Semi-Supervised Half-Quadratic Nonnegative Matrix Factorization for Face Recognition
Alghamdi, Masheal M.
2014-05-01
Face recognition is a challenging problem in computer vision. Difficulties such as slight differences between similar faces of different people, changes in facial expressions, light and illumination condition, and pose variations add extra complications to the face recognition research. Many algorithms are devoted to solving the face recognition problem, among which the family of nonnegative matrix factorization (NMF) algorithms has been widely used as a compact data representation method. Different versions of NMF have been proposed. Wang et al. proposed the graph-based semi-supervised nonnegative learning (S2N2L) algorithm that uses labeled data in constructing intrinsic and penalty graph to enforce separability of labeled data, which leads to a greater discriminating power. Moreover the geometrical structure of labeled and unlabeled data is preserved through using the smoothness assumption by creating a similarity graph that conserves the neighboring information for all labeled and unlabeled data. However, S2N2L is sensitive to light changes, illumination, and partial occlusion. In this thesis, we propose a Semi-Supervised Half-Quadratic NMF (SSHQNMF) algorithm that combines the benefits of S2N2L and the robust NMF by the half- quadratic minimization (HQNMF) algorithm.Our algorithm improves upon the S2N2L algorithm by replacing the Frobenius norm with a robust M-Estimator loss function. A multiplicative update solution for our SSHQNMF algorithmis driven using the half- 4 quadratic (HQ) theory. Extensive experiments on ORL, Yale-A and a subset of the PIE data sets for nine M-estimator loss functions for both SSHQNMF and HQNMF algorithms are investigated, and compared with several state-of-the-art supervised and unsupervised algorithms, along with the original S2N2L algorithm in the context of classification, clustering, and robustness against partial occlusion. The proposed algorithm outperformed the other algorithms. Furthermore, SSHQNMF with Maximum Correntropy
Unidimensional nonnegative scaling for genome-wide linkage disequilibrium maps.
Liao, Haiyong; Ng, Michael; Fung, Eric; Sham, Pak C
2008-01-01
The main aim of this paper is to propose and develop a unidimensional nonnegative scaling model to construct Linkage Disequilibrium (LD) maps. The proposed constrained scaling model can be efficiently solved by transforming it to an unconstrained model. The method is implemented in PC Clusters at Hong Kong Baptist University. The LD maps are constructed for four populations from Hapmap data sets with chromosomes of several ten thousand Single Nucleotide Polymorphisms (SNPs). The similarities and dissimilarities of the LD maps are studied and analysed. Computational results are also reported to show the effectiveness of the method using parallel computation.
Combinatorics on Words in Symbolic Dynamics: The Quadratic Map
Institute of Scientific and Technical Information of China (English)
Wan Ji DAI; Kebo L(U); Jun WANG
2008-01-01
This paper is contributed to the combinatorial properties of the MSS sequences, which are the periodic kneading words of quadratic maps denned on a interval. An explicit expression of adjacency relations on MSS sequences of given lengths is established.
SOME DYNAMICAL PROPERTIES OF QUADRATIC RATIONAL MAPS
Institute of Scientific and Technical Information of China (English)
YINYONGCHENG
1994-01-01
This paper studies the dynamics of the analytic family z+1/z+b and describes the topology of the parameter space, structural stability and J-stability. The mapping class group of almost all maps of the above family is determined.
Large Deviation Principle for Benedicks-Carleson Quadratic Maps
Chung, Yong Moo; Takahasi, Hiroki
2012-11-01
Since the pioneering works of Jakobson and Benedicks & Carleson and others, it has been known that a positive measure set of quadratic maps admit invariant probability measures absolutely continuous with respect to Lebesgue. These measures allow one to statistically predict the asymptotic fate of Lebesgue almost every initial condition. Estimating fluctuations of empirical distributions before they settle to equilibrium requires a fairly good control over large parts of the phase space. We use the sub-exponential slow recurrence condition of Benedicks & Carleson to build induced Markov maps of arbitrarily small scale and associated towers, to which the absolutely continuous measures can be lifted. These various lifts together enable us to obtain a control of recurrence that is sufficient to establish a level 2 large deviation principle, for the absolutely continuous measures. This result encompasses dynamics far from equilibrium, and thus significantly extends presently known local large deviations results for quadratic maps.
On the continuity of the map square root of nonnegative isomorphisms in Hilbert spaces
Directory of Open Access Journals (Sweden)
Jeovanny de Jesus Muentes Acevedo
2015-06-01
Full Text Available Let H be a real (or complex Hilbert space. Every nonnegative operator L ∈ L(H admits a unique nonnegative square root R ∈ L(H, i.e., a nonnegative operator R ∈ L(H such that R2 = L. Let GL+ S (H be the set of nonnegative isomorphisms in L(H. First we will show that GL+ S (H is a convex (real Banach manifold. Denoting by L1/2 the nonnegative square root of L. In [3], Richard Bouldin proves that L1/2 depends continuously on L (this proof is non-trivial. This result has several applications. For example, it is used to find the polar decomposition of a bounded operator. This polar decomposition allows us to determine the positive and negative spectral subespaces of any self-adjoint operator, and moreover, allows us to define the Maslov index. The autor of the paper under review provides an alternative proof (and a little more simplified that L1/2 depends continuously on L, and moreover, he shows that the map is a homeomorphism. Resumen. Sea H un espacio de Hilbert real (o complejo. Todo operador no negativo L ∈ L(H admite una única raíz cuadrada no negativa R ∈ L(H, esto es, un operador no negativo R ∈ L(H tal que R2 = L. Sea GL+ S (H el conjunto de los isomorfismos no negativos en L(H. Primero probaremos que GL+ S (H es una variedad de Banach (real. Denotando como L1/2 la raíz cuadrada no negativa de L, en [3] Richard Bouldin prueba que L1/2 depende continuamente de L (esta prueba es no trivial. Este resultado tiene varias aplicaciones. Por ejemplo, es usado para encontrar la descomposición polar de un operador limitado. Esta descomposición polar nos lleva a determinar los subespacios espectrales positivos y negativos de cualquier operador autoadjunto, y además, lleva a definir el índice de Máslov. El autor de este artículo da una prueba alternativa (y un poco más simplificada de que L1/2 depende continuamente de L, y además, prueba que la aplicación es un homeomorfismo
Directory of Open Access Journals (Sweden)
Ruiqi Liao
2014-02-01
Full Text Available In the past decades, advances in high-throughput technologies have led to the generation of huge amounts of biological data that require analysis and interpretation. Recently, nonnegative matrix factorization (NMF has been introduced as an efficient way to reduce the complexity of data as well as to interpret them, and has been applied to various fields of biological research. In this paper, we present CloudNMF, a distributed open-source implementation of NMF on a MapReduce framework. Experimental evaluation demonstrated that CloudNMF is scalable and can be used to deal with huge amounts of data, which may enable various kinds of a high-throughput biological data analysis in the cloud. CloudNMF is freely accessible at http://admis.fudan.edu.cn/projects/CloudNMF.html.
Liao, Ruiqi; Zhang, Yifan; Guan, Jihong; Zhou, Shuigeng
2014-02-01
In the past decades, advances in high-throughput technologies have led to the generation of huge amounts of biological data that require analysis and interpretation. Recently, nonnegative matrix factorization (NMF) has been introduced as an efficient way to reduce the complexity of data as well as to interpret them, and has been applied to various fields of biological research. In this paper, we present CloudNMF, a distributed open-source implementation of NMF on a MapReduce framework. Experimental evaluation demonstrated that CloudNMF is scalable and can be used to deal with huge amounts of data, which may enable various kinds of a high-throughput biological data analysis in the cloud. CloudNMF is freely accessible at http://admis.fudan.edu.cn/projects/CloudNMF.html.
Alternative quadratic programming for non-negative matrix low-order factorization%非负矩阵低秩分解的交替二次规划算法
Institute of Scientific and Technical Information of China (English)
阳明盛; 刘力军
2014-01-01
非负矩阵分解算法有多种，但都存在着各自的缺陷。在现有工作的基础上，将非负矩阵分解(NMF)模型转化为一组(两个)二次凸规划模型，利用二次凸规划有解的充分必要条件推导出迭代公式，进行交替迭代，可求出问题的解。得到的解不仅具有某种最优性、稀疏性，还避免了约束非线性规划求解的复杂过程和大量的计算。证明了迭代的收敛性，且收敛速度快于已知的方法，对于大规模数据模型尤能显示出其优越性。%Many algorithms are available for solving the problem of non-negative matrix factorization (NMF)despite respective shortcomings.Based on existing works,NMF model is transformed into one group of (two ) convex quadratic programming model. Using the sufficient and necessary conditions for quadratic programming problems,iteration formula for NMF is obtained by which the problem is solved after alternative iteration process.The obtained solution reaches its optimality and sparseness while avoiding computational burden and complexity for solving constrained nonlinear programming problems.The iteration convergence can be proved easily and its speed is faster than that of existing approaches.The proposed approach has its superority for large-scale data model.
A Simple Chaotic Image Cryptography Algorithm Based on New Quadratic Chaotic Map
Directory of Open Access Journals (Sweden)
Saad Muhi Falih
2017-07-01
Full Text Available The chaos based cryptographic methods have been suggested some new and efficient algorithms to develop image encryption techniques because of its exceptionally desirable properties of sensitivity to initial condition and parameters of chaotic map. However, this paper proposes a new symmetric image encryption system (SIES that based on a new class of quadratic chaotic map. In this proposed scheme, the image is converted to a stream of serial bits which modulo-2 added with the stream of binary chaotic sequence generated using a new class of quadratic chaotic map. Finally, the proposed system is tested under Matlab environment and results show that the proposed technique is efficient and has high security features.
Message-Passing Algorithms for Quadratic Programming Formulations of MAP Estimation
Kumar, Akshat
2012-01-01
Computing maximum a posteriori (MAP) estimation in graphical models is an important inference problem with many applications. We present message-passing algorithms for quadratic programming (QP) formulations of MAP estimation for pairwise Markov random fields. In particular, we use the concave-convex procedure (CCCP) to obtain a locally optimal algorithm for the non-convex QP formulation. A similar technique is used to derive a globally convergent algorithm for the convex QP relaxation of MAP. We also show that a recently developed expectation-maximization (EM) algorithm for the QP formulation of MAP can be derived from the CCCP perspective. Experiments on synthetic and real-world problems confirm that our new approach is competitive with max-product and its variations. Compared with CPLEX, we achieve more than an order-of-magnitude speedup in solving optimally the convex QP relaxation.
Strictly nonnegative tensors and nonnegative tensor partition
Institute of Scientific and Technical Information of China (English)
HU ShengLong; HUANG ZhengHai; QI LiQun
2014-01-01
We introduce a new class of nonnegative tensors—strictly nonnegative tensors.A weakly irreducible nonnegative tensor is a strictly nonnegative tensor but not vice versa.We show that the spectral radius of a strictly nonnegative tensor is always positive.We give some necessary and su？cient conditions for the six wellconditional classes of nonnegative tensors,introduced in the literature,and a full relationship picture about strictly nonnegative tensors with these six classes of nonnegative tensors.We then establish global R-linear convergence of a power method for finding the spectral radius of a nonnegative tensor under the condition of weak irreducibility.We show that for a nonnegative tensor T,there always exists a partition of the index set such that every tensor induced by the partition is weakly irreducible;and the spectral radius of T can be obtained from those spectral radii of the induced tensors.In this way,we develop a convergent algorithm for finding the spectral radius of a general nonnegative tensor without any additional assumption.Some preliminary numerical results show the feasibility and effectiveness of the algorithm.
