-d wave-functions. (K.A.) 44 refs.; 6 figs
International Nuclear Information System (INIS)
Shuen Wei Li.
1991-08-01
The crystal-field and spin-orbit matrix for d 1 or d 9 configuration with D 2 symmetry has been derived. By diagonalizing the matrix, the energy level of C 2+ u in Cs 2 CuCl 4 and its eigenfunctions have been obtained with the aid of the approximate SCF d-orbit. Furthermore, by suing the eigenfunctions, the EPR g-factors and the magnetic susceptibilities at different temperatures have been calculated. The calculated results are in good agreement with the experimental findings. The calculation only needs two adjustable parameters and can give more theoretical results than those of previous work which introduced 11 adjustable parameters. (author). 16 refs, 3 tabs
Semi-analytic modeling of tokamak particle transport
International Nuclear Information System (INIS)
Shi Bingren; Long Yongxing; Li Jiquan
2000-01-01
The linear particle transport equation of tokamak plasma is analyzed. Particle flow consists of an outward diffusion and an inward convection. General solution is expressed in terms of a Green function constituted by eigen-functions of corresponding Sturm-Liouville problem. For a particle source near the plasma edge (shadow fueling), a well-behaved solution in terms of Fourier series can be constituted by using the complementarity relation. It can be seen from the lowest eigen-function that the particle density becomes peaked when the wall recycling reduced. For a transient point source in the inner region, a well-behaved solution can be obtained by the complementarity as well
Generalized perturbation theory using two-dimensional, discrete ordinates transport theory
International Nuclear Information System (INIS)
Childs, R.L.
1979-01-01
Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using two-dimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions Λ and Λ*. Demonstration calculations were performed for changes in a reaction-rate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions
Interbasis expansions for isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Dong, Shi-Hai, E-mail: dongsh2@yahoo.com [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, Mexico D.F. 07738 (Mexico)
2012-03-12
The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n. -- Highlights: ► Exact solutions of harmonic oscillator are reviewed in three coordinates. ► Interbasis expansions of the eigenfunctions is solved completely. ► This is occurred only for those degenerated states for given quantum number n.
Fluctuations of wavefunctions about their classical average
International Nuclear Information System (INIS)
Benet, L; Flores, J; Hernandez-Saldana, H; Izrailev, F M; Leyvraz, F; Seligman, T H
2003-01-01
Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations of the quantum wavefunctions around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes whose width is determined by the classical shape of the eigenfunction. To compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators, we develop a rescaling method for the components. The expectations are broadly confirmed, but deviations due to scars are observed. This effect is much reduced when both Hamiltonians have chaotic dynamics
Closure of the squared Zakharov--Shabat eigenstates
International Nuclear Information System (INIS)
Kaup, D.J.
1976-01-01
By solution of the inverse scattering problem for a third-order (degenerate) eigenvalue problem, the closure of the squared eigenfunctions of the Zakharov--Shabat equations is found. The question of the completeness of squared eigenstates occurs in many aspects of ''inverse scattering transforms'' (solving nonlinear evolution equations exactly by inverse scattering techniques), as well as in various aspects of the inverse scattering problem. The method used here is quite suggestive as to how one might find the closure of the squared eigenfunctions of other eigenvalue equations, and the strong analogy between these results and the problem of finding the closure of the eigenvectors of a nonself-adjoint matrix is pointed out
Cseh, Maria; Manikoth, Nisha N.
2011-01-01
As the authors of the preceding article (Choi and Jacobs, 2011) have noted, the workplace learning literature shows evidence of the complementary and integrated nature of formal and informal learning in the development of employee competencies. The importance of supportive learning environments in the workplace and of employees' personal learning…
Missouri Univ., Columbia. Coll. of Education.
Information is provided regarding major learning styles and other factors important to student learning. Several typically asked questions are presented regarding different learning styles (visual, auditory, tactile and kinesthetic, and multisensory learning), associated considerations, determining individuals' learning styles, and appropriate…
Adventure Learning: Theory and Implementation of Hybrid Learning
Doering, A.
