Embedded random matrix ensembles in quantum physics
Kota, V K B
2014-01-01
Although used with increasing frequency in many branches of physics, random matrix ensembles are not always sufficiently specific to account for important features of the physical system at hand. One refinement which retains the basic stochastic approach but allows for such features consists in the use of embedded ensembles. The present text is an exhaustive introduction to and survey of this important field. Starting with an easy-to-read introduction to general random matrix theory, the text then develops the necessary concepts from the beginning, accompanying the reader to the frontiers of present-day research. With some notable exceptions, to date these ensembles have primarily been applied in nuclear spectroscopy. A characteristic example is the use of a random two-body interaction in the framework of the nuclear shell model. Yet, topics in atomic physics, mesoscopic physics, quantum information science and statistical mechanics of isolated finite quantum systems can also be addressed using these ensemb...
Group theory for embedded random matrix ensembles
Kota, V. K. B.
2015-04-01
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated quantum many-particle systems. For the simplest spinless fermion (or boson) systems with say m fermions (or bosons) in N single particle states and interacting with say k-body interactions, we have EGUE(k) [embedded GUE of k-body interactions) with GUE embedding and the embedding algebra is U(N). In this paper, using EGUE(k) representation for a Hamiltonian that is fc-body and an independent EGUE(t) representation for a transition operator that is t-body and employing the embedding U(N) algebra, finite-N formulas for moments up to order four are derived, for the first time, for the transition strength densities (transition strengths multiplied by the density of states at the initial and final energies). In the asymptotic limit, these formulas reduce to those derived for the EGOE version and establish that in general bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extension of these results for other types of transition operators and EGUE ensembles with further symmetries are discussed.
Applications of Random Matrix Ensembles in Nuclear Systems
Duras, Maciej M.
2003-01-01
The random matrix ensembles (RME), especially Gaussian RME and Ginibre RME, are applied to nuclear systems, molecular systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integrability with respect to eigenergies of quantum systems are defined and calculated.
Inner structure of vehicular ensembles and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Krbálek, Milan, E-mail: milan.krbalek@fjfi.cvut.cz; Hobza, Tomáš
2016-05-06
Highlights: • New class of random matrices (DUE) is proposed and analyzed in detail. • Approximation formula for level spacing distribution in DUE ensembles is analytically derived. • Connection between DUE and vehicular systems (analogical to a well-known link between GUE and Mexico buses) is presented. • It is shown that LS distribution of DUE matrices is the same as clearance distribution measured on expressways. - Abstract: We introduce a special class of random matrices (DUE) whose spectral statistics corresponds to statistics of microscopical quantities detected in vehicular flows. Comparing the level spacing distribution (for ordered eigenvalues in unfolded spectra of DUE matrices) with the time-clearance distribution extracted from various areas of the flux-density diagram (evaluated from original traffic data measured on Czech expressways with high occupancies) we demonstrate that the set of classical systems showing an universality associated with Random Matrix Ensembles can be extended by traffic systems.
Inner structure of vehicular ensembles and random matrix theory
Krbálek, Milan; Hobza, Tomáš
2016-05-01
We introduce a special class of random matrices (DUE) whose spectral statistics corresponds to statistics of microscopical quantities detected in vehicular flows. Comparing the level spacing distribution (for ordered eigenvalues in unfolded spectra of DUE matrices) with the time-clearance distribution extracted from various areas of the flux-density diagram (evaluated from original traffic data measured on Czech expressways with high occupancies) we demonstrate that the set of classical systems showing an universality associated with Random Matrix Ensembles can be extended by traffic systems.
Random matrix ensembles with random interactions: Results for ...
Indian Academy of Sciences (India)
quadrupole. (Q · Q) operator over the EGOE(1+2)-SU(4) ensemble. Finally, going beyond. EGUE(2)-SU(4), it is both interesting and possible (by extending and applying the SU(4) ⊃ SUS(2) ⊗ SUT (2) Wigner–Racah algebra developed by Hecht and.
Analogies between random matrix ensembles and the one-component plasma in two-dimensions
Directory of Open Access Journals (Sweden)
Peter J. Forrester
2016-03-01
Full Text Available The eigenvalue PDF for some well known classes of non-Hermitian random matrices — the complex Ginibre ensemble for example — can be interpreted as the Boltzmann factor for one-component plasma systems in two-dimensional domains. We address this theme in a systematic fashion, identifying the plasma system for the Ginibre ensemble of non-Hermitian Gaussian random matrices G, the spherical ensemble of the product of an inverse Ginibre matrix and a Ginibre matrix G1−1G2, and the ensemble formed by truncating unitary matrices, as well as for products of such matrices. We do this when each has either real, complex or real quaternion elements. One consequence of this analogy is that the leading form of the eigenvalue density follows as a corollary. Another is that the eigenvalue correlations must obey sum rules known to characterise the plasma system, and this leads us to an exhibit of an integral identity satisfied by the two-particle correlation for real quaternion matrices in the neighbourhood of the real axis. Further random matrix ensembles investigated from this viewpoint are self dual non-Hermitian matrices, in which a previous study has related to the one-component plasma system in a disk at inverse temperature β=4, and the ensemble formed by the single row and column of quaternion elements from a member of the circular symplectic ensemble.
Energy Technology Data Exchange (ETDEWEB)
Macedo-Junior, A.F. [Departamento de Fisica, Laboratorio de Fisica Teorica e Computacional, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil)]. E-mail: ailton@df.ufpe.br; Macedo, A.M.S. [Departamento de Fisica, Laboratorio de Fisica Teorica e Computacional, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil)
2006-09-25
We study a class of Brownian-motion ensembles obtained from the general theory of Markovian stochastic processes in random-matrix theory. The ensembles admit a complete classification scheme based on a recent multivariable generalization of classical orthogonal polynomials and are closely related to Hamiltonians of Calogero-Sutherland-type quantum systems. An integral transform is proposed to evaluate the n-point correlation function for a large class of initial distribution functions. Applications of the classification scheme and of the integral transform to concrete physical systems are presented in detail.
Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory
Pato, Mauricio P.; Oshanin, Gleb
2013-03-01
We study the probability distribution function P(β)n(w) of the Schmidt-like random variable w = x21/(∑j = 1nx2j/n), where xj, (j = 1, 2, …, n), are unordered eigenvalues of a given n × n β-Gaussian random matrix, β being the Dyson symmetry index. This variable, by definition, can be considered as a measure of how any individual (randomly chosen) eigenvalue deviates from the arithmetic mean value of all eigenvalues of a given random matrix, and its distribution is calculated with respect to the ensemble of such β-Gaussian random matrices. We show that in the asymptotic limit n → ∞ and for arbitrary β the distribution P(β)n(w) converges to the Marčenko-Pastur form, i.e. is defined as P_{n}^{( \\beta )}(w) \\sim \\sqrt{(4 - w)/w} for w ∈ [0, 4] and equals zero outside of the support, despite the fact that formally w is defined on the interval [0, n]. Furthermore, for Gaussian unitary ensembles (β = 2) we present exact explicit expressions for P(β = 2)n(w) which are valid for arbitrary n and analyse their behaviour.
Quasiclassical Random Matrix Theory
Prange, R. E.
1996-01-01
We directly combine ideas of the quasiclassical approximation with random matrix theory and apply them to the study of the spectrum, in particular to the two-level correlator. Bogomolny's transfer operator T, quasiclassically an NxN unitary matrix, is considered to be a random matrix. Rather than rejecting all knowledge of the system, except for its symmetry, [as with Dyson's circular unitary ensemble], we choose an ensemble which incorporates the knowledge of the shortest periodic orbits, th...
Random matrix theory and multivariate statistics
Diaz-Garcia, Jose A.; Jáimez, Ramon Gutiérrez
2009-01-01
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases the classical random matrix ensembles, are proposed. Some properties of these classes of ensemble are analysed. In addition, the random matrix ensemble approach is extended and a unified theory proposed for the study of distributions for real normed divisio...
Tailored Random Graph Ensembles
Roberts, E. S.; Annibale, A.; Coolen, A. C. C.
2013-02-01
Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.
Deift, Percy
2009-01-01
This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles-orthogonal, unitary, and symplectic. The authors follow the approach of Tracy and Widom, but the exposition here contains a substantial amount of additional material, in particular, facts from functional analysis and the theory of Pfaffians. The main result in the book is a proof of universality for orthogonal and symplectic ensembles corresponding to generalized Gaussian type weights following the authors' prior work. New, quantitative error estimates are derive
Pan, Guangming; Wang, Shaochen; Zhou, Wang
2017-10-01
In this paper, we consider the asymptotic behavior of Xfn (n )≔∑i=1 nfn(xi ) , where xi,i =1 ,…,n form orthogonal polynomial ensembles and fn is a real-valued, bounded measurable function. Under the condition that Var Xfn (n )→∞ , the Berry-Esseen (BE) bound and Cramér type moderate deviation principle (MDP) for Xfn (n ) are obtained by using the method of cumulants. As two applications, we establish the BE bound and Cramér type MDP for linear spectrum statistics of Wigner matrix and sample covariance matrix in the complex cases. These results show that in the edge case (which means fn has a particular form f (x ) I (x ≥θn ) where θn is close to the right edge of equilibrium measure and f is a smooth function), Xfn (n ) behaves like the eigenvalues counting function of the corresponding Wigner matrix and sample covariance matrix, respectively.
Octonions in random matrix theory
Forrester, Peter J.
2016-01-01
The octonions are one of the four normed division algebras, together with the real, complex and quaternion number systems. The latter three hold a primary place in random matrix theory, where in applications to quantum physics they are determined as the entries of ensembles of Hermitian random by symmetry considerations. Only for $N=2$ is there an existing analytic theory of Hermitian random matrices with octonion entries. We use a Jordan algebra viewpoint to provide an analytic theory for $N...
Matrix averages relating to Ginibre ensembles
Energy Technology Data Exchange (ETDEWEB)
Forrester, Peter J [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia); Rains, Eric M [Department of Mathematics, California Institute of Technology, Pasadena, CA 91125 (United States)], E-mail: p.forrester@ms.unimelb.edu.au
2009-09-25
The theory of zonal polynomials is used to compute the average of a Schur polynomial of argument AX, where A is a fixed matrix and X is from the real Ginibre ensemble. This generalizes a recent result of Sommers and Khoruzhenko (2009 J. Phys. A: Math. Theor. 42 222002), and furthermore allows analogous results to be obtained for the complex and real quaternion Ginibre ensembles. As applications, the positive integer moments of the general variance Ginibre ensembles are computed in terms of generalized hypergeometric functions; these are written in terms of averages over matrices of the same size as the moment to give duality formulas, and the averages of the power sums of the eigenvalues are expressed as finite sums of zonal polynomials.
A random matrix theory of decoherence
Energy Technology Data Exchange (ETDEWEB)
Gorin, T [Departamento de FIsica, Universidad de Guadalajara, Blvd Marcelino GarcIa Barragan y Calzada OlImpica, Guadalajara CP 44840, JalIsco (Mexico); Pineda, C [Institut fuer Physik und Astronomie, University of Potsdam, 14476 Potsdam (Germany); Kohler, H [Fachbereich Physik, Universitaet Duisburg-Essen, D-47057 Duisburg (Germany); Seligman, T H [Instituto de Ciencias FIsicas, Universidad Nacional Autonoma de Mexico (Mexico)], E-mail: thomas.gorin@red.cucei.udg.mx, E-mail: carlospgmat03@gmail.com
2008-11-15
Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix arising from the ensemble induced, in contrast to previous studies where the average values of purity, concurrence and entropy were considered; we further discuss when one or the other approach is relevant. The two approaches agree in the limit of large environments. Analytic results for the average density matrix and its purity are presented in linear response approximation. The two-qubit system is analysed, mainly numerically, in more detail.
Logarithmic universality in random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Splittorff, K. E-mail: split@alf.nbi.dk
1999-05-24
Universality in unitary invariant random matrix ensembles with complex matrix elements is considered. We treat two general ensembles which have a determinant factor in the weight. These ensembles are relevant, e.g., for spectra of the Dirac operator in QCD. In addition to the well established universality with respect to the choice of potential, we prove that microscopic spectral correlators are unaffected when the matrix in the determinant is replaced by an expansion in powers of the matrix. We refer to this invariance as logarithmic universality. The result is used in proving that a simple random matrix model with Ginsparg-Wilson symmetry has the same microscopic spectral correlators as chiral random matrix theory.
Supersymmetry in random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Kieburg, Mario
2010-05-04
I study the applications of supersymmetry in random matrix theory. I generalize the supersymmetry method and develop three new approaches to calculate eigenvalue correlation functions. These correlation functions are averages over ratios of characteristic polynomials. In the first part of this thesis, I derive a relation between integrals over anti-commuting variables (Grassmann variables) and differential operators with respect to commuting variables. With this relation I rederive Cauchy- like integral theorems. As a new application I trace the supermatrix Bessel function back to a product of two ordinary matrix Bessel functions. In the second part, I apply the generalized Hubbard-Stratonovich transformation to arbitrary rotation invariant ensembles of real symmetric and Hermitian self-dual matrices. This extends the approach for unitarily rotation invariant matrix ensembles. For the k-point correlation functions I derive supersymmetric integral expressions in a unifying way. I prove the equivalence between the generalized Hubbard-Stratonovich transformation and the superbosonization formula. Moreover, I develop an alternative mapping from ordinary space to superspace. After comparing the results of this approach with the other two supersymmetry methods, I obtain explicit functional expressions for the probability densities in superspace. If the probability density of the matrix ensemble factorizes, then the generating functions exhibit determinantal and Pfaffian structures. For some matrix ensembles this was already shown with help of other approaches. I show that these structures appear by a purely algebraic manipulation. In this new approach I use structures naturally appearing in superspace. I derive determinantal and Pfaffian structures for three types of integrals without actually mapping onto superspace. These three types of integrals are quite general and, thus, they are applicable to a broad class of matrix ensembles. (orig.)
Octonions in random matrix theory
Forrester, Peter J.
2017-04-01
The octonions are one of the four normed division algebras, together with the real, complex and quaternion number systems. The latter three hold a primary place in random matrix theory, where in applications to quantum physics they are determined as the entries of ensembles of Hermitian random matrices by symmetry considerations. Only for N=2 is there an existing analytic theory of Hermitian random matrices with octonion entries. We use a Jordan algebra viewpoint to provide an analytic theory for N=3. We then proceed to consider the matrix structure X†X, when X has random octonion entries. Analytic results are obtained from N=2, but are observed to break down in the 3×3 case.
Random matrix model for disordered conductors
Indian Academy of Sciences (India)
Keywords. Disordered conductors; random matrix theory; Dyson's Coulomb gas model. ... An interesting random walk problem associated with the joint probability distribution of the ensuing ensemble is discussed and its connection with level dynamics is brought out. It is further proved that Dyson's Coulomb gas analogy ...
Supersymmetric SYK model and random matrix theory
Li, Tianlin; Liu, Junyu; Xin, Yuan; Zhou, Yehao
2017-06-01
In this paper, we investigate the effect of supersymmetry on the symmetry classification of random matrix theory ensembles. We mainly consider the random matrix behaviors in the N=1 supersymmetric generalization of Sachdev-Ye-Kitaev (SYK) model, a toy model for two-dimensional quantum black hole with supersymmetric constraint. Some analytical arguments and numerical results are given to show that the statistics of the supersymmetric SYK model could be interpreted as random matrix theory ensembles, with a different eight-fold classification from the original SYK model and some new features. The time-dependent evolution of the spectral form factor is also investigated, where predictions from random matrix theory are governing the late time behavior of the chaotic hamiltonian with supersymmetry.
Random matrix theory for underwater sound propagation
Hegewisch, K. C.; Tomsovic, S.
2012-02-01
Ocean acoustic propagation can be formulated as a wave guide with a weakly random medium generating multiple scattering. Twenty years ago, this was recognized as a quantum chaos problem, and yet random matrix theory, one pillar of quantum or wave chaos studies, has never been introduced into the subject. The modes of the wave guide provide a representation for the propagation, which in the parabolic approximation is unitary. Scattering induced by the ocean's internal waves leads to a power-law random banded unitary matrix ensemble for long-range deep-ocean acoustic propagation. The ensemble has similarities, but differs, from those introduced for studying the Anderson metal-insulator transition. The resulting long-range propagation ensemble statistics agree well with those of full wave propagation using the parabolic equation.
A Random Matrix Approach to Credit Risk
Guhr, Thomas
2014-01-01
We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided. PMID:24853864
A random matrix approach to credit risk.
Directory of Open Access Journals (Sweden)
Michael C Münnix
Full Text Available We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided.
Indian Academy of Sciences (India)
chaos to galaxies. We demonstrate the applicability of random matrix theory for networks by pro- viding a new dimension to complex systems research. We show that in spite of huge differences ... as mentioned earlier, different types of networks can be constructed based on the nature of connections. For example,.
Statistical properties of random matrix product states
Garnerone, Silvano; de Oliveira, Thiago R.; Haas, Stephan; Zanardi, Paolo
2010-11-01
We study the set of random matrix product states (RMPS) introduced by Garnerone, de Oliveira, and Zanardi [S. Garnerone, T. R. de Oliveira, and P. Zanardi, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.81.032336 81, 032336 (2010)] as a tool to explore foundational aspects of quantum statistical mechanics. In the present work, we provide an accurate numerical and analytical investigation of the properties of RMPS. We calculate the average state of the ensemble in the nonhomogeneous case, and numerically check the validity of this result. We also suggest using RMPS as a tool to approximate properties of general quantum random states. The numerical simulations presented here support the accuracy and efficiency of this approximation. These results suggest that any generalized canonical state can be approximated with high probability by the reduced density matrix of a RMPS, if the average matrix product states coincide with the associated microcanonical ensemble.
Random matrix theory and symmetric spaces
Energy Technology Data Exchange (ETDEWEB)
Caselle, M.; Magnea, U
2004-05-01
In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing the ensembles are in strict correspondence with symmetric spaces and the intrinsic characteristics of their restricted root lattices. Several important results can be obtained from this identification. In particular the Cartan classification of triplets of symmetric spaces with positive, zero and negative curvature gives rise to a new classification of random matrix ensembles. The review is organized into two main parts. In Part I the theory of symmetric spaces is reviewed with particular emphasis on the ideas relevant for appreciating the correspondence with random matrix theories. In Part II we discuss various applications of symmetric spaces to random matrix theories and in particular the new classification of disordered systems derived from the classification of symmetric spaces. We also review how the mapping from integrable Calogero-Sutherland models to symmetric spaces can be used in the theory of random matrices, with particular consequences for quantum transport problems. We conclude indicating some interesting new directions of research based on these identifications.
Spectrum of the QCD Dirac operator and chiral random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Verbaarschot, J. (Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794 (United States))
1994-04-18
We argue that the spectrum of the QCD Dirac operator near zero virtuality can be described by random matrix theory. As in the case of the classical random matrix ensembles of Dyson we have three different cases: the chiral orthogonal ensemble, the chiral unitary ensemble, and the chiral symplectic ensemble. They correspond to gauge groups SU(2) in the fundamental representation, SU([ital N][sub [ital c
Quantum Chaos and Random Matrix Theory Some New Results
Smilansky, U
1996-01-01
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which are the quantum versions of area preserving maps. The relevant Random Matrix ensembles are the Circular ensembles. The resulting semiclassical expressions depend on the symmetry of the system with respect to time reversal, and on a classical parameter $\\mu = tr U -1$ where U is the classical 1-step evolution operator. For system without time reversal symmetry, we are able to reproduce the exact Random Matrix predictions in the limit $\\mu \\to 0$. For systems with time reversal symmetry we can reproduce only some of the features of Random Matrix Theory. For both classes we obtain the leading corrections in $\\mu$. The semiclassical theory for integrable systems is also developed, resulting in expressions which reproduce the theory for the Poissonian ensemble to leading order i...
Discrete Painlev\\'e equations and random matrix averages
Forrester, P. J.; Witte, N. S.
2003-01-01
The $\\tau$-function theory of Painlev\\'e systems is used to derive recurrences in the rank $n$ of certain random matrix averages over U(n). These recurrences involve auxilary quantities which satisfy discrete Painlev\\'e equations. The random matrix averages include cases which can be interpreted as eigenvalue distributions at the hard edge and in the bulk of matrix ensembles with unitary symmetry. The recurrences are illustrated by computing the value of a sequence of these distributions as $...
Solutions of matrix models in the DIII generator ensemble
Roussel, Harold
1994-01-01
In this paper we solve two matrix models, using standard and new techniques. The two models are represented by special form of antisymmetric matrices and are classified in the DIII generator ensemble. It is shown that, in the double scaling limit, their free energy has the same behavior as previous models describing oriented and unoriented surfaces. We also found an additional solution for the first model.
S-AMP: Approximate Message Passing for General Matrix Ensembles
DEFF Research Database (Denmark)
Cakmak, Burak; Winther, Ole; Fleury, Bernard H.
2014-01-01
We propose a novel iterative estimation algorithm for linear observation models called S-AMP. The fixed points of S-AMP are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends...... the approximate message-passing (AMP) algorithm to general matrix ensembles with a well-defined large system size limit. The generalization is based on the S-transform (in free probability) of the spectrum of the measurement matrix. Furthermore, we show that the optimality of S-AMP follows directly from its...
Wigner surmise for mixed symmetry classes in random matrix theory
Schierenberg, Sebastian; Bruckmann, Falk; Wettig, Tilo
2012-06-01
We consider the nearest-neighbor spacing distributions of mixed random matrix ensembles interpolating between different symmetry classes or between integrable and nonintegrable systems. We derive analytical formulas for the spacing distributions of 2×2 or 4×4 matrices and show numerically that they provide very good approximations for those of random matrices with large dimension. This generalizes the Wigner surmise, which is valid for pure ensembles that are recovered as limits of the mixed ensembles. We show how the coupling parameters of small and large matrices must be matched depending on the local eigenvalue density.
Developments in Random Matrix Theory
Snaith, N. C.; Forrester, P. J.; Verbaarschot, J. J. M.
2003-01-01
In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also given.
Energy Technology Data Exchange (ETDEWEB)
Jackson, A.D. [Niels Bohr Inst., Copenhagen (Denmark)
1998-08-10
Chiral random matrix theory has recently been shown to provide a tool useful for both modeling chiral symmetry restoration in QCD and for providing analytic descriptions of the microscopic spectral content of lattice gauge simulations. The basic ideas of chiral random matrix theory and some recent results are discussed. (orig.) 24 refs.
Phenotype Recognition with Combined Features and Random Subspace Classifier Ensemble
Directory of Open Access Journals (Sweden)
Pham Tuan D
2011-04-01
Full Text Available Abstract Background Automated, image based high-content screening is a fundamental tool for discovery in biological science. Modern robotic fluorescence microscopes are able to capture thousands of images from massively parallel experiments such as RNA interference (RNAi or small-molecule screens. As such, efficient computational methods are required for automatic cellular phenotype identification capable of dealing with large image data sets. In this paper we investigated an efficient method for the extraction of quantitative features from images by combining second order statistics, or Haralick features, with curvelet transform. A random subspace based classifier ensemble with multiple layer perceptron (MLP as the base classifier was then exploited for classification. Haralick features estimate image properties related to second-order statistics based on the grey level co-occurrence matrix (GLCM, which has been extensively used for various image processing applications. The curvelet transform has a more sparse representation of the image than wavelet, thus offering a description with higher time frequency resolution and high degree of directionality and anisotropy, which is particularly appropriate for many images rich with edges and curves. A combined feature description from Haralick feature and curvelet transform can further increase the accuracy of classification by taking their complementary information. We then investigate the applicability of the random subspace (RS ensemble method for phenotype classification based on microscopy images. A base classifier is trained with a RS sampled subset of the original feature set and the ensemble assigns a class label by majority voting. Results Experimental results on the phenotype recognition from three benchmarking image sets including HeLa, CHO and RNAi show the effectiveness of the proposed approach. The combined feature is better than any individual one in the classification accuracy. The
Ensembles of physical states and random quantum circuits on graphs
Hamma, Alioscia; Santra, Siddhartha; Zanardi, Paolo
2012-11-01
In this paper we continue and extend the investigations of the ensembles of random physical states introduced in Hamma [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.109.040502 109, 040502 (2012)]. These ensembles are constructed by finite-length random quantum circuits (RQC) acting on the (hyper)edges of an underlying (hyper)graph structure. The latter encodes for the locality structure associated with finite-time quantum evolutions generated by physical, i.e., local, Hamiltonians. Our goal is to analyze physical properties of typical states in these ensembles; in particular here we focus on proxies of quantum entanglement as purity and α-Renyi entropies. The problem is formulated in terms of matrix elements of superoperators which depend on the graph structure, choice of probability measure over the local unitaries, and circuit length. In the α=2 case these superoperators act on a restricted multiqubit space generated by permutation operators associated to the subsets of vertices of the graph. For permutationally invariant interactions the dynamics can be further restricted to an exponentially smaller subspace. We consider different families of RQCs and study their typical entanglement properties for finite time as well as their asymptotic behavior. We find that area law holds in average and that the volume law is a typical property (that is, it holds in average and the fluctuations around the average are vanishing for the large system) of physical states. The area law arises when the evolution time is O(1) with respect to the size L of the system, while the volume law arises as is typical when the evolution time scales like O(L).
Fuzzy Field Theory as a Random Matrix Model
Tekel, Juraj
This dissertation considers the theory of scalar fields on fuzzy spaces from the point of view of random matrices. First we define random matrix ensembles, which are natural description of such theory. These ensembles are new and the novel feature is a presence of kinetic term in the probability measure, which couples the random matrix to a set of external matrices and thus breaks the original symmetry. Considering the case of a free field ensemble, which is generalization of a Gaussian matrix ensemble, we develop a technique to compute expectation values of the observables of the theory based on explicit Wick contractions and we write down recursion rules for these. We show that the eigenvalue distribution of the random matrix follows the Wigner semicircle distribution with a rescaled radius. We also compute distributions of the matrix Laplacian of the random matrix given by the new term and demonstrate that the eigenvalues of these two matrices are correlated. We demonstrate the robustness of the method by computing expectation values and distributions for more complicated observables. We then consider the ensemble corresponding to an interacting field theory, with a quartic interaction. We use the same method to compute the distribution of the eigenvalues and show that the presence of the kinetic terms rescales the distribution given by the original theory, which is a polynomially deformed Wigner semicircle. We compute the eigenvalue distribution of the matrix Laplacian and the joint distribution up to second order in the correlation and we show that the correlation between the two changes from the free field case. Finally, as an application of these results, we compute the phase diagram of the fuzzy scalar field theory, we find multiscaling which stabilizes this diagram in the limit of large matrices and compare it with the results obtained numerically and by considering the kinetic part as a perturbation.
two-body random matrix ensembles
Indian Academy of Sciences (India)
2015-02-03
Feb 3, 2015 ... Abstract. Probability distribution (P(r)) of the level spacing ratios has been introduced recently and is used to investigate many-body localization as well as to quantify the distance from inte- grability on finite size lattices. In this paper, we study the distribution of the ratio of consecutive level spacings using ...
Nonextensive random-matrix theory based on Kaniadakis entropy
Abul-Magd, A. Y.
2006-01-01
The joint eigenvalue distributions of random-matrix ensembles are derived by applying the principle maximum entropy to the Renyi, Abe and Kaniadakis entropies. While the Renyi entropy produces essentially the same matrix-element distributions as the previously obtained expression by using the Tsallis entropy, and the Abe entropy does not lead to a closed form expression, the Kaniadakis entropy leads to a new generalized form of the Wigner surmise that describes a transition of the spacing dis...
Superstatistics in Random Matrix Theory
Abul-Magd, A. Y.
2011-01-01
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed several attempts to extend RMT to describe quantum systems with mixed regular-chaotic dynamics. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented other versions of the theory that keep...
Universality of S-matrix correlations for deterministic plus random Hamiltonians.
Mae, N; Iida, S
2001-04-01
We study S-matrix correlations for random matrix ensembles with a Hamiltonian H=H(0)+straight phi, in which H0 is a deterministic NxN matrix and straight phi belongs to a Gaussian random matrix ensemble. Using Efetov's supersymmetry formalism, we show that in the limit N-->infinity correlation functions of S-matrix elements are universal on the scale of the local mean level spacing: the dependence of H0 enters into these correlation functions only through the average S matrix and the average level density. This statement applies to each of the three symmetry classes (unitary, orthogonal, and symplectic).
Grand-canonical-ensemble representability problem for the one-electron reduced density matrix
Alcoba, D. R.; Bochicchio, R. C.; Massacessi, G. E.; Lain, L.; Torre, A.
2007-01-01
We deal with many-electron systems having a noninteger number of electrons, which cannot be described properly by means of pure states or by canonical statistical ensemble states. The study of the one-electron reduced density matrix for these systems raises the problem of its representability in statistical ensembles of grand canonical type. We derive the necessary and sufficient conditions for the representability of the one-electron reduced density matrix of grand-canonical statistical ensembles.
Supersymmetry in Random Matrix Theory
Guhr, Thomas
2010-01-01
Supersymmetry is nowadays indispensable for many problems in Random Matrix Theory. It is presented here with an emphasis on conceptual and structural issues. An introduction to supermathematics is given. The Hubbard-Stratonovich transformation as well as its generalization and superbosonization are explained. The supersymmetric non-linear sigma model, Brownian motion in superspace and the color-flavor transformation are discussed.
Low-temperature random matrix theory at the soft edge
Energy Technology Data Exchange (ETDEWEB)
Edelman, Alan [Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Persson, Per-Olof [Department of Mathematics, University of California, Berkeley, California 94720 (United States); Sutton, Brian D. [Department of Mathematics, Randolph-Macon College, Ashland, Virginia 23005 (United States)
2014-06-15
“Low temperature” random matrix theory is the study of random eigenvalues as energy is removed. In standard notation, β is identified with inverse temperature, and low temperatures are achieved through the limit β → ∞. In this paper, we derive statistics for low-temperature random matrices at the “soft edge,” which describes the extreme eigenvalues for many random matrix distributions. Specifically, new asymptotics are found for the expected value and standard deviation of the general-β Tracy-Widom distribution. The new techniques utilize beta ensembles, stochastic differential operators, and Riccati diffusions. The asymptotics fit known high-temperature statistics curiously well and contribute to the larger program of general-β random matrix theory.
Low-temperature random matrix theory at the soft edge
Edelman, Alan; Persson, Per-Olof; Sutton, Brian D.
2014-06-01
"Low temperature" random matrix theory is the study of random eigenvalues as energy is removed. In standard notation, β is identified with inverse temperature, and low temperatures are achieved through the limit β → ∞. In this paper, we derive statistics for low-temperature random matrices at the "soft edge," which describes the extreme eigenvalues for many random matrix distributions. Specifically, new asymptotics are found for the expected value and standard deviation of the general-β Tracy-Widom distribution. The new techniques utilize beta ensembles, stochastic differential operators, and Riccati diffusions. The asymptotics fit known high-temperature statistics curiously well and contribute to the larger program of general-β random matrix theory.
Random matrix improved subspace clustering
Couillet, Romain
2017-03-06
This article introduces a spectral method for statistical subspace clustering. The method is built upon standard kernel spectral clustering techniques, however carefully tuned by theoretical understanding arising from random matrix findings. We show in particular that our method provides high clustering performance while standard kernel choices provably fail. An application to user grouping based on vector channel observations in the context of massive MIMO wireless communication networks is provided.
Random matrix theory within superstatistics
Abul-Magd, A. Y.
2005-01-01
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted averages of the corresponding quantities in the standard theory assuming that the mean level spacing itself is a stochastic variable. We illustrate the method by calculating the level density, the nearest-neighbor-spacing distributions and the two-level co...
Staggered chiral random matrix theory
Osborn, James C.
2010-01-01
We present a random matrix theory (RMT) for the staggered lattice QCD Dirac operator. The staggered RMT is equivalent to the zero-momentum limit of the staggered chiral Lagrangian and includes all taste breaking terms at their leading order. This is an extension of previous work which only included some of the taste breaking terms. We will also present some results for the taste breaking contributions to the partition function and the Dirac eigenvalues.
Generalized Random Matrix Theory:. a Mathematical Probe for Complexity
Shukla, Pragya
2012-07-01
The ubiquitous presence of complexity in nature makes it necessary to seek new mathematical tools which can probe physical systems beyond linear or perturbative approximations. The random matrix theory is one such tool in which the statistical behavior of a system is modeled by an ensemble of its replicas. This paper is an attempt to review the basic aspects of the theory in a simplified language, aimed at students from diverse areas of physics.
Random forest ensemble classification based fuzzy logic
Ben Ayed, Abdelkarim; Benhammouda, Marwa; Ben Halima, Mohamed; Alimi, Adel M.
2017-03-01
In this paper, we treat the supervised data classification, while using the fuzzy random forests that combine the hardiness of the decision trees, the power of the random selection that increases the diversity of the trees in the forest as well as the flexibility of the fuzzy logic for noise. We will be interested in the construction of a forest of fuzzy decision trees. Our system is validated on nine standard classification benchmarks from UCI repository and have the specificity to control some data, to reduce the rate of mistakes and to put in evidence more of hardiness and more of interoperability.
Superstatistics in Random Matrix Theory
Directory of Open Access Journals (Sweden)
A.Y. Abul-Magd
2012-12-01
Full Text Available Random matrix theory (RMT provides a successful model for quantum systems, whose classical counterpart has chaotic dynamics. It is based on two assumptions: (1 matrix-element independence, and (2 base invariance. The last decade witnessed several attempts to extend RMT to describe quantum systems with mixed regular-chaotic dynamics. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors have presented other versions of the theory that keep base invariance at the expense of allowing correlations between matrix elements. This is achieved by starting from non-extensive entropies rather than the standard Shannon entropy, or by following the basic prescription of the recently suggested concept of superstatistics. The latter concept was introduced as a generalization of equilibrium thermodynamics to describe non-equilibrium systems by allowing the temperature to fluctuate. We here review the superstatistical generalizations of RMT and illustrate their value by calculating the nearest-neighbor-spacing distributions and comparing the results of calculation with experiments on billiards modeling systems in transition from order to chaos.
Large N (=3) neutrinos and random matrix theory
Bai, Yang; Torroba, Gonzalo
2012-12-01
The large N limit has been successfully applied to QCD, leading to qualitatively correct results even for N = 3. In this work, we propose to treat the number N = 3 of Standard Model generations as a large number. Specifically, we apply this idea to the neutrino anarchy scenario and study neutrino physics using Random Matrix Theory, finding new results in both areas. For neutrino physics, we obtain predictions for the masses and mixing angles as a function of the generation number N. The Seesaw mechanism produces a hierarchy of order 1 /N 3 between the lightest and heaviest neutrino, and a θ 13 mixing angle of order 1 /N, in parametric agreement with experimental data when N goes to 3. For Random Matrix Theory, this motivates the introduction of a new type of ensemble of random matrices, the "Seesaw ensemble." Basic properties of such matrices are studied, including the eigenvalue density and the interpretation as a Coulomb gas system. Besides its mathematical interest, the Seesaw ensemble may be useful in random systems where two hierarchical scales exist.
Nonextensive random-matrix theory based on Kaniadakis entropy
Abul-Magd, A. Y.
2007-02-01
The joint eigenvalue distributions of random-matrix ensembles are derived by applying the principle maximum entropy to the Rényi, Abe and Kaniadakis entropies. While the Rényi entropy produces essentially the same matrix-element distributions as the previously obtained expression by using the Tsallis entropy, and the Abe entropy does not lead to a closed form expression, the Kaniadakis entropy leads to a new generalized form of the Wigner surmise that describes a transition of the spacing distribution from chaos to order. This expression is compared with the corresponding expression obtained by assuming Tsallis' entropy as well as the results of a previous numerical experiment.
Nonextensive random-matrix theory based on Kaniadakis entropy
Energy Technology Data Exchange (ETDEWEB)
Abul-Magd, A.Y. [Department of Mathematics, Faculty of Science, Zagazig University, Zagazig (Egypt)]. E-mail: a_y_abul_magd@hotmail.com
2007-02-12
The joint eigenvalue distributions of random-matrix ensembles are derived by applying the principle maximum entropy to the Renyi, Abe and Kaniadakis entropies. While the Renyi entropy produces essentially the same matrix-element distributions as the previously obtained expression by using the Tsallis entropy, and the Abe entropy does not lead to a closed form expression, the Kaniadakis entropy leads to a new generalized form of the Wigner surmise that describes a transition of the spacing distribution from chaos to order. This expression is compared with the corresponding expression obtained by assuming Tsallis' entropy as well as the results of a previous numerical experiment.
Surprising Pfaffian factorizations in random matrix theory with Dyson index β = 2
Kieburg, Mario
2012-03-01
In recent decades, determinants and Pfaffians were found for eigenvalue correlations of various random matrix ensembles. These structures simplify the average over a large number of ratios of characteristic polynomials to integrations over one and two characteristic polynomials only. Up to now it was thought that determinants occur for ensembles with Dyson index β = 2, whereas Pfaffians only for ensembles with β = 1, 4. We derive a non-trivial Pfaffian determinant for β = 2 random matrix ensembles which is similar to the one for β = 1, 4. Thus, it unveils a hidden universality of this structure. We also give a general relation between the orthogonal polynomials related to the determinantal structure and the skew-orthogonal polynomials corresponding to the Pfaffian. As a particular example, we consider the chiral unitary ensembles in great detail.
Fast Constrained Spectral Clustering and Cluster Ensemble with Random Projection
Directory of Open Access Journals (Sweden)
Wenfen Liu
2017-01-01
Full Text Available Constrained spectral clustering (CSC method can greatly improve the clustering accuracy with the incorporation of constraint information into spectral clustering and thus has been paid academic attention widely. In this paper, we propose a fast CSC algorithm via encoding landmark-based graph construction into a new CSC model and applying random sampling to decrease the data size after spectral embedding. Compared with the original model, the new algorithm has the similar results with the increase of its model size asymptotically; compared with the most efficient CSC algorithm known, the new algorithm runs faster and has a wider range of suitable data sets. Meanwhile, a scalable semisupervised cluster ensemble algorithm is also proposed via the combination of our fast CSC algorithm and dimensionality reduction with random projection in the process of spectral ensemble clustering. We demonstrate by presenting theoretical analysis and empirical results that the new cluster ensemble algorithm has advantages in terms of efficiency and effectiveness. Furthermore, the approximate preservation of random projection in clustering accuracy proved in the stage of consensus clustering is also suitable for the weighted k-means clustering and thus gives the theoretical guarantee to this special kind of k-means clustering where each point has its corresponding weight.
Random matrix theory in biological nuclear magnetic resonance spectroscopy.
Lacelle, S
1984-01-01
The statistical theory of energy levels or random matrix theory is presented in the context of the analysis of chemical shifts of nuclear magnetic resonance (NMR) spectra of large biological systems. Distribution functions for the spacing between nearest-neighbor energy levels are discussed for uncorrelated, correlated, and random superposition of correlated energy levels. Application of this approach to the NMR spectra of a vitamin, an antibiotic, and a protein demonstrates the state of correlation of an ensemble of energy levels that characterizes each system. The detection of coherent and dissipative structures in proteins becomes feasible with this statistical spectroscopic technique. PMID:6478032
Neutron resonance data exclude random matrix theory
Koehler, P. E.; Bečvář, F.; Krtička, M.; Guber, K. H.; Ullmann, J. L.
2013-02-01
Almost since the time it was formulated, the overwhelming consensus has been that random matrix theory (RMT) is in excellent agreement with neutron resonance data. However, over the past few years, we have obtained new neutron-width data at Oak Ridge and Los Alamos National Laboratories that are in stark disagreement with this theory. We also have reanalyzed neutron widths in the most famous data set, the nuclear data ensemble (NDE), and found that it is seriously flawed, and, when analyzed carefully, excludes RMT with high confidence. More recently, we carefully examined energy spacings for these same resonances in the NDE using the $\\Delta_{3}$ statistic. We conclude that the data can be found to either confirm or refute the theory depending on which nuclides and whether known or suspected p-wave resonances are included in the analysis, in essence confirming results of our neutron-width analysis of the NDE. We also have examined radiation widths resulting from our Oak Ridge and Los Alamos measurements, and find that in some cases they do not agree with RMT. Although these disagreements presently are not understood, they could have broad impact on basic and applied nuclear physics, from nuclear astrophysics to nuclear criticality safety.
Neutron resonance data exclude random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Koehler, P.E. [Physics Division, Oak Ridge National Laboratory, MailStop 6356, Oak Ridge, Tennessee 37831 (United States); Becvar, F.; Krticka, M. [Charles University, Faculty of Mathematics and Physics, 180 00 Prague 8 (Czech Republic); Guber, K.H. [Reactor and Nuclear Systems Division, Oak Ridge National Laboratory, Mail Stop 6356, Oak Ridge, Tennessee 37831 (United States); Ullmann, J.L. [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2013-02-15
Almost since the time it was formulated, the overwhelming consensus has been that random matrix theory (RMT) is in excellent agreement with neutron resonance data. However, over the past few years, we have obtained new neutron-width data at Oak Ridge and Los Alamos National Laboratories that are in stark disagreement with this theory. We also have reanalyzed neutron widths in the most famous data set, the nuclear data ensemble (NDE), and found that it is seriously flawed, and, when analyzed carefully, excludes RMT with high confidence. More recently, we carefully examined energy spacings for these same resonances in the NDE using the {Delta}{sub 3} statistic. We conclude that the data can be found to either confirm or refute the theory depending on which nuclides and whether known or suspected p-wave resonances are included in the analysis, in essence confirming results of our neutron-width analysis of the NDE. We also have examined radiation widths resulting from our Oak Ridge and Los Alamos measurements, and find that in some cases they do not agree with RMT. Although these disagreements presently are not understood, they could have broad impact on basic and applied nuclear physics, from nuclear astrophysics to nuclear criticality safety. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Skew-orthogonal polynomials and random matrix theory
Ghosh, Saugata
2009-01-01
Orthogonal polynomials satisfy a three-term recursion relation irrespective of the weight function with respect to which they are defined. This gives a simple formula for the kernel function, known in the literature as the Christoffel-Darboux sum. The availability of asymptotic results of orthogonal polynomials and the simple structure of the Christoffel-Darboux sum make the study of unitary ensembles of random matrices relatively straightforward. In this book, the author develops the theory of skew-orthogonal polynomials and obtains recursion relations which, unlike orthogonal polynomials, depend on weight functions. After deriving reduced expressions, called the generalized Christoffel-Darboux formulas (GCD), he obtains universal correlation functions and non-universal level densities for a wide class of random matrix ensembles using the GCD. The author also shows that once questions about higher order effects are considered (questions that are relevant in different branches of physics and mathematics) the ...
Random matrix ensembles with random interactions: Results for ...
Indian Academy of Sciences (India)
4); Wigner–Racah algebra; covariances; chaos. ... these covariances increase in magnitude as we go from EGUE(2) to EGUE(2)-s to EGUE(2)-(4) implying that symmetries may be responsible for chaos in finite interacting quantum systems.
Directory of Open Access Journals (Sweden)
Elias D. Nino-Ruiz
2017-07-01
Full Text Available In this paper, a matrix-free posterior ensemble Kalman filter implementation based on a modified Cholesky decomposition is proposed. The method works as follows: the precision matrix of the background error distribution is estimated based on a modified Cholesky decomposition. The resulting estimator can be expressed in terms of Cholesky factors which can be updated based on a series of rank-one matrices in order to approximate the precision matrix of the analysis distribution. By using this matrix, the posterior ensemble can be built by either sampling from the posterior distribution or using synthetic observations. Furthermore, the computational effort of the proposed method is linear with regard to the model dimension and the number of observed components from the model domain. Experimental tests are performed making use of the Lorenz-96 model. The results reveal that, the accuracy of the proposed implementation in terms of root-mean-square-error is similar, and in some cases better, to that of a well-known ensemble Kalman filter (EnKF implementation: the local ensemble transform Kalman filter. In addition, the results are comparable to those obtained by the EnKF with large ensemble sizes.
Random-matrix-theory approach to mesoscopic fluctuations of heat current
Schmidt, Martin; Kottos, Tsampikos; Shapiro, Boris
2013-08-01
We consider an ensemble of fully connected networks of N oscillators coupled harmonically with random springs and show, using random-matrix-theory considerations, that both the average phonon heat current and its variance are scale invariant and take universal values in the large N limit. These anomalous mesoscopic fluctuations is the hallmark of strong correlations between normal modes.
Distribution of local density of states in superstatistical random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Abul-Magd, A.Y. [Department of Mathematics, Faculty of Science, Zagazig University, Zagazig (Egypt)]. E-mail: a_y_abul_magd@hotmail.com
2007-07-02
We expose an interesting connection between the distribution of local spectral density of states arising in the theory of disordered systems and the notion of superstatistics introduced by Beck and Cohen and recently incorporated in random matrix theory. The latter represents the matrix-element joint probability density function as an average of the corresponding quantity in the standard random-matrix theory over a distribution of level densities. We show that this distribution is in reasonable agreement with the numerical calculation for a disordered wire, which suggests to use the results of theory of disordered conductors in estimating the parameter distribution of the superstatistical random-matrix ensemble.
Diffusion method in random matrix theory
Grela, Jacek
2016-01-01
We introduce a calculational tool useful in computing ratios and products of characteristic polynomials averaged over Gaussian measures with an external source. The method is based on Dyson’s Brownian motion and Grassmann/complex integration formulas for determinants. The resulting formulas are exact for finite matrix size N and form integral representations convenient for large N asymptotics. Quantities obtained by the method are interpreted as averages over standard matrix models. We provide several explicit and novel calculations with special emphasis on the β =2 Girko-Ginibre ensembles.
Random matrix theory, interacting particle systems and integrable systems
Forrester, Peter
2014-01-01
Random matrix theory is at the intersection of linear algebra, probability theory and integrable systems, and has a wide range of applications in physics, engineering, multivariate statistics and beyond. This volume is based on a Fall 2010 MSRI program which generated the solution of long-standing questions on universalities of Wigner matrices and beta-ensembles and opened new research directions especially in relation to the KPZ universality class of interacting particle systems and low-rank perturbations. The book contains review articles and research contributions on all these topics, in addition to other core aspects of random matrix theory such as integrability and free probability theory. It will give both established and new researchers insights into the most recent advances in the field and the connections among many subfields.
Density Functional Approach and Random Matrix Theory in Proteogenesis
Yamanaka, Masanori
2017-02-01
We study the energy-level statistics of amino acids by random matrix theory. The molecular orbital and the Kohn-Sham orbital energies are calculated using ab initio and density-functional formalisms for 20 different amino acids. To generate statistical data, we performed a multipoint calculation on 10000 molecular structures produced via a molecular dynamics simulation. For the valence orbitals, the energy-level statistics exhibit repulsion, but the universality in the random matrix cannot be determined. For the unoccupied orbitals, the energy-level statistics indicate an intermediate distribution between the Gaussian orthogonal ensemble and the semi-Poisson statistics for all 20 different amino acids. These amino acids are considered to be in a type of critical state.
Finitely connected vector spin systems with random matrix interactions
Energy Technology Data Exchange (ETDEWEB)
Coolen, A C C [Department of Mathematics, King' s College London, The Strand, London WC2R 2LS (United Kingdom); Skantzos, N S [Institute for Theoretical Physics, Celestijnenlaan 200D, Katholieke Universiteit Leuven, B-3001 (Belgium); Castillo, I Perez [Rudolf Peierls Center for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP (United Kingdom); Vicente, C J Perez [Departament de FIsica Fonamental, Facultat de FIsica, Universitat de Barcelona, 08028 Barcelona (Spain); Hatchett, J P L [Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Hirosawa 2-1, Wako-Shi, Saitama 351-0198 (Japan); Wemmenhove, B [Department of Medical Physics and Biophysics, Radboud University Nijmegen, Geert Grooteplein 21, NL 6525 EZ Nijmegen (Netherlands); Nikoletopoulos, T [Department of Mathematics, King' s College London, The Strand, London WC2R 2LS (United Kingdom)
2005-09-30
We use finite connectivity equilibrium replica theory to solve models of finitely connected unit-length vectorial spins, with random pair-interactions which are of the orthogonal matrix type. Finitely connected spin models, although still of a mean-field nature, can be regarded as a convenient level of description in between fully connected and finite-dimensional ones. Since the spins are continuous and the connectivity c remains finite in the thermodynamic limit, the replica-symmetric order parameter is a functional. The general theory is developed for arbitrary values of the dimension d of the spins, and arbitrary choices of the ensemble of random orthogonal matrices. We calculate phase diagrams and the values of moments of the order parameter explicitly for d = 2 (finitely connected XY spins with random chiral interactions) and for d = 3 (finitely connected classical Heisenberg spins with random chiral interactions). Numerical simulations are shown to support our predictions quite satisfactorily.
U(1) staggered Dirac operator and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Berg, Bernd A.; Markum, Harald; Pullirsch, Rainer; Wettig, Tilo
2000-03-01
We investigate the spectrum of the staggered Dirac operator in 4d quenched U(1) lattice gauge theory and its relationship to random matrix theory. In the confined as well as in the Coulomb phase the nearest-neighbor spacing distribution of the unfolded eigenvalues is well described by the chiral unitary ensemble. The same is true for the distribution of the smallest eigenvalue and the microscopic spectral density in the confined phase. The physical origin of the chiral condensate in this phase deserves further study.
Application of random matrix theory to biological networks
Energy Technology Data Exchange (ETDEWEB)
Luo Feng [Department of Computer Science, Clemson University, 100 McAdams Hall, Clemson, SC 29634 (United States); Department of Pathology, U.T. Southwestern Medical Center, 5323 Harry Hines Blvd. Dallas, TX 75390-9072 (United States); Zhong Jianxin [Department of Physics, Xiangtan University, Hunan 411105 (China) and Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States)]. E-mail: zhongjn@ornl.gov; Yang Yunfeng [Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Scheuermann, Richard H. [Department of Pathology, U.T. Southwestern Medical Center, 5323 Harry Hines Blvd. Dallas, TX 75390-9072 (United States); Zhou Jizhong [Department of Botany and Microbiology, University of Oklahoma, Norman, OK 73019 (United States) and Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States)]. E-mail: zhouj@ornl.gov
2006-09-25
We show that spectral fluctuation of interaction matrices of a yeast protein-protein interaction network and a yeast metabolic network follows the description of the Gaussian orthogonal ensemble (GOE) of random matrix theory (RMT). Furthermore, we demonstrate that while the global biological networks evaluated belong to GOE, removal of interactions between constituents transitions the networks to systems of isolated modules described by the Poisson distribution. Our results indicate that although biological networks are very different from other complex systems at the molecular level, they display the same statistical properties at network scale. The transition point provides a new objective approach for the identification of functional modules.
Spectral rigidity of vehicular streams (random matrix theory approach)
Energy Technology Data Exchange (ETDEWEB)
Krbalek, Milan [Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Prague (Czech Republic); Seba, Petr [Doppler Institute for Mathematical Physics and Applied Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Prague (Czech Republic)
2009-08-28
Using a method originally developed for the random matrix theory, we derive an approximate mathematical formula for the number variance {delta}{sub N}(L) describing the rigidity of particle ensembles with a power-law repulsion. The resulting relation is compared with the relevant statistics of the single-vehicle data measured on the Dutch freeway A9. The detected value of the inverse temperature {beta}, which can be identified as a coefficient of the mental strain of the car drivers, is then discussed in detail with the relation to the traffic density {rho} and flow J.
Importance of randomness in biological networks: A random matrix ...
Indian Academy of Sciences (India)
2015-01-29
Jan 29, 2015 ... We show that in spite of huge differences these interaction networks, representing real-world systems, posses from random matrix models, the spectral properties of the underlying matrices of these networks follow random matrix theory bringing them into the same universality class. We further demonstrate ...
Universality in Chiral Random Matrix Theory at {beta} = 1 and {beta} = 4
Energy Technology Data Exchange (ETDEWEB)
Sener, M.K.; Verbaarschot, J.J. [Department of Physics and Astronomy, SUNY, Stony Brook, New York 11794 (United States)
1998-07-01
In this paper the kernel for the spectral correlation functions of invariant chiral random matrix ensembles with real ({beta}=1 ) and quaternion real ({beta}=4 ) matrix elements is expressed in terms of the kernel of the corresponding complex Hermitian random matrix ensembles ({beta}=2 ). Such identities are exact in case of a Gaussian probability distribution and, under certain smoothness assumptions, they are shown to be valid asymptotically for an arbitrary finite polynomial potential. They are proved by means of a construction proposed by Brezin and Neuberger. Universal behavior of the eigenvalues close to zero for all three chiral ensembles then follows from microscopic universality for {beta}=2 as shown by Akemann, Damgaard, Magnea, and Nishigaki. {copyright} {ital 1998} {ital The American Physical Society}
Random matrix theory and the sixth Painleve equation
Energy Technology Data Exchange (ETDEWEB)
Forrester, P J; Witte, N S [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia)
2006-09-29
A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realized by matrices with Gaussian entries leads to statistical quantities related to the eigenspectrum, such as the distribution of the largest eigenvalue, which can be expressed as multidimensional integrals or equivalently as determinants. These distributions are well known to be {tau}-functions for Painleve systems, allowing for the former to be characterized as the solution of certain nonlinear equations. We consider the random matrix ensembles for which the nonlinear equation is the {sigma} form of P{sub VI}. Known results are reviewed, as is their implication by way of series expansions for the distributions. New results are given for the boundary conditions in the neighbourhood of the fixed singularities at t = 0, 1, {infinity} of {sigma}P{sub VI} displayed by a generalization of the generating function for the distributions. The structure of these expansions is related to Jimbo's general expansions for the {tau}-function of {sigma}P{sub VI} in the neighbourhood of its fixed singularities, and this theory is itself put in its context of the linear isomonodromy problem relating to P{sub VI}.