The dynamics of a symmetric coupling of three modified quadratic maps
Institute of Scientific and Technical Information of China (English)
Paulo C.Rech
2013-01-01
We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms,and identify various interesting features as a function of two control parameters.In particular,we investigate the emergence of quasiperiodic states arising from Naimark-Sacker bifurcations of stable period-1,period-2,and period-3 orbits.We also investigate the multistability in the same coupling.Lyapunov exponents,parameter planes,phase space portraits,and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states,from quasiperiodic to mode-locked states and to chaotic states,and from chaotic to hyperchaotic states.
Fixed points for alpha-psi contractive mappings with an application to quadratic integral equations
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Bessem Samet
2014-06-01
Full Text Available Recently, Samet et al [24] introduced the concept of alpha-psi contractive mappings and studied the existence of fixed points for such mappings. In this article, we prove three fixed point theorems for this class of operators in complete metric spaces. Our results extend the results in [24] and well known fixed point theorems due to Banach, Kannan, Chatterjea, Zamfirescu, Berinde, Suzuki, Ciric, Nieto, Lopez, and many others. We prove that alpha-psi contractions unify large classes of contractive type operators, whose fixed points can be obtained by means of the Picard iteration. Finally, we utilize our results to discuss the existence and uniqueness of solutions to a class of quadratic integral equations.
Fernández-Guasti, M.
The quadratic iteration is mapped within a nondistributive imaginary scator algebra in 1 + 2 dimensions. The Mandelbrot set is identically reproduced at two perpendicular planes where only the scalar and one of the hypercomplex scator director components are present. However, the bound three-dimensional S set projections change dramatically even for very small departures from zero of the second hypercomplex plane. The S set exhibits a rich fractal-like boundary in three dimensions. Periodic points with period m, are shown to be necessarily surrounded by points that produce a divergent magnitude after m iterations. The scator set comprises square nilpotent elements that ineluctably belong to the bound set. Points that are square nilpotent on the mth iteration, have preperiod 1 and period m. Two-dimensional plots are presented to show some of the main features of the set. A three-dimensional rendering reveals the highly complex structure of its boundary.
Soelter, Jan; Schumacher, Jan; Spors, Hartwig; Schmuker, Michael
2014-09-01
Segmentation of functional parts in image series of functional activity is a common problem in neuroscience. Here we apply regularized non-negative matrix factorization (rNMF) to extract glomeruli in intrinsic optical signal (IOS) images of the olfactory bulb. Regularization allows us to incorporate prior knowledge about the spatio-temporal characteristics of glomerular signals. We demonstrate how to identify suitable regularization parameters on a surrogate dataset. With appropriate regularization segmentation by rNMF is more resilient to noise and requires fewer observations than conventional spatial independent component analysis (sICA). We validate our approach in experimental data using anatomical outlines of glomeruli obtained by 2-photon imaging of resting synapto-pHluorin fluorescence. Taken together, we show that rNMF provides a straightforward method for problem tailored source separation that enables reliable automatic segmentation of functional neural images, with particular benefit in situations with low signal-to-noise ratio as in IOS imaging.
A model for the parabolic slices Per1(e2πip/q) in moduli space of quadratic rational maps
DEFF Research Database (Denmark)
Uhre, Eva
2010-01-01
The notion of relatedness loci in the parabolic slices Per1(e2πip/q) in moduli space of quadratic rational maps is introduced. They are counterparts of the disconnectedness or escape locus in the slice of quadratic polynomials. A model for these loci is presented, and a strategy of proof of the f...
Takahasi, Hiroki
2016-09-01
It is well-known that the geometric pressure function tin {{R}}mapsto sup _{μ }{ h_μ (T_2)-tint log |dT_2(x)|dμ (x)} of the Chebyshev quadratic map T_2(x)=1-2x^2 (xin {{R}}) is not differentiable at t=-1. We show that this phase transition can be "removed", by an arbitrarily small singular perturbation of the map T_2 into Hénon-like diffeomorphisms. A proof of this result relies on an elaboration of the well-known inducing techniques adapted to Hénon-like dynamics near the first bifurcation.
Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping
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Hassan Azadi Kenary
2012-01-01
Full Text Available Using fixed point method and direct method, we prove the Hyers-Ulam stability of the following additive-quadratic functional equation 2((++/+2((−+/+2((+−/+2((−++/=4(+4(+4(, where is a positive real number, in non-Archimedean normed spaces.
ON THE MINIMAL NONNEGATIVE SOLUTION OF NONSYMMETRIC ALGEBRAIC RICCATI EQUATION
Institute of Scientific and Technical Information of China (English)
Xiao-xia Guo; Zhong-zhi Bai
2005-01-01
We study perturbation bound and structured condition number about the minimal nonnegative solution of nonsymmetric algebraic Riccati equation, obtaining a sharp perturbation bound and an accurate condition number. By using the matrix sign function method we present a new method for finding the minimal nonnegative solution of this algebraic Riccati equation. Based on this new method, we show how to compute the desired M-matrix solution of the quadratic matrix equation X2 - EX - F -= 0 by connecting it with the nonsymmetric algebraic Riccati equation, where E is a diagonal matrix and F is an M-matrix.
Geometric quadratic stochastic operator on countable infinite set
Energy Technology Data Exchange (ETDEWEB)
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar [Department of Computational and Theoretical Sciences, Kulliyyah of Science, International Islamic University, Jalan Sultan Ahmad Shah, Bandar InderaMahkota, 25200 Kuantan, Pahang (Malaysia)
2015-02-03
In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.
Jurenko, Robert J.; Bush, T. Jason; Ottander, John A.
2014-01-01
A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes both quadratically constrained least squares (LSQI) and Direct Shape Mapping (DSM) algorithms to determine physical displacements. This approach is applicable to the simulation of the elastic behavior of launch vehicles and other structures that utilize multiple LTI finite element model (FEM) derived mode sets that are propagated throughout time. The time invariant nature of the elastic data for discrete segments of the launch vehicle trajectory presents a problem of how to properly transition between models while preserving motion across the transition. In addition, energy may vary between flex models when using a truncated mode set. The LSQI-DSM algorithm can accommodate significant changes in energy between FEM models and carries elastic motion across FEM model transitions. Compared with previous approaches, the LSQI-DSM algorithm shows improvements ranging from a significant reduction to a complete removal of transients across FEM model transitions as well as maintaining elastic motion from the prior state.
Nonnegativity of uncertain polynomials
Directory of Open Access Journals (Sweden)
iljak Dragoslav D.
1998-01-01
Full Text Available The purpose of this paper is to derive tests for robust nonnegativity of scalar and matrix polynomials, which are algebraic, recursive, and can be completed in finite number of steps. Polytopic families of polynomials are considered with various characterizations of parameter uncertainty including affine, multilinear, and polynomic structures. The zero exclusion condition for polynomial positivity is also proposed for general parameter dependencies. By reformulating the robust stability problem of complex polynomials as positivity of real polynomials, we obtain new sufficient conditions for robust stability involving multilinear structures, which can be tested using only real arithmetic. The obtained results are applied to robust matrix factorization, strict positive realness, and absolute stability of multivariable systems involving parameter dependent transfer function matrices.
Ryckelynck, Philippe
2011-01-01
This paper addresses the classical and discrete Euler-Lagrange equations for systems of $n$ particles interacting quadratically in $\\mathbb{R}^d$. By highlighting the role played by the center of mass of the particles, we solve the previous systems via the classical quadratic eigenvalue problem (QEP) and its discrete transcendental generalization. The roots of classical and discrete QEP being given, we state some conditional convergence results. Next, we focus especially on periodic and choreographic solutions and we provide some numerical experiments which confirm the convergence.
Nonnegative and Compartmental Dynamical Systems
Haddad, Wassim M; Hui, Qing
2010-01-01
This comprehensive book provides the first unified framework for stability and dissipativity analysis and control design for nonnegative and compartmental dynamical systems, which play a key role in a wide range of fields, including engineering, thermal sciences, biology, ecology, economics, genetics, chemistry, medicine, and sociology. Using the highest standards of exposition and rigor, the authors explain these systems and advance the state of the art in their analysis and active control design. Nonnegative and Compartmental Dynamical Systems presents the most complete treatment available o
Form Sums of Nonnegative Selfadjoint Operators
Hassi, S.; Sandovici, A.; Snoo, H.S.V. de; Winkler, Henrik; Sandovici, 27740
2006-01-01
The sum of two unbounded nonnegative selfadjoint operators is a nonnegative operator which is not necessarily densely defined. In general its selfadjoint extensions exist in the sense of linear relations (multivalued operators). One of its nonnegative selfadjoint extensions is constructed via the fo
Computing a Nonnegative Matrix Factorization -- Provably
Arora, Sanjeev; Kannan, Ravi; Moitra, Ankur
2011-01-01
In the Nonnegative Matrix Factorization (NMF) problem we are given an $n \\times m$ nonnegative matrix $M$ and an integer $r > 0$. Our goal is to express $M$ as $A W$ where $A$ and $W$ are nonnegative matrices of size $n \\times r$ and $r \\times m$ respectively. In some applications, it makes sense to ask instead for the product $AW$ to approximate $M$ -- i.e. (approximately) minimize $\
Solvable quadratic Lie algebras
Institute of Scientific and Technical Information of China (English)
ZHU; Linsheng
2006-01-01
A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.
Coefficient Conditions for Starlikeness of Nonnegative Order
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Rosihan M. Ali
2012-01-01
Full Text Available Sufficient conditions on a sequence {ak} of nonnegative numbers are obtained that ensures f(z=∑k=1∞akzk is starlike of nonnegative order in the unit disk. A result of Vietoris on trigonometric sums is extended in this pursuit. Conditions for close to convexity and convexity in the direction of the imaginary axis are also established. These results are applied to investigate the starlikeness of functions involving the Gaussian hypergeometric functions.
Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems
Opmeer, MR; Curtain, RF
2004-01-01
In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show
Non-negative Matrix Factorization for Binary Data
DEFF Research Database (Denmark)
Larsen, Jacob Søgaard; Clemmensen, Line Katrine Harder
We propose the Logistic Non-negative Matrix Factorization for decomposition of binary data. Binary data are frequently generated in e.g. text analysis, sensory data, market basket data etc. A common method for analysing non-negative data is the Non-negative Matrix Factorization, though this is in......We propose the Logistic Non-negative Matrix Factorization for decomposition of binary data. Binary data are frequently generated in e.g. text analysis, sensory data, market basket data etc. A common method for analysing non-negative data is the Non-negative Matrix Factorization, though...
When to call a linear system nonnegative
Nieuwenhuis, J.W.
1998-01-01
In this paper we will consider discrete time invariant linear systems that allow for an input-state-output representation with a finite dimensional state space, and that have a finite number of inputs and outputs. The basic issue in this paper is when to call these systems nonnegative. An important
Max–min distance nonnegative matrix factorization
Wang, Jim Jing-Yan
2014-10-26
Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problems. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basis matrix and a nonnegative coefficient matrix. The columns of the coefficient matrix can be used as new representations of these data samples. However, traditional NMF methods ignore class labels of the data samples. In this paper, we propose a novel supervised NMF algorithm to improve the discriminative ability of the new representation by using the class labels. Using the class labels, we separate all the data sample pairs into within-class pairs and between-class pairs. To improve the discriminative ability of the new NMF representations, we propose to minimize the maximum distance of the within-class pairs in the new NMF space, and meanwhile to maximize the minimum distance of the between-class pairs. With this criterion, we construct an objective function and optimize it with regard to basis and coefficient matrices, and slack variables alternatively, resulting in an iterative algorithm. The proposed algorithm is evaluated on three pattern classification problems and experiment results show that it outperforms the state-of-the-art supervised NMF methods.