2008-12-01
Adventure Learning (AL), a hybrid distance education approach, provides students and teachers with the opportunity to learn about authentic curricular content areas while interacting with adventurers, students, and content experts at various locations throughout the world within an online learning environment (Doering, 2006). An AL curriculum and online environment provides collaborative community spaces where traditional hierarchical classroom roles are blurred and learning is transformed. AL has most recently become popular in K-12 classrooms nationally and internationally with millions of students participating online. However, in the literature, the term "adventure learning" many times gets confused with phrases such as "virtual fieldtrip" and activities where someone "exploring" is posting photos and text. This type of "adventure learning" is not "Adventure Learning" (AL), but merely a slideshow of their activities. The learning environment may not have any curricular and/or social goals, and if it does, the environment design many times does not support these objectives. AL, on the other hand, is designed so that both teachers and students understand that their online and curriculum activities are in synch and supportive of the curricular goals. In AL environments, there are no disparate activities as the design considers the educational, social, and technological affordances (Kirschner, Strijbos, Kreijns, & Beers, 2004); in other words, the artifacts of the learning environment encourage and support the instructional goals, social interactions, collaborative efforts, and ultimately learning. AL is grounded in two major theoretical approaches to learning - experiential and inquiry-based learning. As Kolb (1984) noted, in experiential learning, a learner creates meaning from direct experiences and reflections. Such is the goal of AL within the classroom. Additionally, AL affords learners a real-time authentic online learning experience concurrently as they
Emergent Learning and Learning Ecologies in Web 2.0
Directory of Open Access Journals (Sweden)
Roy Williams
2011-03-01
Full Text Available This paper describes emergent learning and situates it within learning networks and systems and the broader learning ecology of Web 2.0. It describes the nature of emergence and emergent learning and the conditions that enable emergent, self-organised learning to occur and to flourish. Specifically, it explores whether emergent learning can be validated and self-correcting and whether it is possible to link or integrate emergent and prescribed learning. It draws on complexity theory, communities of practice, and the notion of connectivism to develop some of the foundations for an analytic framework, for enabling and managing emergent learning and networks in which agents and systems co-evolve. It then examines specific cases of learning to test and further develop the analytic framework.The paper argues that although social networking media increase the potential range and scope for emergent learning exponentially, considerable effort is required to ensure an effective balance between openness and constraint. It is possible to manage the relationship between prescriptive and emergent learning, both of which need to be part of an integrated learning ecology.
Semantic modelling for learning styles and learning material in an e-learning environment
Alhasan, K.; Chen, Liming; Chen, Feng
2017-01-01
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the URI link. Various learners with various requirements have led to the raise of a crucial concern in the area of e-learning. A new technology for propagating learning to learners worldwide, has led to an evolution in the e-learning industry that takes into account all the requirements of the learning process. In spite of the wide growing, the e-learning te...
Directory of Open Access Journals (Sweden)
Muhammad RUSLI
2017-10-01
Full Text Available The effectiveness of a learning depends on four main elements, they are content, desired learning outcome, instructional method and the delivery media. The integration of those four elements can be manifested into a learning modul which is called multimedia learning or learning by using multimedia. In learning context by using computer-based multimedia, there are two main things that need to be noticed so that the learning process can run effectively: how the content is presented, and what the learner’s chosen way in accepting and processing the information into a meaningful knowledge. First it is related with the way to visualize the content and how people learn. The second one is related with the learning style of the learner. This research aims to investigate the effect of the type of visualization—static vs animated—on a multimedia computer-based learning, and learning styles—visual vs verbal, towards the students’ capability in applying the concepts, procedures, principles of Java programming. Visualization type act as independent variables, and learning styles of the students act as a moderator variable. Moreover, the instructional strategies followed the Component Display Theory of Merril, and the format of presentation of multimedia followed the Seven Principles of Multimedia Learning of Mayer and Moreno. Learning with the multimedia computer-based learning has been done in the classroom. The subject of this research was the student of STMIK-STIKOM Bali in odd semester 2016-2017 which followed the course of Java programming. The Design experiments used multivariate analysis of variance, MANOVA 2 x 2, with a large sample of 138 students in 4 classes. Based on the results of the analysis, it can be concluded that the animation in multimedia interactive learning gave a positive effect in improving students’ learning outcomes, particularly in the applying the concepts, procedures, and principles of Java programming. The
Learning Analytics for Networked Learning Models
Joksimovic, Srecko; Hatala, Marek; Gaševic, Dragan
2014-01-01
Teaching and learning in networked settings has attracted significant attention recently. The central topic of networked learning research is human-human and human-information interactions occurring within a networked learning environment. The nature of these interactions is highly complex and usually requires a multi-dimensional approach to…
Semantic Modelling for Learning Styles and Learning Material in an E-Learning Environment
Alhasan, Khawla; Chen, Liming; Chen, Feng
2017-01-01
Various learners with various requirements have led to the raise of a crucial concern in the area of e-learning. A new technology for propagating learning to learners worldwide, has led to an evolution in the e-learning industry that takes into account all the requirements of the learning process. In spite of the wide growing, the e-learning…
J.G. Bagi; N.K. Hashilkar
2014-01-01
Background: Blended learning includes an integration of face to face classroom learning with technology enhanced online material. It provides the convenience, speed and cost effectiveness of e-learning with the personal touch of traditional learning. Objective: The objective of the present study was to assess the effectiveness of a combination of e-learning module and traditional teaching (Blended learning) as compared to traditional teaching alone to teach acid base homeostasis to Phase I MB...
Poell, R.F.; Moorsel, M.A.A.H. van
1996-01-01
This paper discusses the relevance of Van der Krogt's learning network theory (1995) for our understanding of the concepts of work-related learning projects and learning climate in organisations. The main assumptions of the learning network theory are presented and transferred to the level of learning groups in organisations. Four theoretical types of learning projects are distinguished. Four different approaches to the learning climate of work groups are compared to the approach offered by t...