Typicality in random matrix product states
Garnerone, Silvano; de Oliveira, Thiago R.; Zanardi, Paolo
2010-03-01
Recent results suggest that the use of ensembles in statistical mechanics may not be necessary for isolated systems, since typically the states of the Hilbert space would have properties similar to those of the ensemble. Nevertheless, it is often argued that most of the states of the Hilbert space are nonphysical and not good descriptions of realistic systems. Therefore, to better understand the actual power of typicality it is important to ask if it is also a property of a set of physically relevant states. Here we address this issue, studying if and how typicality emerges in the set of matrix product states. We show analytically that typicality occurs for the expectation value of subsystems’ observables when the rank of the matrix product state scales polynomially with the size of the system with a power greater than 2. We illustrate this result numerically and present some indications that typicality may appear already for a linear scaling of the rank of the matrix product state.
Non-hermitian random matrix theory: Method of hermitian reduction
Energy Technology Data Exchange (ETDEWEB)
Feinberg, J. [California Univ., Santa Barbara, CA (United States). Inst. for Theoretical Physics; Zee, A. [California Univ., Santa Barbara, CA (United States). Inst. for Theoretical Physics]|[Institute for Advanced Study, Olden Lane, Princeton, NJ 08540 (United States)
1997-11-03
We consider random non-hermitian matrices in the large-N limit. The power of analytic function theory cannot be brought to bear directly to analyze non-hermitian random matrices, in contrast to hermitian random matrices. To overcome this difficulty, we show that associated to each ensemble of non-hermitian matrices there is an auxiliary ensemble of random hermitian matrices which can be analyzed by the usual methods. We then extract the Green function and the density of eigenvalues of the non-hermitian ensemble from those of the auxiliary ensemble. We apply this ``method of hermitization`` to several examples, and discuss a number of related issues. (orig.). 25 refs.
Non-extensive random matrix theory--a bridge connecting chaotic and regular dynamics
Energy Technology Data Exchange (ETDEWEB)
Abul-Magd, A.Y. [Faculty of Science, Zagazig University, Zagazig (Egypt)]. E-mail: a_y_abul_magd@hotmail.com
2004-11-29
We consider a possible generalization of the random matrix theory, which involves the maximization of Tsallis' q-parametrized entropy. We discuss the dependence of the spacing distribution on q using a non-extensive generalization of Wigner's surmises for ensembles belonging to the orthogonal, unitary and symplectic symmetry universal classes.
Random matrix techniques in quantum information theory
Collins, Benoît; Nechita, Ion
2016-01-01
The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.
Random matrix techniques in quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Collins, Benoît, E-mail: collins@math.kyoto-u.ac.jp [Department of Mathematics, Kyoto University, Kyoto 606-8502 (Japan); Département de Mathématique et Statistique, Université d’Ottawa, 585 King Edward, Ottawa, Ontario K1N6N5 (Canada); CNRS, Lyon (France); Nechita, Ion, E-mail: nechita@irsamc.ups-tlse.fr [Zentrum Mathematik, M5, Technische Universität München, Boltzmannstrasse 3, 85748 Garching (Germany); Laboratoire de Physique Théorique, CNRS, IRSAMC, Université de Toulouse, UPS, F-31062 Toulouse (France)
2016-01-15
The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.
Effective Lagrangians and chiral random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Halasz, M.A.; Verbaarschot, J.J.M. [Department of Physics, State University of New York, Stony Brook, New York 11794 (United States)
1995-08-15
Recently, sum rules were derived for the inverse eigenvalues of the Dirac operator. They were obtained in two different ways: (i) starting from the low-energy effective Lagrangian and (ii) starting from a random matrix theory with the symmetries of the Dirac operator. This suggests that the effective theory can be obtained directly from the random matrix theory. Previously, this was shown for three or more colors with fundamental fermions. In this paper we construct the effective theory from a random matrix theory for two colors in the fundamental representation and for an arbitrary number of colors in the adjoint representation. We construct a fermionic partition function for Majorana fermions in Euclidean spacetime. Their reality condition is formulated in terms of complex conjugation of the second kind.
Random matrix theory with an external source
Brézin, Edouard
2016-01-01
This is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. The main interest is to use this freedom to compute various topological invariants for surfaces such as the intersection numbers for curves drawn on a surface of given genus with marked points, Euler characteristics, and the Gromov–Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries.
Nonequilibrium random matrix theory: Transition probabilities
Pedro, Francisco Gil; Westphal, Alexander
2017-03-01
In this paper we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large N limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.
Quark Spectra, Topology, and Random Matrix Theory
Energy Technology Data Exchange (ETDEWEB)
Edwards, R.G.; Heller, U.M. [SCRI, Florida State University, Tallahassee, Florida 32306-4130 (United States); Kiskis, J. [Department of Physics, University of California, Davis, California 95616 (United States); Narayanan, R. [Department of Physics, Building 510A, Brookhaven National Laboratory, P.O. Box 5000, Upton, New York 11973 (United States)
1999-05-01
Quark spectra in QCD are linked to fundamental properties of the theory including the identification of pions as the Goldstone bosons of spontaneously broken chiral symmetry. The lattice overlap Dirac operator provides a nonperturbative, ultraviolet-regularized description of quarks with the correct chiral symmetry. Properties of the spectrum of this operator and their relation to random matrix theory are studied here. In particular, the predictions from chiral random matrix theory in topologically nontrivial gauge field sectors are tested for the first time. {copyright} {ital 1999} {ital The American Physical Society}
An ensemble method with hybrid features to identify extracellular matrix proteins.
Yang, Runtao; Zhang, Chengjin; Gao, Rui; Zhang, Lina
2015-01-01
The extracellular matrix (ECM) is a dynamic composite of secreted proteins that play important roles in numerous biological processes such as tissue morphogenesis, differentiation and homeostasis. Furthermore, various diseases are caused by the dysfunction of ECM proteins. Therefore, identifying these important ECM proteins may assist in understanding related biological processes and drug development. In view of the serious imbalance in the training dataset, a Random Forest-based ensemble method with hybrid features is developed in this paper to identify ECM proteins. Hybrid features are employed by incorporating sequence composition, physicochemical properties, evolutionary and structural information. The Information Gain Ratio and Incremental Feature Selection (IGR-IFS) methods are adopted to select the optimal features. Finally, the resulting predictor termed IECMP (Identify ECM Proteins) achieves an balanced accuracy of 86.4% using the 10-fold cross-validation on the training dataset, which is much higher than results obtained by other methods (ECMPRED: 71.0%, ECMPP: 77.8%). Moreover, when tested on a common independent dataset, our method also achieves significantly improved performance over ECMPP and ECMPRED. These results indicate that IECMP is an effective method for ECM protein prediction, which has a more balanced prediction capability for positive and negative samples. It is anticipated that the proposed method will provide significant information to fully decipher the molecular mechanisms of ECM-related biological processes and discover candidate drug targets. For public access, we develop a user-friendly web server for ECM protein identification that is freely accessible at http://iecmp.weka.cc.
Random-matrix theory of quantum transport
Energy Technology Data Exchange (ETDEWEB)
Beenakker, C.W. [Instituut-Lorentz, University of Leiden, 2300 RA Leiden, (The Netherlands)
1997-07-01
This is a review of the statistical properties of the scattering matrix of a mesoscopic system. Two geometries are contrasted: A quantum dot and a disordered wire. The quantum dot is a confined region with a chaotic classical dynamics, which is coupled to two electron reservoirs via point contacts. The disordered wire also connects two reservoirs, either directly or via a point contact or tunnel barrier. One of the two reservoirs may be in the superconducting state, in which case conduction involves Andreev reflection at the interface with the superconductor. In the case of the quantum dot, the distribution of the scattering matrix is given by either Dyson{close_quote}s circular ensemble for ballistic point contacts or the Poisson kernel for point contacts containing a tunnel barrier. In the case of the disordered wire, the distribution of the scattering matrix is obtained from the Dorokhov-Mello-Pereyra-Kumar equation, which is a one-dimensional scaling equation. The equivalence is discussed with the nonlinear {sigma} model, which is a supersymmetric field theory of localization. The distribution of scattering matrices is applied to a variety of physical phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction. {copyright} {ital 1997} {ital The American Physical Society}
NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES
Directory of Open Access Journals (Sweden)
Sachin Kumar
2017-12-01
Full Text Available We investigate spacing statistics for ensembles of various real random matrices where the matrix-elements have various Probability Distribution Function (PDF: f(x including Gaussian. For two modifications of 2 × 2 matrices with various PDFs, we derive the spacing distributions p(s of adjacent energy eigenvalues. Nevertheless, they show the linear level repulsion near s = 0 as αs where α depends on the choice of the PDF. More interestingly when f(x = xe−x2 (f(0 = 0, we get cubic level repulsion near s = 0: p(s ~ s3e−s2.We also derive the distribution of eigenvalues D(ε for these matrices.
Social patterns revealed through random matrix theory
Sarkar, Camellia; Jalan, Sarika
2014-11-01
Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real-world systems. Using random matrix analysis of a weighted social network, we demonstrate the profound impact of weights in interactions on emerging structural properties. The analysis reveals that randomness existing in particular time frame affects the decisions of individuals rendering them more freedom of choice in situations of financial security. While the structural organization of networks remains the same throughout all datasets, random matrix theory provides insight into the interaction pattern of individuals of the society in situations of crisis. It has also been contemplated that individual accountability in terms of weighted interactions remains as a key to success unless segregation of tasks comes into play.
Random matrix theory for transition strengths: Applications and open questions
Kota, V. K. B.
2017-12-01
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different) and so on. Using embedded ensembles (EE), there are efforts to derive a good statistical theory for transition strengths. With m fermions (or bosons) in N mean-field single particle levels and interacting via two-body forces, we have with GOE embedding, the so called EGOE(1+2). Now, the transition strength density (transition strength multiplied by the density of states at the initial and final energies) is a convolution of the density generated by the mean-field one-body part with a bivariate spreading function due to the two-body interaction. Using the embedding U(N) algebra, it is established, for a variety of transition operators, that the spreading function, for sufficiently strong interactions, is close to a bivariate Gaussian. Also, as the interaction strength increases, the spreading function exhibits a transition from bivariate Breit-Wigner to bivariate Gaussian form. In appropriate limits, this EE theory reduces to the polynomial theory of Draayer, French and Wong on one hand and to the theory due to Flambaum and Izrailev for one-body transition operators on the other. Using spin-cutoff factors for projecting angular momentum, the theory is applied to nuclear matrix elements for neutrinoless double beta decay (NDBD). In this paper we will describe: (i) various developments in the EE theory for transition strengths; (ii) results for nuclear matrix elements for 130Te and 136Xe NDBD; (iii) important open questions in the current form of the EE theory.
Riemannian symmetric superspaces and their origin in random-matrix theory
Energy Technology Data Exchange (ETDEWEB)
Zirnbauer, M.R. [Institute for Theoretical Physics, University of California at Santa Barbara, Santa Barbara, California 93106 (United States)
1996-10-01
Gaussian random-matrix ensembles defined over the tangent spaces of the large families of Cartan{close_quote}s symmetric spaces are considered. Such ensembles play a central role in mesoscopic physics, as they describe the universal ergodic limit of disordered and chaotic single-particle systems. The generating function for the spectral correlations of each ensemble is reduced to an integral over a Riemannian symmetric superspace in the limit of large matrix dimension. Such a space is defined as a pair ({ital G}/{ital H},{ital M}{sub {ital r}}), where {ital G}/{ital H} is a complex-analytic graded manifold homogeneous with respect to the action of a complex Lie supergroup {ital G}, and {ital M}{sub {ital r}} is a maximal Riemannian submanifold of the support of {ital G}/{ital H}. {copyright} {ital 1996 American Institute of Physics.}
Using histograms to introduce randomization in the generation of ensembles of decision trees
Kamath, Chandrika; Cantu-Paz, Erick; Littau, David
2005-02-22
A system for decision tree ensembles that includes a module to read the data, a module to create a histogram, a module to evaluate a potential split according to some criterion using the histogram, a module to select a split point randomly in an interval around the best split, a module to split the data, and a module to combine multiple decision trees in ensembles. The decision tree method includes the steps of reading the data; creating a histogram; evaluating a potential split according to some criterion using the histogram, selecting a split point randomly in an interval around the best split, splitting the data, and combining multiple decision trees in ensembles.
Random Matrix Theory and Elliptic Curves
2014-11-24
lecture on random matrix models for elliptic curves at the combined meeting of the Australian and New Zealand mathematical societies Melbourne, Australia...organizer). Associated with the Chichely meeting will be a special volume of the Philosophical Transactions of the Royal Society (the world’s oldest...Distribution A: Approved for public release; distribution is unlimited. 5 USE OF SUPPORT 8 • JPK was awarded a Royal Society Wolfson Research Merit
Pseudo-Hermitian random matrix theory
Srivastava, S. C. L.; Jain, S. R.
2013-02-01
Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present applications to problems in statistical mechanics where new results have become possible. We have found it important to mention the precise directions where advances could be made if further results become available.
Pseudo-Hermitian random matrix theory
Srivastava, Shashi C. L.; Jain, S. R.
2013-01-01
Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present applications to problems in statistical mechanics where new results have become possible. We have found it important to mention the precise directions where advances could be made if further results become available.
Overlap Dirac operator, eigenvalues and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Edwards, Robert G.; Heller, Urs M.; Kiskis, Joe; Narayanan, Rajamani
2000-03-01
The properties of the spectrum of the overlap Dirac operator and their relation to random matrix theory are studied. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are tested.
Durner, Maximilian; Márton, Zoltán.; Hillenbrand, Ulrich; Ali, Haider; Kleinsteuber, Martin
2017-03-01
In this work, a new ensemble method for the task of category recognition in different environments is presented. The focus is on service robotic perception in an open environment, where the robot's task is to recognize previously unseen objects of predefined categories, based on training on a public dataset. We propose an ensemble learning approach to be able to flexibly combine complementary sources of information (different state-of-the-art descriptors computed on color and depth images), based on a Markov Random Field (MRF). By exploiting its specific characteristics, the MRF ensemble method can also be executed as a Dynamic Classifier Selection (DCS) system. In the experiments, the committee- and topology-dependent performance boost of our ensemble is shown. Despite reduced computational costs and using less information, our strategy performs on the same level as common ensemble approaches. Finally, the impact of large differences between datasets is analyzed.
Random matrix approach to categorical data analysis
Patil, Aashay; Santhanam, M. S.
2015-09-01
Correlation and similarity measures are widely used in all the areas of sciences and social sciences. Often the variables are not numbers but are instead qualitative descriptors called categorical data. We define and study similarity matrix, as a measure of similarity, for the case of categorical data. This is of interest due to a deluge of categorical data, such as movie ratings, top-10 rankings, and data from social media, in the public domain that require analysis. We show that the statistical properties of the spectra of similarity matrices, constructed from categorical data, follow random matrix predictions with the dominant eigenvalue being an exception. We demonstrate this approach by applying it to the data for Indian general elections and sea level pressures in the North Atlantic ocean.
The intersection numbers of the p-spin curves from random matrix theory
Brézin, E.; Hikami, S.
2013-02-01
The intersection numbers of p-spin curves are computed through correlation functions of Gaussian ensembles of random matrices in an external matrix source. The p-dependence of intersection numbers is determined as polynomial in p; the large p behavior is also considered. The analytic continuation of intersection numbers to negative values of p is discussed in relation to SL(2,R)/U(1) black hole sigma model.
Application of random matrix theory to microarray data for discovering functional gene modules
Energy Technology Data Exchange (ETDEWEB)
Luo, F. [Xiangtan University, Xiangtan Hunan, China; Zhong, Jianxin [ORNL; Yang, Y. F. [unknown; Zhou, Jizhong [ORNL
2006-03-01
We show that spectral fluctuation of coexpression correlation matrices of yeast gene microarray profiles follows the description of the Gaussian orthogonal ensemble (GOE) of the random matrix theory (RMT) and removal of small values of the correlation coefficients results in a transition from the GOE statistics to the Poisson statistics of the RMT. This transition is directly related to the structural change of the gene expression network from a global network to a network of isolated modules.
Heavy-tailed chiral random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Kanazawa, Takuya [iTHES Research Group and Quantum Hadron Physics Laboratory, RIKEN,Wako, Saitama, 351-0198 (Japan)
2016-05-27
We study an unconventional chiral random matrix model with a heavy-tailed probabilistic weight. The model is shown to exhibit chiral symmetry breaking with no bilinear condensate, in analogy to the Stern phase of QCD. We solve the model analytically and obtain the microscopic spectral density and the smallest eigenvalue distribution for an arbitrary number of flavors and arbitrary quark masses. Exotic behaviors such as non-decoupling of heavy flavors and a power-law tail of the smallest eigenvalue distribution are illustrated.
Open quantum systems and random matrix theory
Mulhall, Declan
2015-01-01
A simple model for open quantum systems is analyzed with random matrix theory. The system is coupled to the continuum in a minimal way. In this paper the effect on the level statistics of opening the system is seen. In particular the Δ3(L ) statistic, the width distribution and the level spacing are examined as a function of the strength of this coupling. The emergence of a super-radiant transition is observed. The level spacing and Δ3(L ) statistics exhibit the signatures of missed levels or intruder levels as the super-radiant state is formed.
Heavy-tailed chiral random matrix theory
Kanazawa, Takuya
2016-05-01
We study an unconventional chiral random matrix model with a heavy-tailed probabilistic weight. The model is shown to exhibit chiral symmetry breaking with no bilinear condensate, in analogy to the Stern phase of QCD. We solve the model analytically and obtain the microscopic spectral density and the smallest eigenvalue distribution for an arbitrary number of flavors and arbitrary quark masses. Exotic behaviors such as non-decoupling of heavy flavors and a power-law tail of the smallest eigenvalue distribution are illustrated.
Pseudo-Hermitian random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Srivastava, S.C.L. [RIBFG, Variable Energy Cyclotron Centre, 1/AF Bidhan nagar, Kolkata-700 064 (India); Jain, S.R. [NPD, Bhabha Atomic Research Centre, Mumbai-400 085 (India)
2013-02-15
Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present applications to problems in statistical mechanics where new results have become possible. We have found it important to mention the precise directions where advances could be made if further results become available. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Random Coding Bounds for DNA Codes Based on Fibonacci Ensembles of DNA Sequences
2008-07-01
Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188) Washington, DC...COVERED (From - To) 6 Jul 08 – 11 Jul 08 4. TITLE AND SUBTITLE RANDOM CODING BOUNDS FOR DNA CODES BASED ON FIBONACCI ENSEMBLES OF DNA SEQUENCES...sequences which are generalizations of the Fibonacci sequences. 15. SUBJECT TERMS DNA Codes, Fibonacci Ensembles, DNA Computing, Code Optimization 16
Yamanaka, Masanori
2013-08-01
We apply the random matrix theory to analyze the molecular dynamics simulation of macromolecules, such as proteins. The eigensystem of the cross-correlation matrix for the time series of the atomic coordinates is analyzed. We study a data set with seven different sampling intervals to observe the characteristic motion at each time scale. In all cases, the unfolded eigenvalue spacings are in agreement with the predictions of random matrix theory. In the short-time scale, the cross-correlation matrix has the universal properties of the Gaussian orthogonal ensemble. The eigenvalue distribution and inverse participation ratio have a crossover behavior between the universal and nonuniversal classes, which is distinct from the known results such as the financial time series. Analyzing the inverse participation ratio, we extract the correlated cluster of atoms and decompose it to subclusters.
Action correlations and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Smilansky, Uzy; Verdene, Basile [Department of Physics of Complex Systems, The Weizmann Institute of Science, Rehovot 76100 (Israel)
2003-03-28
The correlations in the spectra of quantum systems are intimately related to correlations which are of genuine classical origin, and which appear in the spectra of actions of the classical periodic orbits of the corresponding classical systems. We review this duality and the semiclassical theory which brings it about. The conjecture that the quantum spectral statistics are described in terms of random matrix theory, leads to the proposition that the classical two-point correlation function is also given in terms of a universal function. We study in detail the spectrum of actions of the Baker map, and use it to illustrate the steps needed to reveal the classical correlations, their origin and their relation to symbolic dynamics00.
Quantum graphs and random-matrix theory
Pluhař, Z.; Weidenmüller, H. A.
2015-07-01
For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas-Giannoni-Schmit (BGS) conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that the generating function for every (P,Q) correlation function for both closed and open graphs coincides with the corresponding expression of random-matrix theory. We show that the classical Perron-Frobenius operator is bistochastic and possesses a single eigenvalue +1. In the quantum case that implies the existence of a zero (or massless) mode of the effective action. That mode causes universal fluctuation properties. Avoiding the saddle-point approximation we show that for graphs that are classically mixing (i.e. for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap) and that do not carry a special class of bound states, the zero mode dominates in the limit of infinite graph size.
A random matrix approach to language acquisition
Nicolaidis, A.; Kosmidis, Kosmas; Argyrakis, Panos
2009-12-01
Since language is tied to cognition, we expect the linguistic structures to reflect patterns that we encounter in nature and are analyzed by physics. Within this realm we investigate the process of lexicon acquisition, using analytical and tractable methods developed within physics. A lexicon is a mapping between sounds and referents of the perceived world. This mapping is represented by a matrix and the linguistic interaction among individuals is described by a random matrix model. There are two essential parameters in our approach. The strength of the linguistic interaction β, which is considered as a genetically determined ability, and the number N of sounds employed (the lexicon size). Our model of linguistic interaction is analytically studied using methods of statistical physics and simulated by Monte Carlo techniques. The analysis reveals an intricate relationship between the innate propensity for language acquisition β and the lexicon size N, N~exp(β). Thus a small increase of the genetically determined β may lead to an incredible lexical explosion. Our approximate scheme offers an explanation for the biological affinity of different species and their simultaneous linguistic disparity.
Raney Distributions and Random Matrix Theory
Forrester, Peter J.; Liu, Dang-Zheng
2015-03-01
Recent works have shown that the family of probability distributions with moments given by the Fuss-Catalan numbers permit a simple parameterized form for their density. We extend this result to the Raney distribution which by definition has its moments given by a generalization of the Fuss-Catalan numbers. Such computations begin with an algebraic equation satisfied by the Stieltjes transform, which we show can be derived from the linear differential equation satisfied by the characteristic polynomial of random matrix realizations of the Raney distribution. For the Fuss-Catalan distribution, an equilibrium problem characterizing the density is identified. The Stieltjes transform for the limiting spectral density of the singular values squared of the matrix product formed from inverse standard Gaussian matrices, and standard Gaussian matrices, is shown to satisfy a variant of the algebraic equation relating to the Raney distribution. Supported on , we show that it too permits a simple functional form upon the introduction of an appropriate choice of parameterization. As an application, the leading asymptotic form of the density as the endpoints of the support are approached is computed, and is shown to have some universal features.
Improving the ensemble optimization method through covariance matrix adaptation (CMA-EnOpt)
Fonseca, R.M.; Leeuwenburgh, O.; Hof, P.M.J. van den; Jansen, J.D.
2013-01-01
Ensemble Optimization (EnOpt) is a rapidly emerging method for reservoir model based production optimization. EnOpt uses an ensemble of controls to approximate the gradient of the objective function with respect to the controls. Current implementations of EnOpt use a Gaussian ensemble with a
Universality in random matrix theory and chiral symmetry breaking in QCD
Energy Technology Data Exchange (ETDEWEB)
Akemann, G.
2000-05-01
In this work we review the topic of random matrix model universality with particular stress on its application to the study of chiral symmetry breaking in QCD. We highlight the role of microscopic and macroscopic matrix model correlation functions played in the description of the deep infrared eigenvalue spectrum of the Dirac operator. The universal microscopic correlation functions are presented for all three chiral symmetry breaking patterns, and the corresponding random matrix universality proofs are given for massless and massive fermions in a unified way. These analytic results have been widely confirmed from QCD lattice data and we present a comparison with the most recent analytic calculations describing data for dynamical SU(2) staggered fermions. The microscopic matrix model results are then re-expressed in terms of the finite-volume partition functions of Leutwyler and Smilga, where some of these expressions have been recently obtained using field theory only. The macroscopic random matrix universality is reviewed for the most simplest examples of bosonic and supersymmetric models. We also give an example for a non-universal deformation of a random matrix model - the restricted trace ensemble. (orig.)
Random matrix theory and three-dimensional QCD
Energy Technology Data Exchange (ETDEWEB)
Verbaarschot, J.J.M.; Zahed, I. (Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794 (United States))
1994-10-24
We suggest that the spectral properties near zero virtuality of three-dimensional QCD follow from a Hermitian random matrix model. The exact spectral density is derived for this family of random matrix models for both even and odd number of fermions. New sum rules for the inverse powers of the eigenvalues of the Dirac operator are obtained. The issue of anomalies in random matrix theories is discussed.
Construction of random perfect phylogeny matrix
Directory of Open Access Journals (Sweden)
Mehdi Sadeghi
2010-11-01
Full Text Available Mehdi Sadeghi1,2, Hamid Pezeshk4, Changiz Eslahchi3,5, Sara Ahmadian6, Sepideh Mah Abadi61National Institute of Genetic Engineering and Biotechnology, Tehran, Iran; 2School of Computer Science, 3School of Mathematics, Institute for Research in Fundamental Sciences (IPM, Tehran, Iran; 4School of Mathematics, Statistics and Computer Sciences, Center of Excellence in Biomathematics, College of Science, University of Tehran, Tehran, Iran; 5Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran; 6Department of Computer Engineering, Sharif University of Technology, Tehran, IranPurpose: Interest in developing methods appropriate for mapping increasing amounts of genome-wide molecular data are increasing rapidly. There is also an increasing need for methods that are able to efficiently simulate such data.Patients and methods: In this article, we provide a graph-theory approach to find the necessary and sufficient conditions for the existence of a phylogeny matrix with k nonidentical haplotypes, n single nucleotide polymorphisms (SNPs, and a population size of m for which the minimum allele frequency of each SNP is between two specific numbers a and b.Results: We introduce an O(max(n2, nm algorithm for the random construction of such a phylogeny matrix. The running time of any algorithm for solving this problem would be Ω (nm.Conclusion: We have developed software, RAPPER, based on this algorithm, which is available at http://bioinf.cs.ipm.ir/softwares/RAPPER.Keywords: perfect phylogeny, minimum allele frequency (MAF, tree, recursive algorithm
The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights
Kaymak, Vural; Kieburg, Mario; Guhr, Thomas
2014-07-01
In the past few years, the supersymmetry method has been generalized to real symmetric, Hermitian, and Hermitian self-dual random matrices drawn from ensembles invariant under the orthogonal, unitary, and unitary symplectic groups, respectively. We extend this supersymmetry approach to chiral random matrix theory invariant under the three chiral unitary groups in a unifying way. Thereby we generalize a projection formula providing a direct link and, hence, a ‘short cut’ between the probability density in ordinary space and that in superspace. We emphasize that this point was one of the main problems and shortcomings of the supersymmetry method, since only implicit dualities between ordinary space and superspace were known before. To provide examples, we apply this approach to the calculation of the supersymmetric analogue of a Lorentzian (Cauchy) ensemble and an ensemble with a quartic potential. Moreover, we consider the partially quenched partition function of the three chiral Gaussian ensembles corresponding to four-dimensional continuum quantum chromodynamics. We identify a natural splitting of the chiral Lagrangian in its lowest order into a part for the physical mesons and a part associated with source terms generating the observables, e.g. the level density of the Dirac operator.
Logistic ensembles of Random Spherical Linear Oracles for microarray classification.
Peterson, Leif E; Coleman, Matthew A
2009-01-01
Random Spherical Linear Oracles (RSLO) for DNA microarray gene expression data are proposed for classifier fusion. RSLO employs random hyperplane splits of samples in the principal component score space based on the first three principal components (X, Y, Z) of the input feature set. Hyperplane splits are used to assign training(testing) samples to separate logistic regression mini-classifiers, which increases the diversity of voting results since errors are not shared across mini-classifiers. We recommend use of RSLO with 3-4 10-fold CV and re-partitioning samples randomly every ten iterations prior to each 10-fold CV. This equates to a total of 30-40 iterations.
Directory of Open Access Journals (Sweden)
Tzu-Chien Hsiao
2013-11-01
Full Text Available Excitation-emission matrix (EEM fluorescence spectroscopy is a noninvasive method for tissue diagnosis and has become important in clinical use. However, the intrinsic characterization of EEM fluorescence remains unclear. Photobleaching and the complexity of the chemical compounds make it difficult to distinguish individual compounds due to overlapping features. Conventional studies use principal component analysis (PCA for EEM fluorescence analysis, and the relationship between the EEM features extracted by PCA and diseases has been examined. The spectral features of different tissue constituents are not fully separable or clearly defined. Recently, a non-stationary method called multi-dimensional ensemble empirical mode decomposition (MEEMD was introduced; this method can extract the intrinsic oscillations on multiple spatial scales without loss of information. The aim of this study was to propose a fluorescence spectroscopy system for EEM measurements and to describe a method for extracting the intrinsic characteristics of EEM by MEEMD. The results indicate that, although PCA provides the principal factor for the spectral features associated with chemical compounds, MEEMD can provide additional intrinsic features with more reliable mapping of the chemical compounds. MEEMD has the potential to extract intrinsic fluorescence features and improve the detection of biochemical changes.
A trivial observation on time reversal in random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Kaplan, L [Department of Physics, Tulane University, New Orleans, LA (United States); Leyvraz, F [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico (Mexico); Pineda, C [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico (Mexico); Seligman, T H [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico (Mexico)
2007-12-07
It is commonly thought that a state-dependent quantity, after being averaged over a classical ensemble of random Hamiltonians, will always become independent of the state. We point out that this is in general incorrect: if the ensemble of Hamiltonians is time-reversal invariant, and the quantity involves the state in higher than bilinear order, then we show that the quantity is only a constant over the orbits of the invariance group on the Hilbert space. Examples include fidelity and decoherence in appropriate models. (fast track communication)
Transition from Poisson to circular unitary ensemble
Indian Academy of Sciences (India)
Transitions to universality classes of random matrix ensembles have been useful in the study of weakly-broken symmetries in quantum chaotic systems. Transitions involving Poisson as the initial ensemble have been particularly interesting. The exact two-point correlation function was derived by one of the present authors ...
Transition from Poisson to circular unitary ensemble
Indian Academy of Sciences (India)
Abstract. Transitions to universality classes of random matrix ensembles have been useful in the study of weakly-broken symmetries in quantum chaotic systems. Transitions involving Poisson as the initial ensemble have been particularly interesting. The exact two-point correlation function was derived by one of the present ...
Random matrix theory and higher genus integrability: the quantum chiral Potts model
Energy Technology Data Exchange (ETDEWEB)
Angles d' Auriac, J.Ch. [Centre de Recherches sur les Tres Basses Temperatures, BP 166, Grenoble (France)]. E-mail: dauriac@polycnrs-gre.fr; Maillard, J.M.; Viallet, C.M. [LPTHE, Tour 16, Paris (France)]. E-mails: maillard@lpthe.jussieu.fr; viallet@lpthe.jussieu.fr
2002-06-14
We perform a random matrix theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L 8. Our analysis gives clear evidence of a Gaussian orthogonal ensemble (GOE) statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore, a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of 'higher genus integrability'. (author)
Energy Technology Data Exchange (ETDEWEB)
Edwards, R.G.; Heller, U.M. [SCRI, Florida State University, Tallahassee, Florida 32306-4130 (United States); Narayanan, R. [Department of Physics, Building 510A, Brookhaven National Laboratory, P. O. Box 5000, Upton, New York 11973 (United States)
1999-10-01
The low-lying spectrum of the Dirac operator is predicted to be universal, within three classes, depending on symmetry properties specified according to random matrix theory. The three universal classes are the orthogonal, unitary and symplectic ensembles. Lattice gauge theory with staggered fermions has verified two of the cases so far, unitary and symplectic, with staggered fermions in the fundamental representation of SU(3) and SU(2). We verify the missing case here, namely orthogonal, with staggered fermions in the adjoint representation of SU(N{sub c}), N{sub c}=2,3. {copyright} {ital 1999} {ital The American Physical Society}
Application of Random Matrix Theory to Complex Networks
Rai, Aparna; Jalan, Sarika
The present article provides an overview of recent developments in spectral analysis of complex networks under random matrix theory framework. Adjacency matrix of unweighted networks, reviewed here, differ drastically from a random matrix, as former have only binary entries. Remarkably, short range correlations in corresponding eigenvalues of such matrices exhibit Gaussian orthogonal statistics of RMT and thus bring them into the universality class. Spectral rigidity of spectra provides measure of randomness in underlying networks. We will consider several examples of model networks vastly studied in last two decades. To the end we would provide potential of RMT framework and obtained results to understand and predict behavior of complex systems with underlying network structure.
Vibrations in glasses and Euclidean random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Grigera, T.S.; Martin-Mayor, V.; Parisi, G. [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , Rome (Italy); INFN Sezione di Roma - INFM Unita di Roma, Rome (Italy); Verrocchio, P. [Dipartimento di Fisica, Universita di Trento, Povo, Trento (Italy); INFM Unita di Trento, Trento (Italy)
2002-03-11
We study numerically and analytically a simple off-lattice model of scalar harmonic vibrations by means of Euclidean random matrix theory. Since the spectrum of this model shares the most puzzling spectral features with the high-frequency domain of glasses (non-Rayleigh broadening of the Brillouin peak, boson peak and secondary peak), Euclidean random matrix theory provides a single and fairly simple theoretical framework for their explanation. (author)
Random matrix model for disordered conductors
Indian Academy of Sciences (India)
1. Introduction. Matrix models are being successfully employed in a variety of domains of physics includ- ing studies on heavy nuclei [1], mesoscopic disordered conductors [2,3], two-dimensional quantum gravity [4], and chaotic quantum systems [5]. Universal conductance fluctuations in metals [6] and spectral fluctuations in ...
Energy Technology Data Exchange (ETDEWEB)
Berkolaiko, G., E-mail: berko@math.tamu.edu [Department of Mathematics, Texas A and M University, College Station, Texas 77843-3368 (United States); Kuipers, J., E-mail: Jack.Kuipers@physik.uni-regensburg.de [Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg (Germany)
2013-11-15
To study electronic transport through chaotic quantum dots, there are two main theoretical approaches. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other treats the transport in the semiclassical approximation and studies correlations among sets of classical trajectories. There are established evaluation procedures within the semiclassical evaluation that, for several linear and nonlinear transport moments to which they were applied, have always resulted in the agreement with random matrix predictions. We prove that this agreement is universal: any semiclassical evaluation within the accepted procedures is equivalent to the evaluation within random matrix theory. The equivalence is shown by developing a combinatorial interpretation of the trajectory sets as ribbon graphs (maps) with certain properties and exhibiting systematic cancellations among their contributions. Remaining trajectory sets can be identified with primitive (palindromic) factorisations whose number gives the coefficients in the corresponding expansion of the moments of random matrices. The equivalence is proved for systems with and without time reversal symmetry.
Berkolaiko, G.; Kuipers, J.
2013-11-01
To study electronic transport through chaotic quantum dots, there are two main theoretical approaches. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other treats the transport in the semiclassical approximation and studies correlations among sets of classical trajectories. There are established evaluation procedures within the semiclassical evaluation that, for several linear and nonlinear transport moments to which they were applied, have always resulted in the agreement with random matrix predictions. We prove that this agreement is universal: any semiclassical evaluation within the accepted procedures is equivalent to the evaluation within random matrix theory. The equivalence is shown by developing a combinatorial interpretation of the trajectory sets as ribbon graphs (maps) with certain properties and exhibiting systematic cancellations among their contributions. Remaining trajectory sets can be identified with primitive (palindromic) factorisations whose number gives the coefficients in the corresponding expansion of the moments of random matrices. The equivalence is proved for systems with and without time reversal symmetry.
Kappa-Deformed Random-Matrix Theory Based on Kaniadakis Statistics
Abul-Magd, A. Y.; Abdel-Mageed, M.
We present a possible extension of the random-matrix theory, which is widely used to describe spectral fluctuations of chaotic systems. By considering the Kaniadakis non-Gaussian statistics, characterized by the index κ (Boltzmann-Gibbs entropy is recovered in the limit κ → 0), we propose the non-Gaussian deformations (κ ≠ 0) of the conventional orthogonal and unitary ensembles of random matrices. The joint eigenvalue distributions for the κ-deformed ensembles are derived by applying the principle maximum entropy to Kaniadakis entropy. The resulting distribution functions are base invariant as they depend on the matrix elements in a trace form. Using these expressions, we introduce a new generalized form of the Wigner surmise valid for nearly-chaotic mixed systems, where a basis-independent description is still expected to hold. We motivate the necessity of such generalization by the need to describe the transition of the spacing distribution from chaos to order, at least in the initial stage. We show several examples about the use of the generalized Wigner surmise to the analysis of the results of a number of previous experiments and numerical experiments. Our results suggest the entropic index κ as a measure for deviation from the state of chaos. We also introduce a κ-deformed Porter-Thomas distribution of transition intensities, which fits the experimental data for mixed systems better than the commonly-used gamma-distribution.
Prediction of Protein Hotspots from Whole Protein Sequences by a Random Projection Ensemble System
Directory of Open Access Journals (Sweden)
Jinjian Jiang
2017-07-01
Full Text Available Hotspot residues are important in the determination of protein-protein interactions, and they always perform specific functions in biological processes. The determination of hotspot residues is by the commonly-used method of alanine scanning mutagenesis experiments, which is always costly and time consuming. To address this issue, computational methods have been developed. Most of them are structure based, i.e., using the information of solved protein structures. However, the number of solved protein structures is extremely less than that of sequences. Moreover, almost all of the predictors identified hotspots from the interfaces of protein complexes, seldom from the whole protein sequences. Therefore, determining hotspots from whole protein sequences by sequence information alone is urgent. To address the issue of hotspot predictions from the whole sequences of proteins, we proposed an ensemble system with random projections using statistical physicochemical properties of amino acids. First, an encoding scheme involving sequence profiles of residues and physicochemical properties from the AAindex1 dataset is developed. Then, the random projection technique was adopted to project the encoding instances into a reduced space. Then, several better random projections were obtained by training an IBk classifier based on the training dataset, which were thus applied to the test dataset. The ensemble of random projection classifiers is therefore obtained. Experimental results showed that although the performance of our method is not good enough for real applications of hotspots, it is very promising in the determination of hotspot residues from whole sequences.
Prediction of Protein Hotspots from Whole Protein Sequences by a Random Projection Ensemble System
Jiang, Jinjian; Wang, Nian; Chen, Peng; Zheng, Chunhou; Wang, Bing
2017-01-01
Hotspot residues are important in the determination of protein-protein interactions, and they always perform specific functions in biological processes. The determination of hotspot residues is by the commonly-used method of alanine scanning mutagenesis experiments, which is always costly and time consuming. To address this issue, computational methods have been developed. Most of them are structure based, i.e., using the information of solved protein structures. However, the number of solved protein structures is extremely less than that of sequences. Moreover, almost all of the predictors identified hotspots from the interfaces of protein complexes, seldom from the whole protein sequences. Therefore, determining hotspots from whole protein sequences by sequence information alone is urgent. To address the issue of hotspot predictions from the whole sequences of proteins, we proposed an ensemble system with random projections using statistical physicochemical properties of amino acids. First, an encoding scheme involving sequence profiles of residues and physicochemical properties from the AAindex1 dataset is developed. Then, the random projection technique was adopted to project the encoding instances into a reduced space. Then, several better random projections were obtained by training an IBk classifier based on the training dataset, which were thus applied to the test dataset. The ensemble of random projection classifiers is therefore obtained. Experimental results showed that although the performance of our method is not good enough for real applications of hotspots, it is very promising in the determination of hotspot residues from whole sequences. PMID:28718782
Random matrix theory for pseudo-Hermitian systems: Cyclic blocks
Indian Academy of Sciences (India)
We discuss the relevance of random matrix theory for pseudo-Hermitian systems, and, for Hamiltonians that break parity and time-reversal invariance . In an attempt to understand the random Ising model, we present the treatment of cyclic asymmetric matrices with blocks and show that the nearest-neighbour spacing ...
Random matrix theory for heavy-tailed time series
DEFF Research Database (Denmark)
Heiny, Johannes
2017-01-01
This paper is a review of recent results for large random matrices with heavy-tailed entries. First, we outline the development of and some classical results in random matrix theory. We focus on large sample covariance matrices, their limiting spectral distributions, the asymptotic behavior...... of their largest and smallest eigenvalues and their eigenvectors. The limits significantly depend on the finite or infiniteness of the fourth moment of the entries of the random matrix. We compare the results for these two regimes which give rise to completely different asymptotic theories. Finally, the limits...
Huang, Weimin; Yang, Yongzhong; Lin, Zhiping; Huang, Guang-Bin; Zhou, Jiayin; Duan, Yuping; Xiong, Wei
2014-01-01
This paper presents a new approach to detect and segment liver tumors. The detection and segmentation of liver tumors can be formulized as novelty detection or two-class classification problem. Each voxel is characterized by a rich feature vector, and a classifier using random feature subspace ensemble is trained to classify the voxels. Since Extreme Learning Machine (ELM) has advantages of very fast learning speed and good generalization ability, it is chosen to be the base classifier in the ensemble. Besides, majority voting is incorporated for fusion of classification results from the ensemble of base classifiers. In order to further increase testing accuracy, ELM autoencoder is implemented as a pre-training step. In automatic liver tumor detection, ELM is trained as a one-class classifier with only healthy liver samples, and the performance is compared with two-class ELM. In liver tumor segmentation, a semi-automatic approach is adopted by selecting samples in 3D space to train the classifier. The proposed method is tested and evaluated on a group of patients' CT data and experiment show promising results.
Random discrete Schroedinger operators from random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Breuer, Jonathan [Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Forrester, Peter J [Department of Mathematics and Statistics, University of Melbourne, Parkville, Vic 3010 (Australia); Smilansky, Uzy [Department of Physics of Complex Systems, Weizmann Institute, Rehovot 76100 (Israel)
2007-02-02
We investigate random, discrete Schroedinger operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature {beta}. They are similar to the class of 'critical' random Schroedinger operators with random potentials which diminish as vertical bar x vertical bar{sup -1/2}. We show that as a function of {beta} they undergo a transition from a regime of (power-law) localized eigenstates with a pure point spectrum for {beta} < 2 to a regime of extended states with a singular continuous spectrum for {beta} {>=} 2. (fast track communication)
Ling, Qing-Hua; Song, Yu-Qing; Han, Fei; Yang, Dan; Huang, De-Shuang
2016-01-01
For ensemble learning, how to select and combine the candidate classifiers are two key issues which influence the performance of the ensemble system dramatically. Random vector functional link networks (RVFL) without direct input-to-output links is one of suitable base-classifiers for ensemble systems because of its fast learning speed, simple structure and good generalization performance. In this paper, to obtain a more compact ensemble system with improved convergence performance, an improved ensemble of RVFL based on attractive and repulsive particle swarm optimization (ARPSO) with double optimization strategy is proposed. In the proposed method, ARPSO is applied to select and combine the candidate RVFL. As for using ARPSO to select the optimal base RVFL, ARPSO considers both the convergence accuracy on the validation data and the diversity of the candidate ensemble system to build the RVFL ensembles. In the process of combining RVFL, the ensemble weights corresponding to the base RVFL are initialized by the minimum norm least-square method and then further optimized by ARPSO. Finally, a few redundant RVFL is pruned, and thus the more compact ensemble of RVFL is obtained. Moreover, in this paper, theoretical analysis and justification on how to prune the base classifiers on classification problem is presented, and a simple and practically feasible strategy for pruning redundant base classifiers on both classification and regression problems is proposed. Since the double optimization is performed on the basis of the single optimization, the ensemble of RVFL built by the proposed method outperforms that built by some single optimization methods. Experiment results on function approximation and classification problems verify that the proposed method could improve its convergence accuracy as well as reduce the complexity of the ensemble system.
Analysis of symmetry breaking in quartz blocks using superstatistical random-matrix theory
Abul-Magd, A. Y.; Mazen, S. A.; Abdel-Mageed, M.
2012-06-01
We study the symmetry breaking of acoustic resonances measured by Ellegaard et al. (1996) [1] in quartz blocks. The observed resonance spectra show a gradual transition from a superposition of two uncoupled components, one for each symmetry realization, to a single component that is well represented by a Gaussian orthogonal ensemble (GOE) of random matrices. We discuss the applicability of superstatistical random-matrix theory to the final stages of the symmetry-breaking transition. A comparison is made between the formula from superstatistics and that from a previous work by Abd El-Hady et al. (2002) [7], which describes the same data by introducing a third GOE component. Our results suggest that the inverse chi-squared superstatistics could be used for studying the whole symmetry-breaking process.
Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States
Ambainis, Andris; Harrow, Aram W.; Hastings, Matthew B.
2012-02-01
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in {(mathbb {C}^d)^{⊗ k}}, where k and p/ d k are fixed while d → ∞. When k = 1, the Marčenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ({(1+sqrt{p/d^k})^2}) but the smallest eigenvalue {(min(0,1-sqrt{p/d^k})^2)} and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately {(1+sqrt{p/d^k})^2} and the spectral density approaches that of the Marčenko-Pastur law, generalizing the random matrix theory result to the random tensor case. Our bound on the largest eigenvalue has implications both for sampling from a particular heavy-tailed distribution and for a recently proposed quantum data-hiding and correlation-locking scheme due to Leung and Winter. Since the matrices we consider have neither independent entries nor unitary invariance, we need to develop new techniques for their analysis. The main contribution of this paper is to give three different methods for analyzing mixtures of random product states: a diagrammatic approach based on Gaussian integrals, a combinatorial method that looks at the cycle decompositions of permutations and a recursive method that uses a variant of the Schwinger-Dyson equations.
Vertices from replica in a random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Brezin, E [Laboratoire de Physique Theorique, Ecole Normale Superieure, 24 rue Lhomond 75231, Paris Cedex 05 (France); Hikami, S [Department of Basic Sciences, University of Tokyo, Meguro-ku, Komaba, Tokyo 153 (Japan)
2007-11-09
Kontsevich's work on Airy matrix integrals has led to explicit results for the intersection numbers of the moduli space of curves. In a subsequent work Okounkov rederived these results from the edge behavior of a Gaussian matrix integral. In our work we consider the correlation functions of vertices in a Gaussian random matrix theory, with an external matrix source. We deal with operator products of the form <{pi}{sub i=1}{sup n}1/N tr M{sup k{sub i}}>, in a 1/N expansion. For large values of the powers k{sub i}, in an appropriate scaling limit relating large k's to large N, universal scaling functions are derived. Furthermore, we show that the replica method applied to characteristic polynomials of the random matrices, together with a duality exchanging N and the number of points, provides a new way to recover Kontsevich's results on these intersection numbers.
Non-equilibrium random matrix theory. Transition probabilities
Energy Technology Data Exchange (ETDEWEB)
Pedro, Francisco Gil [Univ. Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie
2016-06-15
In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large N limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.
Skew-orthogonal polynomials, differential systems and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Saugata [Abdus Salam ICTP, Strada Costiera 11, 34100, Trieste (Italy)
2007-01-26
We study skew-orthogonal polynomials with respect to the weight function exp [ - 2V(x)], with V(x) = {sigma}{sup 2d}{sub K=1}(u{sub K}/K)x{sup K}, u{sub 2d} > 0, d > 0. A finite subsequence of such skew-orthogonal polynomials arising in the study of orthogonal and symplectic ensembles of random matrices satisfies a system of differential-difference-deformation equation. The vectors formed by such subsequence have the rank equal to the degree of the potential in the quaternion sense. These solutions satisfy certain compatibility condition and hence admit a simultaneous fundamental system of solutions.
Enumeration of RNA complexes via random matrix theory
DEFF Research Database (Denmark)
Andersen, Jørgen E; Chekhov, Leonid O.; Penner, Robert C
2013-01-01
In the present article, we review a derivation of the numbers of RNA complexes of an arbitrary topology. These numbers are encoded in the free energy of the Hermitian matrix model with potential V(x)=x(2)/2 - stx/(1 - tx), where s and t are respective generating parameters for the number of RNA...... molecules and hydrogen bonds in a given complex. The free energies of this matrix model are computed using the so-called topological recursion, which is a powerful new formalism arising from random matrix theory. These numbers of RNA complexes also have profound meaning in mathematics: they provide...
Random matrix analysis for gene interaction networks in cancer cells
Kikkawa, Ayumi
2016-01-01
Motivation: The investigation of topological modifications of the gene interaction networks in cancer cells is essential for understanding the desease. We study gene interaction networks in various human cancer cells with the random matrix theory. This study is based on the Cancer Network Galaxy (TCNG) database which is the repository of huge gene interactions inferred by Bayesian network algorithms from 256 microarray experimental data downloaded from NCBI GEO. The original GEO data are provided by the high-throughput microarray expression experiments on various human cancer cells. We apply the random matrix theory to the computationally inferred gene interaction networks in TCNG in order to detect the universality in the topology of the gene interaction networks in cancer cells. Results: We found the universal behavior in almost one half of the 256 gene interaction networks in TCNG. The distribution of nearest neighbor level spacing of the gene interaction matrix becomes the Wigner distribution when the net...
Optimum allocation in multivariate stratified random sampling: Stochastic matrix optimisation
Diaz-Garcia, Jose A.; Ramos-Quiroga, Rogelio
2011-01-01
The allocation problem for multivariate stratified random sampling as a problem of stochastic matrix integer mathematical programming is considered. With these aims the asymptotic normality of sample covariance matrices for each strata is established. Some alternative approaches are suggested for its solution. An example is solved by applying the proposed techniques.
QCD Dirac spectra with and without random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Damgaard, P.H. [Niels Bohr Institute, Copenhagen (Denmark)
1999-07-01
Recent work on the spectrum of the Euclidean Dirac operator spectrum show that the exact microscopic spectral density can be computed in both random matrix theory, and directly from field theory. Exact relations to effective Lagrangians with additional quark species form the bridge between the two formulations. (author)
Partial Discharge Detection and Recognition in Random Matrix Theory Paradigm
National Research Council Canada - National Science Library
Luo, Lingen; Han, Bei; Chen, Jingde; Sheng, Gehao; Jiang, Xiuchen
.... Take advantage of the affluent results from random matrix theory (RMT), such as eigenvalue analysis, M-P law, the ring law, and so on, a novel methodology in RMT paradigm is proposed for fast PD pulse detection in this paper...
Random matrix theory approach to vibrations near the jamming transition
Beltukov, Y. M.
2015-03-01
It has been shown that the dynamical matrix M describing harmonic oscillations in granular media can be represented in the form M = AA T, where the rows of the matrix A correspond to the degrees of freedom of individual granules and its columns correspond to elastic contacts between granules. Such a representation of the dynamical matrix makes it possible to estimate the density of vibrational states with the use of the random matrix theory. The found density of vibrational states is approximately constant in a wide frequency range ω- < ω < ω+, which is determined by the ratio of the number of degrees of freedom to the total number of contacts in the system, which is in good agreement with the results of the numerical experiments.
Random matrix theory for the analysis of the performance of an analog computer: a scaling theory
Energy Technology Data Exchange (ETDEWEB)
Ben-Hur, Asa; Feinberg, Joshua; Fishman, Shmuel; Siegelmann, Hava T
2004-03-22
The phase space flow of a dynamical system, leading to the solution of linear programming (LP) problems, is explored as an example of complexity analysis in an analog computation framework. In this framework, computation by physical devices and natural systems, evolving in continuous phase space and time (in contrast to the digital computer where these are discrete), is explored. A Gaussian ensemble of LP problems is studied. The convergence time of a flow to the fixed point representing the optimal solution, is computed. The cumulative distribution function of the convergence time is calculated in the framework of random matrix theory (RMT) in the asymptotic limit of large problem size. It is found to be a scaling function, of the form obtained in the theories of critical phenomena and Anderson localization. It demonstrates a correspondence between problems of computer science and physics.
Transmission eigenvalue densities and moments in chaotic cavities from random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Vivo, Pierpaolo [School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge, Middlesex, UB8 3PH (United Kingdom); Vivo, Edoardo [Universita degli Studi di Parma, Dipartimento di Fisica Teorica, Viale GP Usberti n.7/A (Parco Area delle Scienze), Parma (Italy)
2008-03-28
We point out that the transmission eigenvalue density and higher order correlation functions in chaotic cavities for an arbitrary number of incoming and outgoing leads (N{sub 1}, N{sub 2}) are analytically known from the Jacobi ensemble of random matrix theory. Using this result and a simple linear statistic, we give an exact and non-perturbative expression for moments of the form ({lambda}{sup m}{sub 1}) for m > -|N{sub 1} - N{sub 2}| - 1 and {beta} = 2, thus improving the existing results in the literature. Secondly, we offer an independent derivation of the average density and higher order correlation function for {beta} = 2, 4 which does not make use of the orthogonal polynomials technique. This result may be relevant for an efficient numerical implementation avoiding determinants. (fast track communication)
Odd-flavored QCD{sub 3} and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Christiansen, Jesper E-mail: jeschris@nbi.dk
1999-05-10
We consider QCD{sub 3} with an odd number of flavors in the mesoscopic scaling region where the field theory finite-volume partition function is equivalent to a random matrix theory partition function. We argue that the theory is parity invariant at the classical level if an odd number of masses are zero. By introducing so-called pseudo-orthogonal polynomials we are able to relate the kernel to the kernel of the chiral unitary ensemble with {beta} = 2 in the sector of topological charge {nu} = ((1)/(2)). We prove universality and are able to write the kernel in the microscopic limit in terms of field theory finite-volume partition functions.