On affine non-negative matrix factorization
DEFF Research Database (Denmark)
Laurberg, Hans; Hansen, Lars Kai
2007-01-01
We generalize the non-negative matrix factorization (NMF) generative model to incorporate an explicit offset. Multiplicative estimation algorithms are provided for the resulting sparse affine NMF model. We show that the affine model has improved uniqueness properties and leads to more accurate...
Accardi, Luigi
2009-01-01
We construct the quadratic analogue of the boson Fock functor. While in the first order case all contractions on the 1--particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. Within this semigroup we characterize the unitary and the isometric elements.
Quadratic eigenvalue problems.
Energy Technology Data Exchange (ETDEWEB)
Walsh, Timothy Francis; Day, David Minot
2007-04-01
In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In the context of object-oriented video coding, the encoding of segmentation maps defined by contour networks is particularly critical. In this paper, we present a lossy contour network encoding algorithm where both the rate distortion contour encoding based on maximum operator and the prediction error for the current frame based on quadratic motion model are combined into a optimal polygon contour network compression scheme. The bit rate for the contour network can be further reduced by about 20% in comparison with that in the optimal polygonal boundary encoding scheme using maximum operator in the rate distortion sense.
Nonnegative Matrix Factorizations Performing Object Detection and Localization
Directory of Open Access Journals (Sweden)
G. Casalino
2012-01-01
Full Text Available We study the problem of detecting and localizing objects in still, gray-scale images making use of the part-based representation provided by nonnegative matrix factorizations. Nonnegative matrix factorization represents an emerging example of subspace methods, which is able to extract interpretable parts from a set of template image objects and then to additively use them for describing individual objects. In this paper, we present a prototype system based on some nonnegative factorization algorithms, which differ in the additional properties added to the nonnegative representation of data, in order to investigate if any additional constraint produces better results in general object detection via nonnegative matrix factorizations.
The explicit dependence of quadrat variance on the ratio of clump size to quadrat size.
Ferrandino, Francis J
2005-05-01
ABSTRACT In the past decade, it has become common practice to pool mapped binary epidemic data into quadrats. The resultant "quadrat counts" can then be analyzed by fitting them to a probability distribution (i.e., betabinomial). Often a binary form of Taylor's power law is used to relate the quadrat variance to the quadrat mean. The fact that there is an intrinsic dependence of such analyses on quadrat size and shape is well known. However, a clear-cut exposition of the direct connection between the spatial properties of the two-dimensional pattern of infected plants in terms of the geometry of the quadrat and the results of quadrat-based analyses is lacking. This problem was examined both empirically and analytically. The empirical approach is based on a set of stochastically generated "mock epidemics" using a Neyman-Scott cluster process. The resultant spatial point-patterns of infected plants have a fixed number of disease foci characterized by a known length scale (monodisperse) and saturated to a known disease level. When quadrat samples of these epidemics are fit to a beta-binomial distribution, the resulting measures of aggregation are totally independent of disease incidence and most strongly dependent on the ratio of the length scale of the quadrat to the length scale of spatial aggregation and to a lesser degree on disease saturation within individual foci. For the analytical approach, the mathematical form for the variation in the sum of random variates is coupled to the geometry of a quadrat through an assumed exponential autocorrelation function. The net result is an explicit equation expressing the intraquadrat correlation, quadrat variance, and the index of dispersion in terms of the ratio of the quadrat length scale to the correlative length scale.
Multistage quadratic stochastic programming
Lau, Karen K.; Womersley, Robert S.
2001-04-01
Quadratic stochastic programming (QSP) in which each subproblem is a convex piecewise quadratic program with stochastic data, is a natural extension of stochastic linear programming. This allows the use of quadratic or piecewise quadratic objective functions which are essential for controlling risk in financial and project planning. Two-stage QSP is a special case of extended linear-quadratic programming (ELQP). The recourse functions in QSP are piecewise quadratic convex and Lipschitz continuous. Moreover, they have Lipschitz gradients if each QP subproblem is strictly convex and differentiable. Using these properties, a generalized Newton algorithm exhibiting global and superlinear convergence has been proposed recently for the two stage case. We extend the generalized Newton algorithm to multistage QSP and show that it is globally and finitely convergent under suitable conditions. We present numerical results on randomly generated data and modified publicly available stochastic linear programming test sets. Efficiency schemes on different scenario tree structures are discussed. The large-scale deterministic equivalent of the multistage QSP is also generated and their accuracy compared.
An Alternating Direction Algorithm for Matrix Completion with Nonnegative Factors
Xu, Yangyang; Wen, Zaiwen; Zhang, Yin
2011-01-01
This paper introduces a novel algorithm for the nonnegative matrix factorization and completion problem, which aims to find nonnegative matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates M. This problem is closely related to the two existing problems: nonnegative matrix factorization and low-rank matrix completion, in the sense that it kills two birds with one stone. As it takes advantages of both nonnegativity and low rank, its results can be superior than those of the two problems alone. Our algorithm is applied to minimizing a non-convex constrained least-squares formulation and is based on the classic alternating direction augmented Lagrangian method. Preliminary convergence properties and numerical simulation results are presented. Compared to a recent algorithm for nonnegative random matrix factorization, the proposed algorithm yields comparable factorization through accessing only half of the matrix entries. On tasks of recovering incomplete grayscale and hypers...
Distortion control of conjugacies between quadratic polynomials
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We use a new type of distortion control of univalent functions to give an alternative proof of Douady-Hubbard’s ray-landing theorem for quadratic Misiurewicz polynomials. The univalent maps arise from Thurston’s iterated algorithm on perturbation of such polynomials.
Semidefinite programming for quadratically constrained quadratic programs
Olkin, Julia A.; Titterton, Paul J., Jr.
1995-06-01
We consider the linear least squares problem subject to multiple quadratic constraints, which is motivated by a practical application in controller design. We use the techniques of convex optimization, in particluar, interior-point methods for semi-definite programming. We reduce a quasi-convex potential function. Each iteration requires calculating a primal and dual search direction and minimizing along the plane defined by these search directions. The primal search direction requires solving a least squares problem whose matrix is composed of a block- Toeplitz portion plus other structured matrices. We make use of Kronecker products and FFTs to greatly reduce the calculation. In addition, the matrix updates and matrix inverses in the plane search are actually low-rank updates to structured matrices so we are able to further reduce the flops required. Consequently, we can design controllers for problems of considerable size.
Totally nonnegative Grassmannian and Grassmann polytopes
Lam, Thomas
2015-01-01
These are lecture notes intended to supplement my second lecture at the Current Developments in Mathematics conference in 2014. In the first half of article, we give an introduction to the totally nonnegative Grassmannian together with a survey of some more recent work. In the second half of the article, we give a definition of a Grassmann polytope motivated by work of physicists on the amplituhedron. We propose to use Schubert calculus and canonical bases to replace linear algebra and convexity in the theory of polytopes.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
On Quadratic Differential Forms
Willems, J.C.; Trentelman, H.L.
1998-01-01
This paper develops a theory around the notion of quadratic differential forms in the context of linear differential systems. In many applications, we need to not only understand the behavior of the system variables but also the behavior of certain functionals of these variables. The obvious cases w
Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio
2016-01-01
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...
ON CONVERGENCE OF MULTIGRID METHOD FOR NONNEGATIVE DEFINITE SYSTEMS
Institute of Scientific and Technical Information of China (English)
Qian-shun Chang; Wei-wei Sun
2005-01-01
In this paper, we consider multigrid methods for solving symmetric nonnegative definite matrix equations. We present some interesting features of the multigrid method and prove that the method is convergent in L2 space and the convergent solution is unique for such nonnegative definite system and given initial guess.
Incremental Nonnegative Matrix Factorization for Face Recognition
Directory of Open Access Journals (Sweden)
Wen-Sheng Chen
2008-01-01
Full Text Available Nonnegative matrix factorization (NMF is a promising approach for local feature extraction in face recognition tasks. However, there are two major drawbacks in almost all existing NMF-based methods. One shortcoming is that the computational cost is expensive for large matrix decomposition. The other is that it must conduct repetitive learning, when the training samples or classes are updated. To overcome these two limitations, this paper proposes a novel incremental nonnegative matrix factorization (INMF for face representation and recognition. The proposed INMF approach is based on a novel constraint criterion and our previous block strategy. It thus has some good properties, such as low computational complexity, sparse coefficient matrix. Also, the coefficient column vectors between different classes are orthogonal. In particular, it can be applied to incremental learning. Two face databases, namely FERET and CMU PIE face databases, are selected for evaluation. Compared with PCA and some state-of-the-art NMF-based methods, our INMF approach gives the best performance.
How quantum are non-negative wavefunctions?
Energy Technology Data Exchange (ETDEWEB)
Hastings, M. B. [Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA and Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052 (United States)
2016-01-15
We consider wavefunctions which are non-negative in some tensor product basis. We study what possible teleportation can occur in such wavefunctions, giving a complete answer in some cases (when one system is a qubit) and partial answers elsewhere. We use this to show that a one-dimensional wavefunction which is non-negative and has zero correlation length can be written in a “coherent Gibbs state” form, as explained later. We conjecture that such holds in higher dimensions. Additionally, some results are provided on possible teleportation in general wavefunctions, explaining how Schmidt coefficients before measurement limit the possible Schmidt coefficients after measurement, and on the absence of a “generalized area law” [D. Aharonov et al., in Proceedings of Foundations of Computer Science (FOCS) (IEEE, 2014), p. 246; e-print arXiv.org:1410.0951] even for Hamiltonians with no sign problem. One of the motivations for this work is an attempt to prove a conjecture about ground state wavefunctions which have an “intrinsic” sign problem that cannot be removed by any quantum circuit. We show a weaker version of this, showing that the sign problem is intrinsic for commuting Hamiltonians in the same phase as the double semion model under the technical assumption that TQO-2 holds [S. Bravyi et al., J. Math. Phys. 51, 093512 (2010)].
On Nonnegative Signed Domination in Graphs and its Algorithmic Complexity
Directory of Open Access Journals (Sweden)
Zhongsheng Huang
2013-02-01
Full Text Available Let G = (V, E be a simple graph with vertex set V and edge set E. A function f from V to a set {-1, 1} is said to be a nonnegative signed dominating function (NNSDF if the sum of its function values over any closed neighborhood is at least zero. The weight of f is the sum of function values of vertices in V. The nonnegative signed domination number for a graph G equals the minimum weight of a nonnegative signed dominating function of G. In this paper, exact values are found for cycles, stars, wheels, spiders and complete equally bipartite graphs and we present some lower bounds for nonnegative signed domination number in terms of the order and the maximum and minimum degree. Fothermore, we show that the decision problem corresponding to the problem of computing the nonnegative signed domination number is NP-complete.
Hidden conic quadratic representation of some nonconvex quadratic optimization problems
Ben-Tal, A.; den Hertog, D.
2014-01-01
The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated S-lemma
Extended gcd of quadratic integers
Miled, Abdelwaheb
2010-01-01
Computation of the extended gcd of two quadratic integers. The ring of integers considered is principal but could be euclidean or not euclidean ring. This method rely on principal ideal ring and reduction of binary quadratic forms.