Learning about Learning: A Conundrum and a Possible Resolution
Barnett, Ronald
2011-01-01
What is it to learn in the modern world? We can identify four "learning epochs" through which our understanding of learning has passed: a metaphysical view; an empirical view; an experiential view; and, currently, a "learning-amid-contestation" view. In this last and current view, learning has its place in a world in which, the more one learns,…
Emergent learning and learning ecologies in Web 2.0
Williams, Roy; Karousou, Regina; Mackness, J.
2011-01-01
This paper describes emergent learning and situates it within learning networks and systems and the broader learning ecology of Web 2.0. It describes the nature of emergence and emergent learning and the conditions that enable emergent, self-organised learning to occur and to flourish. Specifically, it explores whether emergent learning can be validated and self-correcting and whether it is possible to link or integrate emergent and prescribed learning. It draws on complexity theory, commu...
Directory of Open Access Journals (Sweden)
Sabina Jelenc Krašovec
2000-12-01
Full Text Available A vast array of economical, social, political, cultural and other factors influences the transformed role of learning and education in the society, as well as the functioning of local community and its social and communication patterns. The influences which are manifested as global problems can only be successfully solved on the level of local community. Analogously with the society in general, there is a great need of transforming a local community into a learning, flexible and interconnected environment which takes into account different interests, wishes and needs regarding learning and being active. The fundamental answer to changes is the strategy of lifelong learning and education which requires reorganisation of all walks of life (work, free time, family, mass media, culture, sport, education and transforming of organisations into learning organisations. With learning society based on networks of knowledge individuals are turning into learning individuals, and organisations into learning organisations; people who learn take the responsibility of their progress, learning denotes partnership among learning people, teachers, parents, employers and local community, so that they work together to achieve better results.
New designing of E-Learning systems with using network learning
Malayeri, Amin Daneshmand; Abdollahi, Jalal
2010-01-01
One of the most applied learning in virtual spaces is using E-Learning systems. Some E-Learning methodologies has been introduced, but the main subject is the most positive feedback from E-Learning systems. In this paper, we introduce a new methodology of E-Learning systems entitle "Network Learning" with review of another aspects of E-Learning systems. Also, we present benefits and advantages of using these systems in educating and fast learning programs. Network Learning can be programmable...
[Learning how to learn for specialist further education].
Breuer, G; Lütcke, B; St Pierre, M; Hüttl, S
2017-02-01
The world of medicine is becoming from year to year more complex. This necessitates efficient learning processes, which incorporate the principles of adult education but with unchanged periods of further education. The subject matter must be processed, organized, visualized, networked and comprehended. The learning process should be voluntary and self-driven with the aim of learning the profession and becoming an expert in a specialist field. Learning is an individual process. Despite this, the constantly cited learning styles are nowadays more controversial. An important factor is a healthy mixture of blended learning methods, which also use new technical possibilities. These include a multitude of e‑learning options and simulations, which partly enable situative learning in a "shielded" environment. An exemplary role model of the teacher and feedback for the person in training also remain core and sustainable aspects in medical further education.
Using Learning Games to Meet Learning Objectives
DEFF Research Database (Denmark)
Henriksen, Thomas Duus
2013-01-01
This paper addresses the question on how learning games can be used to meet with the different levels in Bloom’s and the SOLO taxonomy, which are commonly used for evaluating the learning outcome of educational activities. The paper discusses the quality of game-based learning outcomes based on a...... on a case study of the learning game 6Styles....
Siegler, Robert S.
2004-01-01
The field of children's learning was thriving when the Merrill-Palmer Quarterly was launched; the field later went into eclipse and now is in the midst of a resurgence. This commentary examines reasons for these trends, and describes the emerging field of children's learning. In particular, the new field is seen as differing from the old in its…
Skill learning and the evolution of social learning mechanisms.
van der Post, Daniel J; Franz, Mathias; Laland, Kevin N
2016-08-24
Social learning is potentially advantageous, but evolutionary theory predicts that (i) its benefits may be self-limiting because social learning can lead to information parasitism, and (ii) these limitations can be mitigated via forms of selective copying. However, these findings arise from a functional approach in which learning mechanisms are not specified, and which assumes that social learning avoids the costs of asocial learning but does not produce information about the environment. Whether these findings generalize to all kinds of social learning remains to be established. Using a detailed multi-scale evolutionary model, we investigate the payoffs and information production processes of specific social learning mechanisms (including local enhancement, stimulus enhancement and observational learning) and their evolutionary consequences in the context of skill learning in foraging groups. We find that local enhancement does not benefit foraging success, but could evolve as a side-effect of grouping. In contrast, stimulus enhancement and observational learning can be beneficial across a wide range of environmental conditions because they generate opportunities for new learning outcomes. In contrast to much existing theory, we find that the functional outcomes of social learning are mechanism specific. Social learning nearly always produces information about the environment, and does not always avoid the costs of asocial learning or support information parasitism. Our study supports work emphasizing the value of incorporating mechanistic detail in functional analyses.