Random matrix theory and acoustic resonances in plates with an approximate symmetry
DEFF Research Database (Denmark)
Andersen, Anders Peter; Ellegaard, C.; Jackson, A.D.
2001-01-01
We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminum plate may have an approximate symmetry. We have measured the frequency spectrum...... and the widths for acoustic resonances in thin aluminum plates, cut in the shape of the so-called three-leaf clover. Due to the mirror symmetry through the middle plane of the plate, each resonance of the plate belongs to one of two mode classes and we show how to separate the modes into these two classes using...... their measured widths. We compare the spectral statistics of each mode class with results for the Gaussian orthogonal ensemble. By cutting a slit of increasing depth on one face of the plate, we gradually break the mirror symmetry and study the transition that takes place as the two classes are mixed. Presenting...
A Secure LFSR Based Random Measurement Matrix for Compressive Sensing
George, Sudhish N.; Pattathil, Deepthi P.
2014-11-01
In this paper, a novel approach for generating the secure measurement matrix for compressive sensing (CS) based on linear feedback shift register (LFSR) is presented. The basic idea is to select the different states of LFSR as the random entries of the measurement matrix and normalize these values to get independent and identically distributed (i.i.d.) random variables with zero mean and variance , where N is the number of input samples. The initial seed for the LFSR system act as the key to the user to provide security. Since the measurement matrix is generated from the LFSR system, and memory overload to store the measurement matrix is avoided in the proposed system. Moreover, the proposed system can provide security maintaining the robustness to noise of the CS system. The proposed system is validated through different block-based CS techniques of images. To enhance security, the different blocks of images are measured with different measurement matrices so that the proposed encryption system can withstand known plaintext attack. A modulo division circuit is used to reseed the LFSR system to generate multiple random measurement matrices, whereby after each fundamental period of LFSR, the feedback polynomial of the modulo circuit is modified in terms of a chaotic value. The proposed secure robust CS paradigm for images is subjected to several forms of attacks and is proven to be resistant against the same. From experimental analysis, it is proven that the proposed system provides better performance than its counterparts.
Ensemble of Neural Network Conditional Random Fields for Self-Paced Brain Computer Interfaces
Directory of Open Access Journals (Sweden)
Hossein Bashashati
2017-07-01
Full Text Available Classification of EEG signals in self-paced Brain Computer Interfaces (BCI is an extremely challenging task. The main diﬃculty stems from the fact that start time of a control task is not defined. Therefore it is imperative to exploit the characteristics of the EEG data to the extent possible. In sensory motor self-paced BCIs, while performing the mental task, the user’s brain goes through several well-defined internal state changes. Applying appropriate classifiers that can capture these state changes and exploit the temporal correlation in EEG data can enhance the performance of the BCI. In this paper, we propose an ensemble learning approach for self-paced BCIs. We use Bayesian optimization to train several different classifiers on different parts of the BCI hyper- parameter space. We call each of these classifiers Neural Network Conditional Random Field (NNCRF. NNCRF is a combination of a neural network and conditional random field (CRF. As in the standard CRF, NNCRF is able to model the correlation between adjacent EEG samples. However, NNCRF can also model the nonlinear dependencies between the input and the output, which makes it more powerful than the standard CRF. We compare the performance of our algorithm to those of three popular sequence labeling algorithms (Hidden Markov Models, Hidden Markov Support Vector Machines and CRF, and to two classical classifiers (Logistic Regression and Support Vector Machines. The classifiers are compared for the two cases: when the ensemble learning approach is not used and when it is. The data used in our studies are those from the BCI competition IV and the SM2 dataset. We show that our algorithm is considerably superior to the other approaches in terms of the Area Under the Curve (AUC of the BCI system.
Random Vector and Matrix Theories: A Renormalization Group Approach
Zinn-Justin, Jean
2014-09-01
Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has generated a tremendous expansion of random matrix theory, tackled with increasingly sophisticated mathematical methods and number of matrix models have been solved exactly. However, the somewhat paradoxical situation is that either models can be solved exactly or little can be said. Since the solved models display critical points and universal properties, it is tempting to use renormalization group ideas to determine universal properties, without solving models explicitly. Initiated by Br\\'ezin and Zinn-Justin, the approach has led to encouraging results, first for matrix integrals and then quantum mechanics with matrices, but has not yet become a universal tool as initially hoped. In particular, general quantum field theories with matrix fields require more detailed investigations. To better understand some of the encountered difficulties, we first apply analogous ideas to the simpler O(N) symmetric vector models, models that can be solved quite generally in the large N limit. Unlike other attempts, our method is a close extension of Br\\'ezin and Zinn-Justin. Discussing vector and matrix models with similar approximation scheme, we notice that in all cases (vector and matrix integrals, vector and matrix path integrals in the local approximation), at leading order, non-trivial fixed points satisfy the same universal algebraic equation, and this is the main result of this work. However, its precise meaning and role have still to be better understood.
Random matrix approach to the distribution of genomic distance.
Alexeev, Nikita; Zograf, Peter
2014-08-01
The cycle graph introduced by Bafna and Pevzner is an important tool for evaluating the distance between two genomes, that is, the minimal number of rearrangements needed to transform one genome into another. We interpret this distance in topological terms and relate it to the random matrix theory. Namely, the number of genomes at a given 2-break distance from a fixed one (the Hultman number) is represented by a coefficient in the genus expansion of a matrix integral over the space of complex matrices with the Gaussian measure. We study generating functions for the Hultman numbers and prove that the two-break distance distribution is asymptotically normal.
Random matrix theory and portfolio optimization in Moroccan stock exchange
El Alaoui, Marwane
2015-09-01
In this work, we use random matrix theory to analyze eigenvalues and see if there is a presence of pertinent information by using Marčenko-Pastur distribution. Thus, we study cross-correlation among stocks of Casablanca Stock Exchange. Moreover, we clean correlation matrix from noisy elements to see if the gap between predicted risk and realized risk would be reduced. We also analyze eigenvectors components distributions and their degree of deviations by computing the inverse participation ratio. This analysis is a way to understand the correlation structure among stocks of Casablanca Stock Exchange portfolio.
Generalized Christoffel-Darboux formula for skew-orthogonal polynomials and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Saugata [Abdus Salam ICTP, Strada Costiera 11, 34100, Trieste (Italy)
2006-07-14
We obtain a generalized Christoffel-Darboux (GCD) formula for skew-orthogonal polynomials. Using this, we present an alternative derivation of the level density and two-point function for Gaussian orthogonal ensembles and Gaussian symplectic ensembles of random matrices.
Super Yang-Mills theory as a random matrix model
Energy Technology Data Exchange (ETDEWEB)
Siegel, W. [Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11794-3840 (United States)
1995-07-15
We generalize the Gervais-Neveu gauge to four-dimensional {ital N}=1 superspace. The model describes an {ital N}=2 super Yang-Mills theory. All chiral superfields ({ital N}=2 matter and ghost multiplets) exactly cancel to all loops. The remaining Hermitian scalar superfield (matrix) has a renormalizable massive propagator and simplified vertices. These properties are associated with {ital N}=1 supergraphs describing a superstring theory on a random lattice world sheet. We also consider all possible finite matrix models, and find they have a universal large-color limit. These could describe gravitational strings if the matrix-model coupling is fixed to unity, for exact electric-magnetic self-duality.
Random matrix theory and acoustic resonances in plates with an approximate symmetry
Energy Technology Data Exchange (ETDEWEB)
Andersen, A.; Ellegaard, C.; Jackson, A. D.; Schaadt, K.
2001-06-01
We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminum plate may have an approximate symmetry. We have measured the frequency spectrum and the widths for acoustic resonances in thin aluminum plates, cut in the shape of the so-called three-leaf clover. Due to the mirror symmetry through the middle plane of the plate, each resonance of the plate belongs to one of two mode classes and we show how to separate the modes into these two classes using their measured widths. We compare the spectral statistics of each mode class with results for the Gaussian orthogonal ensemble. By cutting a slit of increasing depth on one face of the plate, we gradually break the mirror symmetry and study the transition that takes place as the two classes are mixed. Presenting the spectral fluctuation statistics and the distribution of widths for the resonances, we find that this transition is well described by the random matrix model.
Analysis of the {sup 238}U resonance parameters using random-matrix theory
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Courcelle, A. [CEA Cadarache, 13 - Saint Paul lez Durance (France); Derrien, H.; Leal, L.C.; Larson, N.M. [Oak Ridge National Laboratory, Oak Ridge, TN (United States)
2005-07-01
Random-matrix theories (RMTs) provide valuable statistical tools to analyze neutron-resonance data. The predictive power of the random-matrix theories, which do not contain any adjustable parameters, is striking, and the application is rather simple and fast. A new evaluation of {sup 238}U resonance parameters has recently been performed at the Oak Ridge National Laboratory; the objective of this paper is to illustrate the use of RMT in the field of resonance-parameter evaluation with the newly evaluated {sup 239}U energy levels and widths. Several statistics were computed using the s-wave resonances up to 20 keV and compared to the Gaussian Orthogonal Ensemble predictions. It is shown that a good agreement is observed between RMT and the experimental data up to 2.5 keV. The F-Dyson statistic was especially investigated because of its claimed ability to detect locally missed and spurious levels in the sample (p-resonances contamination or unresolved multiplets). As expected, the entire set of evaluated {sup 238}U s-wave resonances up to 20 keV disagrees significantly with the theory. There are two reasons for this: First, it is difficult to distinguish s- and p-wave resonances in the analysis. Secondly, especially above 10 keV, it is impossible to determine reliable resonance energies from the available experimental data. It is concluded that the use of RMT can help nuclear data specialists to improve their evaluations in the resonance range. (authors)
Nishigaki, Shinsuke M.
2012-12-01
Schierenberg [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.061130 85, 061130 (2012)] recently applied the Wigner surmise, i.e., substitution of ∞×∞ matrices by their 2×2 counterparts for the computation of level spacing distributions, to random matrix ensembles in transition between two universality classes. I examine the accuracy and the range of validity of the surmise for the crossover between the Gaussian orthogonal and unitary ensembles by contrasting them with the large-N results that I evaluated using the Nyström-type method for the Fredholm determinant. The surmised expression at the best-fitting parameter provides a good approximation for 0≲s≲2, i.e., the validity range of the original surmise.
Random-matrix theory of Majorana fermions and topological superconductors
Beenakker, C. W. J.
2015-07-01
The theory of random matrices originated half a century ago as a universal description of the spectral statistics of atoms and nuclei, dependent only on the presence or absence of fundamental symmetries. Applications to quantum dots (artificial atoms) followed, stimulated by developments in the field of quantum chaos, as well as applications to Andreev billiards—quantum dots with induced superconductivity. Superconductors with topologically protected subgap states, Majorana zero modes, and Majorana edge modes, provide a new arena for applications of random-matrix theory. These recent developments are reviewed, with an emphasis on electrical and thermal transport properties that can probe the Majorana fermions.
Chiral random matrix theory and effective theories of QCD
Energy Technology Data Exchange (ETDEWEB)
Takahashi, K.; Iida, S
2000-05-08
The correlations of the QCD Dirac eigenvalues are studied with use of an extended chiral random matrix model. The inclusion of spatial dependence which the original model lacks enables us to investigate the effects of diffusion modes. We get analytical expressions of level correlation functions with non-universal behavior caused by diffusion modes which is characterized by Thouless energy. Pion mode is shown to be responsible for these diffusion effects when QCD vacuum is considered a disordered medium.
Chiral Random Matrix Theory and Chiral Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Damgaard, Poul H, E-mail: phdamg@nbi.dk [Niels Bohr International Academy and Discovery Center, The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark)
2011-04-01
Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.
Comparing lattice Dirac operators with Random Matrix Theory
Energy Technology Data Exchange (ETDEWEB)
Farchioni, F.; Hipt, I.; Lang, C.B
2000-03-01
We study the eigenvalue spectrum of different lattice Dirac operators (staggered, fixed point, overlap) and discuss their dependence on the topological sectors. Although the model is 2D (the Schwinger model with massless fermions) our observations indicate possible problems in 4D applications. In particular misidentification of the smallest eigenvalues due to non-identification of the topological sector may hinder successful comparison with Random Matrix Theory (RMT)
Random matrix theory and the spectra of overlap fermions
Energy Technology Data Exchange (ETDEWEB)
Shcheredin, S.; Bietenholz, W.; Chiarappa, T.; Jansen, K.; Nagai, K.-I
2004-03-01
The application of Random Matrix Theory to the Dirac operator of QCD yields predictions for the probability distributions of the lowest eigenvalues. We measured Dirac operator spectra using massless overlap fermions in quenched QCD at topological charge {nu} = 0, {+-} 1 and {+-}2, and found agreement with those predictions -- at least for the first non-zero eigenvalue -- if the volume exceeds about (1.2 fm){sup 4}.
Page 1 contents v Random matrix theory and the statistical ...
Indian Academy of Sciences (India)
contents v. Random matrix theory and the statistical mechanics of disordered systems , k. & & & è è & e * * • • • * * * * * * * w * • • s • * • * • • a • » • • • • • • • • « • « Jitendra C Parikh 467—476. Statistical Physics. On information, negentropy and thermostatistics.... C G Chakrabarti 65-72. Connectivity constant of the kagomé lattice.
Moments of the transmission eigenvalues, proper delay times and random matrix theory II
Mezzadri, F.; Simm, N. J.
2012-05-01
We systematically study the first three terms in the asymptotic expansions of the moments of the transmission eigenvalues and proper delay times as the number of quantum channels n in the leads goes to infinity. The computations are based on the assumption that the Landauer-Büttiker scattering matrix for chaotic ballistic cavities can be modelled by the circular ensembles of random matrix theory. The starting points are the finite-n formulae that we recently discovered [F. Mezzadri and N. J. Simm, "Moments of the transmission eigenvalues, proper delay times and random matrix theory," J. Math. Phys. 52, 103511 (2011)], 10.1063/1.3644378. Our analysis includes all the symmetry classes β ∈ {1, 2, 4}; in addition, it applies to the transmission eigenvalues of Andreev billiards, whose symmetry classes were classified by Zirnbauer ["Riemannian symmetric superspaces and their origin in random-matrix theory," J. Math. Phys. 37(10), 4986 (1996)], 10.1063/1.531675 and Altland and Zirnbauer ["Random matrix theory of a chaotic Andreev quantum dot," Phys. Rev. Lett. 76(18), 3420 (1996), 10.1103/PhysRevLett.76.3420; Altland and Zirnbauer "Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures," Phys. Rev. B 55(2), 1142 (1997)], 10.1103/PhysRevB.55.1142. Where applicable, our results are in complete agreement with the semiclassical theory of mesoscopic systems developed by Berkolaiko et al. ["Full counting statistics of chaotic cavities from classical action correlations," J. Phys. A: Math. Theor. 41(36), 365102 (2008)], 10.1088/1751-8113/41/36/365102 and Berkolaiko and Kuipers ["Moments of the Wigner delay times," J. Phys. A: Math. Theor. 43(3), 035101 (2010), 10.1088/1751-8113/43/3/035101; Berkolaiko and Kuipers "Transport moments beyond the leading order," New J. Phys. 13(6), 063020 (2011)], 10.1088/1367-2630/13/6/063020. Our approach also applies to the Selberg-like integrals. We calculate the first two terms in their asymptotic expansion
Random matrix theory of quantum transport in chaotic cavities with nonideal leads
Jarosz, Andrzej; Vidal, Pedro; Kanzieper, Eugene
2015-05-01
We determine the joint probability density function (JPDF) of reflection eigenvalues in three Dyson's ensembles of normal-conducting chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Expressing the JPDF in terms of hypergeometric functions of matrix arguments (labeled by the Dyson index β ), we further show that reflection eigenvalues form a determinantal ensemble at β =2 and a new type of a Pfaffian ensemble at β =4 . As an application, we derive a simple analytic expression for the concurrence distribution describing production of orbitally entangled electrons in chaotic cavities with tunnel point contacts when time-reversal symmetry is preserved.
Exploring multicollinearity using a random matrix theory approach.
Feher, Kristen; Whelan, James; Müller, Samuel
2012-01-01
Clustering of gene expression data is often done with the latent aim of dimension reduction, by finding groups of genes that have a common response to potentially unknown stimuli. However, what is poorly understood to date is the behaviour of a low dimensional signal embedded in high dimensions. This paper introduces a multicollinear model which is based on random matrix theory results, and shows potential for the characterisation of a gene cluster's correlation matrix. This model projects a one dimensional signal into many dimensions and is based on the spiked covariance model, but rather characterises the behaviour of the corresponding correlation matrix. The eigenspectrum of the correlation matrix is empirically examined by simulation, under the addition of noise to the original signal. The simulation results are then used to propose a dimension estimation procedure of clusters from data. Moreover, the simulation results warn against considering pairwise correlations in isolation, as the model provides a mechanism whereby a pair of genes with `low' correlation may simply be due to the interaction of high dimension and noise. Instead, collective information about all the variables is given by the eigenspectrum.
Random matrix theory and fund of funds portfolio optimisation
Conlon, T.; Ruskin, H. J.; Crane, M.
2007-08-01
The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a fund of hedge funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper, random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers. The inverse participation ratio is used to quantify the number of components that participate in each eigenvector. Finally, the correlation matrix is cleaned by separating the noisy part from the non-noisy part of C. This technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio, leading to an improved risk profile for a fund of hedge funds.
Optimization of MIMO Systems Capacity Using Large Random Matrix Methods
Directory of Open Access Journals (Sweden)
Philippe Loubaton
2012-11-01
Full Text Available This paper provides a comprehensive introduction of large random matrix methods for input covariance matrix optimization of mutual information of MIMO systems. It is first recalled informally how large system approximations of mutual information can be derived. Then, the optimization of the approximations is discussed, and important methodological points that are not necessarily covered by the existing literature are addressed, including the strict concavity of the approximation, the structure of the argument of its maximum, the accuracy of the large system approach with regard to the number of antennas, or the justification of iterative water-filling optimization algorithms. While the existing papers have developed methods adapted to a specific model, this contribution tries to provide a unified view of the large system approximation approach.
Random Matrix Theory of Rigidity in Soft Matter
Yamanaka, Masanori
2015-06-01
We study the rigidity or softness of soft matter using the characteristic scale of coupling formation developed in random matrix theory. The eigensystems of the timescale-dependent cross-correlation matrix, which are obtained from the time series data of the atomic coordinates of a protein produced by the all-atom molecular dynamics of the solvent, are analyzed. As an example, we present a result for a protein lysozyme, PDBID:1AKI. We find that there are at least three different time scales involved in the coupling formation of correlated sectors of atoms and at least two different time scales for the size of the correlated sectors. These five time scales coexist simultaneously. We compare the results with those of the normal mode analysis and find a crossover of the distribution of the dominant vibrational components.
Taste breaking in staggered fermions from random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Osborna, James C
2004-03-01
We discuss the construction of a chiral random matrix model for staggered fermions. This model includes O(a{sup 2}) corrections to the continuum limit of staggered fermions and is related to the zero momentum limit of the Lee-Sharpe Lagrangian for staggered fermions. The naive construction based on a specific expansion in lattice spacing (a) of the Dirac matrix produces the term which gives the dominant contribution to the observed taste splitting in the pion masses. A more careful analysis can include extra terms which are also consistent with the symmetries of staggered fermions. Lastly I will mention possible uses of the model including studies of topology and fractional powers of the fermion determinant.
A random-matrix theory of the number sense.
Hannagan, T; Nieder, A; Viswanathan, P; Dehaene, S
2017-02-19
Number sense, a spontaneous ability to process approximate numbers, has been documented in human adults, infants and newborns, and many other animals. Species as distant as monkeys and crows exhibit very similar neurons tuned to specific numerosities. How number sense can emerge in the absence of learning or fine tuning is currently unknown. We introduce a random-matrix theory of self-organized neural states where numbers are coded by vectors of activation across multiple units, and where the vector codes for successive integers are obtained through multiplication by a fixed but random matrix. This cortical implementation of the 'von Mises' algorithm explains many otherwise disconnected observations ranging from neural tuning curves in monkeys to looking times in neonates and cortical numerotopy in adults. The theory clarifies the origin of Weber-Fechner's Law and yields a novel and empirically validated prediction of multi-peak number neurons. Random matrices constitute a novel mechanism for the emergence of brain states coding for quantity.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).
Chen, Peng
2014-12-03
Background Protein-ligand binding is important for some proteins to perform their functions. Protein-ligand binding sites are the residues of proteins that physically bind to ligands. Despite of the recent advances in computational prediction for protein-ligand binding sites, the state-of-the-art methods search for similar, known structures of the query and predict the binding sites based on the solved structures. However, such structural information is not commonly available. Results In this paper, we propose a sequence-based approach to identify protein-ligand binding residues. We propose a combination technique to reduce the effects of different sliding residue windows in the process of encoding input feature vectors. Moreover, due to the highly imbalanced samples between the ligand-binding sites and non ligand-binding sites, we construct several balanced data sets, for each of which a random forest (RF)-based classifier is trained. The ensemble of these RF classifiers forms a sequence-based protein-ligand binding site predictor. Conclusions Experimental results on CASP9 and CASP8 data sets demonstrate that our method compares favorably with the state-of-the-art protein-ligand binding site prediction methods.
Macroscopic and microscopic (non-)universality of compact support random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Akemann, G.; Vernizzi, G
2000-09-11
A random matrix model with a {sigma}-model like constraint, the restricted trace ensemble (RTE), is solved in the large-n limit. In the macroscopic limit the smooth connected two-point resolvent G(z,w) is found to be non-universal, extending previous results from monomial to arbitrary polynomial potentials. Using loop equation techniques we give a closed though non-universal expression for G(z,w), which extends recursively to all higher k-point resolvents. These findings are in contrast to the usual unconstrained one-matrix model. However, in the microscopic large-n limit, which probes only correlations at distance of the mean level spacing, we are able to show that the constraint does not modify the universal sine-law. In the case of monomial potentials V(M)=M{sup 2p}, we provide a relation valid for finite-n between the k-point correlation function of the RTE and the unconstrained model. In the microscopic large-n limit they coincide which proves the microscopic universality of RTEs.
Matrix and discrepancy view of generalized random and quasirandom graphs
Directory of Open Access Journals (Sweden)
Bolla Marianna
2016-01-01
Full Text Available We will discuss how graph based matrices are capable to find classification of the graph vertices with small within- and between-cluster discrepancies. The structural eigenvalues together with the corresponding spectral subspaces of the normalized modularity matrix are used to find a block-structure in the graph. The notions are extended to rectangular arrays of nonnegative entries and to directed graphs. We also investigate relations between spectral properties, multiway discrepancies, and degree distribution of generalized random graphs. These properties are regarded as generalized quasirandom properties, and we conjecture and partly prove that they are also equivalent for certain deterministic graph sequences, irrespective of stochastic models.
Random Matrix Theory Approach to Chaotic Coherent Perfect Absorbers
Li, Huanan; Suwunnarat, Suwun; Fleischmann, Ragnar; Schanz, Holger; Kottos, Tsampikos
2017-01-01
We employ random matrix theory in order to investigate coherent perfect absorption (CPA) in lossy systems with complex internal dynamics. The loss strength γCPA and energy ECPA, for which a CPA occurs, are expressed in terms of the eigenmodes of the isolated cavity—thus carrying over the information about the chaotic nature of the target—and their coupling to a finite number of scattering channels. Our results are tested against numerical calculations using complex networks of resonators and chaotic graphs as CPA cavities.
Complex Langevin dynamics for chiral random matrix theory
Mollgaard, A.; Splittorff, K.
2013-12-01
We apply complex Langevin dynamics to chiral random matrix theory at nonzero chemical potential. At large quark mass, the simulations agree with the analytical results while incorrect convergence is found for small quark masses. The region of quark masses for which the complex Langevin dynamics converges incorrectly is identified as the region where the fermion determinant frequently traces out a path surrounding the origin of the complex plane during the Langevin flow. This links the incorrect convergence to an ambiguity in the Langevin force due to the presence of the logarithm of the fermion determinant in the action.
Index Theorem and Random Matrix Theory for Improved Staggered Quarks
Energy Technology Data Exchange (ETDEWEB)
Follana, E. [Department of Physics and Astronomy, University of Glasgow (United Kingdom); Hart, A. [School of Physics, University of Edinburgh (United Kingdom); Davies, C.T.H. [Department of Physics and Astronomy, University of Glasgow (United Kingdom)
2006-03-15
We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD. We find a clear separation of the spectrum of eigenvalues into high chirality, would-be zero modes and others, in accordance with the Index Theorem. We find the expected clustering of the non-zero modes into quartets as we approach the continuum limit. The predictions of random matrix theory for the epsilon regime are well reproduced. We conclude that improved staggered quarks near the continuum limit respond correctly to QCD topology.
Random matrix theory and QCD at nonzero chemical potential
Energy Technology Data Exchange (ETDEWEB)
Verbaarschot, J.J.M. [State Univ. of New York, Stony Brook, NY (United States). Dept. of Physics and Astronomy
1998-11-02
In this lecture we give a brief review of chiral random matrix theory (chRMT) and its applications to QCD at nonzero chemical potential. We present both analytical arguments involving chiral perturbation theory and numerical evidence from lattice QCD simulations showing that correlations of the smallest Dirac eigenvalues are described by chRMT. We discuss the range of validity of chRMT and emphasize the importance of universality. For chRMT`s at {mu}{ne}0 we identify universal properties of the Dirac eigenvalues and study the effect of quenching on the distribution of Yang-Lee zeros. (orig.) 86 refs.
Charting an Inflationary Landscape with Random Matrix Theory
Energy Technology Data Exchange (ETDEWEB)
Marsh, M.C. David [Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP (United Kingdom); McAllister, Liam [Department of Physics, Cornell University, Ithaca, NY 14853 (United States); Pajer, Enrico [Department of Physics, Princeton University, Princeton, NJ 08544 (United States); Wrase, Timm, E-mail: david.marsh1@physics.ox.ac.uk, E-mail: mcallister@cornell.edu, E-mail: epajer@princeton.edu, E-mail: timm.wrase@stanford.edu [Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305 (United States)
2013-11-01
We construct a class of random potentials for N >> 1 scalar fields using non-equilibrium random matrix theory, and then characterize multifield inflation in this setting. By stipulating that the Hessian matrices in adjacent coordinate patches are related by Dyson Brownian motion, we define the potential in the vicinity of a trajectory. This method remains computationally efficient at large N, permitting us to study much larger systems than has been possible with other constructions. We illustrate the utility of our approach with a numerical study of inflation in systems with up to 100 coupled scalar fields. A significant finding is that eigenvalue repulsion sharply reduces the duration of inflation near a critical point of the potential: even if the curvature of the potential is fine-tuned to be small at the critical point, small cross-couplings in the Hessian cause the curvature to grow in the neighborhood of the critical point.
Particle diagrams and embedded many-body random matrix theory
Small, R. A.; Müller, S.
2014-07-01
We present a method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplifications. We use it here to find the fourth, sixth, and eighth moments of the level density of an m-body system with k fermions or bosons interacting through a random Hermitian potential (k ≤m) in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k=m, from moments arising from a semicircular level density to Gaussian moments. The results also reveal a striking feature; the domain of the 2nth moment is naturally divided into n subdomains specified by the points 2k=m,3k=m,...,nk=m.
Energy Technology Data Exchange (ETDEWEB)
Agassi, D.; Ko, C.M.; Weidenmueller, H.A.
1977-09-06
A random-matrix model is used to describe the transformation of kinetic energy of relative motion into intrinsic excitation energy typical of a deeply inelastic heavy-ion collision. The random-matrix model is based upon statistical assumptions regarding the form factors coupling relative motion with intrinsic excitation of either fragment. Average cross sections are calculated by means of an ensemble average over the random matrix model. Summations over intermediate and final intrinsic spin values are performed. As a result, average cross sections are given by the asymptotic behavior of a probability density which in turn obeys a transport equation. In the transport equation there is no further reference to intrinsic spins. The physical and mathematical properties of this equation are exhibited.
Statistics of resonances and delay times in random media: beyond random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Kottos, Tsampikos [Department of Physics, Wesleyan University, Middletown, CT 06459-0155 (United States); Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstrasse 10, D-37073 Goettingen (Germany)
2005-12-09
We review recent developments in quantum scattering from mesoscopic systems. Various spatial geometries whose closed analogues show diffusive, localized or critical behaviour are considered. These are the features that cannot be described by the universal random matrix theory results. Instead, one has to go beyond this approximation and incorporate them in a non-perturbative way. Here, we pay particular attention to the traces of these non-universal characteristics, in the distribution of the Wigner delay times and resonance widths. The former quantity captures time-dependent aspects of quantum scattering while the latter is associated with the poles of the scattering matrix.
Blind Measurement Selection: A Random Matrix Theory Approach
Elkhalil, Khalil
2016-12-14
This paper considers the problem of selecting a set of $k$ measurements from $n$ available sensor observations. The selected measurements should minimize a certain error function assessing the error in estimating a certain $m$ dimensional parameter vector. The exhaustive search inspecting each of the $n\\\\choose k$ possible choices would require a very high computational complexity and as such is not practical for large $n$ and $k$. Alternative methods with low complexity have recently been investigated but their main drawbacks are that 1) they require perfect knowledge of the measurement matrix and 2) they need to be applied at the pace of change of the measurement matrix. To overcome these issues, we consider the asymptotic regime in which $k$, $n$ and $m$ grow large at the same pace. Tools from random matrix theory are then used to approximate in closed-form the most important error measures that are commonly used. The asymptotic approximations are then leveraged to select properly $k$ measurements exhibiting low values for the asymptotic error measures. Two heuristic algorithms are proposed: the first one merely consists in applying the convex optimization artifice to the asymptotic error measure. The second algorithm is a low-complexity greedy algorithm that attempts to look for a sufficiently good solution for the original minimization problem. The greedy algorithm can be applied to both the exact and the asymptotic error measures and can be thus implemented in blind and channel-aware fashions. We present two potential applications where the proposed algorithms can be used, namely antenna selection for uplink transmissions in large scale multi-user systems and sensor selection for wireless sensor networks. Numerical results are also presented and sustain the efficiency of the proposed blind methods in reaching the performances of channel-aware algorithms.
Index Theorem and Random Matrix Theory for Improved Staggered Quarks
Energy Technology Data Exchange (ETDEWEB)
Follana, E. [Department of Physics and Astronomy, University of Glasgow, G12 8QQ Glasgow (United Kingdom)
2005-03-15
We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We find a clear separation of the spectrum of eigenvalues into would-be zero modes and others. The number of would-be zero modes depends on the topological charge as expected from the Index Theorem, and their chirality expectation value is large. The remaining modes have low chirality and show clear signs of clustering into quartets and approaching the random matrix theory predictions for all topological charge sectors. We conclude that improvement of the fermionic and gauge actions moves the staggered quarks closer to the continuum limit where they respond correctly to QCD topology.
Random matrix theory of a chaotic Andreev quantum dot
Energy Technology Data Exchange (ETDEWEB)
Altland, A.; Zirnbauer, M.R. [Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Str.77, 50937 Koeln (Germany)
1996-04-01
A new universality class distinct from the standard Wigner-Dyson class is identified. This class is realized by putting a metallic quantum dot in contact with a superconductor, while applying a magnetic field so as to make the pairing field effectively vanish on average. A random-matrix description of the spectral and transport properties of such a quantum dot is proposed. The weak-localization correction to the tunnel conductance is nonzero and results from the depletion of the density of states due to the coupling with the superconductor. Semiclassically, the depletion is caused by a singular mode of phase-coherent long-range propagation of particles and holes. {copyright} {ital 1996 The American Physical Society.}
Perturbation treatment of symmetry breaking within random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Carvalho, J.X. de [Max-Planck-Institut fuer Physik komplexer Systeme, Noethnitzer Strasse 38, D-01187 Dresden (Germany); Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, S.P. (Brazil); Hussein, M.S. [Max-Planck-Institut fuer Physik komplexer Systeme, Noethnitzer Strasse 38, D-01187 Dresden (Germany); Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, S.P. (Brazil)], E-mail: mhussein@mpipks-dresden.mpg.de; Pato, M.P.; Sargeant, A.J. [Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, S.P. (Brazil)
2008-07-07
We discuss the applicability, within the random matrix theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both two-fold and three-fold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an appropriate number of eigenfrequencies is considered to be missing in the sample. Our findings are relevant for symmetry violation studies in general.
Large-Nc Gauge Theory and Chiral Random Matrix Theory
Hanada, Masanori; Lee, Jong-Wan; Yamada, Norikazu
Effective theory approaches and the large-Nc limit are useful for studying the strongly coupled gauge theories. In this talk we consider how the chiral random matrix theory (χRMT) can be used in the study of large-Nc gauge theories. It turns out the parameter regions, in which each of these two approaches are valid, are different. Still, however, we show that the breakdown of chiral symmetry can be detected by combining the large-Nc argument and the χRMT with some cares. As a demonstration, we numerically study the four dimensional SU(Nc) gauge theory with Nf = 2 heavy adjoint fermions on a 24 lattice by using Monte-Carlo simulations, which is related to the infinite volume lattice through the Eguchi-Kawai equivalence.
From gap probabilities in random matrix theory to eigenvalue expansions
Bothner, Thomas
2016-02-01
We present a method to derive asymptotics of eigenvalues for trace-class integral operators K :{L}2(J;{{d}}λ )\\circlearrowleft , acting on a single interval J\\subset {{R}}, which belongs to the ring of integrable operators (Its et al 1990 Int. J. Mod. Phys. B 4 1003-37 ). Our emphasis lies on the behavior of the spectrum \\{{λ }i(J)\\}{}i=0∞ of K as | J| \\to ∞ and i is fixed. We show that this behavior is intimately linked to the analysis of the Fredholm determinant {det}(I-γ K){| }{L2(J)} as | J| \\to ∞ and γ \\uparrow 1 in a Stokes type scaling regime. Concrete asymptotic formulæ are obtained for the eigenvalues of Airy and Bessel kernels in random matrix theory. Dedicated to Percy Deift and Craig Tracy on the occasion of their 70th birthdays.
Cleaning large correlation matrices: Tools from Random Matrix Theory
Bun, Joël; Bouchaud, Jean-Philippe; Potters, Marc
2017-01-01
This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marčenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent "Rotationally Invariant" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.
Random-matrix theory of amplifying and absorbing resonators with {PT} or {PTT}^{\\prime } symmetry
Birchall, Christopher; Schomerus, Henning
2012-11-01
We formulate Gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical realizations of such systems we consider a {PT} or a {PTT}^{\\prime } time-reversal symmetry, which impose different constraints on magneto-optical effects, and then focus on five common settings. For each of these, we determine the eigenvalue distribution in the complex plane in the short-wavelength limit, which reveals that the fraction of real eigenvalues among all eigenvalues in the spectrum vanishes if all classical scales are kept fixed. Numerically, we find that the transition from real to complex eigenvalues in the various ensembles display a different dependence on the coupling strength between the two resonators. These differences can be linked to the level spacing statistics in the Hermitian limit of the considered models. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Suliman, Mohamed
2016-01-01
In this supplementary appendix we provide proofs and additional simulation results that complement the paper (constrained perturbation regularization approach for signal estimation using random matrix theory).
Kernel Factory: An Ensemble of Kernel Machines
M. BALLINGS; D. VAN DEN POEL
2012-01-01
We propose an ensemble method for kernel machines. The training data is randomly split into a number of mutually exclusive partitions defined by a row and column parameter. Each partition forms an input space and is transformed by a kernel function into a kernel matrix K. Subsequently, each K is used as training data for a base binary classifier (Random Forest). This results in a number of predictions equal to the number of partitions. A weighted average combines the predictions into one fina...
Random matrix approach to the dynamics of stock inventory variations
Zhou, Wei-Xing; Mu, Guo-Hua; Kertész, János
2012-09-01
It is well accepted that investors can be classified into groups owing to distinct trading strategies, which forms the basic assumption of many agent-based models for financial markets when agents are not zero-intelligent. However, empirical tests of these assumptions are still very rare due to the lack of order flow data. Here we adopt the order flow data of Chinese stocks to tackle this problem by investigating the dynamics of inventory variations for individual and institutional investors that contain rich information about the trading behavior of investors and have a crucial influence on price fluctuations. We find that the distributions of cross-correlation coefficient Cij have power-law forms in the bulk that are followed by exponential tails, and there are more positive coefficients than negative ones. In addition, it is more likely that two individuals or two institutions have a stronger inventory variation correlation than one individual and one institution. We find that the largest and the second largest eigenvalues (λ1 and λ2) of the correlation matrix cannot be explained by random matrix theory and the projections of investors' inventory variations on the first eigenvector u(λ1) are linearly correlated with stock returns, where individual investors play a dominating role. The investors are classified into three categories based on the cross-correlation coefficients CV R between inventory variations and stock returns. A strong Granger causality is unveiled from stock returns to inventory variations, which means that a large proportion of individuals hold the reversing trading strategy and a small part of individuals hold the trending strategy. Our empirical findings have scientific significance in the understanding of investors' trading behavior and in the construction of agent-based models for emerging stock markets.
Porcine collagen matrix for treating gingival recession. Randomized clinical trial.
Directory of Open Access Journals (Sweden)
Yuri Castro
2014-03-01
Full Text Available Achieving root coverage after exposure caused by gingival recession is one of the main goals of reconstructive periodontal surgery. Even though a large variety of techniques and mucogingival grafting procedures are available, their long-term results are not clear yet. Therefore, this study aimed to compare clinical effectiveness of the porcine collagen matrix with subepithelial connective graft for treating Miller class I and II gingival recessions. Materials and methods: The randomized clinical trial included twelve patients assigned to two groups. In the first group (experimental, six patients were treated using collagen matrix (mean age, 54.3±5.6 years; mean recession 2. 67±1.03mm. Another group (control of six patients was treated using connective grafts (mean age, 57.1± 2.7 years; mean recession 4.33±1.03mm. All patients underwent periodontal evaluation and pre-surgical preparation including oral hygiene instruction and supragingival scaling. Gingival recessions were exposed through partial thickness flaps where the grafts and matrices were placed. Patients were assessed periodically until complete healing of tissue. Results: Root coverage parameters, amount of keratinized gingiva, gingival biotype and clinical attachment level were evaluated. The root coverage percentage for the group using connective graft was 24.7±13.5% and 16.6±26.8% for the one treated with the matrix. The amount of increased keratinized tissue was 4.33±2.06mm and 4.5±0.83mm for the control and experimental group respectively. Both groups increased gingival biotypes from thin to thick at 100%. The final clinical attachment level was 4.17±3.17±04mm for the control group and 0.98mm for the experimental group. There were significant differences between the outcome of gingival recession and clinical attachment. Conclusion: Results indicate both techniques, besides being predictable, are useful for improving clinical parameters when treating gingival recessions
Advances in random matrix theory, zeta functions, and sphere packing
Hales, T. C.; Sarnak, P.; Pugh, M. C.
2000-01-01
Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks. PMID:11058156
Random matrix theory filters and currency portfolio optimisation
Daly, J.; Crane, M.; Ruskin, H. J.
2010-04-01
Random matrix theory (RMT) filters have recently been shown to improve the optimisation of financial portfolios. This paper studies the effect of three RMT filters on realised portfolio risk, using bootstrap analysis and out-of-sample testing. We considered the case of a foreign exchange and commodity portfolio, weighted towards foreign exchange, and consisting of 39 assets. This was intended to test the limits of RMT filtering, which is more obviously applicable to portfolios with larger numbers of assets. We considered both equally and exponentially weighted covariance matrices, and observed that, despite the small number of assets involved, RMT filters reduced risk in a way that was consistent with a much larger S&P 500 portfolio. The exponential weightings indicated showed good consistency with the value suggested by Riskmetrics, in contrast to previous results involving stocks. This decay factor, along with the low number of past moves preferred in the filtered, equally weighted case, displayed a trend towards models which were reactive to recent market changes. On testing portfolios with fewer assets, RMT filtering provided less or no overall risk reduction. In particular, no long term out-of-sample risk reduction was observed for a portfolio consisting of 15 major currencies and commodities.
Novaes, Marcel
2015-06-01
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = - iħS†dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.
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Novaes, Marcel [Instituto de Física, Universidade Federal de Uberlândia, Ave. João Naves de Ávila, 2121, Uberlândia, MG 38408-100 (Brazil)
2015-06-15
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS{sup †}dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.
Rotationally invariant ensembles of integrable matrices.
Yuzbashyan, Emil A; Shastry, B Sriram; Scaramazza, Jasen A
2016-05-01
We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT)-a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M family of integrable matrices consists of exactly N-M independent commuting N×N matrices linear in a real parameter. We first develop a rotationally invariant parametrization of such matrices, previously only constructed in a preferred basis. For example, an arbitrary choice of a vector and two commuting Hermitian matrices defines a type-1 family and vice versa. Higher types similarly involve a random vector and two matrices. The basis-independent formulation allows us to derive the joint probability density for integrable matrices, similar to the construction of Gaussian ensembles in the RMT.
Energy Technology Data Exchange (ETDEWEB)
Suleymanov, Mais [CIIT, Islamabad (Pakistan); Shahaliev, Ehtiram [HEPL, JINR, Dubna (Russian Federation)
2009-07-01
Over the last 25 years a lot of efforts have been made to search for new phases of strongly interacting matter. Heavy ion collisions are of great importance since they open a way to reproduce these phases in the Earth laboratory. But in this case the volume of information increases sharply as well as the background information. A method was introduced a method on the basic of Random Matrix Theory to study the fluctuations of neutron resonances in compound nuclei which doesn't depend on the background of measurements. To analyze the energetic levels of compound nuclei the function of distances between two energetic levels p(s{sub i}) is defined as the general distributions for probability of all kinds of ensembles. At values of the index of universality {nu}=0 it will change to Poisson type distributions pointing to absence of any correlations in the system and at the values of {nu}=1 it will change to Wigner type behavior directing to some correlation in the studying ensemble. We discuss that the experimental study of the behavior of p(s{sub i}) distribution for secondary particles could give a signal on the phase transitions.
Andric, I; Jurman, D; Nielsen, H B
2007-01-01
We discuss a dynamical matrix model by which probability distribution is associated with Gaussian ensembles from random matrix theory. We interpret the matrix M as a Hamiltonian representing interaction of a bosonic system with a single fermion. We show that a system of second-quantized fermions influences the ground state of the whole system by producing a gap between the highest occupied eigenvalue and the lowest unoccupied eigenvalue.
Ensemble global ocean forecasting
Brassington, G. B.
2016-02-01
A novel time-lagged ensemble system based on multiple independent cycles has been performed in operations at the Australian Bureau of Meteorology for the past 3 years. Despite the use of only four cycles the ensemble mean provided robustly higher skill and the ensemble variance was a reliable predictor of forecast errors. A spectral analysis comparing the ensemble mean with the members demonstrated the gradual increase in power of random errors with wavenumber up to a saturation length scale imposed by the resolution of the observing system. This system has been upgraded to a near-global 0.1 degree system in a new hybrid six-member ensemble system configuration including a new data assimilation system, cycling pattern and initialisation. The hybrid system consists of two ensemble members per day each with a 3 day cycle. We will outline the performance of both the deterministic and ensemble ocean forecast system.
Spectra of large time-lagged correlation matrices from random matrix theory
Nowak, Maciej A.; Tarnowski, Wojciech
2017-06-01
We analyze the spectral properties of large, time-lagged correlation matrices using the tools of random matrix theory. We compare predictions of the one-dimensional spectra, based on approaches already proposed in the literature. Employing the methods of free random variables and diagrammatic techniques, we solve a general random matrix problem, namely the spectrum of a matrix \\frac{1}{T}XA{{X}\\dagger} , where X is an N× T Gaussian random matrix and A is any T× T , not necessarily symmetric (Hermitian) matrix. Using this result, we study the spectral features of the large lagged correlation matrices as a function of the depth of the time-lag. We also analyze the properties of left and right eigenvector correlations for the time-lagged matrices. We positively verify our results by the numerical simulations.
Online Learning with Ensembles
Urbanczik, R.
1999-01-01
Supervised online learning with an ensemble of students randomized by the choice of initial conditions is analyzed. For the case of the perceptron learning rule, asymptotically the same improvement in the generalization error of the ensemble compared to the performance of a single student is found as in Gibbs learning. For more optimized learning rules, however, using an ensemble yields no improvement. This is explained by showing that for any learning rule $f$ a transform $\\tilde{f}$ exists,...
Constrained Perturbation Regularization Approach for Signal Estimation Using Random Matrix Theory
Suliman, Mohamed; Ballal, Tarig; Kammoun, Abla; Al-Naffouri, Tareq Y.
2016-12-01
In this supplementary appendix we provide proofs and additional extensive simulations that complement the analysis of the main paper (constrained perturbation regularization approach for signal estimation using random matrix theory).
Density of state in a complex random matrix theory with external source
Energy Technology Data Exchange (ETDEWEB)
Hikami, S. [Department of Pure and Applied Sciences, University of Tokyo, Meguro-ku, Komaba, Tokyo (Japan); Pnini, R. [Department of Pure and Applied Sciences, University of Tokyo, Meguro-ku, Komaba, Tokyo (Japan); CREST, Japan Science and Technology Cooperation (Japan)
1998-09-04
The density of state for a complex NxN random matrix coupled to an external deterministic source is considered for a finite N, and a compact expression in an integral representation is obtained. (author). Letter-to-the-editor.
Considering Horn’s parallel analysis from a random matrix theory point of view
Saccenti, Edoardo; Timmerman, Marieke E.
Horn’s parallel analysis is a widely used method for assessing the number of principal components and common factors. We discuss the theoretical foundations of parallel analysis for principal components based on a covariance matrix by making use of arguments from random matrix theory. In particular,
Considering Horn’s Parallel Analysis from a Random Matrix Theory Point of View
Saccenti, Edoardo; Timmerman, Marieke E.
2017-01-01
Horn’s parallel analysis is a widely used method for assessing the number of principal components and common factors. We discuss the theoretical foundations of parallel analysis for principal components based on a covariance matrix by making use of arguments from random matrix theory. In
A random matrix approach to RNA folding with interaction
Indian Academy of Sciences (India)
2015-11-27
Nov 27, 2015 ... In the matrix model of RNA [G Vernizzi, H Orland and A Zee, Phys. Rev. Lett. 94, 168103 (2005)] we introduce external interactions on n bases in the action of the partition function where ≤ and is the length of the polymer chain. The RNA structures found in the model can be separated into two ...
A random matrix approach to RNA folding with interaction
Indian Academy of Sciences (India)
Abstract. In the matrix model of RNA [G Vernizzi, H Orland and A Zee, Phys. Rev. Lett. 94, 168103 (2005)] we introduce external interactions on n bases in the action of the partition function where n ≤ L and L is the length of the polymer chain. The RNA structures found in the model can be separated into two regimes: (i) 0 ...
Abbout, Adel
2016-08-05
Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and connected through a low-density-of-states two-level quantum dot that acts as a conducting chaotic cavity. Our exact treatment of the chaotic behavior in such devices lies on the scattering matrix formalism and yields analytical expressions for the joint probability distribution functions of the Seebeck coefficient and the transmission profile, as well as the marginal distributions, at arbitrary Fermi energy. The scattering matrices belong to circular ensembles which we sample to numerically compute the transmission function, the Seebeck coefficient, and their relationship. The exact transport coefficients probability distributions are found to be highly non-Gaussian for small numbers of conduction modes, and the analytical and numerical results are in excellent agreement. The system performance is also studied, and we find that the optimum performance is obtained for half-transparent quantum dots; further, this optimum may be enhanced for systems with few conduction modes.
A generalization of random matrix theory and its application to statistical physics
Wang, Duan; Zhang, Xin; Horvatic, Davor; Podobnik, Boris; Eugene Stanley, H.
2017-02-01
To study the statistical structure of crosscorrelations in empirical data, we generalize random matrix theory and propose a new method of cross-correlation analysis, known as autoregressive random matrix theory (ARRMT). ARRMT takes into account the influence of auto-correlations in the study of cross-correlations in multiple time series. We first analytically and numerically determine how auto-correlations affect the eigenvalue distribution of the correlation matrix. Then we introduce ARRMT with a detailed procedure of how to implement the method. Finally, we illustrate the method using two examples taken from inflation rates for air pressure data for 95 US cities.
Random matrix theory for pseudo-Hermitian systems: Cyclic blocks
Indian Academy of Sciences (India)
tems, and, for Hamiltonians that break parity P and time-reversal invariance T. In an attempt to understand the ... Keywords. Random matrices; circulants; quantum chaos; PT symmetry; pseudo-. Hermiticity. ... local fluctuation properties of complex quantum systems have universal properties, independent of the details of the ...
Local random quantum circuits: Ensemble completely positive maps and swap algebras
Energy Technology Data Exchange (ETDEWEB)
Zanardi, Paolo [Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA and Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore)
2014-08-15
We define different classes of local random quantum circuits (L-RQC) and show that (a) statistical properties of L-RQC are encoded into an associated family of completely positive maps and (b) average purity dynamics can be described by the action of these maps on operator algebras of permutations (swap algebras). An exactly solvable one-dimensional case is analyzed to illustrate the power of the swap algebra formalism. More in general, we prove short time area-law bounds on average purity for uncorrelated L-RQC and infinite time results for both the uncorrelated and correlated cases.
Local random quantum circuits: Ensemble completely positive maps and swap algebras
Zanardi, Paolo
2014-08-01
We define different classes of local random quantum circuits (L-RQC) and show that (a) statistical properties of L-RQC are encoded into an associated family of completely positive maps and (b) average purity dynamics can be described by the action of these maps on operator algebras of permutations (swap algebras). An exactly solvable one-dimensional case is analyzed to illustrate the power of the swap algebra formalism. More in general, we prove short time area-law bounds on average purity for uncorrelated L-RQC and infinite time results for both the uncorrelated and correlated cases.
Directory of Open Access Journals (Sweden)
Debesh Jha
2017-01-01
Full Text Available Accurate diagnosis of pathological brain images is important for patient care, particularly in the early phase of the disease. Although numerous studies have used machine-learning techniques for the computer-aided diagnosis (CAD of pathological brain, previous methods encountered challenges in terms of the diagnostic efficiency owing to deficiencies in the choice of proper filtering techniques, neuroimaging biomarkers, and limited learning models. Magnetic resonance imaging (MRI is capable of providing enhanced information regarding the soft tissues, and therefore MR images are included in the proposed approach. In this study, we propose a new model that includes Wiener filtering for noise reduction, 2D-discrete wavelet transform (2D-DWT for feature extraction, probabilistic principal component analysis (PPCA for dimensionality reduction, and a random subspace ensemble (RSE classifier along with the K-nearest neighbors (KNN algorithm as a base classifier to classify brain images as pathological or normal ones. The proposed methods provide a significant improvement in classification results when compared to other studies. Based on 5×5 cross-validation (CV, the proposed method outperforms 21 state-of-the-art algorithms in terms of classification accuracy, sensitivity, and specificity for all four datasets used in the study.
Directory of Open Access Journals (Sweden)
Connie Ko
2016-08-01
selected randomly (with stratified sample size; to 93.8%; when samples were selected with additional criteria; and from 88.4% to 93.8% when an ensemble method was used.
Diffusion MRI noise mapping using random matrix theory
Veraart, Jelle; Fieremans, Els; Novikov, Dmitry S.
2016-01-01
Purpose To estimate the spatially varying noise map using a redundant magnitude MR series. Methods We exploit redundancy in non-Gaussian multi-directional diffusion MRI data by identifying its noise-only principal components, based on the theory of noisy covariance matrices. The bulk of PCA eigenvalues, arising due to noise, is described by the universal Marchenko-Pastur distribution, parameterized by the noise level. This allows us to estimate noise level in a local neighborhood based on the singular value decomposition of a matrix combining neighborhood voxels and diffusion directions. Results We present a model-independent local noise mapping method capable of estimating noise level down to about 1% error. In contrast to current state-of-the art techniques, the resultant noise maps do not show artifactual anatomical features that often reflect physiological noise, the presence of sharp edges, or a lack of adequate a priori knowledge of the expected form of MR signal. Conclusions Simulations and experiments show that typical diffusion MRI data exhibit sufficient redundancy that enables accurate, precise, and robust estimation of the local noise level by interpreting the PCA eigenspectrum in terms of the Marchenko-Pastur distribution. PMID:26599599
Denoising of diffusion MRI using random matrix theory
Veraart, Jelle; Novikov, Dmitry S.; Christiaens, Daan; Ades-aron, Benjamin; Sijbers, Jan; Fieremans, Els
2016-01-01
We introduce and evaluate a post-processing technique for fast denoising diffusion-weighted MR images. By exploiting the intrinsic redundancy in diffusion MRI using universal properties of the eigenspectrum of random covariance matrices, we remove noise-only principal components, thereby enabling signal-to-noise ratio enhancements, yielding parameter maps of improved quality for visual, quantitative, and statistical interpretation. By studying statistics of residuals, we demonstrate that the technique suppresses local signal fluctuations that solely originate from thermal noise rather than from other sources such as anatomical detail. Furthermore, we achieve improved precision in the estimation of diffusion parameters and fiber orientations in the human brain without compromising the accuracy and/or spatial resolution. PMID:27523449
Quantized gauge theory on the fuzzy sphere as random matrix model
Energy Technology Data Exchange (ETDEWEB)
Steinacker, Harold E-mail: harold.steinacker@physik.uni-muenchen.de
2004-02-16
U(n) Yang-Mills theory on the fuzzy sphere S{sup 2}{sub N} is quantized using random matrix methods. The gauge theory is formulated as a matrix model for a single Hermitian matrix subject to a constraint, and a potential with two degenerate minima. This allows to reduce the path integral over the gauge fields to an integral over eigenvalues, which can be evaluated for large N. The partition function of U(n) Yang-Mills theory on the classical sphere is recovered in the large N limit, as a sum over instanton contributions. The monopole solutions are found explicitly.