On Characterization of Quadratic Splines
DEFF Research Database (Denmark)
Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong
2005-01-01
A quadratic spline is a differentiable piecewise quadratic function. Many problems in numerical analysis and optimization literature can be reformulated as unconstrained minimizations of quadratic splines. However, only special cases of quadratic splines are studied in the existing literature...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general......., and algorithms are developed on a case by case basis. There lacks an analytical representation of a general or even a convex quadratic spline. The current paper fills this gap by providing an analytical representation of a general quadratic spline. Furthermore, for convex quadratic spline, it is shown...
Infinity Behavior of Bounded Subharmonic Functions on Ricci Non-negative Manifolds
Institute of Scientific and Technical Information of China (English)
Bao Qiang WU
2004-01-01
In this paper, we study the infinity behavior of the bounded subharmonic functions on a Ricci non-negative Riemannian manifold M. We first show that limr→∞r2/V(r) ∫B(r)△hdv = 0 if h is a bounded subharmonic function. If we further assume that the Laplacian decays pointwisely faster than quadratically we show that h approaches its supremun pointwisely at infinity, under certain auxiliary conditions on the volume growth of M. In particular, our result applies to the case when the Riemannian manifold has maximum volume growth. We also derive a representation formula in our paper, from which one can easily derive Yau's Liouville theorem on bounded harmonic functions.
Multivariate refinement equation with nonnegative masks
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper is concerned with multivariate refinement equations of the type ψ = ∑α∈Zs a(α)ψ(Mx - α),where ψ is the unknown function defined on the s-dimensional Euclidean space Rs, a is a finitely supported nonnegative sequence on Zs, and M is an s × s dilation matrix with m := |detM|. We characterize the existence of L2-solution of refinement equation in terms of spectral radius of a certain finite matrix or transition operator associated with refinement mask a and dilation matrix M. For s = 1 and M = 2, the sufficient and necessary conditions are obtained to characterize the existence of continuous solution of this refinement equation.
On some properties of nonnegative weakly irreducible tensors
Yang, Yuning
2011-01-01
In this paper, we mainly focus on how to generalize some conclusions from \\emph{nonnegative irreducible tensors} to \\emph{nonnegative weakly irreducible tensors}. To do so, a basic lemma as Lemma 3.1 of \\cite{s11} is proven using new tools. First, we define the stochastic tensor. Then we show that every nonnegative weakly irreducible tensor with spectral radius be 1 is diagonally similar to a unique weakly irreducible stochastic tensor. Based on it, we prove some important lemmas, which help us to generalize the results.
Link Prediction via Convex Nonnegative Matrix Factorization on Multiscale Blocks
Directory of Open Access Journals (Sweden)
Enming Dong
2014-01-01
Full Text Available Low rank matrices approximations have been used in link prediction for networks, which are usually global optimal methods and lack of using the local information. The block structure is a significant local feature of matrices: entities in the same block have similar values, which implies that links are more likely to be found within dense blocks. We use this insight to give a probabilistic latent variable model for finding missing links by convex nonnegative matrix factorization with block detection. The experiments show that this method gives better prediction accuracy than original method alone. Different from the original low rank matrices approximations methods for link prediction, the sparseness of solutions is in accord with the sparse property for most real complex networks. Scaling to massive size network, we use the block information mapping matrices onto distributed architectures and give a divide-and-conquer prediction method. The experiments show that it gives better results than common neighbors method when the networks have a large number of missing links.
THE SENSITIVITY OF THE EXPONENTIAL OF AN ESSENTIALLY NONNEGATIVE MATRIX
Institute of Scientific and Technical Information of China (English)
Weifang Zhu; Jungong Xue; Weiguo Gao
2008-01-01
This paper performs perturbation analysis for the exponential of an essentially nonnegative matrix which is perturbed in the way that each entry has a small relative perturbation.For a general essentially nonnegative matrix,we obtain an upper bound for the relative error in 2-norm,which is sharper than the existing perturbation results.For a triangular essentially nonnegative matrix,we obtain an upper bound for the relative error in entrywise sense.This bound indicates that,if the spectral radius of an essentially nonnegative matrix is not large,then small entrywise relative perturbations cause small relative error in each entry of its exponential.Finally,we apply our perturbation results to the sensitivity analysis of RC networks and complementary distribution functions of phase-type distributions.
Recognition of Graphs with Convex Quadratic Stability Number
Pacheco, Maria F.; Cardoso, Domingos M.
2009-09-01
A stable set of a graph is a set of mutually non-adjacent vertices. The determination of a maximum size stable set, which is called maximum stable set, and the determination of its size, which is called stability number, are central combinatorial optimization problems. However, given a nonnegative integer k, to determine if a graph G has a stable set of size k is NP-complete. In this paper we deal with graphs for which the stability number can be determined by solving a convex quadratic programming problem. Such graphs were introduced in [13] and are called graphs with convex-QP stability number. A few algorithmic techniques for the recognition of this type of graphs in particular families are presented.
Non-negative matrix factorization with Gaussian process priors
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Laurberg, Hans
2008-01-01
We present a general method for including prior knowledge in a nonnegative matrix factorization (NMF), based on Gaussian process priors. We assume that the nonnegative factors in the NMF are linked by a strictly increasing function to an underlying Gaussian process specified by its covariance...... function. This allows us to find NMF decompositions that agree with our prior knowledge of the distribution of the factors, such as sparseness, smoothness, and symmetries. The method is demonstrated with an example from chemical shift brain imaging....
Non-negative matrix factorization with Gaussian process priors
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Laurberg, Hans
2008-01-01
We present a general method for including prior knowledge in a nonnegative matrix factorization (NMF), based on Gaussian process priors. We assume that the nonnegative factors in the NMF are linked by a strictly increasing function to an underlying Gaussian process specified by its covariance...... function. This allows us to find NMF decompositions that agree with our prior knowledge of the distribution of the factors, such as sparseness, smoothness, and symmetries. The method is demonstrated with an example from chemical shift brain imaging....
A CLASS OF QUADRATIC HAMILTONIAN SYSTEMS UNDER QUADRATIC PERTURBATION
Institute of Scientific and Technical Information of China (English)
丰建文; 陈士华
2001-01-01
This paper deals with a class of quadratic Hamiltonian systems with quadratic perturbation. The authors prove that if the first order Melnikov function M1(h) = 0 and the second order Melnikov function M2(h) ≡ 0, then the origin of the Hamiltonian system with small perturbation is a center.
Multiple graph regularized nonnegative matrix factorization
Wang, Jim Jing-Yan
2013-10-01
Non-negative matrix factorization (NMF) has been widely used as a data representation method based on components. To overcome the disadvantage of NMF in failing to consider the manifold structure of a data set, graph regularized NMF (GrNMF) has been proposed by Cai et al. by constructing an affinity graph and searching for a matrix factorization that respects graph structure. Selecting a graph model and its corresponding parameters is critical for this strategy. This process is usually carried out by cross-validation or discrete grid search, which are time consuming and prone to overfitting. In this paper, we propose a GrNMF, called MultiGrNMF, in which the intrinsic manifold is approximated by a linear combination of several graphs with different models and parameters inspired by ensemble manifold regularization. Factorization metrics and linear combination coefficients of graphs are determined simultaneously within a unified object function. They are alternately optimized in an iterative algorithm, thus resulting in a novel data representation algorithm. Extensive experiments on a protein subcellular localization task and an Alzheimer\\'s disease diagnosis task demonstrate the effectiveness of the proposed algorithm. © 2013 Elsevier Ltd. All rights reserved.
Minimum-volume-constrained nonnegative matrix factorization: enhanced ability of learning parts.
Zhou, Guoxu; Xie, Shengli; Yang, Zuyuan; Yang, Jun-Mei; He, Zhaoshui
2011-10-01
Nonnegative matrix factorization (NMF) with minimum-volume-constraint (MVC) is exploited in this paper. Our results show that MVC can actually improve the sparseness of the results of NMF. This sparseness is L(0)-norm oriented and can give desirable results even in very weak sparseness situations, thereby leading to the significantly enhanced ability of learning parts of NMF. The close relation between NMF, sparse NMF, and the MVC_NMF is discussed first. Then two algorithms are proposed to solve the MVC_NMF model. One is called quadratic programming_MVC_NMF (QP_MVC_NMF) which is based on quadratic programming and the other is called negative glow_MVC_NMF (NG_MVC_NMF) because it uses multiplicative updates incorporating natural gradient ingeniously. The QP_MVC_NMF algorithm is quite efficient for small-scale problems and the NG_MVC_NMF algorithm is more suitable for large-scale problems. Simulations show the efficiency and validity of the proposed methods in applications of blind source separation and human face images analysis.
On Quadratic Variation of Martingales
Indian Academy of Sciences (India)
Rajeeva L Karandikar; B V Rao
2014-08-01
We give a construction of an explicit mapping $$\\Psi: D([0,∞),\\mathbb{R})→ D([0,∞),\\mathbb{R}),$$ where $D([0,∞), \\mathbb{R})$ denotes the class of real valued r.c.l.l. functions on $[0,∞)$ such that for a locally square integrable martingale $(M_t)$ with r.c.l.l. paths, $$\\Psi(M.())=A.()$$ gives the quadratic variation process (written usually as $[M,M]_t$) of $(M_t)$. We also show that this process $(A_t)$ is the unique increasing process $(B_t)$ such that $M_t^2-B_t$ is a local martingale, $B_0=0$ and $$\\mathbb{P}(( B)_t=[( M)_t]^2, 0 < ∞)=1.$$ Apart from elementary properties of martingales, the only result used is the Doob’s maximal inequality. This result can be the starting point of the development of the stochastic integral with respect to r.c.l.l. martingales.
Quadratic solitons as nonlocal solitons
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov; Neshev, D.; Bang, Ole
2003-01-01
We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for analytical...
On Characterization of Quadratic Splines
DEFF Research Database (Denmark)
Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong
2005-01-01
that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...
The size of quadratic $p$-adic linearization disks
Lindahl, Karl-Olof
2013-01-01
We find the exact radius of linearization disks at indifferent fixed points of quadratic maps in $\\mathbb{C}_p$. We also show that the radius is invariant under power series perturbations. Localizing all periodic orbits of these quadratic-like maps we then show that periodic points are not the only obstruction for linearization. In so doing, we provide the first known examples in the dynamics of polynomials over $\\mathbb{C}_p$ where the boundary of the linearization disk does not contain any ...
Nonnegative matrix factorization and its applications in pattern recognition
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Matrix factorization is an effective tool for large-scale data processing and analysis. Nonnegative matrix factorization (NMF) method, which decomposes the nonnegative matrix into two nonnegative factor matrices, provides a new way for matrix factorization. NMF is significant in intelligent information processing and pattern recognition. This paper firstly introduces the basic idea of NMF and some new relevant methods. Then we discuss the loss functions and relevant algorithms of NMF in the framework of probabilistic models based on our researches, and the relationship between NMF and information processing of perceptual process. Finally, we make use of NMF to deal with some practical questions of pattern recognition and point out some open problems for NMF.
Sparse Non-negative Matrix Factor 2-D Deconvolution
DEFF Research Database (Denmark)
Mørup, Morten; Schmidt, Mikkel N.