Can Social Learning Increase Learning Speed, Performance or Both?
Heinerman, J.V.; Stork, J.; Rebolledo Coy, M.A.; Hubert, J.G.; Eiben, A.E.; Bartz-Beielstein, Thomas; Haasdijk, Evert
2017-01-01
Social learning enables multiple robots to share learned experiences while completing a task. The literature offers contradicting examples of its benefits; robots trained with social learning reach a higher performance, an increased learning speed, or both, compared to their individual learning
A Flow of Entrepreneurial Learning Elements in Experiential Learning Settings
DEFF Research Database (Denmark)
Ramsgaard, Michael Breum; Christensen, Marie Ernst
This paper explored the concept of learning in an experiential learning setting and whether the learning process can be understood as a flow of learning factors influencing the outcome. If many constituting factors lead to the development of learning outcomes, there might need to be developed...... that are a part of experiential learning settings and curriculum development....... a differentiated approach to facilitate experiential learning. Subsequently the paper investigated how facilitators of learning processes can design a learning space where the boundary of what is expected from the learner is challenged. In other words the aim was to explore the transformative learning processes...
DEFF Research Database (Denmark)
Illeris, Knud
How We Learn, deals with the fundamental issues of the processes of learning, critically assessing different types of learning and obstacles to learning. It also considers a broad range of other important questions in relation to learning such as: modern research into learning and brain functions......, self-perception, motivation and competence development, teaching, intelligence and learning style, learning in relation to gender and life age. The book provides a comprehensive introduction to both traditional learning theory and the newest international research into learning processes, while...... at the same time being an innovative contribution to a new and more holistic understanding of learning including discussion on school-based learning, net-based learning, workplace learning and educational politics. How We Learn examines all the key factors that help to create a holistic understanding of what...
From Self-Regulation to Learning to Learn: Observations on the Construction of Self and Learning
Thoutenhoofd, Ernst D.; Pirrie, Anne
2015-01-01
The purpose of this article is to clarify the epistemological basis of self-regulated learning. The authors note that learning to learn, a term that has pervaded education policy at EU and national levels in recent years is often conflated with self-regulated learning. As a result, there has been insufficient attention paid to learning as social…
DEFF Research Database (Denmark)
Hasse, Cathrine
This book shall explore the concept of learning from the new perspective of the posthuman. The vast majority of cognitive, behavioral and part of the constructionist learning theories operate with an autonomous individual who learn in a world of separate objects. Technology is (if mentioned at all......) understood as separate from the individual learner and perceived as tools. Learning theory has in general not been acknowledging materiality in their theorizing about what learning is. A new posthuman learning theory is needed to keep up with the transformations of human learning resulting from new...... technological experiences. One definition of learning is that it is a relatively permanent change in behavior as the result of experience. During the first half of the twentieth century, two theoretical approaches dominated the domain of learning theory: the schools of thought commonly known as behaviorism...
An introduction to machine learning with Scikit-Learn
CERN. Geneva
2015-01-01
This tutorial gives an introduction to the scientific ecosystem for data analysis and machine learning in Python. After a short introduction of machine learning concepts, we will demonstrate on High Energy Physics data how a basic supervised learning analysis can be carried out using the Scikit-Learn library. Topics covered include data loading facilities and data representation, supervised learning algorithms, pipelines, model selection and evaluation, and model introspection.
Students’ Motivation for Learning in Virtual Learning Environments
Beluce, Andrea Carvalho; Oliveira, Katya Luciane de
2015-01-01
The specific characteristics of online education require of the student engagement and autonomy, factors which are related to motivation for learning. This study investigated students’ motivation in virtual learning environments (VLEs). For this, it used the Teaching and Learning Strategy and Motivation to Learn Scale in Virtual Learning Environments (TLSM-VLE). The scale presented 32 items and six dimensions, three of which aimed to measure the variables of autonomous motivation, controlled ...
Yurdugül, Halil; Menzi Çetin, Nihal
2015-01-01
Problem Statement: Learners can access and participate in online learning environments regardless of time and geographical barriers. This brings up the umbrella concept of learner autonomy that contains self-directed learning, self-regulated learning and the studying process. Motivation and learning strategies are also part of this umbrella…
Mapping Students’ Informal Learning Using Personal Learning Environment
Directory of Open Access Journals (Sweden)
Jelena Anđelković Labrović
2014-07-01
Full Text Available Personal learning environments are a widely spared ways of learning, especially for the informal learning process. The aim of this research is to identify the elements of studens’ personal learning environment and to identify the extent to which students use modern technology for learning as part of their non-formal learning. A mapping system was used for gathering data and an analysis of percentages and frequency counts was used for data analysis in the SPSS. The results show that students’ personal learning environment includes the following elements: Wikipedia, Google, YouTube and Facebook in 75% of all cases, and an interesting fact is that all of them belong to a group of Web 2.0 tools and applications.