Full simulation of chiral random matrix theory at nonzero chemical potential by complex Langevin
Mollgaard, A.; Splittorff, K.
2015-02-01
It is demonstrated that the complex Langevin method can simulate chiral random matrix theory at nonzero chemical potential. The successful match with the analytic prediction for the chiral condensate is established through a shift of matrix integration variables and choosing a polar representation for the new matrix elements before complexification. Furthermore, we test the proposal to work with a Langevin-time-dependent quark mass and find that it allows us to control the fluctuations of the phase of the fermion determinant throughout the Langevin trajectory.
On the Marginal Distribution of the Diagonal Blocks in a Blocked Wishart Random Matrix
Directory of Open Access Journals (Sweden)
Kjetil B. Halvorsen
2016-01-01
Full Text Available Let A be a (m1+m2×(m1+m2 blocked Wishart random matrix with diagonal blocks of orders m1×m1 and m2×m2. The goal of the paper is to find the exact marginal distribution of the two diagonal blocks of A. We find an expression for this marginal density involving the matrix-variate generalized hypergeometric function. We became interested in this problem because of an application in spatial interpolation of random fields of positive definite matrices, where this result will be used for parameter estimation, using composite likelihood methods.
Chiral random matrix theory and the spectrum of the Dirac operator near zero virtuality
Energy Technology Data Exchange (ETDEWEB)
Verbaarschot, J. [State Univ. of New York, Stony Brook, NY (United States). Dept. of Physics
1994-01-01
We study the spectrum of the QCD Dirac operator near zero virtuality. We argue that it can be described by a random matrix theory with the chiral structure of QCD. In the large N limit, this model reduces to the low energy limit of the QCD partition function put forward by Leutwyler and Smilga. We conjecture that the microscopic limit of its spectral density is universal and reproduces that of QCD. Using random matrix methods we obtain its exact analytical expression. This results is compared to numerically calculated spectra for a liquid of instantons, and we find a very satisfactory agreement. (author). 26 refs., 2 figs.
Kobayashi, Naohiro
2014-01-01
Superpositioning of atoms in an ensemble of biomolecules is a common task in a variety of fields in structural biology. Although several automated tools exist based on previously established methods, manual operations to define the atoms in the ordered regions are usually preferred. The task is difficult and lacks output efficiency for multi-core proteins having complicated folding topology. The new method presented here can systematically and quantitatively achieve the identification of ordered cores even for molecules containing multiple cores linked with flexible loops. In contrast to established methods, this method treats the variance of inter-atomic distances in an ensemble as information content using a non-linear (NL) function, and then subjects it to multi-dimensional scaling (MDS) to embed the row vectors in the inter-atomic distance variance matrix into a lower dimensional matrix. The plots of the identified atom groups in a one or two-dimensional map enables users to visually and intuitively infer well-ordered atoms in an ensemble, as well as to automatically identify them by the standard clustering methods. The performance of the NL-MDS method has been examined for number of structure ensembles studied by nuclear magnetic resonance, demonstrating that the method can be more suitable for structural analysis of multi-core proteins in comparison to previously established methods.
Photodissociation in quantum chaotic systems: Random-matrix theory of cross-section fluctuations
Energy Technology Data Exchange (ETDEWEB)
Fyodorov, Y.V. [Fachbereich Physik, Universitaet-GH Essen, D-45117 Essen (Germany); Alhassid, Y. [Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520 (United States)
1998-11-01
Using the random matrix description of open quantum chaotic systems we calculate in closed form the universal autocorrelation function and the probability distribution of the total photodissociation cross section in the regime of quantum chaos. {copyright} {ital 1998} {ital The American Physical Society}
Random matrix theory and discrete moments of the Riemann zeta function
Energy Technology Data Exchange (ETDEWEB)
Hughes, C P [Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978 (Israel)
2003-03-28
We calculate the discrete moments of the characteristic polynomial of a random unitary matrix, evaluated a small distance away from an eigenangle. Such results allow us to make conjectures about similar moments for the Riemann zeta function, and provide a uniform approach to understanding moments of the zeta function and its derivative.
Open problems in applying random-matrix theory to nuclear reactions
Weidenmüller, H. A.
2014-09-01
Problems in applying random-matrix theory (RMT) to nuclear reactions arise in two domains. To justify the approach, statistical properties of isolated resonances observed experimentally must agree with RMT predictions. That agreement is less striking than would be desirable. In the implementation of the approach, the range of theoretically predicted observables is too narrow.
Spectra of empirical autocorrelation matrices: A random-matrix-theory-inspired perspective
Jamali, Tayeb; Jafari, G. R.
2015-07-01
We construct an autocorrelation matrix of a time series and analyze it based on the random-matrix theory (RMT) approach. The autocorrelation matrix is capable of extracting information which is not easily accessible by the direct analysis of the autocorrelation function. In order to provide a precise conclusion based on the information extracted from the autocorrelation matrix, the results must be first evaluated. In other words they need to be compared with some sort of criterion to provide a basis for the most suitable and applicable conclusions. In the context of the present study, the criterion is selected to be the well-known fractional Gaussian noise (fGn). We illustrate the applicability of our method in the context of stock markets. For the former, despite the non-Gaussianity in returns of the stock markets, a remarkable agreement with the fGn is achieved.
Energy Technology Data Exchange (ETDEWEB)
Hehl, H.
2002-07-01
This thesis has studied the range of validity of the chiral random matrix theory in QCD on the example of the quenched staggered Dirac operator. The eigenvalues of this operator in the neighbourhood of zero are essential for the understanding of the spontaneous breaking of the chiral symmetry and the phase transition connected with this. The phase transition cannot be understood in the framework of perturbation theory, so that the formulation of QCD on the lattice has been chosen as the only non-perturbative approach. In order to circumvent both the problem of the fermion doubling and to study chiral properties on the lattice with acceptable numerical effort, quenched Kogut-Susskind fermions have been applied. The corresponding Dirac operator can be completely diagonalized by the Lanczos procedure of Cullum and Willoughby. Monte carlo simulations on hypercubic lattice have been performed and the Dirac operators of very much configurations diagonalized at different lattice lengths and coupling constants. The eigenvalue correlations on the microscopic scale are completely described by the chiral random matrix theory for the topological sector zero, which has been studied by means of the distribution of the smallest eigenvalue, the microscopic spectral density and the corresponding 2-point correlation function. The found universal behaviour shows, that on the scale of the lowest eigenvalue only completely general properties of the theory are important, but not the full dynamics. In order to determine the energy scale, from which the chiral random matrix theory losses its validity, - the Thouless energy - with the scalar susceptibilities observables have been analyzed, which are because of their spectral mass dependence sensitive on this. For each combination of the lattice parameter so the deviation point has been identified.
Some Open Problems in Random Matrix Theory and the Theory of Integrable Systems. II
Deift, Percy
2017-03-01
We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de Recherches Mathématiques, Montréal, June 7-11, 2015. We also describe progress that has been made on problems in an earlier list presented by the author on the occasion of his 60^{th} birthday in 2005 (see [Deift P., Contemp. Math., Vol. 458, Amer. Math. Soc., Providence, RI, 2008, 419-430, arXiv:0712.0849]).
Luo, Feng; Yang, Yunfeng; Zhong, Jianxin; Gao, Haichun; Khan, Latifur; Thompson, Dorothea K; Zhou, Jizhong
2007-01-01
Background Large-scale sequencing of entire genomes has ushered in a new age in biology. One of the next grand challenges is to dissect the cellular networks consisting of many individual functional modules. Defining co-expression networks without ambiguity based on genome-wide microarray data is difficult and current methods are not robust and consistent with different data sets. This is particularly problematic for little understood organisms since not much existing biological knowledge can be exploited for determining the threshold to differentiate true correlation from random noise. Random matrix theory (RMT), which has been widely and successfully used in physics, is a powerful approach to distinguish system-specific, non-random properties embedded in complex systems from random noise. Here, we have hypothesized that the universal predictions of RMT are also applicable to biological systems and the correlation threshold can be determined by characterizing the correlation matrix of microarray profiles using random matrix theory. Results Application of random matrix theory to microarray data of S. oneidensis, E. coli, yeast, A. thaliana, Drosophila, mouse and human indicates that there is a sharp transition of nearest neighbour spacing distribution (NNSD) of correlation matrix after gradually removing certain elements insider the matrix. Testing on an in silico modular model has demonstrated that this transition can be used to determine the correlation threshold for revealing modular co-expression networks. The co-expression network derived from yeast cell cycling microarray data is supported by gene annotation. The topological properties of the resulting co-expression network agree well with the general properties of biological networks. Computational evaluations have showed that RMT approach is sensitive and robust. Furthermore, evaluation on sampled expression data of an in silico modular gene system has showed that under-sampled expressions do not affect the
Luo, Feng; Yang, Yunfeng; Zhong, Jianxin; Gao, Haichun; Khan, Latifur; Thompson, Dorothea K; Zhou, Jizhong
2007-08-14
Large-scale sequencing of entire genomes has ushered in a new age in biology. One of the next grand challenges is to dissect the cellular networks consisting of many individual functional modules. Defining co-expression networks without ambiguity based on genome-wide microarray data is difficult and current methods are not robust and consistent with different data sets. This is particularly problematic for little understood organisms since not much existing biological knowledge can be exploited for determining the threshold to differentiate true correlation from random noise. Random matrix theory (RMT), which has been widely and successfully used in physics, is a powerful approach to distinguish system-specific, non-random properties embedded in complex systems from random noise. Here, we have hypothesized that the universal predictions of RMT are also applicable to biological systems and the correlation threshold can be determined by characterizing the correlation matrix of microarray profiles using random matrix theory. Application of random matrix theory to microarray data of S. oneidensis, E. coli, yeast, A. thaliana, Drosophila, mouse and human indicates that there is a sharp transition of nearest neighbour spacing distribution (NNSD) of correlation matrix after gradually removing certain elements insider the matrix. Testing on an in silico modular model has demonstrated that this transition can be used to determine the correlation threshold for revealing modular co-expression networks. The co-expression network derived from yeast cell cycling microarray data is supported by gene annotation. The topological properties of the resulting co-expression network agree well with the general properties of biological networks. Computational evaluations have showed that RMT approach is sensitive and robust. Furthermore, evaluation on sampled expression data of an in silico modular gene system has showed that under-sampled expressions do not affect the recovery of gene
2002-01-01
NYYD Ensemble'i duost Traksmann - Lukk E.-S. Tüüri teosega "Symbiosis", mis on salvestatud ka hiljuti ilmunud NYYD Ensemble'i CDle. 2. märtsil Rakvere Teatri väikeses saalis ja 3. märtsil Rotermanni Soolalaos, kavas Tüür, Kaumann, Berio, Reich, Yun, Hauta-aho, Buckinx
Kanazawa, Takuya; Wettig, Tilo
2014-10-01
We generalize QCD at asymptotically large isospin chemical potential to an arbitrary even number of flavors. We also allow for small quark chemical potentials, which stress the coincident Fermi surfaces of the paired quarks and lead to a sign problem in Monte Carlo simulations. We derive the corresponding low-energy effective theory in both p- and ɛ-expansion and quantify the severity of the sign problem. We construct the random matrix theory describing our physical situation and show that it can be mapped to a known random matrix theory at low baryon density so that new insights can be gained without additional calculations. In particular, we explain the Silver Blaze phenomenon at high isospin density. We also introduce stressed singular values of the Dirac operator and relate them to the pionic condensate. Finally we comment on extensions of our work to two-color QCD.
Random matrix theory and the zeros of {zeta}'(s)
Energy Technology Data Exchange (ETDEWEB)
Mezzadri, Francesco [School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK (United Kingdom)
2003-03-28
We study the density of the roots of the derivative of the characteristic polynomial Z(U, z) of an N x N random unitary matrix with distribution given by Haar measure on the unitary group. Based on previous random matrix theory models of the Riemann zeta function {zeta}(s), this is expected to be an accurate description for the horizontal distribution of the zeros of {zeta}'(s) to the right of the critical line. We show that as N {yields} {infinity} the fraction of the roots of Z'(U, z) that lie in the region 1 - x/(N - 1) {<=} vertical bar z vertical bar < 1 tends to a limit function. We derive asymptotic expressions for this function in the limits x {yields} {infinity} and x {yields} 0 and compare them with numerical experiments.
Testing the Predictions of Random Matrix Theory in Low Loss Wave Chaotic Scattering Systems
Yeh, Jen-Hao; Antonsen, Thomas; Ott, Edward; Anlage, Steven
2013-03-01
Wave chaos is a field where researchers apply random matrix theory (RMT) to predict the statistics of wave properties in complicated wave scattering systems. The RMT predictions have successfully demonstrated universality of the distributions of these wave properties, which only depend on the loss parameter of the system and the physical symmetry. Examination of these predictions in very low loss systems is interesting because extreme limits for the distribution functions and other predictions are encountered. Therefore, we use a wave-chaotic superconducting cavity to establish a low loss environment and test RMT predictions, including the statistics of the scattering (S) matrix and the impedance (Z) matrix, the universality (or lack thereof) of the Z- and S-variance ratios, and the statistics of the proper delay times of the Wigner-Smith time-delay matrix. We have applied an in-situ microwave calibration method (Thru-Reflection-Line method) to calibrate the cryostat system, and we also applied the random coupling model to remove the system-specific features. Our experimental results of different properties agree with the RMT predictions. This work is funded by the ONR/Maryland AppEl Center Task A2 (contract No. N000140911190), the AFOSR under grant FA95500710049, and Center for Nanophysics and Advanced Materials.
Analysis of aeroplane boarding via spacetime geometry and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Bachmat, E [Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105 (Israel); Berend, D [Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105 (Israel); Sapir, L [Department of Management and Industrial Engineering, Ben-Gurion University, Beer-Sheva 84105 (Israel); Skiena, S [Department of Computer science, SUNY at Stony Brook, Stony Brook, NY 11794 (United States); Stolyarov, N [Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105 (Israel)
2006-07-21
We show that aeroplane boarding can be asymptotically modelled by two-dimensional Lorentzian geometry. Boarding time is given by the maximal proper time among curves in the model. Discrepancies between the model and simulation results are closely related to random matrix theory. The models can be used to explain why some commonly practiced airline boarding policies are ineffective and even detrimental. (letter to the editor)
UA(1) breaking and phase transition in chiral random matrix model
Sano, T.; Fujii, H.; Ohtani, M
2009-01-01
We propose a chiral random matrix model which properly incorporates the flavor-number dependence of the phase transition owing to the \\UA(1) anomaly term. At finite temperature, the model shows the second-order phase transition with mean-field critical exponents for two massless flavors, while in the case of three massless flavors the transition turns out to be of the first order. The topological susceptibility satisfies the anomalous \\UA(1) Ward identity and decreases gradually with the temp...
Berkolaiko, Gregory; Kuipers, Jack
2012-04-01
Electronic transport through chaotic quantum dots exhibits universal, system-independent properties, consistent with random-matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the classical scattering trajectories. Correlations between such trajectories can be organized diagrammatically and have been shown to yield universal answers for some observables. Here, we develop the general combinatorial treatment of the semiclassical diagrams, through a connection to factorizations of permutations. We show agreement between the semiclassical and random matrix approaches to the moments of the transmission eigenvalues. The result is valid for all moments to all orders of the expansion in inverse channel number for all three main symmetry classes (with and without time-reversal symmetry and spin-orbit interaction) and extends to nonlinear statistics. This finally explains the applicability of random-matrix theory to chaotic quantum transport in terms of the underlying dynamics as well as providing semiclassical access to the probability density of the transmission eigenvalues.
Spectral properties of the Wilson-Dirac operator and random matrix theory
Kieburg, Mario; Verbaarschot, Jacobus J. M.; Zafeiropoulos, Savvas
2013-11-01
Random matrix theory has been successfully applied to lattice quantum chromodynamics. In particular, a great deal of progress has been made on the understanding, numerically as well as analytically, of the spectral properties of the Wilson-Dirac operator. In this paper, we study the infrared spectrum of the Wilson-Dirac operator via random matrix theory including the three leading order a2 correction terms that appear in the corresponding chiral Lagrangian. A derivation of the joint probability density of the eigenvalues is presented. This result is used to calculate the density of the complex eigenvalues, the density of the real eigenvalues, and the distribution of the chiralities over the real eigenvalues. A detailed discussion of these quantities shows how each low-energy constant affects the spectrum. Especially we consider the limit of small and large (which is almost the mean field limit) lattice spacing. Comparisons with Monte Carlo simulations of the random matrix theory show a perfect agreement with the analytical predictions. Furthermore we present some quantities which can be easily used for comparison of lattice data and the analytical results.
Freezing transitions and extreme values: random matrix theory, and disordered landscapes
Fyodorov, Yan V.; Keating, Jonathan P.
2014-01-01
We argue that the freezing transition scenario, previously conjectured to occur in the statistical mechanics of 1/f-noise random energy models, governs, after reinterpretation, the value distribution of the maximum of the modulus of the characteristic polynomials pN(θ) of large N×N random unitary (circular unitary ensemble) matrices UN; i.e. the extreme value statistics of pN(θ) when . In addition, we argue that it leads to multi-fractal-like behaviour in the total length μN(x) of the intervals in which |pN(θ)|>Nx,x>0, in the same limit. We speculate that our results extend to the large values taken by the Riemann zeta function ζ(s) over stretches of the critical line of given constant length and present the results of numerical computations of the large values of ). Our main purpose is to draw attention to the unexpected connections between these different extreme value problems. PMID:24344336
On Constructing Ensembles for Combinatorial Optimisation.
Hart, Emma; Sim, Kevin
2017-01-10
Although the use of ensemble methods in machine-learning is ubiquitous due to their proven ability to outperform their constituent algorithms, ensembles of optimisation algorithms have received relatively little attention. Existing approaches lag behind machine-learning in both theory and practice, with no principled design guidelines available. In this article, we address fundamental questions regarding ensemble composition in optimisation using the domain of bin-packing as an example. In particular, we investigate the trade-off between accuracy and diversity, and whether diversity metrics can be used as a proxy for constructing an ensemble, proposing a number of novel metrics for comparing algorithm diversity. We find that randomly composed ensembles can outperform ensembles of high-performing algorithms under certain conditions and that judicious choice of diversity metric is required to construct good ensembles. The method and findings can be generalised to any metaheuristic ensemble, and lead to better understanding of how to undertake principled ensemble design.
Kanazawa, Takuya; Yamamoto, Arata
2016-01-01
We apply QCD-inspired techniques to study nonrelativistic N -component degenerate fermions with attractive interactions. By analyzing the singular-value spectrum of the fermion matrix in the Lagrangian, we derive several exact relations that characterize spontaneous symmetry breaking U (1 )×SU (N )→Sp (N ) through bifermion condensates. These are nonrelativistic analogues of the Banks-Casher relation and the Smilga-Stern relation in QCD. Nonlocal order parameters are also introduced and their spectral representations are derived, from which a nontrivial constraint on the phase diagram is obtained. The effective theory of soft collective excitations is derived, and its equivalence to random matrix theory is demonstrated in the ɛ regime. We numerically confirm the above analytical predictions in Monte Carlo simulations.
Energy Technology Data Exchange (ETDEWEB)
Akemann, G.; Kanzieper, E
2001-03-01
The microscopic spectral eigenvalue correlations of QCD Dirac operators in the presence of dynamical fermions are calculated within the framework of Random Matrix Theory (RMT). Our approach treats the low-energy correlation functions of all three chiral symmetry breaking patterns (labeled by the Dyson index {beta} = 1, 2 and 4) on the same footing, offering a unifying description of massive QCD Dirac spectra. RMT universality is explicitly proven for all three symmetry classes and the results are compared to the available lattice data for {beta} = 4.
Lattice QCD in the {epsilon}-regime and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Giusti, L.; Luescher, M. [CERN, Geneva (Switzerland); Weisz, P. [Max-Planck-Institut fuer Physik, Muenchen (Germany); Wittig, H. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2003-11-01
In the {epsilon}-regime of QCD the main features of the spectrum of the low-lying eigenvalues of the (euclidean) Dirac operator are expected to be described by a certain universality class of random matrix models. In particular, the latter predict the joint statistical distribution of the individual eigenvalues in any topological sector of the theory. We compare some of these predictions with high-precision numerical data obtained from quenched lattice QCD for a range of lattice spacings and volumes. While no complete matching is observed, the results agree with theoretical expectations at volumes larger than about 5 fm{sup 4}. (orig.)
Lattice QCD in the {epsilon}-regime and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Giusti, Leonardo; Luescher, Martin [CERN, Theory Division, Geneva (Switzerland)]. E-mail addresses: leonardo.giusti@cern.ch; luscher@mail.cern.ch; Weisz, Peter [Max-Planck-Institut fuer Physik, Munich (Germany)]. E-mail: pew@dmumpiwh.mppmu.mpg.de; Wittig, Hartmut [DESY, Theory Group, Hamburg (Germany)]. E-mail: hartmut.wittig@desy.de
2003-11-01
In the {epsilon}-regime of QCD the main features of the spectrum of the low-lying eigenvalues of the (euclidean) Dirac operator are expected to be described by a certain universality class of random matrix models. In particular, the latter predict the joint statistical distribution of the individual eigenvalues in any topological sector of the theory. We compare some of these predictions with high-precision numerical data obtained from quenched lattice QCD for a range of lattice spacings and volumes. While no complete matching is observed, the results agree with theoretical expectations at volumes larger than about 5 fm{sup 4}. (author)
Hubbard, T J P; Aken, B L; Beal, K; Ballester, B; Caccamo, M; Chen, Y; Clarke, L; Coates, G; Cunningham, F; Cutts, T; Down, T; Dyer, S C; Fitzgerald, S; Fernandez-Banet, J; Graf, S; Haider, S; Hammond, M; Herrero, J; Holland, R; Howe, K; Howe, K; Johnson, N; Kahari, A; Keefe, D; Kokocinski, F; Kulesha, E; Lawson, D; Longden, I; Melsopp, C; Megy, K; Meidl, P; Ouverdin, B; Parker, A; Prlic, A; Rice, S; Rios, D; Schuster, M; Sealy, I; Severin, J; Slater, G; Smedley, D; Spudich, G; Trevanion, S; Vilella, A; Vogel, J; White, S; Wood, M; Cox, T; Curwen, V; Durbin, R; Fernandez-Suarez, X M; Flicek, P; Kasprzyk, A; Proctor, G; Searle, S; Smith, J; Ureta-Vidal, A; Birney, E
2007-01-01
The Ensembl (http://www.ensembl.org/) project provides a comprehensive and integrated source of annotation of chordate genome sequences. Over the past year the number of genomes available from Ensembl has increased from 15 to 33, with the addition of sites for the mammalian genomes of elephant, rabbit, armadillo, tenrec, platypus, pig, cat, bush baby, common shrew, microbat and european hedgehog; the fish genomes of stickleback and medaka and the second example of the genomes of the sea squirt (Ciona savignyi) and the mosquito (Aedes aegypti). Some of the major features added during the year include the first complete gene sets for genomes with low-sequence coverage, the introduction of new strain variation data and the introduction of new orthology/paralog annotations based on gene trees.
Discovering cell types in flow cytometry data with random matrix theory
Shen, Yang; Nussenblatt, Robert; Losert, Wolfgang
Flow cytometry is a widely used experimental technique in immunology research. During the experiments, peripheral blood mononuclear cells (PBMC) from a single patient, labeled with multiple fluorescent stains that bind to different proteins, are illuminated by a laser. The intensity of each stain on a single cell is recorded and reflects the amount of protein expressed by that cell. The data analysis focuses on identifying specific cell types related to a disease. Different cell types can be identified by the type and amount of protein they express. To date, this has most often been done manually by labelling a protein as expressed or not while ignoring the amount of expression. Using a cross correlation matrix of stain intensities, which contains both information on the proteins expressed and their amount, has been largely ignored by researchers as it suffers from measurement noise. Here we present an algorithm to identify cell types in flow cytometry data which uses random matrix theory (RMT) to reduce noise in a cross correlation matrix. We demonstrate our method using a published flow cytometry data set. Compared with previous analysis techniques, we were able to rediscover relevant cell types in an automatic way. Department of Physics, University of Maryland, College Park, MD 20742.
Accounting for Sampling Error in Genetic Eigenvalues Using Random Matrix Theory.
Sztepanacz, Jacqueline L; Blows, Mark W
2017-07-01
The distribution of genetic variance in multivariate phenotypes is characterized by the empirical spectral distribution of the eigenvalues of the genetic covariance matrix. Empirical estimates of genetic eigenvalues from random effects linear models are known to be overdispersed by sampling error, where large eigenvalues are biased upward, and small eigenvalues are biased downward. The overdispersion of the leading eigenvalues of sample covariance matrices have been demonstrated to conform to the Tracy-Widom (TW) distribution. Here we show that genetic eigenvalues estimated using restricted maximum likelihood (REML) in a multivariate random effects model with an unconstrained genetic covariance structure will also conform to the TW distribution after empirical scaling and centering. However, where estimation procedures using either REML or MCMC impose boundary constraints, the resulting genetic eigenvalues tend not be TW distributed. We show how using confidence intervals from sampling distributions of genetic eigenvalues without reference to the TW distribution is insufficient protection against mistaking sampling error as genetic variance, particularly when eigenvalues are small. By scaling such sampling distributions to the appropriate TW distribution, the critical value of the TW statistic can be used to determine if the magnitude of a genetic eigenvalue exceeds the sampling error for each eigenvalue in the spectral distribution of a given genetic covariance matrix. Copyright © 2017 by the Genetics Society of America.
Nobi, Ashadun; Maeng, Seong Eun; Ha, Gyeong Gyun; Lee, Jae Woo
2013-02-01
We analyzed cross-correlations between price fluctuations of global financial indices (20 daily stock indices over the world) and local indices (daily indices of 200 companies in the Korean stock market) by using random matrix theory (RMT). We compared eigenvalues and components of the largest and the second largest eigenvectors of the cross-correlation matrix before, during, and after the global financial the crisis in the year 2008. We find that the majority of its eigenvalues fall within the RMT bounds [ λ -, λ +], where λ - and λ + are the lower and the upper bounds of the eigenvalues of random correlation matrices. The components of the eigenvectors for the largest positive eigenvalues indicate the identical financial market mode dominating the global and local indices. On the other hand, the components of the eigenvector corresponding to the second largest eigenvalue are positive and negative values alternatively. The components before the crisis change sign during the crisis, and those during the crisis change sign after the crisis. The largest inverse participation ratio (IPR) corresponding to the smallest eigenvector is higher after the crisis than during any other periods in the global and local indices. During the global financial the crisis, the correlations among the global indices and among the local stock indices are perturbed significantly. However, the correlations between indices quickly recover the trends before the crisis.
Drouin-Chartier, Jean-Philippe; Tremblay, André J; Maltais-Giguère, Julie; Charest, Amélie; Guinot, Léa; Rioux, Laurie-Eve; Labrie, Steve; Britten, Michel; Lamarche, Benoît; Turgeon, Sylvie L; Couture, Patrick
2017-12-01
Background: In a simulated gastrointestinal environment, the cheese matrix modulates dairy fat digestion. However, to our knowledge, the impact of the cheese matrix on postprandial lipemia in humans has not yet been evaluated.Objective: In healthy subjects, we compared the impact of dairy fat provided from firm cheese, soft cream cheese, and butter on the postprandial response at 4 h and on the incremental area under the curve (iAUC) of plasma triglycerides.Design: Forty-three healthy subjects were recruited to this randomized, crossover, controlled trial. In random order at intervals of 14 d and after a 12-h fast, subjects ingested 33 g fat from a firm cheese (young cheddar), a soft cream cheese (cream cheese), or butter (control) incorporated into standardized meals that were matched for macronutrient content. Plasma concentrations of triglycerides were measured immediately before the meal and 2, 4, 6, and 8 h after the meal.Results: Cheddar cheese, cream cheese, and butter induced similar increases in triglyceride concentrations at 4 h (change from baseline: +59%, +59%, and +62%, respectively; P = 0.9). No difference in the triglyceride iAUC0-8 h (P-meal = 0.9) was observed between the 3 meals. However, at 2 h, the triglyceride response caused by the cream cheese (change from baseline: +44%) was significantly greater than that induced by butter (change from baseline: +24%; P = 0.002) and cheddar cheese (change from baseline: +16%; P = 0.0004). At 6 h, the triglyceride response induced by cream cheese was significantly attenuated compared with that induced by cheddar cheese (change from baseline: +14% compared with +42%; P = 0.0004).Conclusion: This study demonstrates that the cheese matrix modulates the impact of dairy fat on postprandial lipemia in healthy subjects. This trial was registered at clinicaltrials.gov as NCT02623790. © 2017 American Society for Nutrition.
Ramírez, J; Górriz, J M; Ortiz, A; Martínez-Murcia, F J; Segovia, F; Salas-Gonzalez, D; Castillo-Barnes, D; Illán, I A; Puntonet, C G
2017-12-11
Alzheimer's disease (AD) is the most common cause of dementia in the elderly and affects approximately 30 million individuals worldwide. Mild cognitive impairment (MCI) is very frequently a prodromal phase of AD, and existing studies have suggested that people with MCI tend to progress to AD at a rate of about 10-15% per year. However, the ability of clinicians and machine learning systems to predict AD based on MRI biomarkers at an early stage is still a challenging problem that can have a great impact in improving treatments. The proposed system, developed by the SiPBA-UGR team for this challenge, is based on feature standardization, ANOVA feature selection, partial least squares feature dimension reduction and an ensemble of One vs. Rest random forest classifiers. With the aim of improving its performance when discriminating healthy controls (HC) from MCI, a second binary classification level was introduced that reconsiders the HC and MCI predictions of the first level. The system was trained and evaluated on an ADNI datasets that consist of T1-weighted MRI morphological measurements from HC, stable MCI, converter MCI and AD subjects. The proposed system yields a 56.25% classification score on the test subset which consists of 160 real subjects. The classifier yielded the best performance when compared to: (i) One vs. One (OvO), One vs. Rest (OvR) and error correcting output codes (ECOC) as strategies for reducing the multiclass classification task to multiple binary classification problems, (ii) support vector machines, gradient boosting classifier and random forest as base binary classifiers, and (iii) bagging ensemble learning. A robust method has been proposed for the international challenge on MCI prediction based on MRI data. The system yielded the second best performance during the competition with an accuracy rate of 56.25% when evaluated on the real subjects of the test set. Copyright © 2017 Elsevier B.V. All rights reserved.
EnsCat: clustering of categorical data via ensembling.
Clarke, Bertrand S; Amiri, Saeid; Clarke, Jennifer L
2016-09-15
Clustering is a widely used collection of unsupervised learning techniques for identifying natural classes within a data set. It is often used in bioinformatics to infer population substructure. Genomic data are often categorical and high dimensional, e.g., long sequences of nucleotides. This makes inference challenging: The distance metric is often not well-defined on categorical data; running time for computations using high dimensional data can be considerable; and the Curse of Dimensionality often impedes the interpretation of the results. Up to the present, however, the literature and software addressing clustering for categorical data has not yet led to a standard approach. We present software for an ensemble method that performs well in comparison with other methods regardless of the dimensionality of the data. In an ensemble method a variety of instantiations of a statistical object are found and then combined into a consensus value. It has been known for decades that ensembling generally outperforms the components that comprise it in many settings. Here, we apply this ensembling principle to clustering. We begin by generating many hierarchical clusterings with different clustering sizes. When the dimension of the data is high, we also randomly select subspaces also of variable size, to generate clusterings. Then, we combine these clusterings into a single membership matrix and use this to obtain a new, ensembled dissimilarity matrix using Hamming distance. Ensemble clustering, as implemented in R and called EnsCat, gives more clearly separated clusters than other clustering techniques for categorical data. The latest version with manual and examples is available at https://github.com/jlp2duke/EnsCat .
Li, Long; Chen, Guojin; Jin, Tingdu
2017-06-01
As the pile of RNA-Protein complexes sequences mounted, in order to overcome time-consuming problem of the traditional identify RNA-Protein interaction sites (RPIS) method, it is urgent need develop intelligent recognition approach for quickly and reliable recognition of the RNA-Protein interaction sites (RPIS). To settle the question, we developed a new method named iRPIS-PseNNC, in which each sample is a nineteen nucleotides segment that for positive the centre of the segments is RPIS and for negative the segments centre is non-RPIS, and the sample was obtained by sliding window. The RNA sample was formulated by combining the dipeptide position-specific propensity into random forest approach, and by using the random sampling to balance the training dataset. According the voting system, we combine eleven random forest together to construct an ensemble classifier. It is shown that via the rigorous cross validations that the new predictor “iRPIS-PseNNC” achieved very high percentage of accuracy than any other existing algorithms in this field, indicating that the iRPIS-PseNNC predictor will be an effective tool for prediction RNA-Protein interaction sites.
Wang, Rong; Wang, Li; Yang, Yong; Li, Jiajia; Wu, Ying; Lin, Pan
2016-11-01
Attention deficit hyperactivity disorder (ADHD) is the most common childhood neuropsychiatric disorder and affects approximately 6 -7 % of children worldwide. Here, we investigate the statistical properties of undirected and directed brain functional networks in ADHD patients based on random matrix theory (RMT), in which the undirected functional connectivity is constructed based on correlation coefficient and the directed functional connectivity is measured based on cross-correlation coefficient and mutual information. We first analyze the functional connectivity and the eigenvalues of the brain functional network. We find that ADHD patients have increased undirected functional connectivity, reflecting a higher degree of linear dependence between regions, and increased directed functional connectivity, indicating stronger causality and more transmission of information among brain regions. More importantly, we explore the randomness of the undirected and directed functional networks using RMT. We find that for ADHD patients, the undirected functional network is more orderly than that for normal subjects, which indicates an abnormal increase in undirected functional connectivity. In addition, we find that the directed functional networks are more random, which reveals greater disorder in causality and more chaotic information flow among brain regions in ADHD patients. Our results not only further confirm the efficacy of RMT in characterizing the intrinsic properties of brain functional networks but also provide insights into the possibilities RMT offers for improving clinical diagnoses and treatment evaluations for ADHD patients.
On Ensemble Nonlinear Kalman Filtering with Symmetric Analysis Ensembles
Luo, Xiaodong
2010-09-19
The ensemble square root filter (EnSRF) [1, 2, 3, 4] is a popular method for data assimilation in high dimensional systems (e.g., geophysics models). Essentially the EnSRF is a Monte Carlo implementation of the conventional Kalman filter (KF) [5, 6]. It is mainly different from the KF at the prediction steps, where it is some ensembles, rather then the means and covariance matrices, of the system state that are propagated forward. In doing this, the EnSRF is computationally more efficient than the KF, since propagating a covariance matrix forward in high dimensional systems is prohibitively expensive. In addition, the EnSRF is also very convenient in implementation. By propagating the ensembles of the system state, the EnSRF can be directly applied to nonlinear systems without any change in comparison to the assimilation procedures in linear systems. However, by adopting the Monte Carlo method, the EnSRF also incurs certain sampling errors. One way to alleviate this problem is to introduce certain symmetry to the ensembles, which can reduce the sampling errors and spurious modes in evaluation of the means and covariances of the ensembles [7]. In this contribution, we present two methods to produce symmetric ensembles. One is based on the unscented transform [8, 9], which leads to the unscented Kalman filter (UKF) [8, 9] and its variant, the ensemble unscented Kalman filter (EnUKF) [7]. The other is based on Stirling’s interpolation formula (SIF), which results in the divided difference filter (DDF) [10]. Here we propose a simplified divided difference filter (sDDF) in the context of ensemble filtering. The similarity and difference between the sDDF and the EnUKF will be discussed. Numerical experiments will also be conducted to investigate the performance of the sDDF and the EnUKF, and compare them to a well‐established EnSRF, the ensemble transform Kalman filter (ETKF) [2].
A Random Matrix Approach for Quantifying Model-Form Uncertainties in Turbulence Modeling
Xiao, Heng; Ghanem, Roger G
2016-01-01
With the ever-increasing use of Reynolds-Averaged Navier--Stokes (RANS) simulations in mission-critical applications, the quantification of model-form uncertainty in RANS models has attracted attention in the turbulence modeling community. Recently, a physics-based, nonparametric approach for quantifying model-form uncertainty in RANS simulations has been proposed, where Reynolds stresses are projected to physically meaningful dimensions and perturbations are introduced only in the physically realizable limits. However, a challenge associated with this approach is to assess the amount of information introduced in the prior distribution and to avoid imposing unwarranted constraints. In this work we propose a random matrix approach for quantifying model-form uncertainties in RANS simulations with the realizability of the Reynolds stress guaranteed. Furthermore, the maximum entropy principle is used to identify the probability distribution that satisfies the constraints from available information but without int...
Random matrix theory and spectral sum rules for the Dirac operator in QCD
Energy Technology Data Exchange (ETDEWEB)
Shuryak, E.V. (Dept. of Physics, SUNY, Stony Brook, NY (United States)); Verbaarschot, J.J.M. (Dept. of Physics, SUNY, Stony Brook, NY (United States))
1993-07-12
We construct a random matrix model that, in the large-N limit, reduces to the low-energy limit of the QCD partition function put forward by Leutwyler and Smilga. This equivalence holds for an arbitrary number of flavors and any value of the QCD vacuum angle. In this model, moments of the inverse squares of eigenvalues of the Dirac operator obey sum rules, which we conjecture to be universal. In other words, the validity of the sum rules depends only on the symmetries of the theory but not on its details. To illustrate this point we show that the sum rules hold for an interacting liquid of instantons. The physical interpretations is that the way the thermodynamic limit of the spectral density near zero is approached is universal. However, its value, i.e. the chiral condensate, is not. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Liu, Yizhuang, E-mail: yizhuang.liu@stonybrook.edu [Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800 (United States); Nowak, Maciej A., E-mail: maciej.a.nowak@uj.edu.pl [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian University, PL-30348 Krakow (Poland); Zahed, Ismail, E-mail: ismail.zahed@stonybrook.edu [Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800 (United States)
2016-08-15
We derive an exact formula for the stochastic evolution of the characteristic determinant of a class of deformed Wishart matrices following from a chiral random matrix model of QCD at finite chemical potential. In the WKB approximation, the characteristic determinant describes a sharp droplet of eigenvalues that deforms and expands at large stochastic times. Beyond the WKB limit, the edges of the droplet are fuzzy and described by universal edge functions. At the chiral point, the characteristic determinant in the microscopic limit is universal. Remarkably, the physical chiral condensate at finite chemical potential may be extracted from current and quenched lattice Dirac spectra using the universal edge scaling laws, without having to solve the QCD sign problem.
Mussard, Bastien; Jansen, Georg; Angyan, Janos
2016-01-01
Starting from the general expression for the ground state correlation energy in the adiabatic connection fluctuation dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the co...
Random matrix theory of multi-antenna communications: the Ricean channel
Energy Technology Data Exchange (ETDEWEB)
Moustakas, Aris L [Department of Physics, University of Athens, Panepistimiopolis, Athens 15784 (Greece); Simon, Steven H [Bell Labs, Lucent Technologies, 600 Mountain Avenue, Murray Hill, NJ 07974 (United States)
2005-12-09
The use of multi-antenna arrays in wireless communications through disordered media promises huge increases in the information transmission rate. It is therefore important to analyse the information capacity of such systems in realistic situations of microwave transmission, where the statistics of the transmission amplitudes (channel) may be coloured. Here, we present an approach that provides analytic expressions for the statistics, i.e. the moments of the distribution, of the mutual information for general Gaussian channel statistics. The mathematical method applies tools developed originally in the context of coherent wave propagation in disordered media, such as random matrix theory and replicas. Although it is valid formally for large antenna numbers, this approach produces extremely accurate results even for arrays with as few as two antennas. We also develop a method to analytically optimize over the input signal distribution, which enables us to calculate analytic capacities when the transmitter has knowledge of the statistics of the channel. The emphasis of this paper is on elucidating the novel mathematical methods used. We do this by analysing a specific case when the channel matrix is a complex Gaussian with arbitrary mean and unit covariance, which is usually called the Ricean channel.
Global financial indices and twitter sentiment: A random matrix theory approach
García, A.
2016-11-01
We use Random Matrix Theory (RMT) approach to analyze the correlation matrix structure of a collection of public tweets and the corresponding return time series associated to 20 global financial indices along 7 trading months of 2014. In order to quantify the collection of tweets, we constructed daily polarity time series from public tweets via sentiment analysis. The results from RMT analysis support the fact of the existence of true correlations between financial indices, polarities, and the mixture of them. Moreover, we found a good agreement between the temporal behavior of the extreme eigenvalues of both empirical data, and similar results were found when computing the inverse participation ratio, which provides an evidence about the emergence of common factors in global financial information whether we use the return or polarity data as a source. In addition, we found a very strong presumption that polarity Granger causes returns of an Indonesian index for a long range of lag trading days, whereas for Israel, South Korea, Australia, and Japan, the predictive information of returns is also presented but with less presumption. Our results suggest that incorporating polarity as a financial indicator may open up new insights to understand the collective and even individual behavior of global financial indices.
Schweiner, Frank; Laturner, Jeanine; Main, Jörg; Wunner, Günter
2017-11-01
Until now only for specific crossovers between Poissonian statistics (P), the statistics of a Gaussian orthogonal ensemble (GOE), or the statistics of a Gaussian unitary ensemble (GUE) have analytical formulas for the level spacing distribution function been derived within random matrix theory. We investigate arbitrary crossovers in the triangle between all three statistics. To this aim we propose an according formula for the level spacing distribution function depending on two parameters. Comparing the behavior of our formula for the special cases of P→GUE, P→GOE, and GOE→GUE with the results from random matrix theory, we prove that these crossovers are described reasonably. Recent investigations by F. Schweiner et al. [Phys. Rev. E 95, 062205 (2017)2470-004510.1103/PhysRevE.95.062205] have shown that the Hamiltonian of magnetoexcitons in cubic semiconductors can exhibit all three statistics in dependence on the system parameters. Evaluating the numerical results for magnetoexcitons in dependence on the excitation energy and on a parameter connected with the cubic valence band structure and comparing the results with the formula proposed allows us to distinguish between regular and chaotic behavior as well as between existent or broken antiunitary symmetries. Increasing one of the two parameters, transitions between different crossovers, e.g., from the P→GOE to the P→GUE crossover, are observed and discussed.
Random matrix theory, the exceptional Lie groups and L-functions
Energy Technology Data Exchange (ETDEWEB)
Keating, J P [School of Mathematics, University of Bristol, Bristol BS8 1TW, UK (United Kingdom); Linden, N [School of Mathematics, University of Bristol, Bristol BS8 1TW, UK (United Kingdom); Rudnick, Z [Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978 (Israel)
2003-03-28
There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold between the value distributions of the characteristic polynomials of such matrices and value distributions within families of L-functions. These connections are extended here to non-classical groups. We focus on an explicit example: the exceptional Lie group G{sub 2}. The value distributions for characteristic polynomials associated with the 7- and 14-dimensional representations of G{sub 2}, defined with respect to the uniform invariant (Haar) measure, are calculated using two of the Macdonald constant term identities. A one-parameter family of L-functions over a finite field is described whose value distribution in the limit as the size of the finite field grows is related to that of the characteristic polynomials associated with the seven-dimensional representation of G{sub 2}. The random matrix calculations extend to all exceptional Lie groups.
Klopp, Frédéric
The purpose of this paper is to study the transition from the classical to the quantum asymptotics for the integrated density of states of an unbounded random Jacobi matrix. Therefore, we give precise results on the behavior of the tail of the integrated density of states near infinity. We study the evolution of these asymptotics when the decay of the tail of the distribution of the random potential increases. Résumé. Cet article est consacré à l'étude de la transition entre le régime classique et le régime quantique pour la densité d'états intégrée d'une matrice de Jacobi aléatoire non bornée. Pour cela nous donnons des asymptotiques précises du comportement de la densité d'états intégrée au voisinage de l'infini. De plus, nous étudions le comportement de cette asymptotique lorsque la décroissance à l'infini de la distribution du potentiel aléatoire augmente.
Statistical Mechanics of On-line Ensemble Teacher Learning through a Novel Perceptron Learning Rule
Hara, Kazuyuki; Miyoshi, Seiji
2016-01-01
In ensemble teacher learning, ensemble teachers have only uncertain information about the true teacher, and this information is given by an ensemble consisting of an infinite number of ensemble teachers whose variety is sufficiently rich. In this learning, a student learns from an ensemble teacher that is iteratively selected randomly from a pool of many ensemble teachers. An interesting point of ensemble teacher learning is the asymptotic behavior of the student to approach the true teacher ...
Osorio, Ivan; Lai, Ying-Cheng
2011-09-01
We present a general method to analyze multichannel time series that are becoming increasingly common in many areas of science and engineering. Of particular interest is the degree of synchrony among various channels, motivated by the recognition that characterization of synchrony in a system consisting of many interacting components can provide insights into its fundamental dynamics. Often such a system is complex, high-dimensional, nonlinear, nonstationary, and noisy, rendering unlikely complete synchronization in which the dynamical variables from individual components approach each other asymptotically. Nonetheless, a weaker type of synchrony that lasts for a finite amount of time, namely, phase synchronization, can be expected. Our idea is to calculate the average phase-synchronization times from all available pairs of channels and then to construct a matrix. Due to nonlinearity and stochasticity, the matrix is effectively random. Moreover, since the diagonal elements of the matrix can be arbitrarily large, the matrix can be singular. To overcome this difficulty, we develop a random-matrix based criterion for proper choosing of the diagonal matrix elements. Monitoring of the eigenvalues and the determinant provides a powerful way to assess changes in synchrony. The method is tested using a prototype nonstationary noisy dynamical system, electroencephalogram (scalp) data from absence seizures for which enhanced cortico-thalamic synchrony is presumed, and electrocorticogram (intracranial) data from subjects having partial seizures with secondary generalization for which enhanced local synchrony is similarly presumed.
Directory of Open Access Journals (Sweden)
Wanxing Sheng
2016-05-01
Full Text Available In this paper, a reactive power optimization method based on historical data is investigated to solve the dynamic reactive power optimization problem in distribution network. In order to reflect the variation of loads, network loads are represented in a form of random matrix. Load similarity (LS is defined to measure the degree of similarity between the loads in different days and the calculation method of the load similarity of load random matrix (LRM is presented. By calculating the load similarity between the forecasting random matrix and the random matrix of historical load, the historical reactive power optimization dispatching scheme that most matches the forecasting load can be found for reactive power control usage. The differences of daily load curves between working days and weekends in different seasons are considered in the proposed method. The proposed method is tested on a standard 14 nodes distribution network with three different types of load. The computational result demonstrates that the proposed method for reactive power optimization is fast, feasible and effective in distribution network.
Directory of Open Access Journals (Sweden)
A.V. Lebedev
2014-01-01
In the ADNI set, the best AD/HC sensitivity/specificity (88.6%/92.0% — test set was achieved by combining cortical thickness and volumetric measures. The Random Forest model resulted in significantly higher accuracy compared to the reference classifier (linear Support Vector Machine. The models trained using parcelled and high-dimensional (HD input demonstrated equivalent performance, but the former was more effective in terms of computation/memory and time costs. The sensitivity/specificity for detecting MCI-to-AD conversion (but not AD/HC classification performance was further improved from 79.5%/75%–83.3%/81.3% by a combination of morphometric measurements with ApoE-genotype and demographics (age, sex, education. When applied to the independent AddNeuroMed cohort, the best ADNI models produced equivalent performance without substantial accuracy drop, suggesting good robustness sufficient for future clinical implementation.
Thimble regularization at work: From toy models to chiral random matrix theories
Di Renzo, F.; Eruzzi, G.
2015-10-01
We apply the Lefschetz thimble formulation of field theories to a couple of different problems. We first address the solution of a complex zero-dimensional ϕ4 theory. Although very simple, this toy model makes us appreciate a few key issues of the method. In particular, we will solve the model by a correct accounting of all the thimbles giving a contribution to the partition function and we will discuss a number of algorithmic solutions to simulate this (simple) model. We will then move to a chiral random matrix (CRM) theory. This is a somehow more realistic setting, giving us once again the chance to tackle the same couple of fundamental questions: How many thimbles contribute to the solution? How can we make sure that we correctly sample configurations on the thimble? Since the exact result is known for the observable we study (a condensate), we can verify that, in the region of parameters we studied, only one thimble contributes and that the algorithmic solution that we set up works well, despite its very crude nature. The deviation of results from phase quenched ones highlights that in a certain region of parameter space there is a quite important sign problem. In view of this, the success of our thimble approach is quite a significant one.
A global test for gene‐gene interactions based on random matrix theory
Amos, Christopher I.; Moore, Jason H.
2016-01-01
ABSTRACT Statistical interactions between markers of genetic variation, or gene‐gene interactions, are believed to play an important role in the etiology of many multifactorial diseases and other complex phenotypes. Unfortunately, detecting gene‐gene interactions is extremely challenging due to the large number of potential interactions and ambiguity regarding marker coding and interaction scale. For many data sets, there is insufficient statistical power to evaluate all candidate gene‐gene interactions. In these cases, a global test for gene‐gene interactions may be the best option. Global tests have much greater power relative to multiple individual interaction tests and can be used on subsets of the markers as an initial filter prior to testing for specific interactions. In this paper, we describe a novel global test for gene‐gene interactions, the global epistasis test (GET), that is based on results from random matrix theory. As we show via simulation studies based on previously proposed models for common diseases including rheumatoid arthritis, type 2 diabetes, and breast cancer, our proposed GET method has superior performance characteristics relative to existing global gene‐gene interaction tests. A glaucoma GWAS data set is used to demonstrate the practical utility of the GET method. PMID:27386793
Isaacson, Sven; Luo, Feng; Feltus, Frank A.; Smith, Melissa C.
2013-01-01
The study of gene relationships and their effect on biological function and phenotype is a focal point in systems biology. Gene co-expression networks built using microarray expression profiles are one technique for discovering and interpreting gene relationships. A knowledge-independent thresholding technique, such as Random Matrix Theory (RMT), is useful for identifying meaningful relationships. Highly connected genes in the thresholded network are then grouped into modules that provide insight into their collective functionality. While it has been shown that co-expression networks are biologically relevant, it has not been determined to what extent any given network is functionally robust given perturbations in the input sample set. For such a test, hundreds of networks are needed and hence a tool to rapidly construct these networks. To examine functional robustness of networks with varying input, we enhanced an existing RMT implementation for improved scalability and tested functional robustness of human (Homo sapiens), rice (Oryza sativa) and budding yeast (Saccharomyces cerevisiae). We demonstrate dramatic decrease in network construction time and computational requirements and show that despite some variation in global properties between networks, functional similarity remains high. Moreover, the biological function captured by co-expression networks thresholded by RMT is highly robust. PMID:23409071
Large N_c volume reduction and chiral random matrix theory
Lee, J. W.; Hanada, M.; Yamada, N.
Motivated by recent progress on the understanding of the Eguchi-Kawai (EK) volume equivalence and growing interest in conformal window, we simultaneously use the large-Nc volume reduction and Chiral Random Matrix Theory (chRMT) to study the chiral symmetry breaking of four dimensional SU(Nc) gauge theory with adjoint fermions in the large Nc limit. Although some cares are required because the chRMT limit and 't Hooft limit are not compatible in general, we show that the breakdown of the chiral symmetry can be detected in large-Nc gauge theories. As a first step, we mainly focus on the quenched approximation to establish the methodology. We first confirm that heavy adjoint fermions, introduced as the center symmetry preserver, work as expected and thanks to them the volume reduction holds. Using massless overlap fermion as a probe, we then calculate the low-lying Dirac spectrum for fermion in the adjoint representation to compare to that of chRMT, and find that chiral symmetry is indeed broken in the quenched theory.
Disorder in gauge/gravity duality, pole spectrum statistics and random matrix theory
Saremi, Omid
2014-05-01
In condensed-matter, level statistics has long been used to characterize the phases of a disordered system. We provide evidence within the context of a simple model that in a disordered large-N gauge theory with a gravity dual, there exist phases where the nearest neighbor spacing distribution of the unfolded pole spectra of generic two-point correlators is Poisson. This closely resembles the localized phase of the Anderson Hamiltonian. We perform two tests on our statistical hypothesis. One is based on a statistic defined in the context of random matrix theory, the so-called \\overline{\\Delta _3}, or spectral rigidity, proposed by Dyson and Mehta. The second is a χ-squared test. In our model, the results of both tests are consistent with the hypothesis that the pole spectra of two-point functions can be at least in two distinct phases; first a regular sequence and second a completely uncorrelated sequence with a Poisson nearest neighbor spacing distribution.
Thimble regularization at work: from toy models to chiral random matrix theories
Di Renzo, Francesco
2015-01-01
We apply the Lefschetz thimble formulation of field theories to a couple of different problems. We first address the solution of a complex 0-dimensional phi^4 theory. Although very simple, this toy-model makes us appreciate a few key issues of the method. In particular, we will solve the model by a correct accounting of all the thimbles giving a contribution to the partition function and we will discuss a number of algorithmic solutions to simulate this (simple) model. We will then move to a chiral random matrix (CRM) theory. This is a somehow more realistic setting, giving us once again the chance to tackle the same couple of fundamental questions: how many thimbles contribute to the solution? how can we make sure that we correctly sample configurations on the thimble? Since the exact result is known for the observable we study (a condensate), we can verify that, in the region of parameters we studied, only one thimble contributes and that the algorithmic solution that we set up works well, despite its very ...