2006-01-01
We introduce the non-negative matrix factor 2-D deconvolution (NMF2D) model, which decomposes a matrix into a 2-dimensional convolution of two factor matrices. This model is an extension of the non-negative matrix factor deconvolution (NMFD) recently introduced by Smaragdis (2004). We derive...... and prove the convergence of two algorithms for NMF2D based on minimizing the squared error and the Kullback-Leibler divergence respectively. Next, we introduce a sparse non-negative matrix factor 2-D deconvolution model that gives easy interpretable decompositions and devise two algorithms for computing...... this form of factorization. The developed algorithms have been used for source separation and music transcription....
Learning Hidden Markov Models using Non-Negative Matrix Factorization
Cybenko, George
2008-01-01
The Baum-Welsh algorithm together with its derivatives and variations has been the main technique for learning Hidden Markov Models (HMM) from observational data. We present an HMM learning algorithm based on the non-negative matrix factorization (NMF) of higher order Markovian statistics that is structurally different from the Baum-Welsh and its associated approaches. The described algorithm supports estimation of the number of recurrent states of an HMM and iterates the non-negative matrix factorization (NMF) algorithm to improve the learned HMM parameters. Numerical examples are provided as well.
SMOOTHING BY CONVEX QUADRATIC PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Bing-sheng He; Yu-mei Wang
2005-01-01
In this paper, we study the relaxed smoothing problems with general closed convex constraints. It is pointed out that such problems can be converted to a convex quadratic minimization problem for which there are good programs in software libraries.
Quantum quadratic operators and processes
Mukhamedov, Farrukh
2015-01-01
Covering both classical and quantum approaches, this unique and self-contained book presents the most recent developments in the theory of quadratic stochastic operators and their Markov and related processes. The asymptotic behavior of dynamical systems generated by classical and quantum quadratic operators is investigated and various properties of quantum quadratic operators are studied, providing an insight into the construction of quantum channels. This book is suitable as a textbook for an advanced undergraduate/graduate level course or summer school in quantum dynamical systems. It can also be used as a reference book by researchers looking for interesting problems to work on, or useful techniques and discussions of particular problems. Since it includes the latest developments in the fields of quadratic dynamical systems, Markov processes and quantum stochastic processes, researchers at all levels are likely to find the book inspiring and useful.
Quadratic Tangles in Planar Algebras
Jones, Vaughan F R
2010-01-01
In planar algebras, we show how to project certain simple "quadratic" tangles onto the linear space spanned by "linear" and "constant" tangles. We obtain some corollaries about the principal graphs and annular structure of subfactors.
NON-NEGATIVE RADIAL SOLUTION FOR AN ELLIPTIC EQUATION
Institute of Scientific and Technical Information of China (English)
Yang Guoying; Guo Zongming
2005-01-01
We study the structure and behavior of non-negative radial solution for the following elliptic equation △u = uv, x ∈ Rn with 0 ＜ v ＜ 1. We also obtain the detailed asymptotic expansion of u near infinity.
Efficient Nonnegative Matrix Factorization by DC Programming and DCA.
Le Thi, Hoai An; Vo, Xuan Thanh; Dinh, Tao Pham
2016-06-01
In this letter, we consider the nonnegative matrix factorization (NMF) problem and several NMF variants. Two approaches based on DC (difference of convex functions) programming and DCA (DC algorithm) are developed. The first approach follows the alternating framework that requires solving, at each iteration, two nonnegativity-constrained least squares subproblems for which DCA-based schemes are investigated. The convergence property of the proposed algorithm is carefully studied. We show that with suitable DC decompositions, our algorithm generates most of the standard methods for the NMF problem. The second approach directly applies DCA on the whole NMF problem. Two algorithms-one computing all variables and one deploying a variable selection strategy-are proposed. The proposed methods are then adapted to solve various NMF variants, including the nonnegative factorization, the smooth regularization NMF, the sparse regularization NMF, the multilayer NMF, the convex/convex-hull NMF, and the symmetric NMF. We also show that our algorithms include several existing methods for these NMF variants as special versions. The efficiency of the proposed approaches is empirically demonstrated on both real-world and synthetic data sets. It turns out that our algorithms compete favorably with five state-of-the-art alternating nonnegative least squares algorithms.
Nonpolytopal nonsimplicial lattice spheres with nonnegative toric g-vector
Billera, Louis J
2011-01-01
We construct many nonpolytopal nonsimplicial Gorenstein* meet semi-lattices with nonnegative toric g-vector, supporting a conjecture of Stanley. These are formed as Bier spheres over the face posets of multiplexes, polytopes constructed by Bisztriczky as generalizations of simplices.
Automorphisms of semigroups of invertible matrices with nonnegative integer elements
Energy Technology Data Exchange (ETDEWEB)
Semenov, Pavel P [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2012-09-30
Let G{sub n}(Z) be the subsemigroup of GL{sub n}(Z) consisting of the matrices with nonnegative integer coefficients. In the paper, the automorphisms of this semigroup are described for n{>=}2. Bibliography: 5 titles.
Slow features nonnegative matrix factorization for temporal data decomposition
Zafeiriou, Lazaros; Nikitidis, Symeon; Zafeiriou, Stefanos; Pantic, Maja
2014-01-01
In this paper, we combine the principles of temporal slowness and nonnegative parts-based learning into a single framework that aims to learn slow varying parts-based representations of time varying sequences. We demonstrate that the proposed algorithm arises naturally by embedding the Slow Features
On the nonnegative inverse eigenvalue problem of traditional matrices
Directory of Open Access Journals (Sweden)
Alimohammad Nazari
2014-07-01
Full Text Available In this paper, at first for a given set of real or complex numbers $\\sigma$ with nonnegativesummation, we introduce some special conditions that with them there is no nonnegativetridiagonal matrix in which $\\sigma$ is its spectrum. In continue we present some conditions forexistence such nonnegative tridiagonal matrices.
Algorithms for Sparse Non-negative Tucker Decompositions
DEFF Research Database (Denmark)
Mørup, Morten; Hansen, Lars Kai
2008-01-01
for Tucker decompositions when indeed the data and interactions can be considered non-negative. We further illustrate how sparse coding can help identify what model (PARAFAC or Tucker) is the most appropriate for the data as well as to select the number of components by turning off excess components...
Clustered Self Organising Migrating Algorithm for the Quadratic Assignment Problem
Davendra, Donald; Zelinka, Ivan; Senkerik, Roman
2009-08-01
An approach of population dynamics and clustering for permutative problems is presented in this paper. Diversity indicators are created from solution ordering and its mapping is shown as an advantage for population control in metaheuristics. Self Organising Migrating Algorithm (SOMA) is modified using this approach and vetted with the Quadratic Assignment Problem (QAP). Extensive experimentation is conducted on benchmark problems in this area.
Entire functions whose Julia sets include any finitely many copies of quadratic Julia sets
Katagata, Koh
2017-06-01
We prove that for any finite collection of quadratic Julia sets, a polynomial and a transcendental entire function exist whose Julia sets include copies of the given quadratic Julia sets. In order to prove the result, we construct quasiregular maps with required dynamics and employ the quasiconformal surgery to obtain the desired functions.
Students' understanding of quadratic equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-05-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.
Finite dimensional quadratic Lie superalgebras
Jarvis, Peter; Yates, Luke
2010-01-01
We consider a special class of Z_2-graded, polynomial algebras of degree 2, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. Based on the factorisation of the enveloping algebra, we derive the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate the method for one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.
Successive quadratic programming multiuser detector
Institute of Scientific and Technical Information of China (English)
Mu Xuewen; Zhang Yaling; Liu Sanyang
2007-01-01
Based on the semidefinite programming relaxation of the CDMA maximum likelihood multiuser detection problem,a detection strategy by the successive quadratic programming algorithm is presented. Coupled with the randomized cut generation scheme, the suboptimal solution of the multiuser detection problem in obtained. Compared to the interior point methods previously reported based on semidefinite programming, simulations demonstrate that the successive quadratic programming algorithm often yields the similar BER performances of the multiuser detection problem. But the average CPU time of this approach is significantly reduced.
Integer Quadratic Quasi-polyhedra
Letchford, Adam N.
This paper introduces two fundamental families of 'quasi-polyhedra' - polyhedra with a countably infinite number of facets - that arise in the context of integer quadratic programming. It is shown that any integer quadratic program can be reduced to the minimisation of a linear function over a quasi-polyhedron in the first family. Some fundamental properties of the quasi-polyhedra are derived, along with connections to some other well-studied convex sets. Several classes of facet-inducing inequalities are also derived. Finally, extensions to the mixed-integer case are briefly examined.
Impurity solitons with quadratic nonlinearities
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis
1998-01-01
We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton p...
Unramified extensions of quadratic fields
Institute of Scientific and Technical Information of China (English)
Wei Li; Dong Yang; Xianke Zhang
2008-01-01
Let K be a global quadratic field, then every unramified abelian extension of K is proved to be absolutely Galois when K is a number field or under some natural conditions when K is a function field. The absolute Galois group is also determined explicitly.
Quadratic prediction of factor scores
Wansbeek, T
1999-01-01
Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...
Nonnegative spline regression of incomplete tracing data reveals high resolution neural connectivity
Harris, Kameron Decker; Shea-Brown, Eric
2016-01-01
Whole-brain neural connectivity data are now available from viral tracing experiments, which reveal the connections between a source injection site and elsewhere in the brain. These hold the promise of revealing spatial patterns of connectivity throughout the mammalian brain. To achieve this goal, we seek to fit a weighted, nonnegative adjacency matrix among 100 {\\mu}m brain "voxels" using viral tracer data. Despite a multi-year experimental effort, the problem remains severely underdetermined: Injection sites provide incomplete coverage, and the number of voxels is orders of magnitude larger than the number of injections. Furthermore, projection data are missing within the injection site because local connections there are not separable from the injection signal. We use a novel machine-learning algorithm to meet these challenges and develop a spatially explicit, voxel-scale connectivity map of the mouse visual system. Our method combines three features: a matrix completion loss for missing data, a smoothing ...
Sparse and Unique Nonnegative Matrix Factorization Through Data Preprocessing
Gillis, Nicolas
2012-01-01
Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being highly ill-posed, that is, there typically exist many different but equivalent factorizations. In this paper, we introduce a completely new way to obtaining more well-posed NMF problems whose solutions are sparser. Our technique is based on the preprocessing of the nonnegative input data matrix, and relies on the theory of M-matrices and the geometric interpretation of NMF. This approach provably leads to optimal and sparse solutions under the separability assumption of Donoho and Stodden (NIPS, 2003), and, for rank-three matrices, makes the number of exact factorizations finite. We illustrate the effectiveness of our technique on several image datasets.
Algorithms for Sparse Non-negative Tucker Decompositions
DEFF Research Database (Denmark)
Mørup, Morten; Hansen, Lars Kai
2008-01-01
There is a increasing interest in analysis of large scale multi-way data. The concept of multi-way data refers to arrays of data with more than two dimensions, i.e., taking the form of tensors. To analyze such data, decomposition techniques are widely used. The two most common decompositions...... decompositions). To reduce ambiguities of this type of decomposition we develop updates that can impose sparseness in any combination of modalities, hence, proposed algorithms for sparse non-negative Tucker decompositions (SN-TUCKER). We demonstrate how the proposed algorithms are superior to existing algorithms...... for Tucker decompositions when indeed the data and interactions can be considered non-negative. We further illustrate how sparse coding can help identify what model (PARAFAC or Tucker) is the most appropriate for the data as well as to select the number of components by turning off excess components...