A Web-Based Learning Support System for Inquiry-Based Learning
Kim, Dong Won; Yao, Jingtao
The emergence of the Internet and Web technology makes it possible to implement the ideals of inquiry-based learning, in which students seek truth, information, or knowledge by questioning. Web-based learning support systems can provide a good framework for inquiry-based learning. This article presents a study on a Web-based learning support system called Online Treasure Hunt. The Web-based learning support system mainly consists of a teaching support subsystem, a learning support subsystem, and a treasure hunt game. The teaching support subsystem allows instructors to design their own inquiry-based learning environments. The learning support subsystem supports students' inquiry activities. The treasure hunt game enables students to investigate new knowledge, develop ideas, and review their findings. Online Treasure Hunt complies with a treasure hunt model. The treasure hunt model formalizes a general treasure hunt game to contain the learning strategies of inquiry-based learning. This Web-based learning support system empowered with the online-learning game and founded on the sound learning strategies furnishes students with the interactive and collaborative student-centered learning environment.
Designing Learning Resources in Synchronous Learning Environments
DEFF Research Database (Denmark)
Christiansen, Rene B
2015-01-01
Computer-mediated Communication (CMC) and synchronous learning environments offer new solutions for teachers and students that transcend the singular one-way transmission of content knowledge from teacher to student. CMC makes it possible not only to teach computer mediated but also to design...... and create new learning resources targeted to a specific group of learners. This paper addresses the possibilities of designing learning resources within synchronous learning environments. The empirical basis is a cross-country study involving students and teachers in primary schools in three Nordic...... Countries (Denmark, Sweden and Norway). On the basis of these empirical studies a set of design examples is drawn with the purpose of showing how the design fulfills the dual purpose of functioning as a remote, synchronous learning environment and - using the learning materials used and recordings...
Learning paradigms in workplace e-learning research
Directory of Open Access Journals (Sweden)
Isabella Norén Creutz
2014-09-01
Full Text Available The objective of this paper is to explore the discourses of learning that are actualized in workplace e-learning. It aims to understand how learning is defined in research within this field. The empirical material consists of academic research articles on e-learning in the workplace, published from 2000 to 2013. The findings are presented as four metaphors highlighting four overlapping time periods with different truth regimes: Celebration, Questioning, Reflection and Dissolution. It is found that learning as a phenomenon tends to be marginalized in relation to the digital technology used. Based on this, we discuss a proposal for a more critical and problematized approach to e-learning, and a deeper understanding of the challenges and opportunities for employees and organizations to acquire knowledge in the digital age.
Workplace Learning by Action Learning: A Practical Example.
Miller, Peter
2003-01-01
An action learning approach to help managers enhance learning capacity involved a performance management seminar, work by action learning sets, implementation of a new performance management instrument with mentoring by action learning facilitators, and evaluation. Survey responses from 392 participants revealed satisfaction with managerial…
Working memory supports inference learning just like classification learning.
Craig, Stewart; Lewandowsky, Stephan
2013-08-01
Recent research has found a positive relationship between people's working memory capacity (WMC) and their speed of category learning. To date, only classification-learning tasks have been considered, in which people learn to assign category labels to objects. It is unknown whether learning to make inferences about category features might also be related to WMC. We report data from a study in which 119 participants undertook classification learning and inference learning, and completed a series of WMC tasks. Working memory capacity was positively related to people's classification and inference learning performance.
Seamless Language Learning: Second Language Learning with Social Media
Wong, Lung-Hsiang; Chai, Ching Sing; Aw, Guat Poh
2017-01-01
This conceptual paper describes a language learning model that applies social media to foster contextualized and connected language learning in communities. The model emphasizes weaving together different forms of language learning activities that take place in different learning contexts to achieve seamless language learning. it promotes social…
Virtual Learning Environments and Learning Forms -experiments in ICT-based learning
DEFF Research Database (Denmark)
Helbo, Jan; Knudsen, Morten
2004-01-01
This paper report the main results of a three year experiment in ICT-based distance learning. The results are based on a full scale experiment in the education, Master of Industrial Information Technology (MII) and is one of many projects deeply rooted in the project Virtual Learning Environments...... and Learning forms (ViLL). The experiment was to transfer a well functioning on-campus engineering program based on project organized collaborative learning to a technology supported distance education program. After three years the experiments indicate that adjustments are required in this transformation....... The main problem is that we do not find the same self regulatoring learning effect in the group work among the off-campus students as is the case for on-campus students. Based on feedback from evaluation questionnaires and discussions with the students didactic adjustments have been made. The revised...