Asymptotic Analysis of Large Cooperative Relay Networks Using Random Matrix Theory
Directory of Open Access Journals (Sweden)
H. Poor
2008-04-01
Full Text Available Cooperative transmission is an emerging communication technology that takes advantage of the broadcast nature of wireless channels. In cooperative transmission, the use of relays can create a virtual antenna array so that multiple-input/multiple-output (MIMO techniques can be employed. Most existing work in this area has focused on the situation in which there are a small number of sources and relays and a destination. In this paper, cooperative relay networks with large numbers of nodes are analyzed, and in particular the asymptotic performance improvement of cooperative transmission over direction transmission and relay transmission is analyzed using random matrix theory. The key idea is to investigate the eigenvalue distributions related to channel capacity and to analyze the moments of this distribution in large wireless networks. A performance upper bound is derived, the performance in the low signal-to-noise-ratio regime is analyzed, and two approximations are obtained for high and low relay-to-destination link qualities, respectively. Finally, simulations are provided to validate the accuracy of the analytical results. The analysis in this paper provides important tools for the understanding and the design of large cooperative wireless networks.
A multi-platform evaluation of the randomized CX low-rank matrix factorization in Spark
Energy Technology Data Exchange (ETDEWEB)
Gittens, Alex; Kottalam, Jey; Yang, Jiyan; Ringenburg, Michael, F.; Chhugani, Jatin; Racah, Evan; Singh, Mohitdeep; Yao, Yushu; Fischer, Curt; Ruebel, Oliver; Bowen, Benjamin; Lewis, Norman, G.; Mahoney, Michael, W.; Krishnamurthy, Venkat; Prabhat, Mr
2017-07-27
We investigate the performance and scalability of the randomized CX low-rank matrix factorization and demonstrate its applicability through the analysis of a 1TB mass spectrometry imaging (MSI) dataset, using Apache Spark on an Amazon EC2 cluster, a Cray XC40 system, and an experimental Cray cluster. We implemented this factorization both as a parallelized C implementation with hand-tuned optimizations and in Scala using the Apache Spark high-level cluster computing framework. We obtained consistent performance across the three platforms: using Spark we were able to process the 1TB size dataset in under 30 minutes with 960 cores on all systems, with the fastest times obtained on the experimental Cray cluster. In comparison, the C implementation was 21X faster on the Amazon EC2 system, due to careful cache optimizations, bandwidth-friendly access of matrices and vector computation using SIMD units. We report these results and their implications on the hardware and software issues arising in supporting data-centric workloads in parallel and distributed environments.
spam: A Sparse Matrix R Package with Emphasis on MCMC Methods for Gaussian Markov Random Fields
Directory of Open Access Journals (Sweden)
Reinhard Furrer
2010-10-01
Full Text Available spam is an R package for sparse matrix algebra with emphasis on a Cholesky factorization of sparse positive definite matrices. The implemantation of spam is based on the competing philosophical maxims to be competitively fast compared to existing tools and to be easy to use, modify and extend. The first is addressed by using fast Fortran routines and the second by assuring S3 and S4 compatibility. One of the features of spam is to exploit the algorithmic steps of the Cholesky factorization and hence to perform only a fraction of the workload when factorizing matrices with the same sparsity structure. Simulations show that exploiting this break-down of the factorization results in a speed-up of about a factor 5 and memory savings of about a factor 10 for large matrices and slightly smaller factors for huge matrices. The article is motivated with Markov chain Monte Carlo methods for Gaussian Markov random fields, but many other statistical applications are mentioned that profit from an efficient Cholesky factorization as well.
Prognostic interaction patterns in diabetes mellitus II: A random-matrix-theory relation
Rai, Aparna; Pawar, Amit Kumar; Jalan, Sarika
2015-08-01
We analyze protein-protein interactions in diabetes mellitus II and its normal counterpart under the combined framework of random matrix theory and network biology. This disease is the fifth-leading cause of death in high-income countries and an epidemic in developing countries, affecting around 8 % of the total adult population in the world. Treatment at the advanced stage is difficult and challenging, making early detection a high priority in the cure of the disease. Our investigation reveals specific structural patterns important for the occurrence of the disease. In addition to the structural parameters, the spectral properties reveal the top contributing nodes from localized eigenvectors, which turn out to be significant for the occurrence of the disease. Our analysis is time-efficient and cost-effective, bringing a new horizon in the field of medicine by highlighting major pathways involved in the disease. The analysis provides a direction for the development of novel drugs and therapies in curing the disease by targeting specific interaction patterns instead of a single protein.
Energy Technology Data Exchange (ETDEWEB)
Stotland, Alexander; Peer, Tal; Cohen, Doron [Department of Physics, Ben-Gurion University, Beer-Sheva 84005 (Israel); Budoyo, Rangga; Kottos, Tsampikos [Department of Physics, Wesleyan University, Middletown, CT 06459 (United States)
2008-07-11
The calculation of the conductance of disordered rings requires a theory that goes beyond the Kubo-Drude formulation. Assuming 'mesoscopic' circumstances the analysis of the electro-driven transitions shows similarities with a percolation problem in energy space. We argue that the texture and the sparsity of the perturbation matrix dictate the value of the conductance, and study its dependence on the disorder strength, ranging from the ballistic to the Anderson localization regime. An improved sparse random matrix model is introduced to capture the essential ingredients of the problem, and leads to a generalized variable range hopping picture. (fast track communication)
Energy Technology Data Exchange (ETDEWEB)
Verbaarschot, Jacobus (Department of Physics, SUNY, Stony Brook, NY 11794 (United States))
1994-09-19
We study the spectrum of the QCD Dirac operator near zero virtuality for N[sub c] =2. According to a universality argument, it can be described by a random matrix theory with the chiral structure of QCD, but with real matrix elements.Using results derived by Mehta and Mahoux and Nagao and Wadati, we are able to obtain an analytical result for the microscopic spectral density that in turn is the generating function for Leutwyler-Smilga type spectral sum rules. ((orig.))
Ensemble methods for handwritten digit recognition
DEFF Research Database (Denmark)
Hansen, Lars Kai; Liisberg, Christian; Salamon, P.
1992-01-01
by optimizing the receptive fields. It is concluded that it is possible to improve performance significantly by introducing moderate-size ensembles; in particular, a 20-25% improvement has been found. The ensemble random LUTs, when trained on a medium-size database, reach a performance (without rejects) of 94....... It is further shown that it is possible to estimate the ensemble performance as well as the learning curve on a medium-size database. In addition the authors present preliminary analysis of experiments on a large database and show that state-of-the-art performance can be obtained using the ensemble approach...
Schmessane, Andrea; Laboratory of matter out equilibrium Team
2012-11-01
Wave localization explains how a perturbation is trapped by the randomness present in a propagation medium. As it propagates, the localized wave amplitude decreases strongly by multiple internal reflections with randomly positioned scatterers, effectively trapping the perturbation inside the random region. The characteristic length where a localized wave is propagated before being extinguish by randomness is called localization length. We carried experiments in a quasi-onedimensional channel with random bottom in a shallow water regime for surface gravity water waves, using a Perfilometry Fourier Transform method, which enables us to obtain global surface measurements. We discuss keys aspects of the control of variables, the experimental setup and the implementation of the measurement method. Thus, we can control, measure and evaluate fundamental variables present in the localization phenomenon such as the type of randomness, scattering intensity and sample length, which allows us to characterize wave localization. We use the scattering matrix method to compare the experimental measurements with theoretical and numerical predictions, using the Lyapunov exponent of the scattering matrix, and discuss their agreement. Conicyt
Distributions on unbounded moment spaces and random moment sequences
Dette, Holger; Nagel, Jan
2012-01-01
In this paper we define distributions on moment spaces corresponding to measures on the real line with an unbounded support. We identify these distributions as limiting distributions of random moment vectors defined on compact moment spaces and as distributions corresponding to random spectral measures associated with the Jacobi, Laguerre and Hermite ensemble from random matrix theory. For random vectors on the unbounded moment spaces we prove a central limit theorem where the centering vecto...
Wang, Jian-Xun; Xiao, Heng
2016-01-01
Numerical models based on Reynolds-Averaged Navier-Stokes (RANS) equations are widely used in engineering turbulence modeling. However, the RANS predictions have large model-form uncertainties for many complex flows. Quantification of these large uncertainties originating from the modeled Reynolds stresses has attracted attention in turbulence modeling community. Recently, a physics-based Bayesian framework for quantifying model-form uncertainties has been proposed with successful applications to several flows. Nonetheless, how to specify proper priors without introducing unwarranted, artificial information remains challenging to the current form of the physics-based approach. Another recently proposed method based on random matrix theory provides the prior distributions with the maximum entropy, which is an alternative for model-form uncertainty quantification in RANS simulations. In this work, we utilize the random matrix theoretic approach to assess and possibly improve the specification of priors used in ...
Li, Victor C.; Wang, Youjiang; Backer, Stanley
A MICROMECHANICAL model has been formulated for the post-cracking behavior of a brittle matrix composite reinforced with randomly distributed short fibers. This model incorporates the mechanics of pull-out of fibers which are inclined at an angle to the matrix crack plane and which undergo slip-weakening or slip-hardening during the pull-out process. In addition, the random location and orientation of fibers are accounted for. Comparisons of model predictions of post-cracking tension-softening behavior with experimental data appear to support the validity of the model. The model is used to examine the effects of fiber length, snubbing friction coefficient and interfacial bond behavior on composite post-cracking tensile properties. The scaling of the bridging fracture toughening with material parameters is discussed.
Cox, Jeris; Malik, Minnie; Britten, Joy; Lewis, Terrence; Catherino, William H
2018-02-01
In a prior randomized controlled study, patients treated with ulipristal acetate (UPA) or placebo for 3 months had a decrease in leiomyoma size. A total of 10 patients' tissue samples (5 placebo and 5 treated with 10 mg/d UPA) that underwent hysterectomy and tissue preservation were identified from this study. Quantitative real-time reverse transcriptase polymerase chain reaction and Western blotting were used to assess fold gene and protein expression of extracellular membrane (ECM) proteins: collagen 1A (COL1A), fibronectin (FN1), and versican (VCAN) of the samples. Confirmatory immunohistochemical analysis was performed. Changes in total matrix collagen were examined using Masson trichrome staining. Multiplex measurement of the matrix metalloproteinases (MMPs) and tissue inhibitor of metalloproteinases was performed. Compared to placebo-treated surgical specimens, 80% of the treated specimens showed decrease in VCAN protein, 60% showed decrease in FN1, but no consistent alteration in COL1A. This effect was also supported by immunohistochemistry where leiomyoma surgical specimens demonstrated decreased amount of FN1 and VCAN on UPA treatment. Increased MMP2 and decreased MMP9 in treated patient leiomyomas indicate both degradation of the matrix and inhibition of the pathway involved in matrix production. Treatment with UPA decreased fibroid volume in placebo-controlled, randomized trials. Treatment with UPA decreased gene expression and protein production in leiomyoma tissue, suggesting both an impact on water content and ECM protein concentration as a mechanism of ulipristal-mediated decrease in leiomyoma size.
Han, Rui-Qi; Xie, Wen-Jie; Xiong, Xiong; Zhang, Wei; Zhou, Wei-Xing
The correlation structure of a stock market contains important financial contents, which may change remarkably due to the occurrence of financial crisis. We perform a comparative analysis of the Chinese stock market around the occurrence of the 2008 crisis based on the random matrix analysis of high-frequency stock returns of 1228 Chinese stocks. Both raw correlation matrix and partial correlation matrix with respect to the market index in two time periods of one year are investigated. We find that the Chinese stocks have stronger average correlation and partial correlation in 2008 than in 2007 and the average partial correlation is significantly weaker than the average correlation in each period. Accordingly, the largest eigenvalue of the correlation matrix is remarkably greater than that of the partial correlation matrix in each period. Moreover, each largest eigenvalue and its eigenvector reflect an evident market effect, while other deviating eigenvalues do not. We find no evidence that deviating eigenvalues contain industrial sectorial information. Surprisingly, the eigenvectors of the second largest eigenvalues in 2007 and of the third largest eigenvalues in 2008 are able to distinguish the stocks from the two exchanges. We also find that the component magnitudes of the some largest eigenvectors are proportional to the stocks’ capitalizations.
Algorithms on ensemble quantum computers.
Boykin, P Oscar; Mor, Tal; Roychowdhury, Vwani; Vatan, Farrokh
2010-06-01
In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor's factorization algorithm, Grover's search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and σ(z)(¼) as these operations cannot be implemented "bitwise", and their standard fault-tolerant implementations require measurement.
Directory of Open Access Journals (Sweden)
X. Yang
2009-07-01
Full Text Available A new class of ensemble filters, called the Diffuse Ensemble Filter (DEnF, is proposed in this paper. The DEnF assumes that the forecast errors orthogonal to the first guess ensemble are uncorrelated with the latter ensemble and have infinite variance. The assumption of infinite variance corresponds to the limit of "complete lack of knowledge" and differs dramatically from the implicit assumption made in most other ensemble filters, which is that the forecast errors orthogonal to the first guess ensemble have vanishing errors. The DEnF is independent of the detailed covariances assumed in the space orthogonal to the ensemble space, and reduces to conventional ensemble square root filters when the number of ensembles exceeds the model dimension. The DEnF is well defined only in data rich regimes and involves the inversion of relatively large matrices, although this barrier might be circumvented by variational methods. Two algorithms for solving the DEnF, namely the Diffuse Ensemble Kalman Filter (DEnKF and the Diffuse Ensemble Transform Kalman Filter (DETKF, are proposed and found to give comparable results. These filters generally converge to the traditional EnKF and ETKF, respectively, when the ensemble size exceeds the model dimension. Numerical experiments demonstrate that the DEnF eliminates filter collapse, which occurs in ensemble Kalman filters for small ensemble sizes. Also, the use of the DEnF to initialize a conventional square root filter dramatically accelerates the spin-up time for convergence. However, in a perfect model scenario, the DEnF produces larger errors than ensemble square root filters that have covariance localization and inflation. For imperfect forecast models, the DEnF produces smaller errors than the ensemble square root filter with inflation. These experiments suggest that the DEnF has some advantages relative to the ensemble square root filters in the regime of small ensemble size, imperfect model, and copious
Symmetric minimally entangled typical thermal states for canonical and grand-canonical ensembles
Binder, Moritz; Barthel, Thomas
2017-05-01
Based on the density matrix renormalization group (DMRG), strongly correlated quantum many-body systems at finite temperatures can be simulated by sampling over a certain class of pure matrix product states (MPS) called minimally entangled typical thermal states (METTS). When a system features symmetries, these can be utilized to substantially reduce MPS computation costs. It is conceptually straightforward to simulate canonical ensembles using symmetric METTS. In practice, it is important to alternate between different symmetric collapse bases to decrease autocorrelations in the Markov chain of METTS. To this purpose, we introduce symmetric Fourier and Haar-random block bases that are efficiently mixing. We also show how grand-canonical ensembles can be simulated efficiently with symmetric METTS. We demonstrate these approaches for spin-1 /2 X X Z chains and discuss how the choice of the collapse bases influences autocorrelations as well as the distribution of measurement values and, hence, convergence speeds.
Chaos, complexity, and random matrices
Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu; Yoshida, Beni
2017-11-01
Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an O(1) scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us computational traction is the Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics look the same in any basis. Motivated by this property of the GUE, we introduce k-invariance as a precise definition of what it means for the dynamics of a quantum system to be described by random matrix theory. We envision that the dynamical onset of approximate k-invariance will be a useful tool for capturing the transition from early-time chaos, as seen by OTOCs, to late-time chaos, as seen by random matrix theory.
Energy Technology Data Exchange (ETDEWEB)
Yang, Yang [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Aggelen, Helen van [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Department of Inorganic and Physical Chemistry, Ghent University, 9000 Ghent (Belgium); Yang, Weitao, E-mail: weitao.yang@duke.edu [Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708 (United States)
2013-12-14
Double, Rydberg, and charge transfer (CT) excitations have been great challenges for time-dependent density functional theory (TDDFT). Starting from an (N ± 2)-electron single-determinant reference, we investigate excitations for the N-electron system through the pairing matrix fluctuation, which contains information on two-electron addition/removal processes. We adopt the particle-particle random phase approximation (pp-RPA) and the particle-particle Tamm-Dancoff approximation (pp-TDA) to approximate the pairing matrix fluctuation and then determine excitation energies by the differences of two-electron addition/removal energies. This approach captures all types of interesting excitations: single and double excitations are described accurately, Rydberg excitations are in good agreement with experimental data and CT excitations display correct 1/R dependence. Furthermore, the pp-RPA and the pp-TDA have a computational cost similar to TDDFT and consequently are promising for practical calculations.
Muñoz, O.; Volten, H.; Hovenier, J.W.; Laan, E.; Roush, T.; Stam, D.
2008-01-01
We present laboratory measurements for Martian analog particles, consisting of palagonite. We measured all elements of the scattering matrix as functions of the scattering angle from 3 to 174 degrees at a wavelength of 632.8 nm. The results may be used in studies of the Martian atmosphere.
2015-08-24
Squared Error (MSE) tracking performance for direction of arrival estimation in the presence of noise and missing data; see Fig. 5. 6) We have...scatter in random directions, thereby hindering its passage. As the thickness of a slab of highly scattering random medium increases, this effect
World Music Ensemble: Kulintang
Beegle, Amy C.
2012-01-01
As instrumental world music ensembles such as steel pan, mariachi, gamelan and West African drums are becoming more the norm than the exception in North American school music programs, there are other world music ensembles just starting to gain popularity in particular parts of the United States. The kulintang ensemble, a drum and gong ensemble…
Energy Technology Data Exchange (ETDEWEB)
Feinberg, Joshua [Physics Department, University of Haifa at Oranim, Tivon 36006 (Israel); Physics Department, Technion, Israel Institute of Technology, Haifa 32000 (Israel)
2006-08-11
I review aspects of work done in collaboration with A Zee and R Scalettar (1997 Nucl. Phys. B 504 579; 1997 Nucl. Phys. B 501 643; 2001 J. Math. Phys. 42 5718) on complex non-Hermitian random matrices. I open by explaining why the bag of tools used regularly in analysing Hermitian random matrices cannot be applied directly to analyse non-Hermitian matrices, and then introduce the method of Hermitization, which solves this problem. Then, for rotationally invariant ensembles, I derive a master equation for the average density of eigenvalues in the complex plane, in the limit of infinitely large matrices. This is achieved by resumming all the planar diagrams which appear in the perturbative expansion of the Hermitized Green function. Remarkably, this resummation can be carried out explicitly for any rotationally invariant ensemble. I prove that in the limit of infinitely large matrices, the shape of the eigenvalue distribution is either a disc or an annulus. This is the celebrated 'single-ring' theorem. Which of these shapes is realized is determined by the parameters (coupling constants) which determine the ensemble. By varying these parameters a phase transition may occur between the two possible shapes. I briefly discuss the universal features of this transition. As the analysis of this problem relies heavily on summation of planar Feynman diagrams, I make a special effort at presenting a pedagogical exposition of the diagrammatic method, which some readers may find useful.
CMV matrices in random matrix theory and integrable systems: a survey
Energy Technology Data Exchange (ETDEWEB)
Nenciu, Irina [Courant Institute, 251 Mercer St, New York, NY 10012 (United States)
2006-07-14
We present a survey of recent results concerning a remarkable class of unitary matrices, the CMV matrices. We are particularly interested in the role they play in the theory of random matrices and integrable systems. Throughout the paper we also emphasize the analogies and connections to Jacobi matrices.
Resistance of a 1D random chain: Hamiltonian version of the transfer matrix approach
Dossetti-Romero, V.; Izrailev, F. M.; Krokhin, A. A.
2004-01-01
We study some mesoscopic properties of electron transport by employing one-dimensional chains and Anderson tight-binding model. Principal attention is paid to the resistance of finite-length chains with disordered white-noise potential. We develop a new version of the transfer matrix approach based on the equivalency of a discrete Schrödinger equation and a two-dimensional Hamiltonian map describing a parametric kicked oscillator. In the two limiting cases of ballistic and localized regime we demonstrate how analytical results for the mean resistance and its second moment can be derived directly from the averaging over classical trajectories of the Hamiltonian map. We also discuss the implication of the single parameter scaling hypothesis to the resistance.
Random Matrices for Information Processing – A Democratic Vision
DEFF Research Database (Denmark)
Cakmak, Burak
The thesis studies three important applications of random matrices to information processing. Our main contribution is that we consider probabilistic systems involving more general random matrix ensembles than the classical ensembles with iid entries, i.e. models that account for statistical...... dependence between the entries. Specifically, the involved matrices are invariant or fulfill a certain asymptotic freeness condition as their dimensions grow to infinity. Informally speaking, all latent variables contribute to the system model in a democratic fashion – there are no preferred latent variables...... in the system....
Kandaswamy, Krishna Kumar Umar
2013-01-01
The extracellular matrix (ECM) is a major component of tissues of multicellular organisms. It consists of secreted macromolecules, mainly polysaccharides and glycoproteins. Malfunctions of ECM proteins lead to severe disorders such as marfan syndrome, osteogenesis imperfecta, numerous chondrodysplasias, and skin diseases. In this work, we report a random forest approach, EcmPred, for the prediction of ECM proteins from protein sequences. EcmPred was trained on a dataset containing 300 ECM and 300 non-ECM and tested on a dataset containing 145 ECM and 4187 non-ECM proteins. EcmPred achieved 83% accuracy on the training and 77% on the test dataset. EcmPred predicted 15 out of 20 experimentally verified ECM proteins. By scanning the entire human proteome, we predicted novel ECM proteins validated with gene ontology and InterPro. The dataset and standalone version of the EcmPred software is available at http://www.inb.uni-luebeck.de/tools-demos/Extracellular_matrix_proteins/EcmPred. © 2012 Elsevier Ltd.
Liu, Yan-Ping; Gu, Yu-Mei; Thijs, Lutgarde; Knapen, Marjo H J; Salvi, Erika; Citterio, Lorena; Petit, Thibault; Carpini, Simona Delli; Zhang, Zhenyu; Jacobs, Lotte; Jin, Yu; Barlassina, Cristina; Manunta, Paolo; Kuznetsova, Tatiana; Verhamme, Peter; Struijker-Boudier, Harry A; Cusi, Daniele; Vermeer, Cees; Staessen, Jan A
2015-02-01
Matrix Gla-protein is a vitamin K-dependent protein that strongly inhibits arterial calcification. Vitamin K deficiency leads to production of inactive nonphosphorylated and uncarboxylated matrix Gla protein (dp-ucMGP). The risk associated with dp-ucMGP in the population is unknown. In a Flemish population study, we measured circulating dp-ucMGP at baseline (1996-2011), genotyped MGP, recorded adverse health outcomes until December 31, 2012, and assessed the multivariable-adjusted associations of adverse health outcomes with dp-ucMGP. We applied a Mendelian randomization analysis using MGP genotypes as instrumental variables. Among 2318 participants, baseline dp-ucMGP averaged 3.61 μg/L. Over 14.1 years (median), 197 deaths occurred, 58 from cancer and 70 from cardiovascular disease; 85 participants experienced a coronary event. The risk of death and non-cancer mortality curvilinearly increased (P≤0.008) by 15.0% (95% confidence interval, 6.9-25.3) and by 21.5% (11.1-32.9) for a doubling of the nadir (1.43 and 0.97 μg/L, respectively). With higher dp-ucMGP, cardiovascular mortality log-linearly increased (hazard ratio for dp-ucMGP doubling, 1.14 [1.01-1.28]; P=0.027), but coronary events log-linearly decreased (0.93 [0.88-0.99]; P=0.021). dp-ucMGP levels were associated (P≤0.001) with MGP variants rs2098435, rs4236, and rs2430692. For non-cancer mortality and coronary events (P≤0.022), but not for total and cardiovascular mortality (P≥0.13), the Mendelian randomization analysis suggested causality. Higher dp-ucMGP predicts total, non-cancer and cardiovascular mortality, but lower coronary risk. For non-cancer mortality and coronary events, these associations are likely causal. © 2014 American Heart Association, Inc.
Ensemble Machine Learning Methods and Applications
Ma, Yunqian
2012-01-01
It is common wisdom that gathering a variety of views and inputs improves the process of decision making, and, indeed, underpins a democratic society. Dubbed “ensemble learning” by researchers in computational intelligence and machine learning, it is known to improve a decision system’s robustness and accuracy. Now, fresh developments are allowing researchers to unleash the power of ensemble learning in an increasing range of real-world applications. Ensemble learning algorithms such as “boosting” and “random forest” facilitate solutions to key computational issues such as face detection and are now being applied in areas as diverse as object trackingand bioinformatics. Responding to a shortage of literature dedicated to the topic, this volume offers comprehensive coverage of state-of-the-art ensemble learning techniques, including various contributions from researchers in leading industrial research labs. At once a solid theoretical study and a practical guide, the volume is a windfall for r...
Multilevel ensemble Kalman filter
Chernov, Alexey
2016-01-06
This work embeds a multilevel Monte Carlo (MLMC) sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF). In terms of computational cost vs. approximation error the asymptotic performance of the multilevel ensemble Kalman filter (MLEnKF) is superior to the EnKF s.
The Ensembl REST API: Ensembl Data for Any Language.
Yates, Andrew; Beal, Kathryn; Keenan, Stephen; McLaren, William; Pignatelli, Miguel; Ritchie, Graham R S; Ruffier, Magali; Taylor, Kieron; Vullo, Alessandro; Flicek, Paul
2015-01-01
We present a Web service to access Ensembl data using Representational State Transfer (REST). The Ensembl REST server enables the easy retrieval of a wide range of Ensembl data by most programming languages, using standard formats such as JSON and FASTA while minimizing client work. We also introduce bindings to the popular Ensembl Variant Effect Predictor tool permitting large-scale programmatic variant analysis independent of any specific programming language. The Ensembl REST API can be accessed at http://rest.ensembl.org and source code is freely available under an Apache 2.0 license from http://github.com/Ensembl/ensembl-rest. © The Author 2014. Published by Oxford University Press.
The Polyanalytic Ginibre Ensembles
Haimi, Antti; Hedenmalm, Haakan
2013-10-01
For integers n, q=1,2,3,… , let Pol n, q denote the -linear space of polynomials in z and , of degree ≤ n-1 in z and of degree ≤ q-1 in . We supply Pol n, q with the inner product structure of the resulting Hilbert space is denoted by Pol m, n, q . Here, it is assumed that m is a positive real. We let K m, n, q denote the reproducing kernel of Pol m, n, q , and study the associated determinantal process, in the limit as m, n→+∞ while n= m+O(1); the number q, the degree of polyanalyticity, is kept fixed. We call these processes polyanalytic Ginibre ensembles, because they generalize the Ginibre ensemble—the eigenvalue process of random (normal) matrices with Gaussian weight. There is a physical interpretation in terms of a system of free fermions in a uniform magnetic field so that a fixed number of the first Landau levels have been filled. We consider local blow-ups of the polyanalytic Ginibre ensembles around points in the spectral droplet, which is here the closed unit disk . We obtain asymptotics for the blow-up process, using a blow-up to characteristic distance m -1/2; the typical distance is the same both for interior and for boundary points of . This amounts to obtaining the asymptotical behavior of the generating kernel K m, n, q . Following (Ameur et al. in Commun. Pure Appl. Math. 63(12):1533-1584, 2010), the asymptotics of the K m, n, q are rather conveniently expressed in terms of the Berezin measure (and density) [Equation not available: see fulltext.] For interior points | z|1. In contrast, for exterior points | z|>1, we have instead that , where is the harmonic measure at z with respect to the exterior disk . For boundary points, | z|=1, the Berezin measure converges to the unit point mass at z, as with interior points, but the blow-up to the scale m -1/2 exhibits quite different behavior at boundary points compared with interior points. We also obtain the asymptotic boundary behavior of the 1-point function at the coarser local scale q 1
Ensemble approach for differentiation of malignant melanoma
Rastgoo, Mojdeh; Morel, Olivier; Marzani, Franck; Garcia, Rafael
2015-04-01
Melanoma is the deadliest type of skin cancer, yet it is the most treatable kind depending on its early diagnosis. The early prognosis of melanoma is a challenging task for both clinicians and dermatologists. Due to the importance of early diagnosis and in order to assist the dermatologists, we propose an automated framework based on ensemble learning methods and dermoscopy images to differentiate melanoma from dysplastic and benign lesions. The evaluation of our framework on the recent and public dermoscopy benchmark (PH2 dataset) indicates the potential of proposed method. Our evaluation, using only global features, revealed that ensembles such as random forest perform better than single learner. Using random forest ensemble and combination of color and texture features, our framework achieved the highest sensitivity of 94% and specificity of 92%.
Energy-dependent correlations in the S-matrix of chaotic systems
Novaes, Marcel
2016-12-01
The M-dimensional unitary matrix S(E), which describes scattering of waves, is a strongly fluctuating function of the energy for complex systems such as ballistic cavities, whose geometry induces chaotic ray dynamics. Its statistical behaviour can be expressed by means of correlation functions of the kind , which have been much studied within the random matrix approach. In this work, we consider correlations involving an arbitrary number of matrix elements and express them as infinite series in 1/M, whose coefficients are rational functions of ɛ. From a mathematical point of view, this may be seen as a generalization of the Weingarten functions of circular ensembles.
Universality of Wigner random matrices: a survey of recent results
Energy Technology Data Exchange (ETDEWEB)
Erdos, Laszlo [Ludwig-Maximilians-University of Munich (Germany)
2011-06-30
This is a study of the universality of spectral statistics for large random matrices. Considered are NxN symmetric, Hermitian, or quaternion self-dual random matrices with independent identically distributed entries (Wigner matrices), where the probability distribution of each matrix element is given by a measure {nu} with zero expectation and with subexponential decay. The main result is that the correlation functions of the local eigenvalue statistics in the bulk of the spectrum coincide with those of the Gaussian Orthogonal Ensemble (GOE), the Gaussian Unitary Ensemble (GUE), and the Gaussian Symplectic Ensemble (GSE), respectively, in the limit as N {yields} {infinity}. This approach is based on a study of the Dyson Brownian motion via a related new dynamics, the local relaxation flow. As a main input, it is established that the density of the eigenvalues converges to the Wigner semicircle law, and this holds even down to the smallest possible scale. Moreover, it is shown that the eigenvectors are completely delocalized. These results hold even without the condition that the matrix elements are identically distributed: only independence is used. In fact, for the matrix elements of the Green function strong estimates are given that imply that the local statistics of any two ensembles in the bulk are identical if the first four moments of the matrix elements match. Universality at the spectral edges requires matching only two moments. A Wigner-type estimate is also proved, and it is shown that the eigenvalues repel each other on arbitrarily small scales. Bibliography: 108 titles.
Conservation constraints on random matrices
Ma Wen Jong; Hsieh, J
2003-01-01
We study the random matrices constrained by the summation rules that are present in the Hessian of the potential energy surface in the instantaneous normal mode calculations, as a result of momentum conservation. In this paper, we analyse the properties related to such conservation constraints in two classes of real symmetric matrices: one with purely row-wise summation rules and the other with the constraints on the blocks of each matrix, which underscores partially the spatial dimension. We show explicitly that the constraints are removable by separating the degrees of freedom of the zero-eigenvalue modes. The non-spectral degrees of freedom under the constraints can be realized in terms of the ordinary constraint-free orthogonal symmetry but with the rank deducted by the block dimension. We propose that the ensemble of real symmetric matrices with full randomness, constrained by the summation rules, is equivalent to the Gaussian orthogonal ensemble (GOE) with lowered rank. Independent of the joint probabil...
Directory of Open Access Journals (Sweden)
Lev-Tov Hadar
2013-01-01
Full Text Available Abstract Background Diabetic foot ulcers (DFUs represent a significant source of morbidity and an enormous financial burden. Standard care for DFUs involves systemic glucose control, ensuring adequate perfusion, debridement of nonviable tissue, off-loading, control of infection, local wound care and patient education, all administered by a multidisciplinary team. Unfortunately, even with the best standard of care (SOC available, only 24% or 30% of DFUs will heal at weeks 12 or 20, respectively. The extracellular matrix (ECM in DFUs is abnormal and its impairment has been proposed as a key target for new therapeutic devices. These devices intend to replace the aberrant ECM by implanting a matrix, either devoid of cells or enhanced with fibroblasts, keratinocytes or both as well as various growth factors. These new bioengineered skin substitutes are proposed to encourage angiogenesis and in-growth of new tissue, and to utilize living cells to generate cytokines needed for wound repair. To date, the efficacy of bioengineered ECM containing live cellular elements for improving healing above that of a SOC control group has not been compared with the efficacy of an ECM devoid of cells relative to the same SOC. Our hypothesis is that there is no difference in the improved healing effected by either of these two product types relative to SOC. Methods/Design To test this hypothesis we propose a randomized, single-blind, clinical trial with three arms: SOC, SOC plus Dermagraft® (bioengineered ECM containing living fibroblasts and SOC plus Oasis® (ECM devoid of living cells in patients with nonhealing DFUs. The primary outcome is the percentage of subjects that achieved complete wound closure by week 12. Discussion If our hypothesis is correct, then immense cost savings could be realized by using the orders-of-magnitude less expensive acellular ECM device without compromising patient health outcomes. The article describes the protocol proposed to test
Two conjectures about spectral density of diluted sparse Bernoulli random matrices
Nechaev, S. K.
2014-01-01
We consider the ensemble of $N\\times N$ ($N\\gg 1$) symmetric random matrices with the bimodal independent distribution of matrix elements: each element could be either "1" with the probability $p$, or "0" otherwise. We pay attention to the "diluted" sparse regime, taking $p=1/N +\\epsilon$, where $0
Sifaou, Houssem
2016-05-01
Massive MIMO systems are shown to be a promising technology for next generations of wireless communication networks. The realization of the attractive merits promised by massive MIMO systems requires advanced linear precoding and receiving techniques in order to mitigate the interference in downlink and uplink transmissions. This work considers the precoder and receiver design in massive MIMO systems. We first consider the design of the linear precoder and receiver that maximize the minimum signal-to-interference-plus-noise ratio (SINR) subject to a given power constraint. The analysis is carried out under the asymptotic regime in which the number of the BS antennas and that of the users grow large with a bounded ratio. This allows us to leverage tools from random matrix theory in order to approximate the parameters of the optimal linear precoder and receiver by their deterministic approximations. Such a result is of valuable practical interest, as it provides a handier way to implement the optimal precoder and receiver. To reduce further the complexity, we propose to apply the truncated polynomial expansion (TPE) concept on a per-user basis to approximate the inverse of large matrices that appear on the expressions of the optimal linear transceivers. Using tools from random matrix theory, we determine deterministic approximations of the SINR and the transmit power in the asymptotic regime. Then, the optimal per-user weight coe cients that solve the max-min SINR problem are derived. The simulation results show that the proposed precoder and receiver provide very close to optimal performance while reducing signi cantly the computational complexity. As a second part of this work, the TPE technique in a per-user basis is applied to the optimal linear precoding that minimizes the transmit power while satisfying a set of target SINR constraints. Due to the emerging research eld of green cellular networks, such a problem is receiving increasing interest nowadays. Closed
Agarwal, Jayant P; Mendenhall, Shaun D; Anderson, Layla A; Ying, Jian; Boucher, Kenneth M; Liu, Ting; Neumayer, Leigh A
2015-01-01
Recent literature has focused on the advantages and disadvantages of using acellular dermal matrix in breast reconstruction. Many of the reported data are from low level-of-evidence studies, leaving many questions incompletely answered. The present randomized trial provides high-level data on the incidence and severity of complications in acellular dermal matrix breast reconstruction between two commonly used types of acellular dermal matrix. A prospective randomized trial was conducted to compare outcomes of immediate staged tissue expander breast reconstruction using either AlloDerm or DermaMatrix. The impact of body mass index, smoking, diabetes, mastectomy type, radiation therapy, and chemotherapy on outcomes was analyzed. Acellular dermal matrix biointegration was analyzed clinically and histologically. Patient satisfaction was assessed by means of preoperative and postoperative surveys. Logistic regression models were used to identify predictors of complications. This article reports on the study design, surgical technique, patient characteristics, and preoperative survey results, with outcomes data in a separate report. After 2.5 years, we successfully enrolled and randomized 128 patients (199 breasts). The majority of patients were healthy nonsmokers, with 41 percent of patients receiving radiation therapy and 49 percent receiving chemotherapy. Half of the mastectomies were prophylactic, with nipple-sparing mastectomy common in both cancer and prophylactic cases. Preoperative survey results indicate that patients were satisfied with their premastectomy breast reconstruction education. Results from the Breast Reconstruction Evaluation Using Acellular Dermal Matrix as a Sling Trial will assist plastic surgeons in making evidence-based decisions regarding acellular dermal matrix-assisted tissue expander breast reconstruction. Therapeutic, II.
National Aeronautics and Space Administration — Ensemble Data Mining Methods, also known as Committee Methods or Model Combiners, are machine learning methods that leverage the power of multiple models to achieve...
Directory of Open Access Journals (Sweden)
Marin-Garcia Pablo
2010-05-01
Full Text Available Abstract Background The maturing field of genomics is rapidly increasing the number of sequenced genomes and producing more information from those previously sequenced. Much of this additional information is variation data derived from sampling multiple individuals of a given species with the goal of discovering new variants and characterising the population frequencies of the variants that are already known. These data have immense value for many studies, including those designed to understand evolution and connect genotype to phenotype. Maximising the utility of the data requires that it be stored in an accessible manner that facilitates the integration of variation data with other genome resources such as gene annotation and comparative genomics. Description The Ensembl project provides comprehensive and integrated variation resources for a wide variety of chordate genomes. This paper provides a detailed description of the sources of data and the methods for creating the Ensembl variation databases. It also explores the utility of the information by explaining the range of query options available, from using interactive web displays, to online data mining tools and connecting directly to the data servers programmatically. It gives a good overview of the variation resources and future plans for expanding the variation data within Ensembl. Conclusions Variation data is an important key to understanding the functional and phenotypic differences between individuals. The development of new sequencing and genotyping technologies is greatly increasing the amount of variation data known for almost all genomes. The Ensembl variation resources are integrated into the Ensembl genome browser and provide a comprehensive way to access this data in the context of a widely used genome bioinformatics system. All Ensembl data is freely available at http://www.ensembl.org and from the public MySQL database server at ensembldb.ensembl.org.
Hu, Jun; Li, Yang; Yang, Jing-Yu; Shen, Hong-Bin; Yu, Dong-Jun
2016-02-01
G-protein-coupled receptors (GPCRs) are important targets of modern medicinal drugs. The accurate identification of interactions between GPCRs and drugs is of significant importance for both protein function annotations and drug discovery. In this paper, a new sequence-based predictor called TargetGDrug is designed and implemented for predicting GPCR-drug interactions. In TargetGDrug, the evolutionary feature of GPCR sequence and the wavelet-based molecular fingerprint feature of drug are integrated to form the combined feature of a GPCR-drug pair; then, the combined feature is fed to a trained random forest (RF) classifier to perform initial prediction; finally, a novel drug-association-matrix-based post-processing procedure is applied to reduce potential false positive or false negative of the initial prediction. Experimental results on benchmark datasets demonstrate the efficacy of the proposed method, and an improvement of 15% in the Matthews correlation coefficient (MCC) was observed over independent validation tests when compared with the most recently released sequence-based GPCR-drug interactions predictor. The implemented webserver, together with the datasets used in this study, is freely available for academic use at http://csbio.njust.edu.cn/bioinf/TargetGDrug. Copyright © 2015 Elsevier Ltd. All rights reserved.
Cairo, Francesco; Barbato, Luigi; Tonelli, Paolo; Batalocco, Guido; Pagavino, Gabriella; Nieri, Michele
2017-07-01
Peri-implant soft tissue may be critical to prevent inflammation and promote gingival margin stability. The purpose of this randomized clinical trial (RCT) is to compare xenogeneic collagen matrix (XCM) versus connective tissue graft (CTG) to increase buccal soft tissue thickness at implant site. Soft tissue augmentation with XCM (test) or CTG (control) was performed at 60 implants in 60 patients at the time of implant uncovering. Measurements were performed by a blinded examiner at baseline, 3 and 6 months. Outcome measures included buccal soft tissue thickness (GT), apico-coronal keratinized tissue (KT), chair time and post-operative discomfort. Visual Analogue Scale (VAS) was used to evaluate patient satisfaction. After 6 months, the final GT increase was 0.9 ± 0.2 in the XCM group and 1.2 ± 0.3 mm in the CTG group, with a significant difference favouring the control group (0.3 mm; p = .0001). Both procedures resulted in similar final KT amount with no significant difference between treatments. XCM was associated with significant less chair-time (p tissue thickness. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
Meyle, Joerg; Hoffmann, Thomas; Topoll, Heinz; Heinz, Bernd; Al-Machot, Eli; Jervøe-Storm, Pia-Merete; Jepsen, Søren; Eickholz, Peter; Meiss, Christian
2011-01-01
Abstract Objectives: Comparison of clinical and radiographic outcomes of a combination of enamel matrix derivatives (EMD) and a synthetic bone graft (SBG) with EMD alone in wide and deep 1- and 2- wall intrabony defects 12 months after treatment. Method: In 73 patients with chronic periodontitis and one intrabony lesion, defects were randomly assigned to EMD/SBG (test) or EMD (control). Bone sounding, attachment levels, probing pocket depths, bleeding on probing and recessions w...
A new method for determining the optimal lagged ensemble
DelSole, T.; Tippett, M. K.; Pegion, K.
2017-01-01
Abstract We propose a general methodology for determining the lagged ensemble that minimizes the mean square forecast error. The MSE of a lagged ensemble is shown to depend only on a quantity called the cross‐lead error covariance matrix, which can be estimated from a short hindcast data set and parameterized in terms of analytic functions of time. The resulting parameterization allows the skill of forecasts to be evaluated for an arbitrary ensemble size and initialization frequency. Remarkably, the parameterization also can estimate the MSE of a burst ensemble simply by taking the limit of an infinitely small interval between initialization times. This methodology is applied to forecasts of the Madden Julian Oscillation (MJO) from version 2 of the Climate Forecast System version 2 (CFSv2). For leads greater than a week, little improvement is found in the MJO forecast skill when ensembles larger than 5 days are used or initializations greater than 4 times per day. We find that if the initialization frequency is too infrequent, important structures of the lagged error covariance matrix are lost. Lastly, we demonstrate that the forecast error at leads ≥10 days can be reduced by optimally weighting the lagged ensemble members. The weights are shown to depend only on the cross‐lead error covariance matrix. While the methodology developed here is applied to CFSv2, the technique can be easily adapted to other forecast systems. PMID:28580050
The semantic similarity ensemble
Directory of Open Access Journals (Sweden)
Andrea Ballatore
2013-12-01
Full Text Available Computational measures of semantic similarity between geographic terms provide valuable support across geographic information retrieval, data mining, and information integration. To date, a wide variety of approaches to geo-semantic similarity have been devised. A judgment of similarity is not intrinsically right or wrong, but obtains a certain degree of cognitive plausibility, depending on how closely it mimics human behavior. Thus selecting the most appropriate measure for a specific task is a significant challenge. To address this issue, we make an analogy between computational similarity measures and soliciting domain expert opinions, which incorporate a subjective set of beliefs, perceptions, hypotheses, and epistemic biases. Following this analogy, we define the semantic similarity ensemble (SSE as a composition of different similarity measures, acting as a panel of experts having to reach a decision on the semantic similarity of a set of geographic terms. The approach is evaluated in comparison to human judgments, and results indicate that an SSE performs better than the average of its parts. Although the best member tends to outperform the ensemble, all ensembles outperform the average performance of each ensemble's member. Hence, in contexts where the best measure is unknown, the ensemble provides a more cognitively plausible approach.
Ensemble Methods for Classification of Physical Activities from Wrist Accelerometry.
Chowdhury, Alok Kumar; Tjondronegoro, Dian; Chandran, Vinod; Trost, Stewart G
2017-09-01
To investigate whether the use of ensemble learning algorithms improve physical activity recognition accuracy compared to the single classifier algorithms, and to compare the classification accuracy achieved by three conventional ensemble machine learning methods (bagging, boosting, random forest) and a custom ensemble model comprising four algorithms commonly used for activity recognition (binary decision tree, k nearest neighbor, support vector machine, and neural network). The study used three independent data sets that included wrist-worn accelerometer data. For each data set, a four-step classification framework consisting of data preprocessing, feature extraction, normalization and feature selection, and classifier training and testing was implemented. For the custom ensemble, decisions from the single classifiers were aggregated using three decision fusion methods: weighted majority vote, naïve Bayes combination, and behavior knowledge space combination. Classifiers were cross-validated using leave-one subject out cross-validation and compared on the basis of average F1 scores. In all three data sets, ensemble learning methods consistently outperformed the individual classifiers. Among the conventional ensemble methods, random forest models provided consistently high activity recognition; however, the custom ensemble model using weighted majority voting demonstrated the highest classification accuracy in two of the three data sets. Combining multiple individual classifiers using conventional or custom ensemble learning methods can improve activity recognition accuracy from wrist-worn accelerometer data.
Yin, Dong-shan; Gao, Yu-ping; Zhao, Shu-hong
2017-07-01
Millisecond pulsars can generate another type of time scale that is totally independent of the atomic time scale, because the physical mechanisms of the pulsar time scale and the atomic time scale are quite different from each other. Usually the pulsar timing observations are not evenly sampled, and the internals between two data points range from several hours to more than half a month. Further more, these data sets are sparse. All this makes it difficult to generate an ensemble pulsar time scale. Hence, a new algorithm to calculate the ensemble pulsar time scale is proposed. Firstly, a cubic spline interpolation is used to densify the data set, and make the intervals between data points uniform. Then, the Vondrak filter is employed to smooth the data set, and get rid of the high-frequency noises, and finally the weighted average method is adopted to generate the ensemble pulsar time scale. The newly released NANOGRAV (North American Nanohertz Observatory for Gravitational Waves) 9-year data set is used to generate the ensemble pulsar time scale. This data set includes the 9-year observational data of 37 millisecond pulsars observed by the 100-meter Green Bank telescope and the 305-meter Arecibo telescope. It is found that the algorithm used in this paper can reduce effectively the influence caused by the noises in pulsar timing residuals, and improve the long-term stability of the ensemble pulsar time scale. Results indicate that the long-term (> 1 yr) stability of the ensemble pulsar time scale is better than 3.4 × 10-15.
Campitiello, F; Mancone, M; Della Corte, A; Guerniero, R; Canonico, S
2017-12-01
The authors aimed to evaluate the efficacy of an advanced wound matrix (Integra Flowable Wound Matrix, Integra LifeScience Corp, Plainsboro, NJ, USA) for treating wounds with irregular geometries versus a wet dressing in patients with diabetic foot ulcers. Sixty patients with diabetic foot ulcers (Grades 3 Wagner) were included in this randomized clinical trial. The study was conducted in the General Surgery Unit and Geriatric of the Second University of Naples, Italy, in the last 12 months. Forty-six cases of diabetic foot ulcers were equally and randomly divided into control and test groups. The first group treated with Integra Flowable Wound Matrix, while the control group with a wet dressing. Both groups were evaluated once a week for 6 weeks to value the degree of epithelialization and granulation tissue of the wound. The complete healing rate in the whole study population was 69.56% (Integra Flowable Wound Matrix group, 86.95%, control group, 52.17%; p = 0.001). Amputation and rehospitalization rates were higher in the control group compared to the first group, therefore, the difference was statistically significant (p = 0.0019; p = 0.028, respectively). The Integra Flowable Wound Matrix, was significantly superior, compared to the wet dressing, by promoting the complete healing of diabetic foot ulcers. Ease of use, absence of adverse effects, and a facilitated wound healing process are among the properties of the matrix. These characteristics make it appropriate in the management of diabetic foot ulcers. Additional research will shed more light on the promising advantages of this material in healing diabetic foot ulcers.
Shahjahan, S.; Aubry, A.; Rupin, F.; Chassignole, B.; Derode, A.
2014-06-01
We report on ultrasonic imaging in a random heterogeneous medium. The goal is to detect flaws embedded deeply into a polycrystalline material. A 64-element array of piezoelectric transmitters/receivers at a central frequency of 5 MHz is used to capture the Green's matrix in a backscattering configuration. Because of multiple scattering, conventional imaging completely fails to detect the deepest flaws. We utilize a random matrix approach, taking advantage of the deterministic coherence of the backscattered wave-field which is characteristic of single scattering and related to the memory effect. This allows us to separate single and multiple scattering contributions. As a consequence, we show that flaws are detected beyond the conventional limit, as if multiple scattering had been overcome.
Multilevel ensemble Kalman filtering
Hoel, Haakon
2016-01-08
The ensemble Kalman filter (EnKF) is a sequential filtering method that uses an ensemble of particle paths to estimate the means and covariances required by the Kalman filter by the use of sample moments, i.e., the Monte Carlo method. EnKF is often both robust and efficient, but its performance may suffer in settings where the computational cost of accurate simulations of particles is high. The multilevel Monte Carlo method (MLMC) is an extension of classical Monte Carlo methods which by sampling stochastic realizations on a hierarchy of resolutions may reduce the computational cost of moment approximations by orders of magnitude. In this work we have combined the ideas of MLMC and EnKF to construct the multilevel ensemble Kalman filter (MLEnKF) for the setting of finite dimensional state and observation spaces. The main ideas of this method is to compute particle paths on a hierarchy of resolutions and to apply multilevel estimators on the ensemble hierarchy of particles to compute Kalman filter means and covariances. Theoretical results and a numerical study of the performance gains of MLEnKF over EnKF will be presented. Some ideas on the extension of MLEnKF to settings with infinite dimensional state spaces will also be presented.
DEFF Research Database (Denmark)
Hansen, Lars Kai; Salamon, Peter
1990-01-01
We propose several means for improving the performance an training of neural networks for classification. We use crossvalidation as a tool for optimizing network parameters and architecture. We show further that the remaining generalization error can be reduced by invoking ensembles of similar...... networks....
Multivariate localization methods for ensemble Kalman filtering
Roh, S.
2015-12-03
In ensemble Kalman filtering (EnKF), the small number of ensemble members that is feasible to use in a practical data assimilation application leads to sampling variability of the estimates of the background error covariances. The standard approach to reducing the effects of this sampling variability, which has also been found to be highly efficient in improving the performance of EnKF, is the localization of the estimates of the covariances. One family of localization techniques is based on taking the Schur (element-wise) product of the ensemble-based sample covariance matrix and a correlation matrix whose entries are obtained by the discretization of a distance-dependent correlation function. While the proper definition of the localization function for a single state variable has been extensively investigated, a rigorous definition of the localization function for multiple state variables that exist at the same locations has been seldom considered. This paper introduces two strategies for the construction of localization functions for multiple state variables. The proposed localization functions are tested by assimilating simulated observations experiments into the bivariate Lorenz 95 model with their help.
Multivariate localization methods for ensemble Kalman filtering
Roh, S.
2015-05-08
In ensemble Kalman filtering (EnKF), the small number of ensemble members that is feasible to use in a practical data assimilation application leads to sampling variability of the estimates of the background error covariances. The standard approach to reducing the effects of this sampling variability, which has also been found to be highly efficient in improving the performance of EnKF, is the localization of the estimates of the covariances. One family of localization techniques is based on taking the Schur (entry-wise) product of the ensemble-based sample covariance matrix and a correlation matrix whose entries are obtained by the discretization of a distance-dependent correlation function. While the proper definition of the localization function for a single state variable has been extensively investigated, a rigorous definition of the localization function for multiple state variables has been seldom considered. This paper introduces two strategies for the construction of localization functions for multiple state variables. The proposed localization functions are tested by assimilating simulated observations experiments into the bivariate Lorenz 95 model with their help.
ESPC Coupled Global Ensemble Design
2014-09-30
square error of the ensemble mean (RMSE), Continuous Ranked Probability Skill score ( CRPS ), the bias of the ensemble mean, and a measure of the...boundary conditions use a multi-year history of global ocean model output. RESULTS Atmosphere component: 1) Milestone: Develop ensemble...significant improvements, mainly in the ensemble 10m wind speed RMSE and CRPS metrics. An example of these improvements is shown for the case of the
ABCD of Beta Ensembles and Topological Strings
Krefl, Daniel
2012-01-01
We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their relation with refined topological strings. Our results generalize the familiar connections between local topological strings and matrix models leading to An measure, and illustrate that all those classical eigenvalue ensembles, and their topological string counterparts, are related one to another via various deformations and specializations, quantum shifts and discrete quotients. We review the solution of the Gaussian models via Macdonald identities, and interpret them as conifold theories. The interpolation between the various models is plainly apparent in this case. For general polynomial potential, we calculate the partition function in the multi-cut phase in a perturbative fashion, beyond tree-level in the large-N limit. The relation to refined topological string orientifolds on the corresponding local geometry is discussed along the way.
Kingston Soundpainting Ensemble
Minors, Helen Julia; Kingston Soundpainting Ensemble
2012-01-01
This performance is designed to introduce teachers and school musicians to this live multidisciplinary live composing sign language.\\ud \\ud Led by Dr. Helen Julia Minors (soundpainter, trumpet, voice), the Kingston Soundpainting Ensemble, led by Dr. Minors at Kington University, is representated by a section a varied set of performers, using woodwind, brass, voice and percussion, spanning popular, classical and world styles. This performance consists of:\\ud \\ud Philip Warda (electronic instru...
Ensemble Pruning for Glaucoma Detection in an Unbalanced Data Set.