Parallel Nonnegative Least Squares Solvers for Model Order Reduction
2016-03-01
not for the PQN method. For the latter method the size of the active set is controlled to promote sparse solutions. This is described in Section 3.2.1...or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington...21005-5066 primary author’s email: <james.p.collins106.civ@mail.mil>. Parallel nonnegative least squares (NNLS) solvers are developed specifically for
Multiple Kernel Learning for adaptive graph regularized nonnegative matrix factorization
Wang, Jim Jing-Yan
2012-01-01
Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define parts-based, and linear representation of non-negative data. Recently, Graph regularized NMF (GrNMF) is proposed to find a compact representation, which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In GNMF, an affinity graph is constructed from the original data space to encode the geometrical information. In this paper, we propose a novel idea which engages a Multiple Kernel Learning approach into refining the graph structure that reflects the factorization of the matrix and the new data space. The GrNMF is improved by utilizing the graph refined by the kernel learning, and then a novel kernel learning method is introduced under the GrNMF framework. Our approach shows encouraging results of the proposed algorithm in comparison to the state-of-the-art clustering algorithms like NMF, GrNMF, SVD etc.
The Quadratic Graver Cone, Quadratic Integer Minimization, and Extensions
Lee, Jon; Romanchuk, Lyubov; Weismantel, Robert
2010-01-01
We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the system is given, and the quadratic function lies in a suitable {\\em dual Graver cone}, the problem can be solved in polynomial time. We discuss the relation between this cone and the cone of positive semidefinite matrices, and show that none contains the other. So we can minimize in polynomial time some non-convex and some (including all separable) convex quadrics. We conclude by extending our results to efficient integer minimization of multivariate polynomial functions of arbitrary degree lying in suitable cones.
Consensus-ADMM for General Quadratically Constrained Quadratic Programming
Huang, Kejun; Sidiropoulos, Nicholas D.
2016-10-01
Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special cases are NP-hard as well. This paper proposes a new algorithm for general QCQP. The problem is first reformulated in consensus optimization form, to which the alternating direction method of multipliers (ADMM) can be applied. The reformulation is done in such a way that each of the sub-problems is a QCQP with only one constraint (QCQP-1), which is efficiently solvable irrespective of (non-)convexity. The core components are carefully designed to make the overall algorithm more scalable, including efficient methods for solving QCQP-1, memory efficient implementation, parallel/distributed implementation, and smart initialization. The proposed algorithm is then tested in two applications: multicast beamforming and phase retrieval. The results indicate superior performance over prior state-of-the-art methods.
Quadratic and 2-Crossed Modules of Algebras
Institute of Scientific and Technical Information of China (English)
Z. Arvasi; E. Ulualan
2007-01-01
In this work, we define the quadratic modules for commutative algebras and give relations among 2-crossed modules, crossed squares, quadratic modules and simplicial commutative algebras with Moore complex of length 2.
Team Decision Problems with Convex Quadratic Constraints
Gattami, Ather
2015-01-01
In this paper, we consider linear quadratic team problems with an arbitrary number of quadratic constraints in both stochastic and deterministic settings. The team consists of players with different measurements about the state of nature. The objective of the team is to minimize a quadratic cost subject to additional finite number of quadratic constraints. We first consider the problem of countably infinite number of players in the team for a bounded state of nature with a Gaussian distributi...
Sequences of Lower Bounds for the Perron Root of a Nonnegative Irreducible Matrix
Institute of Scientific and Technical Information of China (English)
ZHONG Qin; HUANG Ting Zhu
2009-01-01
Estimate bounds for the Perron root of a nonnegative matrix are important in theory of nonnegative matrices. It is more practical when the bounds are expressed as an easily calculated function in elements of matrices. For the Perron root of nonnegative irreducible matrices,three sequences of lower bounds are presented by means of constructing shifted matrices, whose convergence is studied. The comparisons of the sequences with known ones are supplemented with a numerical example.
A polyhedral approach to quadratic assignment problem
Köksaldı, Ahmet Sertaç Murat
1994-01-01
Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 1994. Thesis (Master's) -- Bilkent University, 1994. Includes bibliographical references. In this thesis, Quadratic Assignment Problem is considered. Since Quadratic Assignment Problem is JVP-bard, no polynomial time exact solution method exists. Proving optimality of solutions to Quadratic Assignment Problems has been limited to instances of small dimension. In...
Orthogonality preserving infinite dimensional quadratic stochastic operators
Energy Technology Data Exchange (ETDEWEB)
Akın, Hasan [Department of Mathematics, Faculty of Education, Zirve University, Gaziantep, 27260 (Turkey); Mukhamedov, Farrukh [Department of Computational & Theoretical Sciences Faculty of Science, International Islamic University Malaysia P.O. Box, 141, 25710, Kuantan Pahang (Malaysia)
2015-09-18
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.
Extending the Scope of Robust Quadratic Optimization
Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand
2017-01-01
In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in ge
Quantum bouncer with quadratic dissipation
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, G. [NanoScience Technology Center, University of Central Florida, Orlando, FL 32826 (United States)]. e-mail: ggonzalez@physics.ucf.edu
2008-07-01
The energy loss due to a quadratic velocity-dependent force on a quantum particle bouncing off a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new, effective, phenomenological Hamiltonian which corresponds to the actual energy of the system and obtain the correction to the eigenvalues of the energy in first-order quantum perturbation theory for the case of weak dissipation. (Author)
Quantum bouncer with quadratic dissipation
González, G.
2008-02-01
The energy loss due to a quadratic velocity dependent force on a quantum particle bouncing on a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new effective phenomenological Hamiltonian which corresponds to the actual energy of the system and obtained the correction to the eigenvalues of the energy in first order quantum perturbation theory for the case of weak dissipation.
Linear Program Relaxation of Sparse Nonnegative Recovery in Compressive Sensing Microarrays
Directory of Open Access Journals (Sweden)
Linxia Qin
2012-01-01
Full Text Available Compressive sensing microarrays (CSM are DNA-based sensors that operate using group testing and compressive sensing principles. Mathematically, one can cast the CSM as sparse nonnegative recovery (SNR which is to find the sparsest solutions subjected to an underdetermined system of linear equations and nonnegative restriction. In this paper, we discuss the l1 relaxation of the SNR. By defining nonnegative restricted isometry/orthogonality constants, we give a nonnegative restricted property condition which guarantees that the SNR and the l1 relaxation share the common unique solution. Besides, we show that any solution to the SNR must be one of the extreme points of the underlying feasible set.
Linear program relaxation of sparse nonnegative recovery in compressive sensing microarrays.
Qin, Linxia; Xiu, Naihua; Kong, Lingchen; Li, Yu
2012-01-01
Compressive sensing microarrays (CSM) are DNA-based sensors that operate using group testing and compressive sensing principles. Mathematically, one can cast the CSM as sparse nonnegative recovery (SNR) which is to find the sparsest solutions subjected to an underdetermined system of linear equations and nonnegative restriction. In this paper, we discuss the l₁ relaxation of the SNR. By defining nonnegative restricted isometry/orthogonality constants, we give a nonnegative restricted property condition which guarantees that the SNR and the l₁ relaxation share the common unique solution. Besides, we show that any solution to the SNR must be one of the extreme points of the underlying feasible set.
Global Optimization of a Class of Nonconvex Quadratically Constrained Quadratic Programming Problems
Institute of Scientific and Technical Information of China (English)
Yong XIA
2011-01-01
In this paper we study a class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems.We show that each problem is polynomially solved.Strong duality holds if a redundant constraint is introduced.As an application,a new lower bound is proposed for the quadratic assignment problem.
A quadratic rate of asymptotic regularity for CAT(0)-spaces
Leustean, Laurentiu
2005-01-01
In this paper we obtain a quadratic bound on the rate of asymptotic regularity for the Krasnoselski-Mann iterations of nonexpansive mappings in CAT(0)-spaces, whereas previous results guarantee only exponential bounds. The method we use is to extend to the more general setting of uniformly convex hyperbolic spaces a quantitative version of a strengthening of Groetsch's theorem obtained by Kohlenbach using methods from mathematical logic (so-called ``proof mining'').
Wind Noise Reduction using Non-negative Sparse Coding
DEFF Research Database (Denmark)
Schmidt, Mikkel N.; Larsen, Jan; Hsiao, Fu-Tien
2007-01-01
We introduce a new speaker independent method for reducing wind noise in single-channel recordings of noisy speech. The method is based on non-negative sparse coding and relies on a wind noise dictionary which is estimated from an isolated noise recording. We estimate the parameters of the model...... and discuss their sensitivity. We then compare the algorithm with the classical spectral subtraction method and the Qualcomm-ICSI-OGI noise reduction method. We optimize the sound quality in terms of signal-to-noise ratio and provide results on a noisy speech recognition task....
Hierarchical subtask discovery with non-negative matrix factorization
CSIR Research Space (South Africa)
Earle, AC
2017-08-01
Full Text Available . Donoho, D. and Stodden, V. When does non-negative matrix factorization give a correct decomposition into parts? Proc. Advances in Neural Information Processing Systems 16, pp. 1141–1148, 2004. Hennequin, R., David, B., and Badeau, R. Beta-divergence as a... with Linearly Solvable Markov Decision Processes. arXiv, 2016. S¸ims¸ek, Ö. and Barto, A.S. Skill Characterization Based on Be- tweenness. Advances in Neural Information Processing Systems, pp. 1497–1504, 2009. Solway, A., Diuk, C., Córdova, N., Yee, D., Barto...
Graph Regularized Nonnegative Matrix Factorization for Hyperspectral Data Unmixing
Rajabi, Roozbeh; Ghassemian, Hassan
2011-01-01
Spectral unmixing is an important tool in hyperspectral data analysis for estimating endmembers and abundance fractions in a mixed pixel. This paper examines the applicability of a recently developed algorithm called graph regularized nonnegative matrix factorization (GNMF) for this aim. The proposed approach exploits the intrinsic geometrical structure of the data besides considering positivity and full additivity constraints. Simulated data based on the measured spectral signatures, is used for evaluating the proposed algorithm. Results in terms of abundance angle distance (AAD) and spectral angle distance (SAD) show that this method can effectively unmix hyperspectral data.
Representations of non-negative polynomials via critical ideals
Hiep, Dang Tuan
2011-01-01
This paper studies the representations of a non-negative polynomial $f$ on a non-compact semi-algebraic set $K$ modulo its critical ideal. Under the assumptions that the semi-algebraic set $K$ is regular and $f$ satisfies the boundary Hessian conditions (BHC) at each zero of $f$ in $K$, we show that $f$ can be represented as a sum of squares (SOS) of real polynomials modulo its critical ideal if $f\\ge 0$ on $K$. In particular, we focus on the polynomial ring $\\mathbb R[x]$.
Asymptotic Normality of Quadratic Estimators.
Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad
2016-12-01
We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.
quadratic spline finite element method
Directory of Open Access Journals (Sweden)
A. R. Bahadir
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
Optimal control linear quadratic methods
Anderson, Brian D O
2007-01-01
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the
Factorization method of quadratic template
Kotyrba, Martin
2017-07-01
Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.