Effective Learning Environments in Relation to Different Learning Theories
Guney, Ali; Al, Selda
2012-01-01
There are diverse learning theories which explain learning processes which are discussed within this paper, through cognitive structure of learning process. Learning environments are usually described in terms of pedagogical philosophy, curriculum design and social climate. There have been only just a few studies about how physical environment is related to learning process. Many researchers generally consider teaching and learning issues as if independent from physical environment, whereas p...
Interorganizational learning systems
DEFF Research Database (Denmark)
Hjalager, Anne-Mette
1999-01-01
The occurrence of organizational and interorganizational learning processes is not only the result of management endeavors. Industry structures and market related issues have substantial spill-over effects. The article reviews literature, and it establishes a learning model in which elements from...... organizational environments are included into a systematic conceptual framework. The model allows four types of learning to be identified: P-learning (professional/craft systems learning), T-learning (technology embedded learning), D-learning (dualistic learning systems, where part of the labor force is exclude...... from learning), and S-learning (learning in social networks or clans). The situation related to service industries illustrates the typology....
When Learning Analytics Meets E-Learning
Czerkawski, Betul C.
2015-01-01
While student data systems are nothing new and most educators have been dealing with student data for many years, learning analytics has emerged as a new concept to capture educational big data. Learning analytics is about better understanding of the learning and teaching process and interpreting student data to improve their success and learning…
Facilitating Learning Organizations. Making Learning Count.
Marsick, Victoria J.; Watkins, Karen E.
This book offers advice to facilitators and change agents who wish to build systems-level learning to create knowledge that can be used to gain a competitive advantage. Chapter 1 describes forces driving companies to build, sustain, and effectively use systems-level learning and presents and links a working definition of the learning organization…
Learning Progressions as Tools for Assessment and Learning
Shepard, Lorrie A.
2018-01-01
This article addresses the teaching and learning side of the learning progressions literature, calling out for measurement specialists the knowledge most needed when collaborating with subject-matter experts in the development of learning progressions. Learning progressions are one of the strongest instantiations of principles from "Knowing…
Enhancing Community Service Learning Via Practical Learning Communities
Directory of Open Access Journals (Sweden)
Ilana Ronen
2015-02-01
Full Text Available The advantages of learning communities focused on analyzing social issues and educational repercussions in the field are presented in this study. The research examines the contribution of a learning community to enhancing student teachers' responsibility and their social involvement. The assumption was that participating in learning community would further implement student teachers' community social involvement while enhancing responsibility in their field of action. A questionnaire aimed to present the student teachers' attitudes involving all aspects of studying in the learning community and their social activity in the community was conducted. The findings pinpointed that there were positive contributions of the learning communities from a personal aspect such as developing self-learning, and learning about “me”, as well as broaden their teaching skills, through methodology for teacher training, and developing reflective thought. These insights can also be implemented in various educational frameworks and during service learning as part of teacher training.
Implicit visual learning and the expression of learning.
Haider, Hilde; Eberhardt, Katharina; Kunde, Alexander; Rose, Michael
2013-03-01
Although the existence of implicit motor learning is now widely accepted, the findings concerning perceptual implicit learning are ambiguous. Some researchers have observed perceptual learning whereas other authors have not. The review of the literature provides different reasons to explain this ambiguous picture, such as differences in the underlying learning processes, selective attention, or differences in the difficulty to express this knowledge. In three experiments, we investigated implicit visual learning within the original serial reaction time task. We used different response devices (keyboard vs. mouse) in order to manipulate selective attention towards response dimensions. Results showed that visual and motor sequence learning differed in terms of RT-benefits, but not in terms of the amount of knowledge assessed after training. Furthermore, visual sequence learning was modulated by selective attention. However, the findings of all three experiments suggest that selective attention did not alter implicit but rather explicit learning processes. Copyright © 2012 Elsevier Inc. All rights reserved.
Collaborative distance learning: Developing an online learning community
Stoytcheva, Maria
2017-12-01
The method of collaborative distance learning has been applied for years in a number of distance learning courses, but they are relatively few in foreign language learning. The context of this research is a hybrid distance learning of French for specific purposes, delivered through the platform UNIV-RcT (Strasbourg University), which combines collaborative activities for the realization of a common problem-solving task online. The study focuses on a couple of aspects: on-line interactions carried out in small, tutored groups and the process of community building online. By analyzing the learner's perceptions of community and collaborative learning, we have tried to understand the process of building and maintenance of online learning community and to see to what extent the collaborative distance learning contribute to the development of the competence expectations at the end of the course. The analysis of the results allows us to distinguish the advantages and limitations of this type of e-learning and thus evaluate their pertinence.