Adler, Werner; Gefeller, Olaf; Gul, Asma; Horn, Folkert K; Khan, Zardad; Lausen, Berthold
2016-12-07
Random forests are successful classifier ensemble methods consisting of typically 100 to 1000 classification trees. Ensemble pruning techniques reduce the computational cost, especially the memory demand, of random forests by reducing the number of trees without relevant loss of performance or even with increased performance of the sub-ensemble. The application to the problem of an early detection of glaucoma, a severe eye disease with low prevalence, based on topographical measurements of the eye background faces specific challenges. We examine the performance of ensemble pruning strategies for glaucoma detection in an unbalanced data situation. The data set consists of 102 topographical features of the eye background of 254 healthy controls and 55 glaucoma patients. We compare the area under the receiver operating characteristic curve (AUC), and the Brier score on the total data set, in the majority class, and in the minority class of pruned random forest ensembles obtained with strategies based on the prediction accuracy of greedily grown sub-ensembles, the uncertainty weighted accuracy, and the similarity between single trees. To validate the findings and to examine the influence of the prevalence of glaucoma in the data set, we additionally perform a simulation study with lower prevalences of glaucoma. In glaucoma classification all three pruning strategies lead to improved AUC and smaller Brier scores on the total data set with sub-ensembles as small as 30 to 80 trees compared to the classification results obtained with the full ensemble consisting of 1000 trees. In the simulation study, we were able to show that the prevalence of glaucoma is a critical factor and lower prevalence decreases the performance of our pruning strategies. The memory demand for glaucoma classification in an unbalanced data situation based on random forests could effectively be reduced by the application of pruning strategies without loss of performance in a population with increased
An estimate of the inflation factor and analysis sensitivity in the ensemble Kalman filter
Directory of Open Access Journals (Sweden)
G. Wu
2017-07-01
Full Text Available The ensemble Kalman filter (EnKF is a widely used ensemble-based assimilation method, which estimates the forecast error covariance matrix using a Monte Carlo approach that involves an ensemble of short-term forecasts. While the accuracy of the forecast error covariance matrix is crucial for achieving accurate forecasts, the estimate given by the EnKF needs to be improved using inflation techniques. Otherwise, the sampling covariance matrix of perturbed forecast states will underestimate the true forecast error covariance matrix because of the limited ensemble size and large model errors, which may eventually result in the divergence of the filter. In this study, the forecast error covariance inflation factor is estimated using a generalized cross-validation technique. The improved EnKF assimilation scheme is tested on the atmosphere-like Lorenz-96 model with spatially correlated observations, and is shown to reduce the analysis error and increase its sensitivity to the observations.
Coherent control of mesoscopic atomic ensembles for quantum information
Beterov, I. I.; Saffman, M.; Zhukov, V. P.; Tretyakov, D. B.; Entin, V. M.; Yakshina, E. A.; Ryabtsev, I. I.; Mansell, C. W.; MacCormick, C.; Bergamini, S.; Fedoruk, M. P.
2013-01-01
We discuss methods for coherently controlling mesoscopic atomic ensembles where the number of atoms varies randomly from one experimental run to the next. The proposed schemes are based on adiabatic passage and Rydberg blockade and can be used for implementation of a scalable quantum register formed by an array of randomly loaded optical dipole traps.
Ensemble Kalman filtering without the intrinsic need for inflation
Directory of Open Access Journals (Sweden)
M. Bocquet
2011-10-01
Full Text Available The main intrinsic source of error in the ensemble Kalman filter (EnKF is sampling error. External sources of error, such as model error or deviations from Gaussianity, depend on the dynamical properties of the model. Sampling errors can lead to instability of the filter which, as a consequence, often requires inflation and localization. The goal of this article is to derive an ensemble Kalman filter which is less sensitive to sampling errors. A prior probability density function conditional on the forecast ensemble is derived using Bayesian principles. Even though this prior is built upon the assumption that the ensemble is Gaussian-distributed, it is different from the Gaussian probability density function defined by the empirical mean and the empirical error covariance matrix of the ensemble, which is implicitly used in traditional EnKFs. This new prior generates a new class of ensemble Kalman filters, called finite-size ensemble Kalman filter (EnKF-N. One deterministic variant, the finite-size ensemble transform Kalman filter (ETKF-N, is derived. It is tested on the Lorenz '63 and Lorenz '95 models. In this context, ETKF-N is shown to be stable without inflation for ensemble size greater than the model unstable subspace dimension, at the same numerical cost as the ensemble transform Kalman filter (ETKF. One variant of ETKF-N seems to systematically outperform the ETKF with optimally tuned inflation. However it is shown that ETKF-N does not account for all sampling errors, and necessitates localization like any EnKF, whenever the ensemble size is too small. In order to explore the need for inflation in this small ensemble size regime, a local version of the new class of filters is defined (LETKF-N and tested on the Lorenz '95 toy model. Whatever the size of the ensemble, the filter is stable. Its performance without inflation is slightly inferior to that of LETKF with optimally tuned inflation for small interval between updates, and
Bata, Ahmed M; Witkowska, Katarzyna J; Wozniak, Piotr A; Fondi, Klemens; Schmidinger, Gerald; Pircher, Niklas; Szegedi, Stephan; Aranha Dos Santos, Valentin; Pantalon, Anca; Werkmeister, René M; Garhofer, Gerhard; Schmetterer, Leopold; Schmidl, Doreen
2016-10-01
Corneal abrasions are frequent after standard (epithelium-off [epi-off]) corneal collagen cross-linking (CXL) in patients with progressive keratoconus. A new matrix therapy agent (ReGeneraTing Agent [RGTA]) has been developed to promote corneal wound healing. To assess the effect of the new type of matrix therapy agent on corneal wound healing after epi-off CXL in patients with keratoconus. This double-masked randomized clinical trial enrolled 40 patients with keratoconus undergoing epi-off CXL from July 18, 2014, to October 21, 2015, when the last follow-up was completed. The analysis of the intention-to-treat population was performed at the Department of Clinical Pharmacology in cooperation with the Center for Medical Physics and Biomedical Engineering and the Department of Ophthalmology and Optometry of the Medical University of Vienna. Patients were randomized to receive the matrix therapy agent or hyaluronic acid-containing eyedrops, 0.1%, every other day starting immediately after surgery. The size of the corneal defect was measured using ultrahigh-resolution optical coherence tomography (OCT) and slitlamp photography (SLP) with fluorescein staining. Corneal wound healing rate, defined as the size of the defect over time. Among the 40 patients undergoing epi-off CXL (31 men; 9 women; mean [SD] age, 31 [10] years), wound healing was significantly faster in the matrix therapy agent group compared with the hyaluronic acid group (4.4 vs 6.1 days; mean difference, 1.7 days; 95% CI, 0.25-3.15 days; P = .008). The defect size was smaller in the matrix therapy agent group than in the hyaluronic acid group as measured with OCT (12.4 vs 23.9 mm2; mean difference, 11.6 mm2; 95% CI, 0.8-23.5 mm2; P = .045) and SLP (11.9 vs 23.5 mm2; mean difference, 11. 6 mm2; 95% CI, 1.3-22.9 mm2; P = .03). A correlation between the defect size measured with OCT and SLP was found (r = 0.89; P matrix therapy agent appears to improve corneal wound healing after CXL in
Weak commutation relations and eigenvalue statistics for products of rectangular random matrices.
Ipsen, Jesper R; Kieburg, Mario
2014-03-01
We study the joint probability density of the eigenvalues of a product of rectangular real, complex, or quaternion random matrices in a unified way. The random matrices are distributed according to arbitrary probability densities, whose only restriction is the invariance under left and right multiplication by orthogonal, unitary, or unitary symplectic matrices, respectively. We show that a product of rectangular matrices is statistically equivalent to a product of square matrices. Hereby we prove a weak commutation relation of the random matrices at finite matrix sizes, which previously has been discussed for infinite matrix size. Moreover, we derive the joint probability densities of the eigenvalues. To illustrate our results, we apply them to a product of random matrices drawn from Ginibre ensembles and Jacobi ensembles as well as a mixed version thereof. For these weights, we show that the product of complex random matrices yields a determinantal point process, while the real and quaternion matrix ensembles correspond to Pfaffian point processes. Our results are visualized by numerical simulations. Furthermore, we present an application to a transport on a closed, disordered chain coupled to a particle bath.
Random point sets and their diffraction
Baake, Michael; Kösters, Holger
2011-07-01
The diffraction of various random subsets of the integer lattice ℤ d , such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in ℝ d . We present several systems with an effective stochastic interaction that still allow for explicit calculations of the autocorrelation and the diffraction measure. We concentrate on one-dimensional examples for illustrative purposes, and briefly indicate possible generalisations to higher dimensions. In particular, we discuss the stationary Poisson process in ℝ d and the renewal process on the line. The latter permits a unified approach to a rather large class of one-dimensional structures, including random tilings. Moreover, we present some stationary point processes that are derived from the classical random matrix ensembles as introduced in the pioneering work of Dyson and Ginibre. Their reconsideration from the diffraction point of view improves the intuition on systems with randomness and mixed spectra.
Imprinting and recalling cortical ensembles.
Carrillo-Reid, Luis; Yang, Weijian; Bando, Yuki; Peterka, Darcy S; Yuste, Rafael
2016-08-12
Neuronal ensembles are coactive groups of neurons that may represent building blocks of cortical circuits. These ensembles could be formed by Hebbian plasticity, whereby synapses between coactive neurons are strengthened. Here we report that repetitive activation with two-photon optogenetics of neuronal populations from ensembles in the visual cortex of awake mice builds neuronal ensembles that recur spontaneously after being imprinted and do not disrupt preexisting ones. Moreover, imprinted ensembles can be recalled by single- cell stimulation and remain coactive on consecutive days. Our results demonstrate the persistent reconfiguration of cortical circuits by two-photon optogenetics into neuronal ensembles that can perform pattern completion. Copyright © 2016, American Association for the Advancement of Science.
Multilevel ensemble Kalman filtering
Hoel, Hakon
2016-06-14
This work embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and noisy discrete-time observations. The signal dynamics is assumed to be governed by a stochastic differential equation (SDE), and a hierarchy of time grids is introduced for multilevel numerical integration of that SDE. The resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.
Mixed learning algorithms and features ensemble in hepatotoxicity prediction.
Liew, Chin Yee; Lim, Yen Ching; Yap, Chun Wei
2011-09-01
Drug-induced liver injury, although infrequent, is an important safety concern that can lead to fatality in patients and failure in drug developments. In this study, we have used an ensemble of mixed learning algorithms and mixed features for the development of a model to predict hepatic effects. This robust method is based on the premise that no single learning algorithm is optimum for all modelling problems. An ensemble model of 617 base classifiers was built from a diverse set of 1,087 compounds. The ensemble model was validated internally with five-fold cross-validation and 25 rounds of y-randomization. In the external validation of 120 compounds, the ensemble model had achieved an accuracy of 75.0%, sensitivity of 81.9% and specificity of 64.6%. The model was also able to identify 22 of 23 withdrawn drugs or drugs with black box warning against hepatotoxicity. Dronedarone which is associated with severe liver injuries, announced in a recent FDA drug safety communication, was predicted as hepatotoxic by the ensemble model. It was found that the ensemble model was capable of classifying positive compounds (with hepatic effects) well, but less so on negatives compounds when they were structurally similar. The ensemble model built in this study is made available for public use. © Springer Science+Business Media B.V. 2011
Wang, Gang-Jin; Xie, Chi; Chen, Shou; Yang, Jiao-Jiao; Yang, Ming-Yan
2013-09-01
In this study, we first build two empirical cross-correlation matrices in the US stock market by two different methods, namely the Pearson’s correlation coefficient and the detrended cross-correlation coefficient (DCCA coefficient). Then, combining the two matrices with the method of random matrix theory (RMT), we mainly investigate the statistical properties of cross-correlations in the US stock market. We choose the daily closing prices of 462 constituent stocks of S&P 500 index as the research objects and select the sample data from January 3, 2005 to August 31, 2012. In the empirical analysis, we examine the statistical properties of cross-correlation coefficients, the distribution of eigenvalues, the distribution of eigenvector components, and the inverse participation ratio. From the two methods, we find some new results of the cross-correlations in the US stock market in our study, which are different from the conclusions reached by previous studies. The empirical cross-correlation matrices constructed by the DCCA coefficient show several interesting properties at different time scales in the US stock market, which are useful to the risk management and optimal portfolio selection, especially to the diversity of the asset portfolio. It will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix R for the DCCA coefficient because it does not obey the Marčenko-Pastur distribution.
Evolutionary Ensemble for In Silico Prediction of Ames Test Mutagenicity
Chen, Huanhuan; Yao, Xin
Driven by new regulations and animal welfare, the need to develop in silico models has increased recently as alternative approaches to safety assessment of chemicals without animal testing. This paper describes a novel machine learning ensemble approach to building an in silico model for the prediction of the Ames test mutagenicity, one of a battery of the most commonly used experimental in vitro and in vivo genotoxicity tests for safety evaluation of chemicals. Evolutionary random neural ensemble with negative correlation learning (ERNE) [1] was developed based on neural networks and evolutionary algorithms. ERNE combines the method of bootstrap sampling on training data with the method of random subspace feature selection to ensure diversity in creating individuals within an initial ensemble. Furthermore, while evolving individuals within the ensemble, it makes use of the negative correlation learning, enabling individual NNs to be trained as accurate as possible while still manage to maintain them as diverse as possible. Therefore, the resulting individuals in the final ensemble are capable of cooperating collectively to achieve better generalization of prediction. The empirical experiment suggest that ERNE is an effective ensemble approach for predicting the Ames test mutagenicity of chemicals.
Distinguishing Two Probability Ensembles with One Sample from each Ensemble
Antunes, L.; Buhrman, H.; Matos, A.; Souto, A.; Teixeira, A.
2016-01-01
We introduced a new method for distinguishing two probability ensembles called one from each method, in which the distinguisher receives as input two samples, one from each ensemble. We compare this new method with multi-sample from the same method already exiting in the literature and prove that
Distinguishing two probability ensembles with one sample from each ensemble
L.F. Antunes (Luis); H. Buhrman (Harry); A. Matos; A. Souto (Andre); A. Teixeira
2016-01-01
htmlabstractWe introduced a new method for distinguishing two probability ensembles called one from each method, in which the distinguisher receives as input two samples, one from each ensemble. We compare this new method with multi-sample from the same method already exiting in the literature
Spectral statistics of the uni-modular ensemble
Joyner, Christopher H.; Smilansky, Uzy; Weidenmüller, Hans A.
2017-09-01
We investigate the spectral statistics of Hermitian matrices in which the elements are chosen uniformly from U(1) , called the uni-modular ensemble (UME), in the limit of large matrix size. Using three complimentary methods; a supersymmetric integration method, a combinatorial graph-theoretical analysis and a Brownian motion approach, we are able to derive expressions for 1 / N corrections to the mean spectral moments and also analyse the fluctuations about this mean. By addressing the same ensemble from three different point of view, we can critically compare their relative advantages and derive some new results.
Inflation with a graceful exit in a random landscape
Energy Technology Data Exchange (ETDEWEB)
Pedro, F.G. [Univ. Autonoma de Madrid (Spain). Dept. de Fisica Teorica y Inst. de Fisica Teorica UAM/CSIC; Westphal, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2016-11-15
We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N<<10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.
Ducote, Martin Paul, Jr.
In this thesis, a papermaking process was used to create two randomly oriented, high performance composite material systems. The primary objective of this was to discover the flexural properties of both composite systems and compare those to reported results from other studies. In addition, the process was evaluated for producing quality, randomly oriented composite panels. Thermoplastic polymers have the toughness and necessary strength to be alternatives to thermosets, but with the promise of lower cycle times and increased recyclability. The wet-lay papermaking process used in this study produces a quality, randomly oriented thermoplastic composite at low cycle times and simple production. The materials chosen represent high performance thermoplastics and carbon fibers. Short chopped carbon fiber filled Nylon 6,6 and PEEK composites were created at varying fiber volume fractions. Ten nylon based panels and five PEEK based panels were subjected to 4-point flexural testing. In several of the nylon-based panels, flexural testing was done in multiple direction to verify the in-plane isotropy of the final composite. The flexural strength performance of both systems showed promise when compared to equivalent products currently available. The flexural modulus results were less than expected and further research should be done into possibly causes. Overall, this research gives good insight into two high performance engineering composites and should aid in continued work.
Jackson, Dan; White, Ian R; Riley, Richard D
2013-03-01
Multivariate meta-analysis is becoming more commonly used. Methods for fitting the multivariate random effects model include maximum likelihood, restricted maximum likelihood, Bayesian estimation and multivariate generalisations of the standard univariate method of moments. Here, we provide a new multivariate method of moments for estimating the between-study covariance matrix with the properties that (1) it allows for either complete or incomplete outcomes and (2) it allows for covariates through meta-regression. Further, for complete data, it is invariant to linear transformations. Our method reduces to the usual univariate method of moments, proposed by DerSimonian and Laird, in a single dimension. We illustrate our method and compare it with some of the alternatives using a simulation study and a real example. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Rovati, L C; Setnikar, I; Genazzani, A R
2000-08-01
New estradiol (E2) transdermal matrix patches developed for once-a-week application, releasing 25 micrograms E2 (7D-25) or 50 micrograms E2 (7D-50) daily, were investigated in comparison with a placebo patch and the twice-weekly parent patch releasing 50 micrograms E2 (Derm-50) daily. Three hundred and eleven postmenopausal patients suffering at least seven hot flushes daily were randomly assigned to the four parallel groups and treated continuously for 12 weeks without progestin opposition. The daily number of hot flushes significantly decreased in all groups. At the 12th week the decrease from a base-line average of eight to nine episodes per day was 78% with 7D-25, 93% and 97% respectively with 7D-50 and Derm-50, and significantly (p fashion and all were well tolerated.
Jackson, Dan; White, Ian R; Riley, Richard D
2013-01-01
Multivariate meta-analysis is becoming more commonly used. Methods for fitting the multivariate random effects model include maximum likelihood, restricted maximum likelihood, Bayesian estimation and multivariate generalisations of the standard univariate method of moments. Here, we provide a new multivariate method of moments for estimating the between-study covariance matrix with the properties that (1) it allows for either complete or incomplete outcomes and (2) it allows for covariates through meta-regression. Further, for complete data, it is invariant to linear transformations. Our method reduces to the usual univariate method of moments, proposed by DerSimonian and Laird, in a single dimension. We illustrate our method and compare it with some of the alternatives using a simulation study and a real example. PMID:23401213
DEFF Research Database (Denmark)
Cherchi, Elisabetta; Guevara, Cristian Angelo
2012-01-01
of parameters increases is usually known as the “curse of dimensionality” in the simulation methods. We investigate this problem in the case of the random coefficients Logit model. We compare the traditional Maximum Simulated Likelihood (MSL) method with two alternative estimation methods: the Expectation......–covariance matrix. Results show that indeed MSL suffers from lack of empirical identification as the dimensionality grows while EM deals much better with this estimation problem. On the other hand, the HH method, although not being simulation-based, showed poor performance with large dimensions, principally because......When the dimension of the vector of estimated parameters increases, simulation based methods become impractical, because the number of draws required for estimation grows exponentially with the number of parameters. In simulation methods, the lack of empirical identification when the number...
Exploring diversity in ensemble classification: Applications in large area land cover mapping
Mellor, Andrew; Boukir, Samia
2017-07-01
Ensemble classifiers, such as random forests, are now commonly applied in the field of remote sensing, and have been shown to perform better than single classifier systems, resulting in reduced generalisation error. Diversity across the members of ensemble classifiers is known to have a strong influence on classification performance - whereby classifier errors are uncorrelated and more uniformly distributed across ensemble members. The relationship between ensemble diversity and classification performance has not yet been fully explored in the fields of information science and machine learning and has never been examined in the field of remote sensing. This study is a novel exploration of ensemble diversity and its link to classification performance, applied to a multi-class canopy cover classification problem using random forests and multisource remote sensing and ancillary GIS data, across seven million hectares of diverse dry-sclerophyll dominated public forests in Victoria Australia. A particular emphasis is placed on analysing the relationship between ensemble diversity and ensemble margin - two key concepts in ensemble learning. The main novelty of our work is on boosting diversity by emphasizing the contribution of lower margin instances used in the learning process. Exploring the influence of tree pruning on diversity is also a new empirical analysis that contributes to a better understanding of ensemble performance. Results reveal insights into the trade-off between ensemble classification accuracy and diversity, and through the ensemble margin, demonstrate how inducing diversity by targeting lower margin training samples is a means of achieving better classifier performance for more difficult or rarer classes and reducing information redundancy in classification problems. Our findings inform strategies for collecting training data and designing and parameterising ensemble classifiers, such as random forests. This is particularly important in large area
Weber, Stephen C; Kauffman, Jeffrey I; Parise, Carol; Weber, Sophia J; Katz, Stephen D
2013-02-01
Arthroscopic rotator cuff repair has a high rate of patient satisfaction. However, multiple studies have shown significant rates of anatomic failure. Biological augmentation would seem to be a reasonable technique to improve clinical outcomes and healing rates. To represent a prospective, double-blinded, randomized study to assess the use of platelet-rich fibrin matrix (PRFM) in rotator cuff surgery. Randomized controlled trial; level of evidence, 1. Prestudy power analysis demonstrated that a sample size of 30 patients in each group (PRFM vs control) would allow recognition of a 20% difference in perioperative pain scores. Sixty consecutive patients were randomized to either receive a commercially available PRFM product or not. Preoperative and postoperative range of motion (ROM), University of California-Los Angeles (UCLA), and simple shoulder test (SST) scores were recorded. Surgery was performed using an arthroscopic single-row technique. Visual analog scale (VAS) pain scores were obtained upon arrival to the recovery room and 1 hour postoperatively, and narcotic consumption was recorded and converted to standard narcotic equivalents. The SST and ROM measurements were taken at 3, 6, 9, and 12 weeks postoperatively, and final (1 year) American shoulder and elbow surgeons (ASES) shoulder and UCLA shoulder scores were assessed. There were no complications. Randomization created comparable groups except that the PRFM group was younger than the control group (mean ± SD, 59.67 ± 8.16 y vs 64.50 ± 8.59 y, respectively; P time was longer for the PRFM group than for the control group (83.28 ± 17.13 min vs 73.28 ± 17.18 min, respectively; P .98). Mean UCLA shoulder scores were 27.94 ± 4.98 for the PRFM group versus 29.59 ± 1.68 for the controls (P matrix was not shown to significantly improve perioperative morbidity, clinical outcomes, or structural integrity. While longer term follow-up or different platelet-rich plasma formulations may show differences, early
Network and Ensemble Enabled Entity Extraction in Informal Text (NEEEEIT) final report
Energy Technology Data Exchange (ETDEWEB)
Kegelmeyer, Philip W. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Shead, Timothy M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Dunlavy, Daniel M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2013-09-01
This SAND report summarizes the activities and outcomes of the Network and Ensemble Enabled Entity Extraction in Information Text (NEEEEIT) LDRD project, which addressed improving the accuracy of conditional random fields for named entity recognition through the use of ensemble methods.
Cieślik-Wegemund, Marta; Wierucka-Młynarczyk, Beata; Tanasiewicz, Marta; Gilowski, Łukasz
2016-12-01
The aim of this study is to compare efficacy of the tunnel technique for root coverage using collagen matrix (CM) versus connective tissue graft (CTG) for treatment of multiple recessions of Miller Classes I and II over a short period of time. Twenty-eight patients were enrolled in the study. Patients in the control group were treated with the tunnel technique using CTGs, whereas patients in the test group were treated with the tunnel technique using xenogeneic CM. Clinical recordings were obtained at baseline and after 3 and 6 months. Percentages of average recession coverage (ARC) and complete recession coverage (CRC) were evaluated 3 and 6 months after surgery. Significant decreases were recorded in both groups of recession parameters compared with baseline measurements. Mean recession depth (0.21 versus 0.39 mm) and recession area (0.31 versus 0.53 mm 2 ) after 6 months were significantly higher in the test group (P tissue width (KTW) increased at a similar rate in both groups (1.0 versus 0.8 mm for control and test groups, respectively). ARC after 6 months was 95% in the control group and 91% in the test group (P <0.05), and CRC was 71.4% (10/14) in the control group and 14.3% (2/14) in the test group (P <0.05). Xenogeneic CM combined with tunnel technique leads to satisfactory ARC and increase in KTW similar to CTG, but yields lower unsatisfactory CRC.
Quantifying Monte Carlo uncertainty in ensemble Kalman filter
Energy Technology Data Exchange (ETDEWEB)
Thulin, Kristian; Naevdal, Geir; Skaug, Hans Julius; Aanonsen, Sigurd Ivar
2009-01-15
This report is presenting results obtained during Kristian Thulin PhD study, and is a slightly modified form of a paper submitted to SPE Journal. Kristian Thulin did most of his portion of the work while being a PhD student at CIPR, University of Bergen. The ensemble Kalman filter (EnKF) is currently considered one of the most promising methods for conditioning reservoir simulation models to production data. The EnKF is a sequential Monte Carlo method based on a low rank approximation of the system covariance matrix. The posterior probability distribution of model variables may be estimated fram the updated ensemble, but because of the low rank covariance approximation, the updated ensemble members become correlated samples from the posterior distribution. We suggest using multiple EnKF runs, each with smaller ensemble size to obtain truly independent samples from the posterior distribution. This allows a point-wise confidence interval for the posterior cumulative distribution function (CDF) to be constructed. We present a methodology for finding an optimal combination of ensemble batch size (n) and number of EnKF runs (m) while keeping the total number of ensemble members ( m x n) constant. The optimal combination of n and m is found through minimizing the integrated mean square error (MSE) for the CDFs and we choose to define an EnKF run with 10.000 ensemble members as having zero Monte Carlo error. The methodology is tested on a simplistic, synthetic 2D model, but should be applicable also to larger, more realistic models. (author). 12 refs., figs.,tabs
Adiabatically deformed ensemble: Engineering nonthermal states of matter
Kennes, D. M.
2017-07-01
We propose a route towards engineering nonthermal states of matter, which show largely unexplored physics. The main idea relies on the adiabatic passage of a thermal ensemble under slow variations of the system Hamiltonian. If the temperature of the initial thermal ensemble is either zero or infinite, the ensemble after the passage is a simple thermal one with the same vanishing or infinite temperature. However, for any finite nonzero temperature, intriguing nonthermal ensembles can be achieved. We exemplify this in (a) a single oscillator, (b) a dimerized interacting one-dimensional chain of spinless fermions, (c) a BCS-type superconductor, and (d) the topological Kitaev chain. We solve these models with a combination of methods: either exactly, numerically using the density matrix renormalization group, or within an approximate functional renormalization group scheme. The designed states show strongly nonthermal behavior in each of the considered models. For example, for the chain of spinless fermions we exemplify how long-ranged nonthermal power-law correlations can be stabilized, and for the Kitaev chain we elucidate how the nonthermal ensemble can largely alter the transition temperature separating topological and trivial phases.
An Adaptive Approach to Mitigate Background Covariance Limitations in the Ensemble Kalman Filter
Song, Hajoon
2010-07-01
A new approach is proposed to address the background covariance limitations arising from undersampled ensembles and unaccounted model errors in the ensemble Kalman filter (EnKF). The method enhances the representativeness of the EnKF ensemble by augmenting it with new members chosen adaptively to add missing information that prevents the EnKF from fully fitting the data to the ensemble. The vectors to be added are obtained by back projecting the residuals of the observation misfits from the EnKF analysis step onto the state space. The back projection is done using an optimal interpolation (OI) scheme based on an estimated covariance of the subspace missing from the ensemble. In the experiments reported here, the OI uses a preselected stationary background covariance matrix, as in the hybrid EnKF–three-dimensional variational data assimilation (3DVAR) approach, but the resulting correction is included as a new ensemble member instead of being added to all existing ensemble members. The adaptive approach is tested with the Lorenz-96 model. The hybrid EnKF–3DVAR is used as a benchmark to evaluate the performance of the adaptive approach. Assimilation experiments suggest that the new adaptive scheme significantly improves the EnKF behavior when it suffers from small size ensembles and neglected model errors. It was further found to be competitive with the hybrid EnKF–3DVAR approach, depending on ensemble size and data coverage.
Diurnal Ensemble Surface Meteorology Statistics
U.S. Environmental Protection Agency — Excel file containing diurnal ensemble statistics of 2-m temperature, 2-m mixing ratio and 10-m wind speed. This Excel file contains figures for Figure 2 in the...
Anderson, Lauren E; Inglehart, Marita R; El-Kholy, Karim; Eber, Robert; Wang, Hom-Lay
2014-08-01
This randomized controlled clinical pilot trial compared the efficacy of 2 soft tissue grafting methods for correcting esthetic discrepancies associated with definitively restored implant crowns. Thirteen patients presenting with implants displaying recession, thin biotype, concavity defects, or a combination thereof associated with single crowned dental implants randomly received subepithelial connective tissue grafts (SCTG) in the control group (N = 7) or acellular dermal matrix (ADM) allografts in the test group (N = 6), both under coronally positioned flaps. Data regarding soft tissue, hard tissue, esthetics, and quality of life (QoL) parameters were collected over 6 months. Both groups gained tissue thickness (SCTG: 63% and ADM: 105%), reduced concavity measures (SCTG: 82% and ADM: 96%), and improved recessions (SCTG: 40% and ADM: 28%) from baseline to 6 months. Clinicians determined improvement in esthetics for both groups (P = 0.001), unlike patients who did not change their esthetic ratings. No statistical differences were noted for QoL assessment; however, ADM subjects had more eventful wound healing (P = 0.021). Within the limitations of this study, both SCTG and ADM result in increased mucosal thickness, reduction in concavity dimensions, and have a potential for recession reduction on definitively restored dental implants.
DEFF Research Database (Denmark)
2004-01-01
Within the framework of the PSO-Ensemble project (FU2101) a demo application has been created. The application use ECMWF ensemble forecasts. Two instances of the application are running; one for Nysted Offshore and one for the total production (except Horns Rev) in the Eltra area. The output is a...... is available via two password-protected web-pages hosted at IMM and is used daily by Elsam and E2....
Energy Technology Data Exchange (ETDEWEB)
McClure, M J; Sell, S A; Bowlin, G L [Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, VA 23284 (United States); Ayres, C E; Simpson, D G, E-mail: glbowlin@vcu.ed [Department of Anatomy and Neurobiology, Virginia Commonwealth University, Richmond, VA 23298 (United States)
2009-10-15
Extracellular matrices are arranged with a specific geometry based on tissue type and mechanical stimulus. For blood vessels in the body, preferential alignment of fibers is in the direction of repetitive force. Electrospinning is a controllable process which can result in fiber alignment and randomization depending on the parameters utilized. In this study, arterial grafts composed of polycaprolactone (PCL), polydioxanone (PDO) and silk fibroin in blends of 100:0 and 50:50 for both PCL:silk and PDO:silk were investigated to determine if fibers could be controllably aligned using a mandrel rotational speed ranging from 500 to 8000 revolutions per minute (RPM). Results revealed that large- and small-diameter mandrels produced different degrees of fiber alignment based on a fast Fourier transform of scanning electron microscope images. Uniaxial tensile testing further demonstrated scaffold anisotropy through changes in peak stress, modulus and strain at break at mandrel rotational speeds of 500 and 8000 RPM, causing peak stress and modulus for PCL to increase 5- and 4.5-fold, respectively, as rotational speed increased. Additional mechanical testing was performed on grafts using dynamic compliance, burst strength and longitudinal strength displaying that grafts electrospun at higher rotational rates produced stiffer conduits which had lower compliance and higher burst strength compared to the lower mandrel rotational rate. Scaffold properties were found to depend on several parameters in the electrospinning process: mandrel rotational rate, polymer type, and mandrel size. Vascular scaffold design under anisotropic conditions provided interesting insights and warrants further investigation.
Deformed Ginibre ensembles and integrable systems
Energy Technology Data Exchange (ETDEWEB)
Orlov, A.Yu., E-mail: orlovs@ocean.ru
2014-01-17
We consider three Ginibre ensembles (real, complex and quaternion-real) with deformed measures and relate them to known integrable systems by presenting partition functions of these ensembles in form of fermionic expectation values. We also introduce double deformed Dyson–Wigner ensembles and compare their fermionic representations with those of Ginibre ensembles.
Daniels, Timothy R; Younger, Alastair S E; Penner, Murray J; Wing, Kevin J; Le, Ian L D; Russell, Iain S; Lalonde, Karl-André; Evangelista, Peter T; Quiton, Jovelyn D; Glazebrook, Mark; DiGiovanni, Christopher W
2015-07-01
Ankle and hindfoot arthrodesis is often supplemented with autograft to promote bony union. Autograft harvest can lead to increased perioperative morbidity. Purified recombinant human platelet-derived growth factor BB homodimer (rhPDGF-BB) has stimulated bone formation in mandibular defects and hindfoot fusion. This randomized controlled trial evaluated the efficacy and safety of rhPDGF-BB combined with an injectable, osteoconductive beta-tricalcium phosphate (β-TCP)-collagen matrix versus autograft in ankle and hindfoot fusions. Seventy-five patients requiring ankle or hindfoot fusion were randomized 5:1 for rhPDGF-BB/β-TCP-collagen (treatment, n = 63) or autograft (control, n = 12). Prospective analysis included 142 autograft control subjects from another clinical trial with identical study protocols. Standardized operative and postoperative protocols were used. Patients underwent standard internal fixation augmented with autograft or 0.3 mg/mL rhPDGF-BB/β-TCP-collagen. Radiologic, clinical, and quality-of-life outcomes were assessed over 52 weeks. Primary outcome was joint fusion (50% or more osseous bridging on computed tomography) at 24 weeks. Secondary outcomes included radiographs, clinical healing status, visual analog scale pain score, American Orthopaedic Foot & Ankle Society Ankle-Hindfoot Scale score, Foot Function Index score, and Short Form-12 score. Noninferiority P values were calculated. Complete fusion of all involved joints at 24 weeks as indicated by computed tomography was achieved in 53 of 63 (84%) rhPDGF-BB/β-TCP-collagen-treated patients and 100 of 154 (65%) autograft-treated patients (P BB/β-TCP-collagen patients versus 19.7 ± 11.5 weeks for autograft patients (P BB/β-TCP-collagen patients and 120 of 154 (78%) autograft patients (P BB/β-TCP-collagen was a safe, effective alternative to autograft for ankle and hindfoot fusions, eliminating the pain and morbidity associated with autograft harvesting. Level I, prospective randomized
Adaptive correction of ensemble forecasts
Pelosi, Anna; Battista Chirico, Giovanni; Van den Bergh, Joris; Vannitsem, Stephane
2017-04-01
Forecasts from numerical weather prediction (NWP) models often suffer from both systematic and non-systematic errors. These are present in both deterministic and ensemble forecasts, and originate from various sources such as model error and subgrid variability. Statistical post-processing techniques can partly remove such errors, which is particularly important when NWP outputs concerning surface weather variables are employed for site specific applications. Many different post-processing techniques have been developed. For deterministic forecasts, adaptive methods such as the Kalman filter are often used, which sequentially post-process the forecasts by continuously updating the correction parameters as new ground observations become available. These methods are especially valuable when long training data sets do not exist. For ensemble forecasts, well-known techniques are ensemble model output statistics (EMOS), and so-called "member-by-member" approaches (MBM). Here, we introduce a new adaptive post-processing technique for ensemble predictions. The proposed method is a sequential Kalman filtering technique that fully exploits the information content of the ensemble. One correction equation is retrieved and applied to all members, however the parameters of the regression equations are retrieved by exploiting the second order statistics of the forecast ensemble. We compare our new method with two other techniques: a simple method that makes use of a running bias correction of the ensemble mean, and an MBM post-processing approach that rescales the ensemble mean and spread, based on minimization of the Continuous Ranked Probability Score (CRPS). We perform a verification study for the region of Campania in southern Italy. We use two years (2014-2015) of daily meteorological observations of 2-meter temperature and 10-meter wind speed from 18 ground-based automatic weather stations distributed across the region, comparing them with the corresponding COSMO
An approach to localization for ensemble-based data assimilation.
Wang, Bin; Liu, Juanjuan; Liu, Li; Xu, Shiming; Huang, Wenyu
2018-01-01
Localization techniques are commonly used in ensemble-based data assimilation (e.g., the Ensemble Kalman Filter (EnKF) method) because of insufficient ensemble samples. They can effectively ameliorate the spurious long-range correlations between the background and observations. However, localization is very expensive when the problem to be solved is of high dimension (say 106 or higher) for assimilating observations simultaneously. To reduce the cost of localization for high-dimension problems, an approach is proposed in this paper, which approximately expands the correlation function of the localization matrix using a limited number of principal eigenvectors so that the Schür product between the localization matrix and a high-dimension covariance matrix is reduced to the sum of a series of Schür products between two simple vectors. These eigenvectors are actually the sine functions with different periods and phases. Numerical experiments show that when the number of principal eigenvectors used reaches 20, the approximate expansion of the correlation function is very close to the exact one in the one-dimensional (1D) and two-dimensional (2D) cases. The new approach is then applied to localization in the EnKF method, and its performance is evaluated in assimilation-cycle experiments with the Lorenz-96 model and single assimilation experiments using a barotropic shallow water model. The results suggest that the approach is feasible in providing comparable assimilation analysis with far less cost.
Introduction to random matrices theory and practice
Livan, Giacomo; Vivo, Pierpaolo
2018-01-01
Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum. The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory). Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.
Barret, M; Bordaçahar, B; Beuvon, F; Terris, B; Camus, M; Coriat, R; Chaussade, S; Batteux, F; Prat, F
2017-05-01
Esophageal stricture formation after extensive endoscopic resection remains a major limitation of endoscopic therapy for early esophageal neoplasia. This study assessed a recently developed self-assembling peptide (SAP) matrix as a wound dressing after endoscopic resection for the prevention of esophageal stricture. Ten pigs were randomly assigned to the SAP or the control group after undergoing a 5-cm-long circumferential endoscopic submucosal dissection of the lower esophagus. Esophageal diameter on endoscopy and esophagogram, weight variation, and histological measurements of fibrosis, granulation tissue, and neoepithelium were assessed in each animal. The rate of esophageal stricture at day 14 was 40% in the SAP-treated group versus 100% in the control group (P = 0.2). Median interquartile range (IQR) esophageal diameter at day 14 was 8 mm (2.5-9) in the SAP-treated group versus 4 mm (3-4) in the control group (P = 0.13). The median (IQR) stricture indexes on esophagograms at day 14 were 0.32 (0.14-0.48) and 0.26 (0.14-0.33) in the SAP-treated and control groups, respectively (P = 0.42). Median (IQR) weight variation during the study was +0.2 (-7.4; +1.8) and -3.8 (-5.4; +0.6) in the SAP-treated and control groups, respectively (P = 0.9). Fibrosis, granulation tissue, and neoepithelium were not significantly different between the groups. The application of SAP matrix on esophageal wounds after a circumferential endoscopic submucosal dissection delayed the onset of esophageal stricture in a porcine model. © International Society for Diseases of the Esophagus 2017. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Fast, low-power manipulation of spin ensembles in superconducting microresonators
Sigillito, A. J.; Malissa, H.; Tyryshkin, A. M.; Riemann, H.; Abrosimov, N. V.; Becker, P.; Pohl, H.-J.; Thewalt, M. L. W.; Itoh, K. M.; Morton, J. J. L.; Houck, A. A.; Schuster, D. I.; Lyon, S. A.
2014-06-01
We demonstrate the use of high-Q superconducting coplanar waveguide (CPW) microresonators to perform rapid manipulations on a randomly distributed spin ensemble using very low microwave power (400 nW). This power is compatible with dilution refrigerators, making microwave manipulation of spin ensembles feasible for quantum computing applications. We also describe the use of adiabatic microwave pulses to overcome microwave magnetic field (B1) inhomogeneities inherent to CPW resonators. This allows for uniform control over a randomly distributed spin ensemble. Sensitivity data are reported showing a single shot (no signal averaging) sensitivity to 107 spins or 3×104spins/√Hz with averaging.
Ensemble algorithms in reinforcement learning.
Wiering, Marco A; van Hasselt, Hado
2008-08-01
This paper describes several ensemble methods that combine multiple different reinforcement learning (RL) algorithms in a single agent. The aim is to enhance learning speed and final performance by combining the chosen actions or action probabilities of different RL algorithms. We designed and implemented four different ensemble methods combining the following five different RL algorithms: Q-learning, Sarsa, actor-critic (AC), QV-learning, and AC learning automaton. The intuitively designed ensemble methods, namely, majority voting (MV), rank voting, Boltzmann multiplication (BM), and Boltzmann addition, combine the policies derived from the value functions of the different RL algorithms, in contrast to previous work where ensemble methods have been used in RL for representing and learning a single value function. We show experiments on five maze problems of varying complexity; the first problem is simple, but the other four maze tasks are of a dynamic or partially observable nature. The results indicate that the BM and MV ensembles significantly outperform the single RL algorithms.
Alexiou, Angeliki; Vouros, Ioannis; Menexes, Georgios; Konstantinidis, Antonis
2017-01-01
The purpose of the present study was to compare the clinical efficiency of enamel matrix derivative (EMD) placed under a coronally advanced flap (CAF; test group), to a connective tissue graft (CTG) placed under a CAF (control group), in patients with multiple recession defects. Twelve patients with multiple Miller's Class I or II gingival recessions in contralateral quadrants of the maxilla were selected. The primary outcome variable was the change in depth of the buccal recession (REC), at 6 months (T6) after surgery. The secondary outcome parameters included the clinical attachment level (CAL), the probing pocket depth (PPD), and the width of keratinized gingiva (WKT) apical to the recession. Recession defects were randomly divided to the test or control group by using a computer-generated randomization list. Data were analyzed within the frame of Mixed Linear Models with the ANOVA method. There were no statistically significantly differences observed between test and control groups in regards with the depth of buccal recession with a mean REC of 1.82 mm (CTG) and 1.72 mm (EMD) respectively. Similarly the mean PPD value was 1.3 mm for both groups at T6, while the respective value for CAL was 1.7 mm (EMD) and 1.8 mm (CTG). Statistically significant differences were observed only for the WKT, which were 3.0 mm and 3.6 mm for the test and control groups respectively (P < .001) at T6. The use of EMD in conjunction with a CAF resulted in similar results as compared to the CTG plus CAF.
Universal critical wrapping probabilities in the canonical ensemble
Directory of Open Access Journals (Sweden)
Hao Hu
2015-09-01
Full Text Available Universal dimensionless quantities, such as Binder ratios and wrapping probabilities, play an important role in the study of critical phenomena. We study the finite-size scaling behavior of the wrapping probability for the Potts model in the random-cluster representation, under the constraint that the total number of occupied bonds is fixed, so that the canonical ensemble applies. We derive that, in the limit L→∞, the critical values of the wrapping probability are different from those of the unconstrained model, i.e. the model in the grand-canonical ensemble, but still universal, for systems with 2yt−d>0 where yt=1/ν is the thermal renormalization exponent and d is the spatial dimension. Similar modifications apply to other dimensionless quantities, such as Binder ratios. For systems with 2yt−d≤0, these quantities share same critical universal values in the two ensembles. It is also derived that new finite-size corrections are induced. These findings apply more generally to systems in the canonical ensemble, e.g. the dilute Potts model with a fixed total number of vacancies. Finally, we formulate an efficient cluster-type algorithm for the canonical ensemble, and confirm these predictions by extensive simulations.
Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach
Energy Technology Data Exchange (ETDEWEB)
Chertkov, Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Skolkovo Inst. of Science and Technology, Moscow (Russia); Chernyak, Vladimir [Wayne State Univ., Detroit, MI (United States). Dept. of Chemistry
2017-01-17
Thermostatically Controlled Loads (TCL), e.g. air-conditioners and heaters, are by far the most wide-spread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control of temperature - changing from on to off , and vice versa, depending on temperature. Aggregation of a large group of similar devices into a statistical ensemble is considered, where the devices operate following the same dynamics subject to stochastic perturbations and randomized, Poisson on/off switching policy. We analyze, using theoretical and computational tools of statistical physics, how the ensemble relaxes to a stationary distribution and establish relation between the re- laxation and statistics of the probability flux, associated with devices' cycling in the mixed (discrete, switch on/off , and continuous, temperature) phase space. This allowed us to derive and analyze spec- trum of the non-equilibrium (detailed balance broken) statistical system. and uncover how switching policy affects oscillatory trend and speed of the relaxation. Relaxation of the ensemble is of a practical interest because it describes how the ensemble recovers from significant perturbations, e.g. forceful temporary switching o aimed at utilizing flexibility of the ensemble in providing "demand response" services relieving consumption temporarily to balance larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.
Similarity measures for protein ensembles
DEFF Research Database (Denmark)
Lindorff-Larsen, Kresten; Ferkinghoff-Borg, Jesper
2009-01-01
a synthetic example from molecular dynamics simulations. We then apply the algorithms to revisit the problem of ensemble averaging during structure determination of proteins, and find that an ensemble refinement method is able to recover the correct distribution of conformations better than standard single....... However, instead of examining individual conformations it is in many cases more relevant to analyse ensembles of conformations that have been obtained either through experiments or from methods such as molecular dynamics simulations. We here present three approaches that can be used to compare......Analyses of similarities and changes in protein conformation can provide important information regarding protein function and evolution. Many scores, including the commonly used root mean square deviation, have therefore been developed to quantify the similarities of different protein conformations...
Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji
2016-07-01
Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a generalized Banks-Casher relation as we confirm explicitly.
Energy Technology Data Exchange (ETDEWEB)
Nagata, Keitaro [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba 305-0801 (Japan); Nishimura, Jun [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba 305-0801 (Japan); Department of Particle and Nuclear Physics, School of High Energy Accelerator Science,Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba 305-0801 (Japan); Shimasaki, Shinji [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba 305-0801 (Japan); Research and Education Center for Natural Sciences, Keio University,Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan)
2016-07-14
Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a generalized Banks-Casher relation as we confirm explicitly.
Kakagia, Despoina D; Kazakos, Konstantinos J; Xarchas, Konstantinos C; Karanikas, Michael; Georgiadis, George S; Tripsiannis, Gregory; Manolas, Constantinos
2007-01-01
This study tests the hypothesis that addition of a protease-modulating matrix enhances the efficacy of autologous growth factors in diabetic ulcers. Fifty-one patients with chronic diabetic foot ulcers were managed as outpatients at the Democritus University Hospital of Alexandroupolis and followed up for 8 weeks. All target ulcers were > or = 2.5 cm in any one dimension and had been previously treated only with moist gauze. Patients were randomly allocated in three groups of 17 patients each: Group A was treated only with the oxidized regenerated cellulose/collagen biomaterial (Promogran, Johnson & Johnson, New Brunswick, NJ), Group B was treated only with autologous growth factors delivered by Gravitational Platelet Separation System (GPS, Biomet), and Group C was managed by a combination of both. All ulcers were digitally photographed at initiation of the study and then at change of dressings once weekly. Computerized planimetry (Texas Health Science Center ImageTool, Version 3.0) was used to assess ulcer dimensions that were analyzed for homogeneity and significance using the Statistical Package for Social Sciences, Version 13.0. Post hoc analysis revealed that there was significantly greater reduction of all three dimensions of the ulcers in Group C compared to Groups A and B (all P<.001). Although reduction of ulcer dimensions was greater in Group A than in Group B, these differences did not reach statistical significance. It is concluded that protease-modulating dressings act synergistically with autologous growth factors and enhance their efficacy in diabetic foot ulcers.
Directory of Open Access Journals (Sweden)
Elyan Al Machot
2014-01-01
Full Text Available Introduction. Periodontitis is an inflammatory process in response to dental biofilm and leads to periodontal tissue destruction. The aim of this study was the comparison of outcomes using either an enamel matrix derivative (EMD or a nanocrystalline hydroxyapatite (NHA in regenerative periodontal therapy after 6 and 12 months. Methods. Using a parallel group, prospective randomized study design, we enrolled 19 patients in each group. The primary outcome was bone fill after 12 months. Attachment gain, probing pocket depth (PPD reduction, and recession were secondary variables. Additionally, early wound healing and adverse events were assessed. Data analysis included test of noninferiority of NHA group (test compared to EMD group (reference in bone fill. Differences in means of secondary variables were compared by paired t-test, frequency data by exact χ2 test. Results. Both groups showed significant bone fill, reduction of PPD, increase in recession, and gain of attachment after 6 and 12 months. No significant differences between groups were found at any time point. Adverse events were comparable between both groups with a tendency of more complaints in the NHA group. Conclusion. The clinical outcomes were similar in both groups. EMD could have some advantage compared to NHA regarding patients comfort and adverse events. The trial is registered with ClinicalTrials.gov NCT00757159.
Al Machot, Elyan; Hoffmann, Thomas; Lorenz, Katrin; Khalili, Ihssan; Noack, Barbara
2014-01-01
Periodontitis is an inflammatory process in response to dental biofilm and leads to periodontal tissue destruction. The aim of this study was the comparison of outcomes using either an enamel matrix derivative (EMD) or a nanocrystalline hydroxyapatite (NHA) in regenerative periodontal therapy after 6 and 12 months. Using a parallel group, prospective randomized study design, we enrolled 19 patients in each group. The primary outcome was bone fill after 12 months. Attachment gain, probing pocket depth (PPD) reduction, and recession were secondary variables. Additionally, early wound healing and adverse events were assessed. Data analysis included test of noninferiority of NHA group (test) compared to EMD group (reference) in bone fill. Differences in means of secondary variables were compared by paired t-test, frequency data by exact χ(2) test. Both groups showed significant bone fill, reduction of PPD, increase in recession, and gain of attachment after 6 and 12 months. No significant differences between groups were found at any time point. Adverse events were comparable between both groups with a tendency of more complaints in the NHA group. The clinical outcomes were similar in both groups. EMD could have some advantage compared to NHA regarding patients comfort and adverse events. The trial is registered with ClinicalTrials.gov NCT00757159.
Santra, Siddhartha; Cruikshank, Benjamin; Balu, Radhakrishnan; Jacobs, Kurt
2017-10-01
Fermi’s golden rule applies to a situation in which a single quantum state \\vert \\psi> is coupled to a near-continuum. This ‘quasi-continuum coupling’ structure results in a rate equation for the population of \\vert \\psi> . Here we show that the coupling of a quantum system to the standard model of a thermal environment, a bath of harmonic oscillators, can be decomposed into a ‘cascade’ made up of the quasi-continuum coupling structures of Fermi’s golden rule. This clarifies the connection between the physics of the golden rule and that of a thermal bath, and provides a non-rigorous but physically intuitive derivation of the Markovian master equation directly from the former. The exact solution to the Hamiltonian of the golden rule, known as the Bixon-Jortner model, generalized for an asymmetric spectrum, provides a window on how the evolution induced by the bath deviates from the master equation as one moves outside the Markovian regime. Our analysis also reveals the relationship between the oscillator bath and the ‘random matrix model’ (RMT) of a thermal bath. We show that the cascade structure is the one essential difference between the two models, and the lack of it prevents the RMT from generating transition rates that are independent of the initial state of the system. We suggest that the cascade structure is one of the generic elements of thermalizing many-body systems.
Abuassba, Adnan O M; Zhang, Dezheng; Luo, Xiong; Shaheryar, Ahmad; Ali, Hazrat
2017-01-01
Extreme Learning Machine (ELM) is a fast-learning algorithm for a single-hidden layer feedforward neural network (SLFN). It often has good generalization performance. However, there are chances that it might overfit the training data due to having more hidden nodes than needed. To address the generalization performance, we use a heterogeneous ensemble approach. We propose an Advanced ELM Ensemble (AELME) for classification, which includes Regularized-ELM, L2-norm-optimized ELM (ELML2), and Kernel-ELM. The ensemble is constructed by training a randomly chosen ELM classifier on a subset of training data selected through random resampling. The proposed AELM-Ensemble is evolved by employing an objective function of increasing diversity and accuracy among the final ensemble. Finally, the class label of unseen data is predicted using majority vote approach. Splitting the training data into subsets and incorporation of heterogeneous ELM classifiers result in higher prediction accuracy, better generalization, and a lower number of base classifiers, as compared to other models (Adaboost, Bagging, Dynamic ELM ensemble, data splitting ELM ensemble, and ELM ensemble). The validity of AELME is confirmed through classification on several real-world benchmark datasets.
Directory of Open Access Journals (Sweden)
Adnan O. M. Abuassba
2017-01-01
Full Text Available Extreme Learning Machine (ELM is a fast-learning algorithm for a single-hidden layer feedforward neural network (SLFN. It often has good generalization performance. However, there are chances that it might overfit the training data due to having more hidden nodes than needed. To address the generalization performance, we use a heterogeneous ensemble approach. We propose an Advanced ELM Ensemble (AELME for classification, which includes Regularized-ELM, L2-norm-optimized ELM (ELML2, and Kernel-ELM. The ensemble is constructed by training a randomly chosen ELM classifier on a subset of training data selected through random resampling. The proposed AELM-Ensemble is evolved by employing an objective function of increasing diversity and accuracy among the final ensemble. Finally, the class label of unseen data is predicted using majority vote approach. Splitting the training data into subsets and incorporation of heterogeneous ELM classifiers result in higher prediction accuracy, better generalization, and a lower number of base classifiers, as compared to other models (Adaboost, Bagging, Dynamic ELM ensemble, data splitting ELM ensemble, and ELM ensemble. The validity of AELME is confirmed through classification on several real-world benchmark datasets.
Compressed sensing of hyperspectral images based on scrambled block Hadamard ensemble
Wang, Li; Feng, Yan
2016-11-01
A fast measurement matrix based on scrambled block Hadamard ensemble for compressed sensing (CS) of hyperspectral images (HSI) is investigated. The proposed measurement matrix offers several attractive features. First, the proposed measurement matrix possesses Gaussian behavior, which illustrates that the matrix is universal and requires a near-optimal number of samples for exact reconstruction. In addition, it could be easily implemented in the optical domain due to its integer-valued elements. More importantly, the measurement matrix only needs small memory for storage in the sampling process. Experimental results on HSIs reveal that the reconstruction performance of the proposed measurement matrix is comparable or better than Gaussian matrix and Bernoulli matrix using different reconstruction algorithms while consuming less computational time. The proposed matrix could be used in CS of HSI, which would save the storage memory on board, improve the sampling efficiency, and ameliorate the reconstruction quality.