The difference between 5 x 5 doubly nonnegative and completely positive matrices
Burer, Samuel; Anstreicher, Kurt M.; Duer, Mirjam
2009-01-01
The convex cone of n x n completely positive (CP) matrices and its dual cone of copositive matrices arise in several areas of applied mathematics, including optimization. Every CP matrix is doubly nonnegative (DNN), i.e., positive semidefinite and component-wise nonnegative, and it is known that, fo
The difference between 5 × 5 doubly nonnegative and completely positive matrices
Burer, Samuel; Anstreicher, Kurt M.; Dür, Mirjam
2009-01-01
The convex cone of n × n completely positive (CP) matrices and its dual cone of copositive matrices arise in several areas of applied mathematics, including optimization. Every CP matrix is doubly nonnegative (DNN), i.e., positive semidefinite and component-wise nonnegative, and it is known that, fo
How to project onto the monotone nonnegative cone using Pool Adjacent Violators type algorithms
Németh, A B
2012-01-01
The metric projection onto an order nonnegative cone from the metric projection onto the corresponding order cone is derived. Particularly, we can use Pool Adjacent Violators-type algorithms developed for projecting onto the monotone cone for projecting onto the monotone nonnegative cone too.
The difference between 5 × 5 doubly nonnegative and completely positive matrices
Burer, Samuel; Anstreicher, Kurt M.; Dür, Mirjam
2009-01-01
The convex cone of n × n completely positive (CP) matrices and its dual cone of copositive matrices arise in several areas of applied mathematics, including optimization. Every CP matrix is doubly nonnegative (DNN), i.e., positive semidefinite and component-wise nonnegative, and it is known that,
The difference between 5 x 5 doubly nonnegative and completely positive matrices
Burer, Samuel; Anstreicher, Kurt M.; Duer, Mirjam
2009-01-01
The convex cone of n x n completely positive (CP) matrices and its dual cone of copositive matrices arise in several areas of applied mathematics, including optimization. Every CP matrix is doubly nonnegative (DNN), i.e., positive semidefinite and component-wise nonnegative, and it is known that,
Quadratic reactivity fuel cycle model
Energy Technology Data Exchange (ETDEWEB)
Lewins, J.D.
1985-11-01
For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau/sup 2/ as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau/sup 2/ in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper.
A flexible R package for nonnegative matrix factorization
Directory of Open Access Journals (Sweden)
Seoighe Cathal
2010-07-01
Full Text Available Abstract Background Nonnegative Matrix Factorization (NMF is an unsupervised learning technique that has been applied successfully in several fields, including signal processing, face recognition and text mining. Recent applications of NMF in bioinformatics have demonstrated its ability to extract meaningful information from high-dimensional data such as gene expression microarrays. Developments in NMF theory and applications have resulted in a variety of algorithms and methods. However, most NMF implementations have been on commercial platforms, while those that are freely available typically require programming skills. This limits their use by the wider research community. Results Our objective is to provide the bioinformatics community with an open-source, easy-to-use and unified interface to standard NMF algorithms, as well as with a simple framework to help implement and test new NMF methods. For that purpose, we have developed a package for the R/BioConductor platform. The package ports public code to R, and is structured to enable users to easily modify and/or add algorithms. It includes a number of published NMF algorithms and initialization methods and facilitates the combination of these to produce new NMF strategies. Commonly used benchmark data and visualization methods are provided to help in the comparison and interpretation of the results. Conclusions The NMF package helps realize the potential of Nonnegative Matrix Factorization, especially in bioinformatics, providing easy access to methods that have already yielded new insights in many applications. Documentation, source code and sample data are available from CRAN.
Tang, Chun-Ming; Jian, Jin-Bao
2008-10-01
Based on an augmented Lagrangian line search function, a sequential quadratically constrained quadratic programming method is proposed for solving nonlinearly constrained optimization problems. Compared to quadratic programming solved in the traditional SQP methods, a convex quadratically constrained quadratic programming is solved here to obtain a search direction, and the Maratos effect does not occur without any other corrections. The "active set" strategy used in this subproblem can avoid recalculating the unnecessary gradients and (approximate) Hessian matrices of the constraints. Under certain assumptions, the proposed method is proved to be globally, superlinearly, and quadratically convergent. As an extension, general problems with inequality and equality constraints as well as nonmonotone line search are also considered.
On Algebraic Approach in Quadratic Systems
Directory of Open Access Journals (Sweden)
Matej Mencinger
2011-01-01
Full Text Available When considering friction or resistance, many physical processes are mathematically simulated by quadratic systems of ODEs or discrete quadratic dynamical systems. Probably the most important problem when such systems are applied in engineering is the stability of critical points and (nonchaotic dynamics. In this paper we consider homogeneous quadratic systems via the so-called Markus approach. We use the one-to-one correspondence between homogeneous quadratic dynamical systems and algebra which was originally introduced by Markus in (1960. We resume some connections between the dynamics of the quadratic systems and (algebraic properties of the corresponding algebras. We consider some general connections and the influence of power-associativity in the corresponding quadratic system.
An Algorithm for Solving Quadratic Programming Problems
Directory of Open Access Journals (Sweden)
V. Moraru
1997-08-01
Full Text Available Herein is investigated the method of solution of quadratic programming problems. The algorithm is based on the effective selection of constraints. Quadratic programming with constraints-equalities are solved with the help of an algorithm, so that matrix inversion is avoided, because of the more convenient organization of the Calculus. Optimal solution is determined in a finite number of iterations. It is discussed the extension of the algorithm over solving quadratic non-convex programming problems.
The Random Quadratic Assignment Problem
Paul, Gerald; Shao, Jia; Stanley, H. Eugene
2011-11-01
The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P. Surprisingly, the QAP has not been studied before using the replica method despite the fact that the QAP was first proposed over 50 years ago and the replica method was developed over 30 years ago. We find simple forms for C min and C max , the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for C min and C max and their dependence on P only through its mean and standard deviation, independent of the details of P.
A fast algorithm for nonnegative matrix factorization and its convergence.
Li, Li-Xin; Wu, Lin; Zhang, Hui-Sheng; Wu, Fang-Xiang
2014-10-01
Nonnegative matrix factorization (NMF) has recently become a very popular unsupervised learning method because of its representational properties of factors and simple multiplicative update algorithms for solving the NMF. However, for the common NMF approach of minimizing the Euclidean distance between approximate and true values, the convergence of multiplicative update algorithms has not been well resolved. This paper first discusses the convergence of existing multiplicative update algorithms. We then propose a new multiplicative update algorithm for minimizing the Euclidean distance between approximate and true values. Based on the optimization principle and the auxiliary function method, we prove that our new algorithm not only converges to a stationary point, but also does faster than existing ones. To verify our theoretical results, the experiments on three data sets have been conducted by comparing our proposed algorithm with other existing methods.
Symmetric nonnegative matrix factorization: algorithms and applications to probabilistic clustering.
He, Zhaoshui; Xie, Shengli; Zdunek, Rafal; Zhou, Guoxu; Cichocki, Andrzej
2011-12-01
Nonnegative matrix factorization (NMF) is an unsupervised learning method useful in various applications including image processing and semantic analysis of documents. This paper focuses on symmetric NMF (SNMF), which is a special case of NMF decomposition. Three parallel multiplicative update algorithms using level 3 basic linear algebra subprograms directly are developed for this problem. First, by minimizing the Euclidean distance, a multiplicative update algorithm is proposed, and its convergence under mild conditions is proved. Based on it, we further propose another two fast parallel methods: α-SNMF and β -SNMF algorithms. All of them are easy to implement. These algorithms are applied to probabilistic clustering. We demonstrate their effectiveness for facial image clustering, document categorization, and pattern clustering in gene expression.
Binary Quadratic Forms: A Historical View
Khosravani, Azar N.; Beintema, Mark B.
2006-01-01
We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…
Quadratic Boost A-Source Impedance Network
DEFF Research Database (Denmark)
Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii
2016-01-01
A novel quadratic boost type A-source impedance network is proposed in this paper for realizing converters that demand a very high voltage gain. To achieve that, the proposed network uses an auto-transformer, whose obtained gain is quadratically dependent on the duty ratio and is presently not ma...
Quadratic Boost A-Source Impedance Network
DEFF Research Database (Denmark)
Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii
2016-01-01
A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance ...
Factorising a Quadratic Expression with Geometric Insights
Joarder, Anwar H.
2015-01-01
An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers. There have been many methods for factorising a quadratic expression described in school text books. However, students often seem to struggle with…
An example in linear quadratic optimal control
Weiss, George; Zwart, Heiko J.
1998-01-01
We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme
An example in linear quadratic optimal control
Weiss, George; Zwart, Heiko J.
1998-01-01
We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme sim
An Effective Hybrid Artificial Bee Colony Algorithm for Nonnegative Linear Least Squares Problems
Directory of Open Access Journals (Sweden)
Xiangyu Kong
2014-07-01
Full Text Available An effective hybrid artificial bee colony algorithm is proposed in this paper for nonnegative linear least squares problems. To further improve the performance of algorithm, orthogonal initialization method is employed to generate the initial swarm. Furthermore, to balance the exploration and exploitation abilities, a new search mechanism is designed. The performance of this algorithm is verified by using 27 benchmark functions and 5 nonnegative linear least squares test problems. And the comparison analyses are given between the proposed algorithm and other swarm intelligence algorithms. Numerical results demonstrate that the proposed algorithm displays a high performance compared with other algorithms for global optimization problems and nonnegative linear least squares problems.
Approximate L0 constrained Non-negative Matrix and Tensor Factorization
DEFF Research Database (Denmark)
Mørup, Morten; Madsen, Kristoffer Hougaard; Hansen, Lars Kai
2008-01-01
Non-negative matrix factorization (NMF), i.e. V = WH where both V, W and H are non-negative has become a widely used blind source separation technique due to its part based representation. The NMF decomposition is not in general unique and a part based representation not guaranteed. However...... path for the L1 norm regularized least squares NMF for fixed W can be calculated at the cost of an ordinary least squares solution based on a modification of the Least Angle Regression and Selection (LARS) algorithm forming a non-negativity constrained LARS (NLARS). With the full regularization path...
Quadratic Hedging of Basis Risk
Directory of Open Access Journals (Sweden)
Hardy Hulley
2015-02-01
Full Text Available This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.
Scalable Linear Visual Feature Learning via Online Parallel Nonnegative Matrix Factorization.
Zhao, Xueyi; Li, Xi; Zhang, Zhongfei; Shen, Chunhua; Zhuang, Yueting; Gao, Lixin; Li, Xuelong
2016-12-01
Visual feature learning, which aims to construct an effective feature representation for visual data, has a wide range of applications in computer vision. It is often posed as a problem of nonnegative matrix factorization (NMF), which constructs a linear representation for the data. Although NMF is typically parallelized for efficiency, traditional parallelization methods suffer from either an expensive computation or a high runtime memory usage. To alleviate this problem, we propose a parallel NMF method called alternating least square block decomposition (ALSD), which efficiently solves a set of conditionally independent optimization subproblems based on a highly parallelized fine-grained grid-based blockwise matrix decomposition. By assigning each block optimization subproblem to an individual computing node, ALSD can be effectively implemented in a MapReduce-based Hadoop framework. In order to cope with dynamically varying visual data, we further present an incremental version of ALSD, which is able to incrementally update the NMF solution with a low computational cost. Experimental results demonstrate the efficiency and scalability of the proposed methods as well as their applications to image clustering and image retrieval.
Von Neumann Regularity and Quadratic Conorms in JB*-triples and C*-algebras
Institute of Scientific and Technical Information of China (English)
Mar(I)a BURGOS; El Amin KAIDI; Antonio Morales CAMPOY; Antonio M. PERALTA; Maribel RAM(I)REZ
2008-01-01
We revise the notion of von Neumann regularity in JB*-triples by finding a new character-isationin terms of the range of the quadratic operator Q(a). We introduce the quadratic conorm of anelement a in a JB*-triple as the minimum reduced modulus of the mapping Q(a). It is shown that thequadratic conorm of a coincides with the infimum of the squares of the points in the triple spectrumof a. It is established that a contractive bijection between JBW*-triples is a triple isomorphism if, andonly if, it preserves quadratic conorms. The continuity of the quadratic conorm and the generalizedinverse are discussed. Some applications to C*-algebras and von Neumann algebras are also studied.