Callanan, Maureen; Cervantes, Christi; Loomis, Molly
2011-11-01
We consider research and theory relevant to the notion of informal learning. Beginning with historical and definitional issues, we argue that learning happens not just in schools or in school-aged children. Many theorists have contrasted informal learning with formal learning. Moving beyond this dichotomy, and away from a focus on where learning occurs, we discuss five dimensions of informal learning that are drawn from the literature: (1) non-didactive, (2) highly socially collaborative, (3) embedded in meaningful activity, (4) initiated by learner's interest or choice, and (5) removed from external assessment. We consider these dimensions in the context of four sample domains: learning a first language, learning about the mind and emotions within families and communities, learning about science in family conversations and museum settings, and workplace learning. Finally, we conclude by considering convergences and divergences across the different literatures and suggesting areas for future research. WIREs Cogni Sci 2011 2 646-655 DOI: 10.1002/wcs.143 For further resources related to this article, please visit the WIREs website. Copyright © 2011 John Wiley & Sons, Ltd.
LEARNING ABOUT LEARNING, A CONFERENCE REPORT.
BRUNER, JEROME
TO EXPLORE THE NATURE OF THE LEARNING PROCESS, THREE IMPORTANT PROBLEM AREAS WERE STUDIED. STUDIES IN THE FIRST AREA, ATTITUDINAL AND AFFECTIVE SKILLS, ARE CONCERNED WITH INDUCING A CHILD TO LEARN AND SUSTAINING HIS ATTENTION. STUDIES IN THE SECOND AREA, COGNITIVE SKILLS, SOUGHT TO DISCOVER WHETHER GENERAL IDEAS AND SKILLS CAN BE LEARNED IN SUCH A…
New learning : three ways to learn in a new balance
Simons, P.R.J.
2000-01-01
Because people are learning all the time, we need criteria that can help us distinguish between better and worse kinds of learning. Organizations and societies as well as the psychology of learning ask for new learning outcomes, new learning processes and new forms of instruction. New learning
DEFF Research Database (Denmark)
Thorhauge, Sally
2014-01-01
"Interface learning - New goals for museum and upper secondary school collaboration" investigates and analyzes the learning that takes place when museums and upper secondary schools in Denmark work together in local partnerships to develop and carry out school-related, museum-based coursework...... for students. The research focuses on the learning that the students experience in the interface of the two learning environments: The formal learning environment of the upper secondary school and the informal learning environment of the museum. Focus is also on the learning that the teachers and museum...... professionals experience as a result of their collaboration. The dissertation demonstrates how a given partnership’s collaboration affects the students’ learning experiences when they are doing the coursework. The dissertation presents findings that museum-school partnerships can use in order to develop...
Online transfer learning with extreme learning machine
Yin, Haibo; Yang, Yun-an
2017-05-01
In this paper, we propose a new transfer learning algorithm for online training. The proposed algorithm, which is called Online Transfer Extreme Learning Machine (OTELM), is based on Online Sequential Extreme Learning Machine (OSELM) while it introduces Semi-Supervised Extreme Learning Machine (SSELM) to transfer knowledge from the source to the target domain. With the manifold regularization, SSELM picks out instances from the source domain that are less relevant to those in the target domain to initialize the online training, so as to improve the classification performance. Experimental results demonstrate that the proposed OTELM can effectively use instances in the source domain to enhance the learning performance.
Zero Learning: Case explorations of barriers to organizational learning
DEFF Research Database (Denmark)
Jørgensen, Frances; S., Jacob
2003-01-01
that the existence of learning barriers may not only inhibit on-going learning process, but also lead to a negative cycle of non-learning in the organization. The implications of a "zero learning" cycle caused by learning barriers are discussed and insights are provided as to how barriers may be resolved so...
M-Learning: The New Horizon of Learning at SQU
Directory of Open Access Journals (Sweden)
Z. Al-Khanjari
2014-12-01
Full Text Available M-learning extends the theory and practice of learning and mobility in converging technological environments. Developing a smart course in order to improve the standard of education at Sultan Qaboos University (SQU is one of the main aims of the current authors. This proposal requires developing innovative applications for ubiquitous, mobile technologies for learning. This kind of development covers new educational and technological methods and concepts for supporting formal and informal learning. SQU is currently using Moodle as the open source e-learning management system to support and enhance traditional learning. Although elearning in SQU has proven its importance in enhancing traditional learning, it is limited to areas and locations where a personal computer exists. This constraint is a burden to many e-learning users who are staff or students, especially if they live in rural areas of Oman. To overcome this drawback, an investigative survey of the importance of m-learning was designed and distributed to SQU students. The results showed that almost all students favored and supported the idea and requested the implementation of a m-learning application. As a step forward, this paper proposes an extension for e-learning—a new m-learning tool to support learners who use mobile device technologies. Our goal in introducing m-learning at SQU is not to replace e-learning but to complement and improve it so both modalities are available, since each grants certain advantages to users.