Ensemble method for dengue prediction.
Buczak, Anna L; Baugher, Benjamin; Moniz, Linda J; Bagley, Thomas; Babin, Steven M; Guven, Erhan
2018-01-01
In the 2015 NOAA Dengue Challenge, participants made three dengue target predictions for two locations (Iquitos, Peru, and San Juan, Puerto Rico) during four dengue seasons: 1) peak height (i.e., maximum weekly number of cases during a transmission season; 2) peak week (i.e., week in which the maximum weekly number of cases occurred); and 3) total number of cases reported during a transmission season. A dengue transmission season is the 12-month period commencing with the location-specific, historical week with the lowest number of cases. At the beginning of the Dengue Challenge, participants were provided with the same input data for developing the models, with the prediction testing data provided at a later date. Our approach used ensemble models created by combining three disparate types of component models: 1) two-dimensional Method of Analogues models incorporating both dengue and climate data; 2) additive seasonal Holt-Winters models with and without wavelet smoothing; and 3) simple historical models. Of the individual component models created, those with the best performance on the prior four years of data were incorporated into the ensemble models. There were separate ensembles for predicting each of the three targets at each of the two locations. Our ensemble models scored higher for peak height and total dengue case counts reported in a transmission season for Iquitos than all other models submitted to the Dengue Challenge. However, the ensemble models did not do nearly as well when predicting the peak week. The Dengue Challenge organizers scored the dengue predictions of the Challenge participant groups. Our ensemble approach was the best in predicting the total number of dengue cases reported for transmission season and peak height for Iquitos, Peru.
Advanced Atmospheric Ensemble Modeling Techniques
Energy Technology Data Exchange (ETDEWEB)
Buckley, R. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Chiswell, S. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Kurzeja, R. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Maze, G. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Viner, B. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Werth, D. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)
2017-09-29
Ensemble modeling (EM), the creation of multiple atmospheric simulations for a given time period, has become an essential tool for characterizing uncertainties in model predictions. We explore two novel ensemble modeling techniques: (1) perturbation of model parameters (Adaptive Programming, AP), and (2) data assimilation (Ensemble Kalman Filter, EnKF). The current research is an extension to work from last year and examines transport on a small spatial scale (<100 km) in complex terrain, for more rigorous testing of the ensemble technique. Two different release cases were studied, a coastal release (SF6) and an inland release (Freon) which consisted of two release times. Observations of tracer concentration and meteorology are used to judge the ensemble results. In addition, adaptive grid techniques have been developed to reduce required computing resources for transport calculations. Using a 20- member ensemble, the standard approach generated downwind transport that was quantitatively good for both releases; however, the EnKF method produced additional improvement for the coastal release where the spatial and temporal differences due to interior valley heating lead to the inland movement of the plume. The AP technique showed improvements for both release cases, with more improvement shown in the inland release. This research demonstrated that transport accuracy can be improved when models are adapted to a particular location/time or when important local data is assimilated into the simulation and enhances SRNL’s capability in atmospheric transport modeling in support of its current customer base and local site missions, as well as our ability to attract new customers within the intelligence community.
Ensembl Genomes: extending Ensembl across the taxonomic space.
Kersey, P J; Lawson, D; Birney, E; Derwent, P S; Haimel, M; Herrero, J; Keenan, S; Kerhornou, A; Koscielny, G; Kähäri, A; Kinsella, R J; Kulesha, E; Maheswari, U; Megy, K; Nuhn, M; Proctor, G; Staines, D; Valentin, F; Vilella, A J; Yates, A
2010-01-01
Ensembl Genomes (http://www.ensemblgenomes.org) is a new portal offering integrated access to genome-scale data from non-vertebrate species of scientific interest, developed using the Ensembl genome annotation and visualisation platform. Ensembl Genomes consists of five sub-portals (for bacteria, protists, fungi, plants and invertebrate metazoa) designed to complement the availability of vertebrate genomes in Ensembl. Many of the databases supporting the portal have been built in close collaboration with the scientific community, which we consider as essential for maintaining the accuracy and usefulness of the resource. A common set of user interfaces (which include a graphical genome browser, FTP, BLAST search, a query optimised data warehouse, programmatic access, and a Perl API) is provided for all domains. Data types incorporated include annotation of (protein and non-protein coding) genes, cross references to external resources, and high throughput experimental data (e.g. data from large scale studies of gene expression and polymorphism visualised in their genomic context). Additionally, extensive comparative analysis has been performed, both within defined clades and across the wider taxonomy, and sequence alignments and gene trees resulting from this can be accessed through the site.
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody
2016-05-03
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Learning ensemble classifiers for diabetic retinopathy assessment.
Saleh, Emran; Błaszczyński, Jerzy; Moreno, Antonio; Valls, Aida; Romero-Aroca, Pedro; de la Riva-Fernández, Sofia; Słowiński, Roman
2017-10-06
Diabetic retinopathy is one of the most common comorbidities of diabetes. Unfortunately, the recommended annual screening of the eye fundus of diabetic patients is too resource-consuming. Therefore, it is necessary to develop tools that may help doctors to determine the risk of each patient to attain this condition, so that patients with a low risk may be screened less frequently and the use of resources can be improved. This paper explores the use of two kinds of ensemble classifiers learned from data: fuzzy random forest and dominance-based rough set balanced rule ensemble. These classifiers use a small set of attributes which represent main risk factors to determine whether a patient is in risk of developing diabetic retinopathy. The levels of specificity and sensitivity obtained in the presented study are over 80%. This study is thus a first successful step towards the construction of a personalized decision support system that could help physicians in daily clinical practice. Copyright © 2017 Elsevier B.V. All rights reserved.
Ensemble algorithms in reinforcement learning
Wiering, Marco A; van Hasselt, Hado
This paper describes several ensemble methods that combine multiple different reinforcement learning (RL) algorithms in a single agent. The aim is to enhance learning speed and final performance by combining the chosen actions or action probabilities of different RL algorithms. We designed and
Truncated Linear Statistics Associated with the Top Eigenvalues of Random Matrices
Grabsch, Aurélien; Majumdar, Satya N.; Texier, Christophe
2017-04-01
Given a certain invariant random matrix ensemble characterised by the joint probability distribution of eigenvalues P(λ _1,\\ldots ,λ _N), many important questions have been related to the study of linear statistics of eigenvalues L=\\sum _{i=1}^Nf(λ _i), where f(λ ) is a known function. We study here truncated linear statistics where the sum is restricted to the N_1analysis of the statistical physics of fluctuating one-dimensional interfaces, we consider the case of the Laguerre ensemble of random matrices with f(λ )=√{λ }. Using the Coulomb gas technique, we study the N→ ∞ limit with N_1/N fixed. We show that the constraint that \\tilde{L}=\\sum _{i=1}^{N_1}f(λ _i) is fixed drives an infinite order phase transition in the underlying Coulomb gas. This transition corresponds to a change in the density of the gas, from a density defined on two disjoint intervals to a single interval. In this latter case the density presents a logarithmic divergence inside the bulk. Assuming that f(λ ) is monotonous, we show that these features arise for any random matrix ensemble and truncated linear statitics, which makes the scenario described here robust and universal.
Global Ensemble Forecast System (GEFS) [1 Deg.
National Oceanic and Atmospheric Administration, Department of Commerce — The Global Ensemble Forecast System (GEFS) is a weather forecast model made up of 21 separate forecasts, or ensemble members. The National Centers for Environmental...
Ensemble Feature Learning of Genomic Data Using Support Vector Machine.
Directory of Open Access Journals (Sweden)
Ali Anaissi
Full Text Available The identification of a subset of genes having the ability to capture the necessary information to distinguish classes of patients is crucial in bioinformatics applications. Ensemble and bagging methods have been shown to work effectively in the process of gene selection and classification. Testament to that is random forest which combines random decision trees with bagging to improve overall feature selection and classification accuracy. Surprisingly, the adoption of these methods in support vector machines has only recently received attention but mostly on classification not gene selection. This paper introduces an ensemble SVM-Recursive Feature Elimination (ESVM-RFE for gene selection that follows the concepts of ensemble and bagging used in random forest but adopts the backward elimination strategy which is the rationale of RFE algorithm. The rationale behind this is, building ensemble SVM models using randomly drawn bootstrap samples from the training set, will produce different feature rankings which will be subsequently aggregated as one feature ranking. As a result, the decision for elimination of features is based upon the ranking of multiple SVM models instead of choosing one particular model. Moreover, this approach will address the problem of imbalanced datasets by constructing a nearly balanced bootstrap sample. Our experiments show that ESVM-RFE for gene selection substantially increased the classification performance on five microarray datasets compared to state-of-the-art methods. Experiments on the childhood leukaemia dataset show that an average 9% better accuracy is achieved by ESVM-RFE over SVM-RFE, and 5% over random forest based approach. The selected genes by the ESVM-RFE algorithm were further explored with Singular Value Decomposition (SVD which reveals significant clusters with the selected data.
Ensemble Feature Learning of Genomic Data Using Support Vector Machine.
Anaissi, Ali; Goyal, Madhu; Catchpoole, Daniel R; Braytee, Ali; Kennedy, Paul J
2016-01-01
The identification of a subset of genes having the ability to capture the necessary information to distinguish classes of patients is crucial in bioinformatics applications. Ensemble and bagging methods have been shown to work effectively in the process of gene selection and classification. Testament to that is random forest which combines random decision trees with bagging to improve overall feature selection and classification accuracy. Surprisingly, the adoption of these methods in support vector machines has only recently received attention but mostly on classification not gene selection. This paper introduces an ensemble SVM-Recursive Feature Elimination (ESVM-RFE) for gene selection that follows the concepts of ensemble and bagging used in random forest but adopts the backward elimination strategy which is the rationale of RFE algorithm. The rationale behind this is, building ensemble SVM models using randomly drawn bootstrap samples from the training set, will produce different feature rankings which will be subsequently aggregated as one feature ranking. As a result, the decision for elimination of features is based upon the ranking of multiple SVM models instead of choosing one particular model. Moreover, this approach will address the problem of imbalanced datasets by constructing a nearly balanced bootstrap sample. Our experiments show that ESVM-RFE for gene selection substantially increased the classification performance on five microarray datasets compared to state-of-the-art methods. Experiments on the childhood leukaemia dataset show that an average 9% better accuracy is achieved by ESVM-RFE over SVM-RFE, and 5% over random forest based approach. The selected genes by the ESVM-RFE algorithm were further explored with Singular Value Decomposition (SVD) which reveals significant clusters with the selected data.
Measuring social interaction in music ensembles
Volpe, Gualtiero; D’Ausilio, Alessandro; Badino, Leonardo; Camurri, Antonio; Fadiga, Luciano
2016-01-01
Music ensembles are an ideal test-bed for quantitative analysis of social interaction. Music is an inherently social activity, and music ensembles offer a broad variety of scenarios which are particularly suitable for investigation. Small ensembles, such as string quartets, are deemed a significant example of self-managed teams, where all musicians contribute equally to a task. In bigger ensembles, such as orchestras, the relationship between a leader (the conductor) and a group of followers ...
Statistical Mechanics of Time Domain Ensemble Learning
Miyoshi, Seiji; Uezu, Tatsuya; Okada, Masato
2006-01-01
Conventional ensemble learning combines students in the space domain. On the other hand, in this paper we combine students in the time domain and call it time domain ensemble learning. In this paper, we analyze the generalization performance of time domain ensemble learning in the framework of online learning using a statistical mechanical method. We treat a model in which both the teacher and the student are linear perceptrons with noises. Time domain ensemble learning is twice as effective ...
Nonparametric resampling of random walks for spectral network clustering
Fallani, Fabrizio De Vico; Nicosia, Vincenzo; Latora, Vito; Chavez, Mario
2014-01-01
Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to replicate structural features of complex networks based on the non-parametric resampling of the transition matrix associated with an unbiased random walk on the graph. We test this bootstrapping technique on synthetic and real-world modular networks and we show that the ensemble of replicates obtained through resampling can be used to improve the performance of standard spectral algorithms for community detection.
Nonparametric resampling of random walks for spectral network clustering.
De Vico Fallani, Fabrizio; Nicosia, Vincenzo; Latora, Vito; Chavez, Mario
2014-01-01
Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to replicate structural features of complex networks based on the non-parametric resampling of the transition matrix associated with an unbiased random walk on the graph. We test this bootstrapping technique on synthetic and real-world modular networks and we show that the ensemble of replicates obtained through resampling can be used to improve the performance of standard spectral algorithms for community detection.
Energy Technology Data Exchange (ETDEWEB)
Deng, Ziwang; Tang, Youmin; Zhou, Xiaobing [University of Northern British Columbia, Environmental Science and Engineering, Prince George, BC (Canada)
2009-02-15
In this study, we assimilated sea surface temperature (SST) data of the past 120 years into an oceanic general circulation model (OGCM) for El Nino-southern oscillation (ENSO) retrospective predictions using ensemble Kalman filter (EnKF). It was found that the ensemble covariance matrix in EnKF can act as a time-variant transfer operator to project the SST corrections onto the subsurface temperatures effectively when initial perturbations of ensemble were constructed using vertically coherent random fields. As such the increments of subsurface temperatures can be obtained via the transfer operator during assimilation cycles. The results show that the SST assimilation improves the model simulation skills significantly, not only for the SST anomalies over the whole assimilated domain, but also for the subsurface temperature anomalies of the upper 100 m over the tropical Pacific off the equator. Along the equator, the improvement of the assimilation is confined within the mixing layer because strong upwelling motions there prevent the downward transfer of SST information. The retrospective prediction skills of ENSO over the past 120 years from 1881 to 2000 were significantly improved by the SST assimilation at all leads of 1-12 months, especially for the 3-6 months leads, compared with those initialized by the control run without assimilation. The skilful predictions by the assimilation allow us to further study ENSO predictability using this coupled model. (orig.)
Roman, A; Soancă, A; Kasaj, A; Stratul, S-I
2013-10-01
The aim of this study was to evaluate whether the combination of enamel matrix derivative (EMD) with subepithelial connective tissue graft (SCTG) plus coronally advanced flap (CAF) would improve the treatment outcomes of Miller class I and II gingival recessions when compared with the same technique (SCTG plus CAF) alone. The study was designed as a randomized, parallel, controlled, double-blinded clinical trial. Forty-two patients were randomly assigned in the test group (SCTG plus EMD) and in the control group (SCTG). Patients had at least one gingival recession ≥ 2 mm. The clinical parameters were evaluated at baseline and at 14 d, 1, 3, 6 and 12 mo follow-up time points. Forty-two patients, 21 in the test group (SCTG plus EMD) and 21 in the control group (SCTG), aged 21-48 years (mean age 31 ± 8.56) were initially included in the study. Both treatments, STCG plus EMD and SCTG, resulted in a significant final mean root coverage (2.91 ± 0.95mm and 2.91 ± 1.29 mm, respectively) (p < 0.001) and in a high mean percentage of root coverage (82.25 ± 22.20% and 89.75 ± 17.33%, respectively) (p < 0.001), 1 year after surgery. The differences in mean root coverage recorded for the two techniques after 1 year, were not statistically significant (p = 0.19). Complete root coverage was achieved in 56.5% of patients treated with SCTG plus EMD and in 70.6% of patients treated with SCTG (p = 0.275), 1 year after treatment. The present study failed to demonstrate any additional clinical benefits when EMD was added to SCTG plus CAF. © 2013 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
McGuire, Michael K; Scheyer, E Todd
2014-10-01
The standard of care for increasing keratinized tissue (KT) and vestibular area is an autogenous free gingival graft (FGG) and vestibuloplasty; however, there is morbidity associated with the harvest of autogenous tissue, and supply is limited. The purpose of this study is to determine if a xenogeneic collagen matrix (CM) might be as effective as FGG. This study is a single-masked, randomized, controlled, split-mouth study of 30 patients with insufficient zones of KT (FGG) therapy. The primary efficacy endpoint was change in KT width (∆KT) from surgery to 6 months post-surgery. Secondary endpoints included traditional periodontal measures, such as clinical attachment level, recession, and bleeding on probing. Patient-reported pain, discomfort, and esthetic satisfaction were also recorded. Biopsies were obtained at 6 months. Surgery and postoperative sequelae were uneventful, with normal healing observed at both test and control sites. The primary outcome, ∆KT width at 6 months, did not establish non-inferiority of CM compared to FGG (P = 0.9992), with the FGG sites averaging 1.5 mm more KT width than CM sites. However, the amount of new KT generated for both therapies averaged ≥2 mm. Secondary outcomes were not significantly different between test and control sites. All site biopsies appeared as normal mucoperiosteum with keratinized epithelium. CM sites achieved better texture and color matches, and more than two-thirds of patients preferred the appearance of their CM sites. With the proviso of sufficient KT (≈2 mm in width) and study goals of lower morbidity, unlimited supply, and patient satisfaction, CM appears to be a suitable substitute for FGG in vestibuloplasty procedures designed to increase KT around teeth.
Aimetti, Mario; Ferrarotti, Francesco; Mariani, Giulia Maria; Romano, Federica
2017-01-01
This investigation was designed to compare the effectiveness of enamel matrix derivative (EMD) proteins in combination with flapless or flap procedure in periodontal regeneration of deep intrabony defects. Thirty chronic periodontitis patients who had at least one residual periodontal defect with an intrabony component of ≥3 mm were consecutively enrolled. Defects were randomly assigned to test or control treatments which both consisted of the use of EMD to reach periodontal regeneration. Test sites (n = 15) were treated according to a novel flapless approach, whereas control sites (n = 15) by means of minimally invasive surgery (MIST). Clinical and radiographic parameters were recorded at baseline, 12 and 24 months post-operatively. Both therapeutic modalities yielded similar probing depth (PD) reduction and clinical attachment level (CAL) gain at 24 months. In flapless-treated sites, a mean PD reduction of 3.6 ± 1.0 mm and a CAL gain of 3.2 ± 1.1 mm were observed. In the MIST group, they were 3.7 ± 0.6 and 3.6 ± 0.9 mm. The operative chair time was twice as long in the MIST compared to the flapless group, whereas comparable patient-oriented outcomes were observed. The flapless procedure may be successfully applied in the regenerative treatment of deep intrabony defects reaching clinical outcomes comparable with those of minimally invasive surgical approaches and may present important advantages in terms of reduction of operative chair time. The use of EMD as an adjunct to non-surgical periodontal treatment may be considered a suitable option to treat defects mainly in the anterior sextants.
Understanding the structural ensembles of a highly extended disordered protein.
Daughdrill, Gary W; Kashtanov, Stepan; Stancik, Amber; Hill, Shannon E; Helms, Gregory; Muschol, Martin; Receveur-Bréchot, Véronique; Ytreberg, F Marty
2012-01-01
Developing a comprehensive description of the equilibrium structural ensembles for intrinsically disordered proteins (IDPs) is essential to understanding their function. The p53 transactivation domain (p53TAD) is an IDP that interacts with multiple protein partners and contains numerous phosphorylation sites. Multiple techniques were used to investigate the equilibrium structural ensemble of p53TAD in its native and chemically unfolded states. The results from these experiments show that the native state of p53TAD has dimensions similar to a classical random coil while the chemically unfolded state is more extended. To investigate the molecular properties responsible for this behavior, a novel algorithm that generates diverse and unbiased structural ensembles of IDPs was developed. This algorithm was used to generate a large pool of plausible p53TAD structures that were reweighted to identify a subset of structures with the best fit to small angle X-ray scattering data. High weight structures in the native state ensemble show features that are localized to protein binding sites and regions with high proline content. The features localized to the protein binding sites are mostly eliminated in the chemically unfolded ensemble; while, the regions with high proline content remain relatively unaffected. Data from NMR experiments support these results, showing that residues from the protein binding sites experience larger environmental changes upon unfolding by urea than regions with high proline content. This behavior is consistent with the urea-induced exposure of nonpolar and aromatic side-chains in the protein binding sites that are partially excluded from solvent in the native state ensemble.
Two-point Correlator Fits on HISQ Ensembles
Bazavov, A; Bouchard, C; DeTar, C; Du, D; El-Khadra, A X; Foley, J; Freeland, E D; Gamiz, E; Gottlieb, Steven; Heller, U M; Hetrick, J E; Kim, J; Kronfeld, A S; Laiho, J; Levkova, L; Lightman, M; Mackenzie, P B; Neil, E T; Oktay, M; Simone, J N; Sugar, R L; Toussaint, D; Van de Water, R S; Zhou, R
2012-01-01
We present our methods to fit the two point correlators for light, strange, and charmed pseudoscalar meson physics with the highly improved staggered quark (HISQ) action. We make use of the least-squares fit including the full covariance matrix of the correlators and including Gaussian constraints on some parameters. We fit the correlators on a variety of the HISQ ensembles. The lattice spacing ranges from 0.15 fm down to 0.06 fm. The light sea quark mass ranges from 0.2 times the strange quark mass down to the physical light quark mass. The HISQ ensembles also include lattices with different volumes and with unphysical values of the strange quark mass. We use the results from this work to obtain our preliminary results of $f_D$, $f_{D_s}$, $f_{D_s}/f_{D}$, and ratios of quark masses presented in another talk [1].
Franklin, Joel N
2003-01-01
Mathematically rigorous introduction covers vector and matrix norms, the condition-number of a matrix, positive and irreducible matrices, much more. Only elementary algebra and calculus required. Includes problem-solving exercises. 1968 edition.
LENUS (Irish Health Repository)
DiFranco, Matthew D
2011-01-01
We present a tile-based approach for producing clinically relevant probability maps of prostatic carcinoma in histological sections from radical prostatectomy. Our methodology incorporates ensemble learning for feature selection and classification on expert-annotated images. Random forest feature selection performed over varying training sets provides a subset of generalized CIEL*a*b* co-occurrence texture features, while sample selection strategies with minimal constraints reduce training data requirements to achieve reliable results. Ensembles of classifiers are built using expert-annotated tiles from training images, and scores for the probability of cancer presence are calculated from the responses of each classifier in the ensemble. Spatial filtering of tile-based texture features prior to classification results in increased heat-map coherence as well as AUC values of 95% using ensembles of either random forests or support vector machines. Our approach is designed for adaptation to different imaging modalities, image features, and histological decision domains.
Ensemble hydromoeteorological forecasting in Denmark
DEFF Research Database (Denmark)
Lucatero Villasenor, Diana
of the main sources of uncertainty in hydrological forecasts. This is the reason why substantiated efforts to include information from Numerical Weather Predictors (NWP) or General Circulation Models (GCM) have been made over the last couple of decades. The present thesis expects to advance the field......teorological extremes such as flood and droughts cause economical and live losses that could be, if not prevented, at least dampened if sufficient time is given to respond to potential threats. This is the ultimate purpose of forecasting which then translates into making reliable predictions...... of ensemble hydrometeorological forecasting by evaluating the added value of NWP and GCM ensemble prediction systems (EPS) for hydrological purposes. The use of NWP EPS that differ in both spatial and temporal resolution to feed a hydrological model for discharge forecasts at specific points, revealed two...
Symanzik flow on HISQ ensembles
Bazavov, A; Brown, N; DeTar, C; Foley, J; Gottlieb, Steven; Heller, U M; Hetrick, J E; Laiho, J; Levkova, L; Oktay, M; Sugar, R L; Toussaint, D; Van de Water, R S; Zhou, R
2013-01-01
We report on a scale determination with gradient-flow techniques on the $N_f = 2 + 1 + 1$ HISQ ensembles generated by the MILC collaboration. The lattice scale $w_0/a$, originally proposed by the BMW collaboration, is computed using Symanzik flow at four lattice spacings ranging from 0.15 to 0.06 fm. With a Taylor series ansatz, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. We give a preliminary determination of the scale $w_0$ in physical units, along with associated systematic errors, and compare with results from other groups. We also present a first estimate of autocorrelation lengths as a function of flowtime for these ensembles.
Nonequilibrium statistical mechanics ensemble method
Eu, Byung Chan
1998-01-01
In this monograph, nonequilibrium statistical mechanics is developed by means of ensemble methods on the basis of the Boltzmann equation, the generic Boltzmann equations for classical and quantum dilute gases, and a generalised Boltzmann equation for dense simple fluids The theories are developed in forms parallel with the equilibrium Gibbs ensemble theory in a way fully consistent with the laws of thermodynamics The generalised hydrodynamics equations are the integral part of the theory and describe the evolution of macroscopic processes in accordance with the laws of thermodynamics of systems far removed from equilibrium Audience This book will be of interest to researchers in the fields of statistical mechanics, condensed matter physics, gas dynamics, fluid dynamics, rheology, irreversible thermodynamics and nonequilibrium phenomena
Multimodel ensembles of wheat growth
DEFF Research Database (Denmark)
Martre, Pierre; Wallach, Daniel; Asseng, Senthold
2015-01-01
, but such studies are difficult to organize and have only recently begun. We report on the largest ensemble study to date, of 27 wheat models tested in four contrasting locations for their accuracy in simulating multiple crop growth and yield variables. The relative error averaged over models was 24...... are applicable to other crop species, and hypothesize that they apply more generally to ecological system models....
Dimensionality Reduction Through Classifier Ensembles
Oza, Nikunj C.; Tumer, Kagan; Norwig, Peter (Technical Monitor)
1999-01-01
In data mining, one often needs to analyze datasets with a very large number of attributes. Performing machine learning directly on such data sets is often impractical because of extensive run times, excessive complexity of the fitted model (often leading to overfitting), and the well-known "curse of dimensionality." In practice, to avoid such problems, feature selection and/or extraction are often used to reduce data dimensionality prior to the learning step. However, existing feature selection/extraction algorithms either evaluate features by their effectiveness across the entire data set or simply disregard class information altogether (e.g., principal component analysis). Furthermore, feature extraction algorithms such as principal components analysis create new features that are often meaningless to human users. In this article, we present input decimation, a method that provides "feature subsets" that are selected for their ability to discriminate among the classes. These features are subsequently used in ensembles of classifiers, yielding results superior to single classifiers, ensembles that use the full set of features, and ensembles based on principal component analysis on both real and synthetic datasets.
Ensemble learning incorporating uncertain registration.
Simpson, Ivor J A; Woolrich, Mark W; Andersson, Jesper L R; Groves, Adrian R; Schnabel, Julia A
2013-04-01
This paper proposes a novel approach for improving the accuracy of statistical prediction methods in spatially normalized analysis. This is achieved by incorporating registration uncertainty into an ensemble learning scheme. A probabilistic registration method is used to estimate a distribution of probable mappings between subject and atlas space. This allows the estimation of the distribution of spatially normalized feature data, e.g., grey matter probability maps. From this distribution, samples are drawn for use as training examples. This allows the creation of multiple predictors, which are subsequently combined using an ensemble learning approach. Furthermore, extra testing samples can be generated to measure the uncertainty of prediction. This is applied to separating subjects with Alzheimer's disease from normal controls using a linear support vector machine on a region of interest in magnetic resonance images of the brain. We show that our proposed method leads to an improvement in discrimination using voxel-based morphometry and deformation tensor-based morphometry over bootstrap aggregating, a common ensemble learning framework. The proposed approach also generates more reasonable soft-classification predictions than bootstrap aggregating. We expect that this approach could be applied to other statistical prediction tasks where registration is important.
Application of Ensemble Learning for Views Generation in Meucci Portfolio Optimization Framework
Didenko, Alexander; Demicheva, Svetlana
2013-01-01
Modern Portfolio Theory assumes that decisions are made by individual agents. In reality most investors are involved in group decision-making. In this research we propose to realize group decision-making process by application of Ensemble Learning algorithm, in particular Random Forest. Predicting accurate asset returns is very important in the process of asset allocation. Most models are based on weak predictors. Ensemble Learning algorithms could significantly improve prediction of weak lea...
Parameter Estimation for Observation Bias with an Ensemble Kalman Filter
Lorente-Plazas, R.; Hacker, J.
2015-12-01
In this work we evaluate a method to estimate systematic errors of individual in-situ observations. The approach is based on parameter estimation using an augmented state in an ensemble adjustment Kalman filter. Biased observations are assimilated in the highly chaotic Lorenz (2005) model that combines small and large scales. For this purpose, synthetic observations are created by introducing a grid-point dependent bias and random errors to a nature run (truth). The sensitivity of the methodology to model error, the number of ensemble members, the number of parameters, and the parameter variance is evaluated. Results demonstrate that the methodology is able to estimate observation bias for a both a perfect model and an imperfect model if the model error is estimated. The parameter estimation and the rms errors are significantly deteriorated if model error is ignored. Errors are qualitatively independent of model forcing when model error is estimated. By contrast, parameter estimation depends on model error when model error is not estimated, especially if observation biases are estimated. Errors increase with the number of estimated parameters, but they are independent of ensemble size as long as the number of ensembles members is large enough. There is an optimum value of parameter variance that minimizes the errors and improves the parameter estimation, but this value depends on observation bias and model error. Overall, the results suggest more accuracy in observation bias estimates than model error estimates.
Path planning in uncertain flow fields using ensemble method
Wang, Tong; Le Maître, Olivier P.; Hoteit, Ibrahim; Knio, Omar M.
2016-10-01
An ensemble-based approach is developed to conduct optimal path planning in unsteady ocean currents under uncertainty. We focus our attention on two-dimensional steady and unsteady uncertain flows, and adopt a sampling methodology that is well suited to operational forecasts, where an ensemble of deterministic predictions is used to model and quantify uncertainty. In an operational setting, much about dynamics, topography, and forcing of the ocean environment is uncertain. To address this uncertainty, the flow field is parametrized using a finite number of independent canonical random variables with known densities, and the ensemble is generated by sampling these variables. For each of the resulting realizations of the uncertain current field, we predict the path that minimizes the travel time by solving a boundary value problem (BVP), based on the Pontryagin maximum principle. A family of backward-in-time trajectories starting at the end position is used to generate suitable initial values for the BVP solver. This allows us to examine and analyze the performance of the sampling strategy and to develop insight into extensions dealing with general circulation ocean models. In particular, the ensemble method enables us to perform a statistical analysis of travel times and consequently develop a path planning approach that accounts for these statistics. The proposed methodology is tested for a number of scenarios. We first validate our algorithms by reproducing simple canonical solutions, and then demonstrate our approach in more complex flow fields, including idealized, steady and unsteady double-gyre flows.
Path planning in uncertain flow fields using ensemble method
Wang, Tong
2016-08-20
An ensemble-based approach is developed to conduct optimal path planning in unsteady ocean currents under uncertainty. We focus our attention on two-dimensional steady and unsteady uncertain flows, and adopt a sampling methodology that is well suited to operational forecasts, where an ensemble of deterministic predictions is used to model and quantify uncertainty. In an operational setting, much about dynamics, topography, and forcing of the ocean environment is uncertain. To address this uncertainty, the flow field is parametrized using a finite number of independent canonical random variables with known densities, and the ensemble is generated by sampling these variables. For each of the resulting realizations of the uncertain current field, we predict the path that minimizes the travel time by solving a boundary value problem (BVP), based on the Pontryagin maximum principle. A family of backward-in-time trajectories starting at the end position is used to generate suitable initial values for the BVP solver. This allows us to examine and analyze the performance of the sampling strategy and to develop insight into extensions dealing with general circulation ocean models. In particular, the ensemble method enables us to perform a statistical analysis of travel times and consequently develop a path planning approach that accounts for these statistics. The proposed methodology is tested for a number of scenarios. We first validate our algorithms by reproducing simple canonical solutions, and then demonstrate our approach in more complex flow fields, including idealized, steady and unsteady double-gyre flows.
Amozegar, M; Khorasani, K
2016-04-01
In this paper, a new approach for Fault Detection and Isolation (FDI) of gas turbine engines is proposed by developing an ensemble of dynamic neural network identifiers. For health monitoring of the gas turbine engine, its dynamics is first identified by constructing three separate or individual dynamic neural network architectures. Specifically, a dynamic multi-layer perceptron (MLP), a dynamic radial-basis function (RBF) neural network, and a dynamic support vector machine (SVM) are trained to individually identify and represent the gas turbine engine dynamics. Next, three ensemble-based techniques are developed to represent the gas turbine engine dynamics, namely, two heterogeneous ensemble models and one homogeneous ensemble model. It is first shown that all ensemble approaches do significantly improve the overall performance and accuracy of the developed system identification scheme when compared to each of the stand-alone solutions. The best selected stand-alone model (i.e., the dynamic RBF network) and the best selected ensemble architecture (i.e., the heterogeneous ensemble) in terms of their performances in achieving an accurate system identification are then selected for solving the FDI task. The required residual signals are generated by using both a single model-based solution and an ensemble-based solution under various gas turbine engine health conditions. Our extensive simulation studies demonstrate that the fault detection and isolation task achieved by using the residuals that are obtained from the dynamic ensemble scheme results in a significantly more accurate and reliable performance as illustrated through detailed quantitative confusion matrix analysis and comparative studies. Copyright © 2016 Elsevier Ltd. All rights reserved.
Mass Conservation and Positivity Preservation with Ensemble-type Kalman Filter Algorithms
Janjic, Tijana; McLaughlin, Dennis B.; Cohn, Stephen E.; Verlaan, Martin
2013-01-01
Maintaining conservative physical laws numerically has long been recognized as being important in the development of numerical weather prediction (NWP) models. In the broader context of data assimilation, concerted efforts to maintain conservation laws numerically and to understand the significance of doing so have begun only recently. In order to enforce physically based conservation laws of total mass and positivity in the ensemble Kalman filter, we incorporate constraints to ensure that the filter ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. We show that the analysis steps of ensemble transform Kalman filter (ETKF) algorithm and ensemble Kalman filter algorithm (EnKF) can conserve the mass integral, but do not preserve positivity. Further, if localization is applied or if negative values are simply set to zero, then the total mass is not conserved either. In order to ensure mass conservation, a projection matrix that corrects for localization effects is constructed. In order to maintain both mass conservation and positivity preservation through the analysis step, we construct a data assimilation algorithms based on quadratic programming and ensemble Kalman filtering. Mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate constraints. Some simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. The results show clear improvements in both analyses and forecasts, particularly in the presence of localized features. Behavior of the algorithm is also tested in presence of model error.
Model error estimation in ensemble data assimilation
Directory of Open Access Journals (Sweden)
S. Gillijns
2007-01-01
Full Text Available A new methodology is proposed to estimate and account for systematic model error in linear filtering as well as in nonlinear ensemble based filtering. Our results extend the work of Dee and Todling (2000 on constant bias errors to time-varying model errors. In contrast to existing methodologies, the new filter can also deal with the case where no dynamical model for the systematic error is available. In the latter case, the applicability is limited by a matrix rank condition which has to be satisfied in order for the filter to exist. The performance of the filter developed in this paper is limited by the availability and the accuracy of observations and by the variance of the stochastic model error component. The effect of these aspects on the estimation accuracy is investigated in several numerical experiments using the Lorenz (1996 model. Experimental results indicate that the availability of a dynamical model for the systematic error significantly reduces the variance of the model error estimates, but has only minor effect on the estimates of the system state. The filter is able to estimate additive model error of any type, provided that the rank condition is satisfied and that the stochastic errors and measurement errors are significantly smaller than the systematic errors. The results of this study are encouraging. However, it remains to be seen how the filter performs in more realistic applications.
Hiding quiet solutions in random constraint satisfaction problems
Energy Technology Data Exchange (ETDEWEB)
Zdeborova, Lenka [Los Alamos National Laboratory; Krzakala, Florent [Los Alamos National Laboratory
2008-01-01
We study constraint satisfaction problems on the so-called planted random ensemble. We show that for a certain class of problems, e.g., graph coloring, many of the properties of the usual random ensemble are quantitatively identical in the planted random ensemble. We study the structural phase transitions and the easy-hard-easy pattern in the average computational complexity. We also discuss the finite temperature phase diagram, finding a close connection with the liquid-glass-solid phenomenology.
Classifier ensembles for land cover mapping using multitemporal SAR imagery
Waske, Björn; Braun, Matthias
SAR data are almost independent from weather conditions, and thus are well suited for mapping of seasonally changing variables such as land cover. In regard to recent and upcoming missions, multitemporal and multi-frequency approaches become even more attractive. In the present study, classifier ensembles (i.e., boosted decision tree and random forests) are applied to multi-temporal C-band SAR data, from different study sites and years. A detailed accuracy assessment shows that classifier ensembles, in particularly random forests, outperform standard approaches like a single decision tree and a conventional maximum likelihood classifier by more than 10% independently from the site and year. They reach up to almost 84% of overall accuracy in rural areas with large plots. Visual interpretation confirms the statistical accuracy assessment and reveals that also typical random noise is considerably reduced. In addition the results demonstrate that random forests are less sensitive to the number of training samples and perform well even with only a small number. Random forests are computationally highly efficient and are hence considered very well suited for land cover classifications of future multifrequency and multitemporal stacks of SAR imagery.
Measuring social interaction in music ensembles.
Volpe, Gualtiero; D'Ausilio, Alessandro; Badino, Leonardo; Camurri, Antonio; Fadiga, Luciano
2016-05-05
Music ensembles are an ideal test-bed for quantitative analysis of social interaction. Music is an inherently social activity, and music ensembles offer a broad variety of scenarios which are particularly suitable for investigation. Small ensembles, such as string quartets, are deemed a significant example of self-managed teams, where all musicians contribute equally to a task. In bigger ensembles, such as orchestras, the relationship between a leader (the conductor) and a group of followers (the musicians) clearly emerges. This paper presents an overview of recent research on social interaction in music ensembles with a particular focus on (i) studies from cognitive neuroscience; and (ii) studies adopting a computational approach for carrying out automatic quantitative analysis of ensemble music performances. © 2016 The Author(s).
Analysis of mesoscale forecasts using ensemble methods
Gross, Markus
2016-01-01
Mesoscale forecasts are now routinely performed as elements of operational forecasts and their outputs do appear convincing. However, despite their realistic appearance at times the comparison to observations is less favorable. At the grid scale these forecasts often do not compare well with observations. This is partly due to the chaotic system underlying the weather. Another key problem is that it is impossible to evaluate the risk of making decisions based on these forecasts because they do not provide a measure of confidence. Ensembles provide this information in the ensemble spread and quartiles. However, running global ensembles at the meso or sub mesoscale involves substantial computational resources. National centers do run such ensembles, but the subject of this publication is a method which requires significantly less computation. The ensemble enhanced mesoscale system presented here aims not at the creation of an improved mesoscale forecast model. Also it is not to create an improved ensemble syste...
Ensemble classifier using GRG algorithm for land cover classification
Abe, Bolanle T.; Jordaan, J. A.; Marwala, Tshilidzi
2013-12-01
Image processing is of great value because it enables satellite images to be translated into useful information. The preprocessing of remotely sensed images before features extraction is important to remove noise and improve the ability to interpret image data more accurately. All images should appear as if they were acquired from the same sensor at the end of image preprocessing. A major challenge associated with hyperspectral imagery in remote sensing analysis is the mixed pixels which are due to huge dimension nature of the data. This study makes a positive contribution to the problem of land cover classification by exploring Generalized Reduced Gradient (GRG) algorithm on hyperspectral datasets by using Washington DC mall and Indiana pines test site of Northwestern Indiana, USA as study sites. The algorithm was used to estimate the fractional abundance in the datasets for land cover classification. Ensemble classifiers such as random forest, bagging and support vector machines were implemented in Waikato Environment for knowledge Analysis (WEKA) to carry out the classification procedures. Experimental results show that random forest ensemble outperformed the other ensemble methods. The comparison of the classifiers is crucial for a decision maker to consider compromises in accuracy technique against complexity technique.
A Localized Ensemble Kalman Smoother
Butala, Mark D.
2012-01-01
Numerous geophysical inverse problems prove difficult because the available measurements are indirectly related to the underlying unknown dynamic state and the physics governing the system may involve imperfect models or unobserved parameters. Data assimilation addresses these difficulties by combining the measurements and physical knowledge. The main challenge in such problems usually involves their high dimensionality and the standard statistical methods prove computationally intractable. This paper develops and addresses the theoretical convergence of a new high-dimensional Monte-Carlo approach called the localized ensemble Kalman smoother.
Wind Power Prediction using Ensembles
DEFF Research Database (Denmark)
Giebel, Gregor; Badger, Jake; Landberg, Lars
2005-01-01
offshore wind farm and the whole Jutland/Funen area. The utilities used these forecasts for maintenance planning, fuel consumption estimates and over-the-weekend trading on the Leipzig power exchange. Othernotable scientific results include the better accuracy of forecasts made up from a simple...... superposition of two NWP provider (in our case, DMI and DWD), an investigation of the merits of a parameterisation of the turbulent kinetic energy within thedelivered wind speed forecasts, and the finding that a “naïve” downscaling of each of the coarse ECMWF ensemble members with higher resolution HIRLAM did...
A Gaussian mixture ensemble transform filter
Reich, Sebastian
2011-01-01
We generalize the popular ensemble Kalman filter to an ensemble transform filter where the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions, ...
Multi-Model Ensemble Wake Vortex Prediction
Koerner, Stephan; Holzaepfel, Frank; Ahmad, Nash'at N.
2015-01-01
Several multi-model ensemble methods are investigated for predicting wake vortex transport and decay. This study is a joint effort between National Aeronautics and Space Administration and Deutsches Zentrum fuer Luft- und Raumfahrt to develop a multi-model ensemble capability using their wake models. An overview of different multi-model ensemble methods and their feasibility for wake applications is presented. The methods include Reliability Ensemble Averaging, Bayesian Model Averaging, and Monte Carlo Simulations. The methodologies are evaluated using data from wake vortex field experiments.
Collective Rabi dynamics of electromagnetically coupled quantum-dot ensembles
Glosser, Connor; Shanker, B.; Piermarocchi, Carlo
2017-09-01
Rabi oscillations typify the inherent nonlinearity of optical excitations in quantum dots. Using an integral kernel formulation to solve the three-dimensional Maxwell-Bloch equations in ensembles of up to 104 quantum dots, we observe features in Rabi oscillations due to the interplay of nonlinearity, nonequilibrium excitation, and electromagnetic coupling between the dots. This approach allows us to observe the dynamics of each dot in the ensemble without resorting to spatial averages. Our simulations predict synchronized multiplets of dots that exchange energy, dots that dynamically couple to screen the effect of incident external radiation, localization of the polarization due to randomness and interactions, as well as wavelength-scale regions of enhanced and suppressed polarization.
Manyfield inflation in random potentials
Bjorkmo, Theodor; Marsh, M. C. David
2018-02-01
We construct models of inflation with many randomly interacting fields and use these to study the generation of cosmological observables. We model the potentials as multi-dimensional Gaussian random fields (GRFs) and identify powerful algebraic simplifications that, for the first time, make it possible to access the manyfield limit of inflation in GRF potentials. Focussing on small-field, slow-roll, approximate saddle-point inflation in potentials with structure on sub-Planckian scales, we construct explicit examples involving up to 100 fields and generate statistical ensembles comprising of 164,000 models involving 5 to 50 fields. For the subset of these that support at least sixty e-folds of inflation, we use the 'transport method' and δ N formalism to determine the predictions for cosmological observables at the end of inflation, including the power spectrum and the local non-Gaussianities of the primordial perturbations. We find three key results: i) Planck compatibility is not rare, but future experiments may rule out this class of models; ii) In the manyfield limit, the predictions from these models agree well with, but are sharper than, previous results derived using potentials constructed through non-equilibrium Random Matrix Theory; iii) Despite substantial multifield effects, non-Gaussianities are typically very small: fNLloc ll 1. We conclude that many of the 'generic predictions' of single-field inflation can be emergent features of complex inflation models.
Directory of Open Access Journals (Sweden)
Rachida El Ouaraini
2015-12-01
Full Text Available The implementation of a regional ensemble data assimilation and forecasting system requires the specification of appropriate perturbations of lateral boundary conditions (LBCs, in order to simulate associated errors. The sensitivity of analysis and 6-h forecast ensemble spread to these perturbations is studied here formally and experimentally by comparing three different LBC configurations for the ensemble data assimilation system of the ALADIN-France limited-area model (LAM. While perturbed initial LBCs are provided by the perturbed LAM analyses in each ensemble, the three ensemble configurations differ with respect to LBCs used at 3- and 6-h forecast ranges, which respectively correspond to: (1 perturbed LBCs provided by the operational global ensemble data assimilation system (GLBC, which is considered as a reference configuration; (2 unperturbed LBCs (ULBC obtained from the global deterministic model; (3 perturbed LBCs obtained by adding random draws of an error covariance model (PLBC to the global deterministic system. A formal analysis of error and perturbation equations is first carried out, in order to provide an insight of the relative effects of observation perturbations and of LBC perturbations at different ranges, in the various ensemble configurations. Horizontal variations of time-averaged ensemble spread are then examined for 6-h forecasts. Despite the use of perturbed initial LBCs, the regional ensemble ULBC is underdispersive not only near the lateral boundaries, but also in approximately one-third of the inner area, due to advection during the data assimilation cycle. This artefact is avoided in PLBC through the additional use of non-zero LBC perturbations at 3- and 6-h ranges, and the sensitivity to the amplitude scaling of the covariance model is illustrated for this configuration. Some aspects of the temporal variation of ensemble spread and associated sensitivities to LBC perturbations are also studied. These results
Automatic Estimation of Osteoporotic Fracture Cases by Using Ensemble Learning Approaches.
Kilic, Niyazi; Hosgormez, Erkan
2016-03-01
Ensemble learning methods are one of the most powerful tools for the pattern classification problems. In this paper, the effects of ensemble learning methods and some physical bone densitometry parameters on osteoporotic fracture detection were investigated. Six feature set models were constructed including different physical parameters and they fed into the ensemble classifiers as input features. As ensemble learning techniques, bagging, gradient boosting and random subspace (RSM) were used. Instance based learning (IBk) and random forest (RF) classifiers applied to six feature set models. The patients were classified into three groups such as osteoporosis, osteopenia and control (healthy), using ensemble classifiers. Total classification accuracy and f-measure were also used to evaluate diagnostic performance of the proposed ensemble classification system. The classification accuracy has reached to 98.85 % by the combination of model 6 (five BMD + five T-score values) using RSM-RF classifier. The findings of this paper suggest that the patients will be able to be warned before a bone fracture occurred, by just examining some physical parameters that can easily be measured without invasive operations.
Joys of Community Ensemble Playing: The Case of the Happy Roll Elastic Ensemble in Taiwan
Hsieh, Yuan-Mei; Kao, Kai-Chi
2012-01-01
The Happy Roll Elastic Ensemble (HREE) is a community music ensemble supported by Tainan Culture Centre in Taiwan. With enjoyment and friendship as its primary goals, it aims to facilitate the joys of ensemble playing and the spirit of social networking. This article highlights the key aspects of HREE's development in its first two years…
A Simple Approach to Account for Climate Model Interdependence in Multi-Model Ensembles
Herger, N.; Abramowitz, G.; Angelil, O. M.; Knutti, R.; Sanderson, B.
2016-12-01
Multi-model ensembles are an indispensable tool for future climate projection and its uncertainty quantification. Ensembles containing multiple climate models generally have increased skill, consistency and reliability. Due to the lack of agreed-on alternatives, most scientists use the equally-weighted multi-model mean as they subscribe to model democracy ("one model, one vote").Different research groups are known to share sections of code, parameterizations in their model, literature, or even whole model components. Therefore, individual model runs do not represent truly independent estimates. Ignoring this dependence structure might lead to a false model consensus, wrong estimation of uncertainty and effective number of independent models.Here, we present a way to partially address this problem by selecting a subset of CMIP5 model runs so that its climatological mean minimizes the RMSE compared to a given observation product. Due to the cancelling out of errors, regional biases in the ensemble mean are reduced significantly.Using a model-as-truth experiment we demonstrate that those regional biases persist into the future and we are not fitting noise, thus providing improved observationally-constrained projections of the 21st century. The optimally selected ensemble shows significantly higher global mean surface temperature projections than the original ensemble, where all the model runs are considered. Moreover, the spread is decreased well beyond that expected from the decreased ensemble size.Several previous studies have recommended an ensemble selection approach based on performance ranking of the model runs. Here, we show that this approach can perform even worse than randomly selecting ensemble members and can thus be harmful. We suggest that accounting for interdependence in the ensemble selection process is a necessary step for robust projections for use in impact assessments, adaptation and mitigation of climate change.
Energy Technology Data Exchange (ETDEWEB)
Cummings, A. [Physics Department, University College Dublin, Dublin (Ireland); Department of Mathematical Physics, National University of Ireland Maynooth, Kildare (Ireland); O' Sullivan, G. [Physics Department, University College Dublin, Dublin (Ireland); Heffernan, D.M. [Department of Mathematical Physics, National University of Ireland Maynooth, Kildare (Ireland); School of Theoretical Physics, Dublin Institute for Advanced Studies, Dublin (Ireland)
2001-09-14
Using the relativistic configuration interaction Hartree-Fock method the Hamiltonian matrices of Ce I, J=4{sup {+-}}, and Pr I, J=11/2{sup {+-}}, are studied. These matrices can be characterized as sparse, banded matrices, with a leading diagonal. Diagonalization of the Hamiltonian results in a set of energy eigenvalues and corresponding eigenvectors and the purpose of this investigation will be to characterize the Hamiltonian matrices and coupling matrices of Ce I and Pr I, for both ls and jj coupling representations, using various statistical predictions of Random Matrix Theory. (author)
Bodewig, E
1959-01-01
Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well
Ping, Jing
2017-05-19
Optimal management of subsurface processes requires the characterization of the uncertainty in reservoir description and reservoir performance prediction. For fractured reservoirs, the location and orientation of fractures are crucial for predicting production characteristics. With the help of accurate and comprehensive knowledge of fracture distributions, early water/CO 2 breakthrough can be prevented and sweep efficiency can be improved. However, since the rock property fields are highly non-Gaussian in this case, it is a challenge to estimate fracture distributions by conventional history matching approaches. In this work, a method that combines vector-based level-set parameterization technique and ensemble Kalman filter (EnKF) for estimating fracture distributions is presented. Performing the necessary forward modeling is particularly challenging. In addition to the large number of forward models needed, each model is used for sampling of randomly located fractures. Conventional mesh generation for such systems would be time consuming if possible at all. For these reasons, we rely on a novel polyhedral mesh method using the mimetic finite difference (MFD) method. A discrete fracture model is adopted that maintains the full geometry of the fracture network. By using a cut-cell paradigm, a computational mesh for the matrix can be generated quickly and reliably. In this research, we apply this workflow on 2D two-phase fractured reservoirs. The combination of MFD approach, level-set parameterization, and EnKF provides an effective solution to address the challenges in the history matching problem of highly non-Gaussian fractured reservoirs.
Improved customer choice predictions using ensemble methods
M.C. van Wezel (Michiel); R. Potharst (Rob)
2005-01-01
textabstractIn this paper various ensemble learning methods from machine learning and statistics are considered and applied to the customer choice modeling problem. The application of ensemble learning usually improves the prediction quality of flexible models like decision trees and thus leads to
Urban runoff forecasting with ensemble weather predictions
DEFF Research Database (Denmark)
Pedersen, Jonas Wied; Courdent, Vianney Augustin Thomas; Vezzaro, Luca
This research shows how ensemble weather forecasts can be used to generate urban runoff forecasts up to 53 hours into the future. The results highlight systematic differences between ensemble members that needs to be accounted for when these forecasts are used in practice....
Ensemble estimators for multivariate entropy estimation.
Sricharan, Kumar; Wei, Dennis; Hero, Alfred O
2013-07-01
The problem of estimation of density functionals like entropy and mutual information has received much attention in the statistics and information theory communities. A large class of estimators of functionals of the probability density suffer from the curse of dimensionality, wherein the mean squared error (MSE) decays increasingly slowly as a function of the sample size T as the dimension d of the samples increases. In particular, the rate is often glacially slow of order O(T(-)(γ)(/)(d) ), where γ > 0 is a rate parameter. Examples of such estimators include kernel density estimators, k-nearest neighbor (k-NN) density estimators, k-NN entropy estimators, intrinsic dimension estimators and other examples. In this paper, we propose a weighted affine combination of an ensemble of such estimators, where optimal weights can be chosen such that the weighted estimator converges at a much faster dimension invariant rate of O(T(-1)). Furthermore, we show that these optimal weights can be determined by solving a convex optimization problem which can be performed offline and does not require training data. We illustrate the superior performance of our weighted estimator for two important applications: (i) estimating the Panter-Dite distortion-rate factor and (ii) estimating the Shannon entropy for testing the probability distribution of a random sample.
Perception of ensemble statistics requires attention.
Jackson-Nielsen, Molly; Cohen, Michael A; Pitts, Michael A
2017-02-01
To overcome inherent limitations in perceptual bandwidth, many aspects of the visual world are represented as summary statistics (e.g., average size, orientation, or density of objects). Here, we investigated the relationship between summary (ensemble) statistics and visual attention. Recently, it was claimed that one ensemble statistic in particular, color diversity, can be perceived without focal attention. However, a broader debate exists over the attentional requirements of conscious perception, and it is possible that some form of attention is necessary for ensemble perception. To test this idea, we employed a modified inattentional blindness paradigm and found that multiple types of summary statistics (color and size) often go unnoticed without attention. In addition, we found attentional costs in dual-task situations, further implicating a role for attention in statistical perception. Overall, we conclude that while visual ensembles may be processed efficiently, some amount of attention is necessary for conscious perception of ensemble statistics. Copyright © 2016 Elsevier Inc. All rights reserved.
Bouallegue, Zied Ben; Theis, Susanne E; Pinson, Pierre
2015-01-01
Probabilistic forecasts in the form of ensemble of scenarios are required for complex decision making processes. Ensemble forecasting systems provide such products but the spatio-temporal structures of the forecast uncertainty is lost when statistical calibration of the ensemble forecasts is applied for each lead time and location independently. Non-parametric approaches allow the reconstruction of spatio-temporal joint probability distributions at a low computational cost.For example, the ensemble copula coupling (ECC) method consists in rebuilding the multivariate aspect of the forecast from the original ensemble forecasts. Based on the assumption of error stationarity, parametric methods aim to fully describe the forecast dependence structures. In this study, the concept of ECC is combined with past data statistics in order to account for the autocorrelation of the forecast error. The new approach which preserves the dynamical development of the ensemble members is called dynamic ensemble copula coupling (...
Ensemble singular vectors and their use as additive inflation in EnKF
Directory of Open Access Journals (Sweden)
Shu-Chih Yang
2015-07-01
Full Text Available Given an ensemble of forecasts, it is possible to determine the leading ensemble singular vector (ESV, that is, the linear combination of the forecasts that, given the choice of the perturbation norm and forecast interval, will maximise the growth of the perturbations. Because the ESV indicates the directions of the fastest growing forecast errors, we explore the potential of applying the leading ESVs in ensemble Kalman filter (EnKF for correcting fast-growing errors. The ESVs are derived based on a quasi-geostrophic multi-level channel model, and data assimilation experiments are carried out under framework of the local ensemble transform Kalman filter. We confirm that even during the early spin-up starting with random initial conditions, the final ESVs of the first analysis with a 12-h window are strongly related to the background errors. Since initial ensemble singular vectors (IESVs grow much faster than Lyapunov Vectors (LVs, and the final ensemble singular vectors (FESVs are close to convergence to leading LVs, perturbations based on leading IESVs grow faster than those based on FESVs, and are therefore preferable as additive inflation. The IESVs are applied in the EnKF framework for constructing flow-dependent additive perturbations to inflate the analysis ensemble. Compared with using random perturbations as additive inflation, a positive impact from using ESVs is found especially in areas with large growing errors. When an EnKF is ‘cold-started’ from random perturbations and poor initial condition, results indicate that using the ESVs as additive inflation has the advantage of correcting large errors so that the spin-up of the EnKF can be accelerated.
Ensemble learning for the detection of facial dysmorphology.
Zhao, Qian; Werghi, Naoufel; Okada, Kazunori; Rosenbaum, Kenneth; Summar, Marshall; Linguraru, Marius George
2014-01-01
Down syndrome is the most common chromosomal condition that presents characteristic facial morphology and texture patterns. The early detection of Down syndrome through an automatic, non-invasive and simple way is desirable and critical to provide the best health management to newborns. In this study, we propose such a computer-aided diagnosis system for Down syndrome from photography based on facial analysis with ensemble learning. First, geometric and texture facial features are extracted based on automatically located facial landmarks, followed by feature fusion and selection. Then multiple classifiers (i.e. support vector machines, random forests and linear discriminant analysis) are adopted to identify patients with Down syndrome. An accurate and reliable decision is finally achieved by optimally combining the outputs of these individual classifiers via ensemble learning that captures both the shared and complementary information from different classifiers. The best performance was achieved by using the median ensemble rule with 0.967 accuracy, 0.977 precision and 0.933 recall.
Ensemble Kinetic Modeling of Metabolic Networks from Dynamic Metabolic Profiles
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Gengjie Jia
2012-11-01
Full Text Available Kinetic modeling of metabolic pathways has important applications in metabolic engineering, but significant challenges still remain. The difficulties faced vary from finding best-fit parameters in a highly multidimensional search space to incomplete parameter identifiability. To meet some of these challenges, an ensemble modeling method is developed for characterizing a subset of kinetic parameters that give statistically equivalent goodness-of-fit to time series concentration data. The method is based on the incremental identification approach, where the parameter estimation is done in a step-wise manner. Numerical efficacy is achieved by reducing the dimensionality of parameter space and using efficient random parameter exploration algorithms. The shift toward using model ensembles, instead of the traditional “best-fit” models, is necessary to directly account for model uncertainty during the application of such models. The performance of the ensemble modeling approach has been demonstrated in the modeling of a generic branched pathway and the trehalose pathway in Saccharomyces cerevisiae using generalized mass action (GMA kinetics.
State estimation for large ensembles
Gill, R.D.; Massar, S.
2000-01-01
We consider the problem of estimating the state of a large but nite number N of identical quantum systems. As N becomes large the problem simplies dramatically. The only relevant measure of the quality of estimation becomes the mean quadratic error matrix. Here we present a bound on this quantity: a
State estimation for large ensembles
Gill, R.D.; Massar, S.
1999-01-01
We consider the problem of estimating the state of a large but nite number N of identical quantum systems In the limit of large N the problem simplies In particular the only relevant measure of the quality of the estimation is the mean quadratic error matrix Here we present a bound on the mean
Stabilizing canonical-ensemble calculations in the auxiliary-field Monte Carlo method
Gilbreth, C. N.; Alhassid, Y.
2015-03-01
Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the auxiliary-field Monte Carlo (AFMC) method, low-temperature or large-model-space calculations require numerically stabilized matrix multiplication. When adapting methods used in the grand-canonical ensemble to the canonical ensemble of fixed particle number, the numerical stabilization increases the number of required floating-point operations for computing observables by a factor of the size of the single-particle model space, and thus can greatly limit the systems that can be studied. We describe an improved method for stabilizing canonical-ensemble calculations in AFMC that exhibits better scaling, and present numerical tests that demonstrate the accuracy and improved performance of the method.
Contributions to Ensemble Classifiers with Image Analysis Applications
Ayerdi Vilches, Borja
2016-01-01
134 p. Ésta tesis tiene dos aspectos fundamentales, por un lado, la propuesta denuevas arquitecturas de clasificadores y, por otro, su aplicación a el análisis deimagen.Desde el punto de vista de proponer nuevas arquitecturas de clasificaciónla tesis tiene dos contribucciones principales. En primer lugar la propuestade un innovador ensemble de clasificadores basado en arquitecturas aleatorias,como pueden ser las Extreme Learning Machines (ELM), Random Forest (RF) yRotation Forest, llamado ...
Fluctuations in a quasi-stationary shallow cumulus cloud ensemble
Directory of Open Access Journals (Sweden)
M. Sakradzija
2015-01-01
Full Text Available We propose an approach to stochastic parameterisation of shallow cumulus clouds to represent the convective variability and its dependence on the model resolution. To collect information about the individual cloud lifecycles and the cloud ensemble as a whole, we employ a large eddy simulation (LES model and a cloud tracking algorithm, followed by conditional sampling of clouds at the cloud-base level. In the case of a shallow cumulus ensemble, the cloud-base mass flux distribution is bimodal, due to the different shallow cloud subtypes, active and passive clouds. Each distribution mode can be approximated using a Weibull distribution, which is a generalisation of exponential distribution by accounting for the change in distribution shape due to the diversity of cloud lifecycles. The exponential distribution of cloud mass flux previously suggested for deep convection parameterisation is a special case of the Weibull distribution, which opens a way towards unification of the statistical convective ensemble formalism of shallow and deep cumulus clouds. Based on the empirical and theoretical findings, a stochastic model has been developed to simulate a shallow convective cloud ensemble. It is formulated as a compound random process, with the number of convective elements drawn from a Poisson distribution, and the cloud mass flux sampled from a mixed Weibull distribution. Convective memory is accounted for through the explicit cloud lifecycles, making the model formulation consistent with the choice of the Weibull cloud mass flux distribution function. The memory of individual shallow clouds is required to capture the correct convective variability. The resulting distribution of the subgrid convective states in the considered shallow cumulus case is scale-adaptive – the smaller the grid size, the broader the distribution.
Physiological evaluation of air-fed ensembles.
Turner, Nina L; Powell, Jeffrey B; Sinkule, Edward J; Novak, Debra A
2014-03-01
The goal of this study was to evaluate the respiratory and metabolic stresses of air-fed ensembles used by workers in the nuclear, chemical, and pharmaceutical industries during rest, low-, and moderate-intensity treadmill exercise. Fourteen men and six women wore two different air-fed ensembles (AFE-1 and AFE-2) and one two-piece supplied-air respirator (SA) at rest (REST) and while walking for 6min at oxygen consumption (V.O2) rates of 1.0 (LOW) and 2.0 l min(-1) (MOD). Inhaled CO2 (FICO2), inhaled O2 (FIO2), pressure, and temperature were measured continuously breath-by-breath. For both LOW and MOD, FICO2 was significantly lower (P ensembles than SA (P REST, LOW, and MOD. Inhaled gas temperature was significantly lower in SA than in either air-fed ensemble (P ensembles in both men and women, an observation that has implications for the design of emergency escape protocols for air-fed ensemble wearers. Results show that inhaled gas concentrations may reach physiologically stressful levels in air-fed ensembles during moderate-intensity treadmill walking.
NIMEFI: gene regulatory network inference using multiple ensemble feature importance algorithms.
Directory of Open Access Journals (Sweden)
Joeri Ruyssinck
Full Text Available One of the long-standing open challenges in computational systems biology is the topology inference of gene regulatory networks from high-throughput omics data. Recently, two community-wide efforts, DREAM4 and DREAM5, have been established to benchmark network inference techniques using gene expression measurements. In these challenges the overall top performer was the GENIE3 algorithm. This method decomposes the network inference task into separate regression problems for each gene in the network in which the expression values of a particular target gene are predicted using all other genes as possible predictors. Next, using tree-based ensemble methods, an importance measure for each predictor gene is calculated with respect to the target gene and a high feature importance is considered as putative evidence of a regulatory link existing between both genes. The contribution of this work is twofold. First, we generalize the regression decomposition strategy of GENIE3 to other feature importance methods. We compare the performance of support vector regression, the elastic net, random forest regression, symbolic regression and their ensemble variants in this setting to the original GENIE3 algorithm. To create the ensemble variants, we propose a subsampling approach which allows us to cast any feature selection algorithm that produces a feature ranking into an ensemble feature importance algorithm. We demonstrate that the ensemble setting is key to the network inference task, as only ensemble variants achieve top performance. As second contribution, we explore the effect of using rankwise averaged predictions of multiple ensemble algorithms as opposed to only one. We name this approach NIMEFI (Network Inference using Multiple Ensemble Feature Importance algorithms and show that this approach outperforms all individual methods in general, although on a specific network a single method can perform better. An implementation of NIMEFI has been made
Durazo, Juan A.; Kostelich, Eric J.; Mahalov, Alex
2017-09-01
We propose a targeted observation strategy, based on the influence matrix diagnostic, that optimally selects where additional observations may be placed to improve ionospheric forecasts. This strategy is applied in data assimilation observing system experiments, where synthetic electron density vertical profiles, which represent those of Constellation Observing System for Meteorology, Ionosphere, and Climate/Formosa satellite 3, are assimilated into the Thermosphere-Ionosphere-Electrodynamics General Circulation Model using the local ensemble transform Kalman filter during the 26 September 2011 geomagnetic storm. During each analysis step, the observation vector is augmented with five synthetic vertical profiles optimally placed to target electron density errors, using our targeted observation strategy. Forecast improvement due to assimilation of augmented vertical profiles is measured with the root-mean-square error (RMSE) of analyzed electron density, averaged over 600 km regions centered around the augmented vertical profile locations. Assimilating vertical profiles with targeted locations yields about 60%-80% reduction in electron density RMSE, compared to a 15% average reduction when assimilating randomly placed vertical profiles. Assimilating vertical profiles whose locations target the zonal component of neutral winds (Un) yields on average a 25% RMSE reduction in Un estimates, compared to a 2% average improvement obtained with randomly placed vertical profiles. These results demonstrate that our targeted strategy can improve data assimilation efforts during extreme events by detecting regions where additional observations would provide the largest benefit to the forecast.
Atomic clock ensemble in space
Cacciapuoti, L.; Salomon, C.
2011-12-01
Atomic Clock Ensemble in Space (ACES) is a mission using high-performance clocks and links to test fundamental laws of physics in space. Operated in the microgravity environment of the International Space Station, the ACES clocks, PHARAO and SHM, will generate a frequency reference reaching instability and inaccuracy at the 1 · 10-16 level. A link in the microwave domain (MWL) and an optical link (ELT) will make the ACES clock signal available to ground laboratories equipped with atomic clocks. Space-to-ground and ground-to-ground comparisons of atomic frequency standards will be used to test Einstein's theory of general relativity including a precision measurement of the gravitational red-shift, a search for time variations of fundamental constants, and Lorentz Invariance tests. Applications in geodesy, optical time transfer, and ranging will also be supported. ACES has now reached an advanced technology maturity, with engineering models completed and successfully tested and flight hardware under development. This paper presents the ACES mission concept and the status of its main instruments.
A Link-Based Cluster Ensemble Approach For Improved Gene Expression Data Analysis
Directory of Open Access Journals (Sweden)
P.Balaji
2015-01-01
Full Text Available Abstract It is difficult from possibilities to select a most suitable effective way of clustering algorithm and its dataset for a defined set of gene expression data because we have a huge number of ways and huge number of gene expressions. At present many researchers are preferring to use hierarchical clustering in different forms this is no more totally optimal. Cluster ensemble research can solve this type of problem by automatically merging multiple data partitions from a wide range of different clusterings of any dimensions to improve both the quality and robustness of the clustering result. But we have many existing ensemble approaches using an association matrix to condense sample-cluster and co-occurrence statistics and relations within the ensemble are encapsulated only at raw level while the existing among clusters are totally discriminated. Finding these missing associations can greatly expand the capability of those ensemble methodologies for microarray data clustering. We propose general K-means cluster ensemble approach for the clustering of general categorical data into required number of partitions.
CA-tree: a hierarchical structure for efficient and scalable coassociation-based cluster ensembles.
Wang, Tsaipei
2011-06-01
Cluster ensembles have attracted a lot of research interests in recent years, and their applications continue to expand. Among the various algorithms for cluster ensembles, those based on coassociation matrices are probably the ones studied and used the most because coassociation matrices are easy to understand and implement. However, the main limitation of coassociation matrices as the data structure for combining multiple clusterings is the complexity that is at least quadratic to the number of patterns N. In this paper, we propose CA-tree, which is a dendogram-like hierarchical data structure, to facilitate efficient and scalable cluster ensembles for coassociation-matrix-based algorithms. All the properties of the CA-tree are derived from base cluster labels and do not require the access to the original data features. We then apply a threshold to the CA-tree to obtain a set of nodes, which are then used in place of the original patterns for ensemble-clustering algorithms. The experiments demonstrate that the complexity for coassociation-based cluster ensembles can be reduced to close to linear to N with minimal loss on clustering accuracy.
Ensemble Weight Enumerators for Protograph LDPC Codes
Divsalar, Dariush
2006-01-01
Recently LDPC codes with projected graph, or protograph structures have been proposed. In this paper, finite length ensemble weight enumerators for LDPC codes with protograph structures are obtained. Asymptotic results are derived as the block size goes to infinity. In particular we are interested in obtaining ensemble average weight enumerators for protograph LDPC codes which have minimum distance that grows linearly with block size. As with irregular ensembles, linear minimum distance property is sensitive to the proportion of degree-2 variable nodes. In this paper the derived results on ensemble weight enumerators show that linear minimum distance condition on degree distribution of unstructured irregular LDPC codes is a sufficient but not a necessary condition for protograph LDPC codes.
Genetic Algorithm Optimized Neural Networks Ensemble as ...
African Journals Online (AJOL)
NJD
Genetic Algorithm Optimized Neural Networks Ensemble as. Calibration Model for Simultaneous Spectrophotometric. Estimation of Atenolol and Losartan Potassium in Tablets. Dondeti Satyanarayana*, Kamarajan Kannan and Rajappan Manavalan. Department of Pharmacy, Annamalai University, Annamalainagar, Tamil ...
Products of rectangular random matrices: Singular values and progressive scattering
Akemann, Gernot; Ipsen, Jesper R.; Kieburg, Mario
2013-11-01
We discuss the product of M rectangular random matrices with independent Gaussian entries, which have several applications, including wireless telecommunication and econophysics. For complex matrices an explicit expression for the joint probability density function is obtained using the Harish-Chandra-Itzykson-Zuber integration formula. Explicit expressions for all correlation functions and moments for finite matrix sizes are obtained using a two-matrix model and the method of biorthogonal polynomials. This generalizes the classical result for the so-called Wishart-Laguerre Gaussian unitary ensemble (or chiral unitary ensemble) at M=1, and previous results for the product of square matrices. The correlation functions are given by a determinantal point process, where the kernel can be expressed in terms of Meijer G-functions. We compare the results with numerical simulations and known results for the macroscopic level density in the limit of large matrices. The location of the end points of support for the latter are analyzed in detail for general M. Finally, we consider the so-called ergodic mutual information, which gives an upper bound for the spectral efficiency of a MIMO communication channel with multifold scattering.
Liu, Li; Xu, Yue-Ping
2017-04-01
Ensemble flood forecasting driven by numerical weather prediction products is becoming more commonly used in operational flood forecasting applications.In this study, a hydrological ensemble flood forecasting system based on Variable Infiltration Capacity (VIC) model and quantitative precipitation forecasts from TIGGE dataset is constructed for Lanjiang Basin, Southeast China. The impacts of calibration strategies and ensemble methods on the performance of the system are then evaluated.The hydrological model is optimized by parallel programmed ɛ-NSGAII multi-objective algorithm and two respectively parameterized models are determined to simulate daily flows and peak flows coupled with a modular approach.The results indicatethat the ɛ-NSGAII algorithm permits more efficient optimization and rational determination on parameter setting.It is demonstrated that the multimodel ensemble streamflow mean have better skills than the best singlemodel ensemble mean (ECMWF) and the multimodel ensembles weighted on members and skill scores outperform other multimodel ensembles. For typical flood event, it is proved that the flood can be predicted 3-4 days in advance, but the flows in rising limb can be captured with only 1-2 days ahead due to the flash feature. With respect to peak flows selected by Peaks Over Threshold approach, the ensemble means from either singlemodel or multimodels are generally underestimated as the extreme values are smoothed out by ensemble process.
Towards a GME ensemble forecasting system: Ensemble initialization using the breeding technique
Directory of Open Access Journals (Sweden)
Jan D. Keller
2008-12-01
Full Text Available The quantitative forecast of precipitation requires a probabilistic background particularly with regard to forecast lead times of more than 3 days. As only ensemble simulations can provide useful information of the underlying probability density function, we built a new ensemble forecasting system (GME-EFS based on the GME model of the German Meteorological Service (DWD. For the generation of appropriate initial ensemble perturbations we chose the breeding technique developed by Toth and Kalnay (1993, 1997, which develops perturbations by estimating the regions of largest model error induced uncertainty. This method is applied and tested in the framework of quasi-operational forecasts for a three month period in 2007. The performance of the resulting ensemble forecasts are compared to the operational ensemble prediction systems ECMWF EPS and NCEP GFS by means of ensemble spread of free atmosphere parameters (geopotential and temperature and ensemble skill of precipitation forecasting. This comparison indicates that the GME ensemble forecasting system (GME-EFS provides reasonable forecasts with spread skill score comparable to that of the NCEP GFS. An analysis with the continuous ranked probability score exhibits a lack of resolution for the GME forecasts compared to the operational ensembles. However, with significant enhancements during the 3 month test period, the first results of our work with the GME-EFS indicate possibilities for further development as well as the potential for later operational usage.
Conductor gestures influence evaluations of ensemble performance.
Morrison, Steven J; Price, Harry E; Smedley, Eric M; Meals, Cory D
2014-01-01
Previous research has found that listener evaluations of ensemble performances vary depending on the expressivity of the conductor's gestures, even when performances are otherwise identical. It was the purpose of the present study to test whether this effect of visual information was evident in the evaluation of specific aspects of ensemble performance: articulation and dynamics. We constructed a set of 32 music performances that combined auditory and visual information and were designed to feature a high degree of contrast along one of two target characteristics: articulation and dynamics. We paired each of four music excerpts recorded by a chamber ensemble in both a high- and low-contrast condition with video of four conductors demonstrating high- and low-contrast gesture specifically appropriate to either articulation or dynamics. Using one of two equivalent test forms, college music majors and non-majors (N = 285) viewed sixteen 30 s performances and evaluated the quality of the ensemble's articulation, dynamics, technique, and tempo along with overall expressivity. Results showed significantly higher evaluations for performances featuring high rather than low conducting expressivity regardless of the ensemble's performance quality. Evaluations for both articulation and dynamics were strongly and positively correlated with evaluations of overall ensemble expressivity.
Ensemble forecasts of road surface temperatures
Sokol, Zbyněk; Bližňák, Vojtěch; Sedlák, Pavel; Zacharov, Petr; Pešice, Petr; Škuthan, Miroslav
2017-05-01
This paper describes a new ensemble technique for road surface temperature (RST) forecasting using an energy balance and heat conduction model. Compared to currently used deterministic forecasts, the proposed technique allows the estimation of forecast uncertainty and probabilistic forecasts. The ensemble technique is applied to the METRo-CZ model and stems from error covariance analyses of the forecasted air temperature and humidity 2 m above the ground, wind speed at 10 m and total cloud cover N in octas by the numerical weather prediction (NWP) model. N is used to estimate the shortwave and longwave radiation fluxes. These variables are used to calculate the boundary conditions in the METRo-CZ model. We found that the variable N is crucial for generating the ensembles. Nevertheless, the ensemble spread is too small and underestimates the uncertainty in the RST forecast. One of the reasons is not considering errors in the rain and snow forecast by the NWP model when generating ensembles. Technical issues, such as incorrect sky view factors and the current state of road surface conditions also contribute to errors. Although the ensemble technique underestimates the uncertainty in the RST forecasts, it provides additional information to road authorities who provide winter road maintenance.
Inflation with a graceful exit in a random landscape
Energy Technology Data Exchange (ETDEWEB)
Pedro, F.G. [Departamento de Física Teórica and Instituto de Física Teórica UAM/CSIC,Universidad Autónoma de Madrid,Cantoblanco, 28049 Madrid (Spain); Westphal, A. [Deutsches Elektronen-Synchrotron DESY, Theory Group,D-22603 Hamburg (Germany)
2017-03-30
We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N≪10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.
Inflation with a graceful exit in a random landscape
Pedro, F. G.; Westphal, A.
2017-03-01
We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N ≪ 10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.
Filter ensemble regularized common spatial pattern for EEG classification
Su, Yuxi; Li, Yali; Wang, Shengjin
2015-07-01
Common Spatial Pattern (CSP) is one of the most effective feature extraction algorithm for Brain-Computer Interfaces (BCI). Despite its advantages of wide versatility and high efficiency, CSP is shown to be non-robust to noise and prone to over fitting when training sample number is limited. In order to overcome these problems, Regularized Common Spatial Pattern (RCSP) is further proposed. RCSP regularized covariance matrix estimation by two parameters, which reduces the estimation difference and improves the stationarity under small sample condition. However, RCSP does not make full use of the frequency information. In this paper, we presents a filter ensemble technique for RCSP (FERCSP) to further extract frequency information and aggregate all the RCSPs efficiently to get an ensemble-based solution. The performance of the proposed algorithm is evaluated on data set IVa of BCI Competition III against other five RCSPbased algorithms. The experimental results show that FERCSP significantly outperforms those of the existing methods in classification accuracy. The FERCSP outperforms the CSP algorithm and R-CSP-A algorithm in all five subjects with an average improvement of 6% in accuracy.
Spatial Ensemble Postprocessing of Precipitation Forecasts Using High Resolution Analyses
Lang, Moritz N.; Schicker, Irene; Kann, Alexander; Wang, Yong
2017-04-01
shows a mean improvement of more than 40% in CRPS when compared to bilinearly interpolated uncalibrated ensemble forecasts. The validation on randomly selected grid points, representing the true height distribution over Austria, still indicates a mean improvement of 35%. The applied statistical model is currently set up for 6-hourly and daily accumulation periods, but will be extended to a temporal resolution of 1-3 hours within a new probabilistic nowcasting system operated by ZAMG.
Improved method for predicting protein fold patterns with ensemble classifiers.
Chen, W; Liu, X; Huang, Y; Jiang, Y; Zou, Q; Lin, C
2012-01-27
Protein folding is recognized as a critical problem in the field of biophysics in the 21st century. Predicting protein-folding patterns is challenging due to the complex structure of proteins. In an attempt to solve this problem, we employed ensemble classifiers to improve prediction accuracy. In our experiments, 188-dimensional features were extracted based on the composition and physical-chemical property of proteins and 20-dimensional features were selected using a coupled position-specific scoring matrix. Compared with traditional prediction methods, these methods were superior in terms of prediction accuracy. The 188-dimensional feature-based method achieved 71.2% accuracy in five cross-validations. The accuracy rose to 77% when we used a 20-dimensional feature vector. These methods were used on recent data, with 54.2% accuracy. Source codes and dataset, together with web server and software tools for prediction, are available at: http://datamining.xmu.edu.cn/main/~cwc/ProteinPredict.html.
Kashtanov, Stepan; Borcherds, Wade; Wu, Hongwei; Daughdrill, Gary W; Ytreberg, F Marty
2012-01-01
The chemical shifts of backbone atoms in polypeptides are sensitive to the dihedral angles phi and psi and can be used to estimate transient secondary structure and to generate structural ensembles of intrinsically disordered proteins (IDPs). In this chapter, several of the random coil reference databases used to estimate transient secondary structure are described, and the procedure is outlined for using these databases to estimate transient secondary structure. A new protocol is also presented for generating a diverse ensemble of structures for an IDP and reweighting these structures to optimize the fit between simulated and experimental chemical shift values.
Energy Technology Data Exchange (ETDEWEB)
Hernandez, R.; Miller, W.H.; Moore, C.B. (Department of Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720 (United States)); Polik, W.F. (Department of Chemistry, Hope College, Holland, Michigan 49423 (United States))
1993-07-15
A previously developed random matrix/transition state theory (RM/TST) model for the probability distribution of state-specific unimolecular decay rates has been generalized to incorporate total angular momentum conservation and other dynamical symmetries. The model is made into a predictive theory by using a semiclassical method to determine the transmission probabilities of a nonseparable rovibrational Hamiltonian at the transition state. The overall theory gives a good description of the state-specific rates for the D[sub 2]CO[r arrow]D[sub 2]+CO unimolecular decay; in particular, it describes the dependence of the distribution of rates on total angular momentum [ital J]. Comparison of the experimental values with results of the RM/TST theory suggests that there is mixing among the rovibrational states.
An Adjoint-Based Adaptive Ensemble Kalman Filter
Song, Hajoon
2013-10-01
A new hybrid ensemble Kalman filter/four-dimensional variational data assimilation (EnKF/4D-VAR) approach is introduced to mitigate background covariance limitations in the EnKF. The work is based on the adaptive EnKF (AEnKF) method, which bears a strong resemblance to the hybrid EnKF/three-dimensional variational data assimilation (3D-VAR) method. In the AEnKF, the representativeness of the EnKF ensemble is regularly enhanced with new members generated after back projection of the EnKF analysis residuals to state space using a 3D-VAR [or optimal interpolation (OI)] scheme with a preselected background covariance matrix. The idea here is to reformulate the transformation of the residuals as a 4D-VAR problem, constraining the new member with model dynamics and the previous observations. This should provide more information for the estimation of the new member and reduce dependence of the AEnKF on the assumed stationary background covariance matrix. This is done by integrating the analysis residuals backward in time with the adjoint model. Numerical experiments are performed with the Lorenz-96 model under different scenarios to test the new approach and to evaluate its performance with respect to the EnKF and the hybrid EnKF/3D-VAR. The new method leads to the least root-mean-square estimation errors as long as the linear assumption guaranteeing the stability of the adjoint model holds. It is also found to be less sensitive to choices of the assimilation system inputs and parameters.
Mondrian Forests: Efficient Online Random Forests
Lakshminarayanan, Balaji; Roy, Daniel M.; Teh, Yee Whye
2014-01-01
Ensembles of randomized decision trees, usually referred to as random forests, are widely used for classification and regression tasks in machine learning and statistics. Random forests achieve competitive predictive performance and are computationally efficient to train and test, making them excellent candidates for real-world prediction tasks. The most popular random forest variants (such as Breiman's random forest and extremely randomized trees) operate on batches of training data. Online ...
Ensemble of randomized soft decision trees for robust classification
Indian Academy of Sciences (India)
G KISHOR KUMAR
τ + w/2 then it belongs to fuzzy block B2 called with a linguistic variable “tall”, otherwise it belongs to both fuzzy blocks “short” and “tall” with some fuzzy membership val- ues as shown in figure 1(b) where w is overlapping width of two fuzzy blocks “short” and “tall”. The fuzzy membership value can be calculated as follows.
Ensemble of randomized soft decision trees for robust classification
Indian Academy of Sciences (India)
For classification, decision trees have become very popular because of its simplicity, interpret-ability and good performance. To induce a decision tree classifier for data having continuous valued attributes, the most common approach is, split the continuous attribute range into a hard (crisp) partition having two or more ...
Fast Constrained Spectral Clustering and Cluster Ensemble with Random Projection
National Research Council Canada - National Science Library
Wenfen Liu; Mao Ye; Jianghong Wei; Xuexian Hu
2017-01-01
Constrained spectral clustering (CSC) method can greatly improve the clustering accuracy with the incorporation of constraint information into spectral clustering and thus has been paid academic attention widely...
Ensemble data assimilation in the Red Sea: sensitivity to ensemble selection and atmospheric forcing
Toye, Habib
2017-05-26
We present our efforts to build an ensemble data assimilation and forecasting system for the Red Sea. The system consists of the high-resolution Massachusetts Institute of Technology general circulation model (MITgcm) to simulate ocean circulation and of the Data Research Testbed (DART) for ensemble data assimilation. DART has been configured to integrate all members of an ensemble adjustment Kalman filter (EAKF) in parallel, based on which we adapted the ensemble operations in DART to use an invariant ensemble, i.e., an ensemble Optimal Interpolation (EnOI) algorithm. This approach requires only single forward model integration in the forecast step and therefore saves substantial computational cost. To deal with the strong seasonal variability of the Red Sea, the EnOI ensemble is then seasonally selected from a climatology of long-term model outputs. Observations of remote sensing sea surface height (SSH) and sea surface temperature (SST) are assimilated every 3 days. Real-time atmospheric fields from the National Center for Environmental Prediction (NCEP) and the European Center for Medium-Range Weather Forecasts (ECMWF) are used as forcing in different assimilation experiments. We investigate the behaviors of the EAKF and (seasonal-) EnOI and compare their performances for assimilating and forecasting the circulation of the Red Sea. We further assess the sensitivity of the assimilation system to various filtering parameters (ensemble size, inflation) and atmospheric forcing.
Ensemble data assimilation in the Red Sea: sensitivity to ensemble selection and atmospheric forcing
Toye, Habib; Zhan, Peng; Gopalakrishnan, Ganesh; Kartadikaria, Aditya R.; Huang, Huang; Knio, Omar; Hoteit, Ibrahim
2017-07-01
We present our efforts to build an ensemble data assimilation and forecasting system for the Red Sea. The system consists of the high-resolution Massachusetts Institute of Technology general circulation model (MITgcm) to simulate ocean circulation and of the Data Research Testbed (DART) for ensemble data assimilation. DART has been configured to integrate all members of an ensemble adjustment Kalman filter (EAKF) in parallel, based on which we adapted the ensemble operations in DART to use an invariant ensemble, i.e., an ensemble Optimal Interpolation (EnOI) algorithm. This approach requires only single forward model integration in the forecast step and therefore saves substantial computational cost. To deal with the strong seasonal variability of the Red Sea, the EnOI ensemble is then seasonally selected from a climatology of long-term model outputs. Observations of remote sensing sea surface height (SSH) and sea surface temperature (SST) are assimilated every 3 days. Real-time atmospheric fields from the National Center for Environmental Prediction (NCEP) and the European Center for Medium-Range Weather Forecasts (ECMWF) are used as forcing in different assimilation experiments. We investigate the behaviors of the EAKF and (seasonal-) EnOI and compare their performances for assimilating and forecasting the circulation of the Red Sea. We further assess the sensitivity of the assimilation system to various filtering parameters (ensemble size, inflation) and atmospheric forcing.
DEFF Research Database (Denmark)
Ben Bouallègue, Zied; Heppelmann, Tobias; Theis, Susanne E.
2016-01-01
Probabilistic forecasts in the form of ensemble of scenarios are required for complex decision making processes. Ensemble forecasting systems provide such products but the spatio-temporal structures of the forecast uncertainty is lost when statistical calibration of the ensemble forecasts...... is applied for each lead time and location independently. Non-parametric approaches allow the reconstruction of spatio-temporal joint probability distributions at a low computational cost. For example, the ensemble copula coupling (ECC) method rebuilds the multivariate aspect of the forecast from...... the original ensemble forecasts. Based on the assumption of error stationarity, parametric methods aim to fully describe the forecast dependence structures. In this study, the concept of ECC is combined with past data statistics in order to account for the autocorrelation of the forecast error. The new...
DEFF Research Database (Denmark)
Ben Bouallègue, Zied; Heppelmann, Tobias; Theis, Susanne E.
2015-01-01
Probabilistic forecasts in the form of ensemble of scenarios are required for complex decision making processes. Ensemble forecasting systems provide such products but the spatio-temporal structures of the forecast uncertainty is lost when statistical calibration of the ensemble forecasts...... is applied for each lead time and location independently. Non-parametric approaches allow the reconstruction of spatio-temporal joint probability distributions at a low computational cost.For example, the ensemble copula coupling (ECC) method consists in rebuilding the multivariate aspect of the forecast...... from the original ensemble forecasts. Based on the assumption of error stationarity, parametric methods aim to fully describe the forecast dependence structures. In this study, the concept of ECC is combined with past data statistics in order to account for the autocorrelation of the forecast error...
Pseudosymmetric random matrices: Semi-Poisson and sub-Wigner statistics
Kumar, Sachin; Ahmed, Zafar
2017-08-01
Real nonsymmetric matrices may have either real or complex conjugate eigenvalues. These matrices can be seen to be pseudosymmetric as η M η-1=Mt , where the metric η could be secular (a constant matrix) or depending upon the matrix elements of M . Here we construct ensembles of a large number N of pseudosymmetric n ×n (n large) matrices using N [n (n +1 ) /2 ≤N ≤n2] independent and identically distributed random numbers as their elements. Based on our numerical calculations, we conjecture that for these ensembles the nearest level spacing distributions [NLSDs, p (s )] are sub-Wigner as pa b c(s ) =a s e-b sc(0 topological transitions in a Josephson junction. Interestingly, p (s ) for c =1 is called semi-Poisson, and we show that it lies close to the form p (s ) =0.59 s K0(0.45 s2) derived for the case of 2 ×2 pseudosymmetric matrix where the eigenvalues are most aptly conditionally real, E1 ,2=a ±√{b2-c2 } , which represent characteristic coalescing of eigenvalues in parity-time (PT) -symmetric systems.
Pseudosymmetric random matrices: Semi-Poisson and sub-Wigner statistics.
Kumar, Sachin; Ahmed, Zafar
2017-08-01
Real nonsymmetric matrices may have either real or complex conjugate eigenvalues. These matrices can be seen to be pseudosymmetric as ηMη^{-1}=M^{t}, where the metric η could be secular (a constant matrix) or depending upon the matrix elements of M. Here we construct ensembles of a large number N of pseudosymmetric n×n (n large) matrices using N[n(n+1)/2≤N≤n^{2}] independent and identically distributed random numbers as their elements. Based on our numerical calculations, we conjecture that for these ensembles the nearest level spacing distributions [NLSDs, p(s)] are sub-Wigner as p_{abc}(s)=ase^{-bs^{c}}(0distributions of their eigenvalues fit well to D(ε)=A[tanh{(ε+B)/C}-tanh{(ε-B)/C}] (exceptions also discussed). These sub-Wigner NLSDs are encountered in Anderson metal-insulator transition and topological transitions in a Josephson junction. Interestingly, p(s) for c=1 is called semi-Poisson, and we show that it lies close to the form p(s)=0.59sK_{0}(0.45s^{2}) derived for the case of 2×2 pseudosymmetric matrix where the eigenvalues are most aptly conditionally real, E_{1,2}=a±sqrt[b^{2}-c^{2}], which represent characteristic coalescing of eigenvalues in parity-time (PT) -symmetric systems.
Directory of Open Access Journals (Sweden)
David eVasmer
2014-05-01
Full Text Available Drosophila represents a model organism to analyze neuronal mechanisms underlying learning and memory. Kenyon cells of the Drosophila mushroom body are required for associative odor learning and memory retrieval. But is the mushroom body sufficient to acquire and retrieve an associative memory? To answer this question we have conceived an experimental approach to bypass olfactory sensory input and to thermogenetically activate sparse and random ensembles of Kenyon cells directly. We found that if the artifical activation of Kenyon cell ensembles coincides with a salient, aversive stimulus learning was induced The animals adjusted their behavior in a subsequent test situation and actively avoided reactivation of these Kenyon cells. Our results show that Kenyon cell activity in coincidence with a salient aversive stimulus can suffice to form an associative memory. Memory retrieval is characterized by a closed feedback loop between a behavioral action and the reactivation of sparse ensembles of Kenyon cells.
Directory of Open Access Journals (Sweden)
Mohammad Nazmul Haque
Full Text Available Classification of datasets with imbalanced sample distributions has always been a challenge. In general, a popular approach for enhancing classification performance is the construction of an ensemble of classifiers. However, the performance of an ensemble is dependent on the choice of constituent base classifiers. Therefore, we propose a genetic algorithm-based search method for finding the optimum combination from a pool of base classifiers to form a heterogeneous ensemble. The algorithm, called GA-EoC, utilises 10 fold-cross validation on training data for evaluating the quality of each candidate ensembles. In order to combine the base classifiers decision into ensemble's output, we used the simple and widely used majority voting approach. The proposed algorithm, along with the random sub-sampling approach to balance the class distribution, has been used for classifying class-imbalanced datasets. Additionally, if a feature set was not available, we used the (α, β - k Feature Set method to select a better subset of features for classification. We have tested GA-EoC with three benchmarking datasets from the UCI-Machine Learning repository, one Alzheimer's disease dataset and a subset of the PubFig database of Columbia University. In general, the performance of the proposed method on the chosen datasets is robust and better than that of the constituent base classifiers and many other well-known ensembles. Based on our empirical study we claim that a genetic algorithm is a superior and reliable approach to heterogeneous ensemble construction and we expect that the proposed GA-EoC would perform consistently in other cases.
Multiscale macromolecular simulation: role of evolving ensembles.
Singharoy, A; Joshi, H; Ortoleva, P J
2012-10-22
Multiscale analysis provides an algorithm for the efficient simulation of macromolecular assemblies. This algorithm involves the coevolution of a quasiequilibrium probability density of atomic configurations and the Langevin dynamics of spatial coarse-grained variables denoted order parameters (OPs) characterizing nanoscale system features. In practice, implementation of the probability density involves the generation of constant OP ensembles of atomic configurations. Such ensembles are used to construct thermal forces and diffusion factors that mediate the stochastic OP dynamics. Generation of all-atom ensembles at every Langevin time step is computationally expensive. Here, multiscale computation for macromolecular systems is made more efficient by a method that self-consistently folds in ensembles of all-atom configurations constructed in an earlier step, history, of the Langevin evolution. This procedure accounts for the temporal evolution of these ensembles, accurately providing thermal forces and diffusions. It is shown that efficiency and accuracy of the OP-based simulations is increased via the integration of this historical information. Accuracy improves with the square root of the number of historical timesteps included in the calculation. As a result, CPU usage can be decreased by a factor of 3-8 without loss of accuracy. The algorithm is implemented into our existing force-field based multiscale simulation platform and demonstrated via the structural dynamics of viral capsomers.
The Hydrologic Ensemble Prediction Experiment (HEPEX)
Wood, A. W.; Thielen, J.; Pappenberger, F.; Schaake, J. C.; Hartman, R. K.
2012-12-01
The Hydrologic Ensemble Prediction Experiment was established in March, 2004, at a workshop hosted by the European Center for Medium Range Weather Forecasting (ECMWF). With support from the US National Weather Service (NWS) and the European Commission (EC), the HEPEX goal was to bring the international hydrological and meteorological communities together to advance the understanding and adoption of hydrological ensemble forecasts for decision support in emergency management and water resources sectors. The strategy to meet this goal includes meetings that connect the user, forecast producer and research communities to exchange ideas, data and methods; the coordination of experiments to address specific challenges; and the formation of testbeds to facilitate shared experimentation. HEPEX has organized about a dozen international workshops, as well as sessions at scientific meetings (including AMS, AGU and EGU) and special issues of scientific journals where workshop results have been published. Today, the HEPEX mission is to demonstrate the added value of hydrological ensemble prediction systems (HEPS) for emergency management and water resources sectors to make decisions that have important consequences for economy, public health, safety, and the environment. HEPEX is now organised around six major themes that represent core elements of a hydrologic ensemble prediction enterprise: input and pre-processing, ensemble techniques, data assimilation, post-processing, verification, and communication and use in decision making. This poster presents an overview of recent and planned HEPEX activities, highlighting case studies that exemplify the focus and objectives of HEPEX.
An ensemble framework for identifying essential proteins.
Zhang, Xue; Xiao, Wangxin; Acencio, Marcio Luis; Lemke, Ney; Wang, Xujing
2016-08-25
Many centrality measures have been proposed to mine and characterize the correlations between network topological properties and protein essentiality. However, most of them show limited prediction accuracy, and the number of common predicted essential proteins by different methods is very small. In this paper, an ensemble framework is proposed which integrates gene expression data and protein-protein interaction networks (PINs). It aims to improve the prediction accuracy of basic centrality measures. The idea behind this ensemble framework is that different protein-protein interactions (PPIs) may show different contributions to protein essentiality. Five standard centrality measures (degree centrality, betweenness centrality, closeness centrality, eigenvector centrality, and subgraph centrality) are integrated into the ensemble framework respectively. We evaluated the performance of the proposed ensemble framework using yeast PINs and gene expression data. The results show that it can considerably improve the prediction accuracy of the five centrality measures individually. It can also remarkably increase the number of common predicted essential proteins among those predicted by each centrality measure individually and enable each centrality measure to find more low-degree essential proteins. This paper demonstrates that it is valuable to differentiate the contributions of different PPIs for identifying essential proteins based on network topological characteristics. The proposed ensemble framework is a successful paradigm to this end.
Meller, Laura; Cabeza, Mar; Pironon, Samuel; Barbet-Massin, Morgane; Maiorano, Luigi; Georges, Damien; Thuiller, Wilfried
2014-01-01
Aim Conservation planning exercises increasingly rely on species distributions predicted either from one particular statistical model or, more recently, from an ensemble of models (i.e. ensemble forecasting). However, it has not yet been explored how different ways of summarizing ensemble predictions affect conservation planning outcomes. We evaluate these effects and compare commonplace consensus methods, applied before the conservation prioritization phase, to a novel method that applies consensus after reserve selection. Location Europe. Methods We used an ensemble of predicted distributions of 146 Western Palaearctic bird species in alternative ways: four different consensus methods, as well as distributions discounted with variability, were used to produce inputs for spatial conservation prioritization. In addition, we developed and tested a novel method, in which we built 100 datasets by sampling the ensemble of predicted distributions, ran a conservation prioritization analysis on each of them and averaged the resulting priority ranks. We evaluated the conservation outcome against three controls: (i) a null control, based on random ranking of cells; (2) the reference solution, based on an expert-refined dataset; and (3) the independent solution, based on an independent dataset. Results Networks based on predicted distributions were more representative of rare species than randomly selected networks. Alternative methods to summarize ensemble predictions differed in representativeness of resulting reserve networks. Our novel method resulted in better representation of rare species than pre-selection consensus methods. Main conclusions Retaining information about the variation in the predicted distributions throughout the conservation prioritization seems to provide better results than summarizing the predictions before conservation prioritization. Our results highlight the need to understand and consider model-based uncertainty when using predicted
The ensemble variance of pure-tone measurements in reverberation rooms
DEFF Research Database (Denmark)
Jacobsen, Finn; Molares, Alfonso Rodriguez
2010-01-01
Reverberation rooms are often used for measuring the sound power emitted by sources of sound. At medium and high frequencies, where the modal overlap is high, a fairly simple model based on sums of waves from random directions having random phase relations gives good predictions of the ensemble...... statistics of measurements in such rooms. Below the Schroeder frequency, the relative variance is much larger, particularly if the source emits a pure-tone. The established theory for this frequency range is based on ensemble statistics of modal sums and requires knowledge of mode shapes and the distribution...... of modal frequencies. This paper extends the far simpler random wave theory to low frequencies. The two theories are compared, and their predictions are found to compare well with experimental and numerical results....
Directory of Open Access Journals (Sweden)
Jennifer R Stapleton
2007-10-01
Full Text Available The gustatory cortex (GC processes chemosensory and somatosensory information and is involved in learning and anticipation. Previously we found that a subpopulation of GC neurons responded to tastants in a single lick (Stapleton et al., 2006. Here we extend this investigation to determine if small ensembles of GC neurons, obtained while rats received blocks of tastants on a fixed ratio schedule (FR5, can discriminate between tastants and their concentrations after a single 50 µL delivery. In the FR5 schedule subjects received tastants every fifth (reinforced lick and the intervening licks were unreinforced. The ensemble firing patterns were analyzed with a Bayesian generalized linear model whose parameters included the firing rates and temporal patterns of the spike trains. We found that when both the temporal and rate parameters were included, 12 of 13 ensembles correctly identified single tastant deliveries. We also found that the activity during the unreinforced licks contained signals regarding the identity of the upcoming tastant, which suggests that GC neurons contain anticipatory information about the next tastant delivery. To support this finding we performed experiments in which tastant delivery was randomized within each block and found that the neural activity following the unreinforced licks did not predict the upcoming tastant. Collectively, these results suggest that after a single lick ensembles of GC neurons can discriminate between tastants, that they may utilize both temporal and rate information, and when the tastant delivery is repetitive ensembles contain information about the identity of the upcoming tastant delivery.
An Intelligent Ensemble Neural Network Model for Wind Speed Prediction in Renewable Energy Systems
Ranganayaki, V.; Deepa, S. N.
2016-01-01
Various criteria are proposed to select the number of hidden neurons in artificial neural network (ANN) models and based on the criterion evolved an intelligent ensemble neural network model is proposed to predict wind speed in renewable energy applications. The intelligent ensemble neural model based wind speed forecasting is designed by averaging the forecasted values from multiple neural network models which includes multilayer perceptron (MLP), multilayer adaptive linear neuron (Madaline), back propagation neural network (BPN), and probabilistic neural network (PNN) so as to obtain better accuracy in wind speed prediction with minimum error. The random selection of hidden neurons numbers in artificial neural network results in overfitting or underfitting problem. This paper aims to avoid the occurrence of overfitting and underfitting problems. The selection of number of hidden neurons is done in this paper employing 102 criteria; these evolved criteria are verified by the computed various error values. The proposed criteria for fixing hidden neurons are validated employing the convergence theorem. The proposed intelligent ensemble neural model is applied for wind speed prediction application considering the real time wind data collected from the nearby locations. The obtained simulation results substantiate that the proposed ensemble model reduces the error value to minimum and enhances the accuracy. The computed results prove the effectiveness of the proposed ensemble neural network (ENN) model with respect to the considered error factors in comparison with that of the earlier models available in the literature. PMID:27034973
An Intelligent Ensemble Neural Network Model for Wind Speed Prediction in Renewable Energy Systems.
Ranganayaki, V; Deepa, S N
2016-01-01
Various criteria are proposed to select the number of hidden neurons in artificial neural network (ANN) models and based on the criterion evolved an intelligent ensemble neural network model is proposed to predict wind speed in renewable energy applications. The intelligent ensemble neural model based wind speed forecasting is designed by averaging the forecasted values from multiple neural network models which includes multilayer perceptron (MLP), multilayer adaptive linear neuron (Madaline), back propagation neural network (BPN), and probabilistic neural network (PNN) so as to obtain better accuracy in wind speed prediction with minimum error. The random selection of hidden neurons numbers in artificial neural network results in overfitting or underfitting problem. This paper aims to avoid the occurrence of overfitting and underfitting problems. The selection of number of hidden neurons is done in this paper employing 102 criteria; these evolved criteria are verified by the computed various error values. The proposed criteria for fixing hidden neurons are validated employing the convergence theorem. The proposed intelligent ensemble neural model is applied for wind speed prediction application considering the real time wind data collected from the nearby locations. The obtained simulation results substantiate that the proposed ensemble model reduces the error value to minimum and enhances the accuracy. The computed results prove the effectiveness of the proposed ensemble neural network (ENN) model with respect to the considered error factors in comparison with that of the earlier models available in the literature.
Statistical ensembles and fragmentation of finite nuclei
Das, P.; Mallik, S.; Chaudhuri, G.
2017-09-01
Statistical models based on different ensembles are very commonly used to describe the nuclear multifragmentation reaction in heavy ion collisions at intermediate energies. Canonical model results are more appropriate for finite nuclei calculations while those obtained from the grand canonical ones are more easily calculable. A transformation relation has been worked out for converting results of finite nuclei from grand canonical to canonical and vice versa. The formula shows that, irrespective of the particle number fluctuation in the grand canonical ensemble, exact canonical results can be recovered for observables varying linearly or quadratically with the number of particles. This result is of great significance since the baryon and charge conservation constraints can make the exact canonical calculations extremely difficult in general. This concept developed in this work can be extended in future for transformation to ensembles where analytical solutions do not exist. The applicability of certain equations (isoscaling, etc.) in the regime of finite nuclei can also be tested using this transformation relation.
Total probabilities of ensemble runoff forecasts
Olav Skøien, Jon; Bogner, Konrad; Salamon, Peter; Smith, Paul; Pappenberger, Florian
2017-04-01
Ensemble forecasting has a long history from meteorological modelling, as an indication of the uncertainty of the forecasts. However, it is necessary to calibrate and post-process the ensembles as the they often exhibit both bias and dispersion errors. Two of the most common methods for this are Bayesian Model Averaging (Raftery et al., 2005) and Ensemble Model Output Statistics (EMOS) (Gneiting et al., 2005). There are also methods for regionalizing these methods (Berrocal et al., 2007) and for incorporating the correlation between lead times (Hemri et al., 2013). Engeland and Steinsland Engeland and Steinsland (2014) developed a framework which can estimate post-processing parameters varying in space and time, while giving a spatially and temporally consistent output. However, their method is computationally complex for our larger number of stations, which makes it unsuitable for our purpose. Our post-processing method of the ensembles is developed in the framework of the European Flood Awareness System (EFAS - http://www.efas.eu), where we are making forecasts for whole Europe, and based on observations from around 700 catchments. As the target is flood forecasting, we are also more interested in improving the forecast skill for high-flows rather than in a good prediction of the entire flow regime. EFAS uses a combination of ensemble forecasts and deterministic forecasts from different meteorological forecasters to force a distributed hydrologic model and to compute runoff ensembles for each river pixel within the model domain. Instead of showing the mean and the variability of each forecast ensemble individually, we will now post-process all model outputs to estimate the total probability, the post-processed mean and uncertainty of all ensembles. The post-processing parameters are first calibrated for each calibration location, but we are adding a spatial penalty in the calibration process to force a spatial correlation of the parameters. The penalty takes
Ensemble simulations with discrete classical dynamics
DEFF Research Database (Denmark)
Toxværd, Søren
2013-01-01
{E}(h)$ is employed to determine the relation with the corresponding energy, $E$ for the analytic dynamics with $h=0$ and the zero-order estimate $E_0(h)$ of the energy for discrete dynamics, appearing in the literature for MD with VA. We derive a corresponding time reversible VA algorithm for canonical dynamics...... for the $(NV\\tilde{T}(h))$ ensemble and determine the relations between the energies and temperatures for the different ensembles, including the $(NVE_0(h))$ and $(NVT_0(h))$ ensembles. The differences in the energies and temperatures are proportional with $h^2$ and they are of the order a few tenths...... of a percent for a traditional value of $h$. The relations between $(NV\\tilde{E}(h))$ and $(NVE)$, and $(NV\\tilde{T}(h))$ and $(NVT)$ are easily determined for a given density and temperature, and allows for using larger time increments in MD. The accurate determinations of the energies are used to determine...
Bhatia, Rajendra
1997-01-01
A good part of matrix theory is functional analytic in spirit. This statement can be turned around. There are many problems in operator theory, where most of the complexities and subtleties are present in the finite-dimensional case. My purpose in writing this book is to present a systematic treatment of methods that are useful in the study of such problems. This book is intended for use as a text for upper division and gradu ate courses. Courses based on parts of the material have been given by me at the Indian Statistical Institute and at the University of Toronto (in collaboration with Chandler Davis). The book should also be useful as a reference for research workers in linear algebra, operator theory, mathe matical physics and numerical analysis. A possible subtitle of this book could be Matrix Inequalities. A reader who works through the book should expect to become proficient in the art of deriving such inequalities. Other authors have compared this art to that of cutting diamonds. One first has to...
Cluster ensembles, quantization and the dilogarithm
DEFF Research Database (Denmark)
Fock, Vladimir; Goncharov, Alexander B.
2009-01-01
A cluster ensemble is a pair of positive spaces (i.e. varieties equipped with positive atlases), coming with an action of a symmetry group . The space is closely related to the spectrum of a cluster algebra [ 12 ]. The two spaces are related by a morphism . The space is equipped with a closed -form......, possibly degenerate, and the space has a Poisson structure. The map is compatible with these structures. The dilogarithm together with its motivic and quantum avatars plays a central role in the cluster ensemble structure. We define a non-commutative -deformation of the -space. When is a root of unity...