Contextual Approach with Guided Discovery Learning and Brain Based Learning in Geometry Learning
Kartikaningtyas, V.; Kusmayadi, T. A.; Riyadi
2017-09-01
The aim of this study was to combine the contextual approach with Guided Discovery Learning (GDL) and Brain Based Learning (BBL) in geometry learning of junior high school. Furthermore, this study analysed the effect of contextual approach with GDL and BBL in geometry learning. GDL-contextual and BBL-contextual was built from the steps of GDL and BBL that combined with the principles of contextual approach. To validate the models, it uses quasi experiment which used two experiment groups. The sample had been chosen by stratified cluster random sampling. The sample was 150 students of grade 8th in junior high school. The data were collected through the student’s mathematics achievement test that given after the treatment of each group. The data analysed by using one way ANOVA with different cell. The result shows that GDL-contextual has not different effect than BBL-contextual on mathematics achievement in geometry learning. It means both the two models could be used in mathematics learning as the innovative way in geometry learning.
Dr. Harmen Schaap; Dr. Liesbeth Baartman; Prof.Dr. Elly de Bruijn
2012-01-01
This article reviews 24 articles in order to get a structured view on student's learning processes when dealing with a combination of school-based learning and workplace learning in vocational education. It focuses on six main themes: students' expertise development, students' learning styles,
Intelligent Web-Based Learning System with Personalized Learning Path Guidance
Chen, C. M.
2008-01-01
Personalized curriculum sequencing is an important research issue for web-based learning systems because no fixed learning paths will be appropriate for all learners. Therefore, many researchers focused on developing e-learning systems with personalized learning mechanisms to assist on-line web-based learning and adaptively provide learning paths…
Learning Networks for Lifelong Learning
Sloep, Peter
2009-01-01
Presentation in a seminar organized by Christopher Hoadley at Penn State University, October 2004.Contains general introduction into the Learning Network Programme and a demonstration of the Netlogo Simulation of a Learning Network.
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Learning Theory Foundations of Simulation-Based Mastery Learning.
McGaghie, William C; Harris, Ilene B
2018-06-01
Simulation-based mastery learning (SBML), like all education interventions, has learning theory foundations. Recognition and comprehension of SBML learning theory foundations are essential for thoughtful education program development, research, and scholarship. We begin with a description of SBML followed by a section on the importance of learning theory foundations to shape and direct SBML education and research. We then discuss three principal learning theory conceptual frameworks that are associated with SBML-behavioral, constructivist, social cognitive-and their contributions to SBML thought and practice. We then discuss how the three learning theory frameworks converge in the course of planning, conducting, and evaluating SBML education programs in the health professions. Convergence of these learning theory frameworks is illustrated by a description of an SBML education and research program in advanced cardiac life support. We conclude with a brief coda.
Blended Learning or E-learning?
Tayebinik, Maryam; Puteh, Marlia
2013-01-01
ICT or Information and Communication Technology has pervaded the fields of education.In recent years the term e-learning has emerged as a result of the integration of ICT in the education fields. Following the application this technology into teaching, some pitfalls have been identified and this have led to the Blended learning phenomenon.However the preference on this new method has been debated quite extensively.The aim of this paper is to investigate the advantages of blended learning over...
On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator
Korda, Milan; Mezić, Igor
2018-04-01
Extended dynamic mode decomposition (EDMD) (Williams et al. in J Nonlinear Sci 25(6):1307-1346, 2015) is an algorithm that approximates the action of the Koopman operator on an N-dimensional subspace of the space of observables by sampling at M points in the state space. Assuming that the samples are drawn either independently or ergodically from some measure μ , it was shown in Klus et al. (J Comput Dyn 3(1):51-79, 2016) that, in the limit as M→ ∞, the EDMD operator K_{N,M} converges to K_N, where K_N is the L_2(μ )-orthogonal projection of the action of the Koopman operator on the finite-dimensional subspace of observables. We show that, as N → ∞, the operator K_N converges in the strong operator topology to the Koopman operator. This in particular implies convergence of the predictions of future values of a given observable over any finite time horizon, a fact important for practical applications such as forecasting, estimation and control. In addition, we show that accumulation points of the spectra of K_N correspond to the eigenvalues of the Koopman operator with the associated eigenfunctions converging weakly to an eigenfunction of the Koopman operator, provided that the weak limit of the eigenfunctions is nonzero. As a by-product, we propose an analytic version of the EDMD algorithm which, under some assumptions, allows one to construct K_N directly, without the use of sampling. Finally, under additional assumptions, we analyze convergence of K_{N,N} (i.e., M=N), proving convergence, along a subsequence, to weak eigenfunctions (or eigendistributions) related to the eigenmeasures of the Perron-Frobenius operator. No assumptions on the observables belonging to a finite-dimensional invariant subspace of the Koopman operator are required throughout.
Web-Based Instruction, Learning Effectiveness and Learning Behavior: The Impact of Relatedness
Shieh, Chich-Jen; Liao, Ying; Hu, Ridong
2013-01-01
This study aims to discuss the effects of Web-based Instruction and Learning Behavior on Learning Effectiveness. Web-based Instruction contains the dimensions of Active Learning, Simulation-based Learning, Interactive Learning, and Accumulative Learning; and, Learning Behavior covers Learning Approach, Learning Habit, and Learning Attitude. The…