Non-negative matrix factorization and term structure of interest rates
Takada, Hellinton H.; Stern, Julio M.
2015-01-01
Non-Negative Matrix Factorization (NNMF) is a technique for dimensionality reduction with a wide variety of applications from text mining to identification of concentrations in chemistry. NNMF deals with non-negative data and results in non-negative factors and factor loadings. Consequently, it is a natural choice when studying the term structure of interest rates. In this paper, NNMF is applied to obtain factors from the term structure of interest rates and the procedure is compared with other very popular techniques: principal component analysis and Nelson-Siegel model. The NNMF approximation for the term structure of interest rates is better in terms of fitting. From a practitioner point of view, the NNMF factors and factor loadings obtained possess straightforward financial interpretations due to their non-negativeness.
Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition
Astakhov, S A; Kraskov, A; Grassberger, P; Astakhov, Sergey A.; St\\"ogbauer, Harald; Kraskov, Alexander; Grassberger, Peter
2006-01-01
We propose a simulated annealing algorithm (called SNICA for "stochastic non-negative independent component analysis") for blind decomposition of linear mixtures of non-negative sources with non-negative coefficients. The de-mixing is based on a Metropolis type Monte Carlo search for least dependent components, with the mutual information between recovered components as a cost function and their non-negativity as a hard constraint. Elementary moves are shears in two-dimensional subspaces and rotations in three-dimensional subspaces. The algorithm is geared at decomposing signals whose probability densities peak at zero, the case typical in analytical spectroscopy and multivariate curve resolution. The decomposition performance on large samples of synthetic mixtures and experimental data is much better than that of traditional blind source separation methods based on principal component analysis (MILCA, FastICA, RADICAL) and chemometrics techniques (SIMPLISMA, ALS, BTEM) The source codes of SNICA, MILCA and th...
Matioc, Bogdan-Vasile
2011-01-01
We prove global existence of nonnegative weak solutions for a strongly coupled, fourth order degenerate parabolic system governing the motion of two thin fluid layers in a porous medium when capillarity is the sole driving mechanism.
COMPUTING A NEAREST P-SYMMETRIC NONNEGATIVE DEFINITE MATRIX UNDER LINEAR RESTRICTION
Institute of Scientific and Technical Information of China (English)
Hua Dai
2004-01-01
Let P be an n × n symmetric orthogonal matrix. A real n × n matrix A is called P-symmetric nonnegative definite if A is symmetric nonnegative definite and (PA)T =PA. This paper is concerned with a kind of inverse problem for P-symmetric nonncgative definite matrices: Given a real n × n matrix A, real n × m matrices X and B, find an n × n P-symmetric nonnegative definite matrix A minimizing ‖A- A‖F subject to AX = B.Necessary and sufficient conditions are presented for the solvability of the problem. The expression of the solution to the problem is given. These results are applied to solve an inverse eigenvalue problem for P-symmetric nonnegative definite matrices.
The Pure Virtual Braid Group Is Quadratic
Lee, Peter
2011-01-01
If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra gr_I K need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a criterion which is equivalent to gr_I K being quadratic. We apply this criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic.
Specialization of Quadratic and Symmetric Bilinear Forms
Knebusch, Manfred
2010-01-01
The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory. This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed for fields of characteristic different from 2, are explored here without this restriction. In addition to chapters on specialization theory, generic splitting t
Quadratic stabilization of switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
DONG YaLi; FAN JiaoJiao; MEI ShengWei
2009-01-01
In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated. When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law. The results of this paper are also applied to switched linear systems.
Two pitfalls of BOLD fMRI magnitude-based neuroimage analysis: non-negativity and edge effect.
Chen, Zikuan; Calhoun, Vince D
2011-08-15
BOLD fMRI is accepted as a noninvasive imaging modality for neuroimaging and brain mapping. A BOLD fMRI dataset consists of magnitude and phase components. Currently, only the magnitude is used for neuroimage analysis. In this paper, we show that the fMRI-magnitude-based neuroimage analysis may suffer two pitfalls: one is that the magnitude is non-negative and cannot differentiate positive from negative BOLD activity; the other is an edge effect that may manifest as an edge enhancement or a spatial interior dip artifact at a local uniform BOLD region. We demonstrate these pitfalls via numeric simulations using a BOLD fMRI model and also via a phantom experiment. We also propose a solution by making use of the fMRI phase image, the counterpart of the fMRI magnitude.
Dictionary Learning Based on Nonnegative Matrix Factorization Using Parallel Coordinate Descent
Directory of Open Access Journals (Sweden)
Zunyi Tang
2013-01-01
Full Text Available Sparse representation of signals via an overcomplete dictionary has recently received much attention as it has produced promising results in various applications. Since the nonnegativities of the signals and the dictionary are required in some applications, for example, multispectral data analysis, the conventional dictionary learning methods imposed simply with nonnegativity may become inapplicable. In this paper, we propose a novel method for learning a nonnegative, overcomplete dictionary for such a case. This is accomplished by posing the sparse representation of nonnegative signals as a problem of nonnegative matrix factorization (NMF with a sparsity constraint. By employing the coordinate descent strategy for optimization and extending it to multivariable case for processing in parallel, we develop a so-called parallel coordinate descent dictionary learning (PCDDL algorithm, which is structured by iteratively solving the two optimal problems, the learning process of the dictionary and the estimating process of the coefficients for constructing the signals. Numerical experiments demonstrate that the proposed algorithm performs better than the conventional nonnegative K-SVD (NN-KSVD algorithm and several other algorithms for comparison. What is more, its computational consumption is remarkably lower than that of the compared algorithms.
Structure of Solvable Quadratic Lie Algebras
Institute of Scientific and Technical Information of China (English)
ZHU Lin-sheng
2005-01-01
@@ Killing form plays a key role in the theory of semisimple Lie algebras. It is natural to extend the study to Lie algebras with a nondegenerate symmetric invariant bilinear form. Such a Lie algebra is generally called a quadratic Lie algebra which occur naturally in physics[10,12,13]. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the Kac-Moody algebras and the Extended Affine Lie algebras.
Compression limits in cascaded quadratic soliton compression
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Krolikowski, Wieslaw;
2008-01-01
Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency.......Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency....
Radiotherapy treatment planning linear-quadratic radiobiology
Chapman, J Donald
2015-01-01
Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil
Quadratic stabilization for uncertain stochastic systems
Institute of Scientific and Technical Information of China (English)
Jun'e FENG; Weihai ZHANG
2005-01-01
This paper discusses the robust quadratic stabilization control problem for stochastic uncertain systems,where the uncertain matrix is norm bounded,and the external disturbance is a stochastic process.Two kinds of controllers are designed,which include state feedback case and output feedback case.The conditions for the robust quadratic stabilization of stochastic uncertain systems are given via linear matrix inequalities.The detailed design methods are presented.Numerical examples show the effectiveness of our results.
Cascaded quadratic soliton compression at 800 nm
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Moses, Jeffrey;
2007-01-01
We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion.......We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....
A NEW INEXACT SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM
Institute of Scientific and Technical Information of China (English)
倪勤
2002-01-01
This paper represents an inexact sequential quadratic programming (SQP ) algorithm which can solve nonlinear programming (NLP ) problems. An inexact solution of the quadratic programming subproblem is determined by a projection and contraction method such that only matrix-vector product is required. Some truncated criteria are chosen such that the algorithm is suitable to large scale NLP problem. The global convergence of the algorithm is proved.
Learning a Nonnegative Sparse Graph for Linear Regression.
Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung
2015-09-01
Previous graph-based semisupervised learning (G-SSL) methods have the following drawbacks: 1) they usually predefine the graph structure and then use it to perform label prediction, which cannot guarantee an overall optimum and 2) they only focus on the label prediction or the graph structure construction but are not competent in handling new samples. To this end, a novel nonnegative sparse graph (NNSG) learning method was first proposed. Then, both the label prediction and projection learning were integrated into linear regression. Finally, the linear regression and graph structure learning were unified within the same framework to overcome these two drawbacks. Therefore, a novel method, named learning a NNSG for linear regression was presented, in which the linear regression and graph learning were simultaneously performed to guarantee an overall optimum. In the learning process, the label information can be accurately propagated via the graph structure so that the linear regression can learn a discriminative projection to better fit sample labels and accurately classify new samples. An effective algorithm was designed to solve the corresponding optimization problem with fast convergence. Furthermore, NNSG provides a unified perceptiveness for a number of graph-based learning methods and linear regression methods. The experimental results showed that NNSG can obtain very high classification accuracy and greatly outperforms conventional G-SSL methods, especially some conventional graph construction methods.
Multiplicative algorithms for constrained non-negative matrix factorization
Peng, Chengbin
2012-12-01
Non-negative matrix factorization (NMF) provides the advantage of parts-based data representation through additive only combinations. It has been widely adopted in areas like item recommending, text mining, data clustering, speech denoising, etc. In this paper, we provide an algorithm that allows the factorization to have linear or approximatly linear constraints with respect to each factor. We prove that if the constraint function is linear, algorithms within our multiplicative framework will converge. This theory supports a large variety of equality and inequality constraints, and can facilitate application of NMF to a much larger domain. Taking the recommender system as an example, we demonstrate how a specialized weighted and constrained NMF algorithm can be developed to fit exactly for the problem, and the tests justify that our constraints improve the performance for both weighted and unweighted NMF algorithms under several different metrics. In particular, on the Movielens data with 94% of items, the Constrained NMF improves recall rate 3% compared to SVD50 and 45% compared to SVD150, which were reported as the best two in the top-N metric. © 2012 IEEE.
A Multidimensional Nonnegative Matrix Factorization Model for Retweeting Behavior Prediction
Directory of Open Access Journals (Sweden)
Mengmeng Wang
2015-01-01
Full Text Available Today microblogging has increasingly become a means of information diffusion via user’s retweeting behavior. As a consequence, exploring on retweeting behavior is a better way to understand microblog’s transmissibility in the network. Hence, targeted at online microblogging, a directed social network, along with user-based features, this paper first built content-based features, which consisted of URL, hashtag, emotion difference, and interest similarity, based on time series of text information that user posts. And then we measure relationship-based factor in social network according to frequency of interactions and network structure which blend with temporal information. Finally, we utilize nonnegative matrix factorization to predict user’s retweeting behavior from user-based dimension and content-based dimension, respectively, by employing strength of social relationship to constrain objective function. The results suggest that our proposed method effectively increases retweeting behavior prediction accuracy and provides a new train of thought for retweeting behavior prediction in dynamic social networks.
Sparse Nonnegative Matrix Factorization Strategy for Cochlear Implants
Directory of Open Access Journals (Sweden)
Hongmei Hu
2015-12-01
Full Text Available Current cochlear implant (CI strategies carry speech information via the waveform envelope in frequency subbands. CIs require efficient speech processing to maximize information transfer to the brain, especially in background noise, where the speech envelope is not robust to noise interference. In such conditions, the envelope, after decomposition into frequency bands, may be enhanced by sparse transformations, such as nonnegative matrix factorization (NMF. Here, a novel CI processing algorithm is described, which works by applying NMF to the envelope matrix (envelopogram of 22 frequency channels in order to improve performance in noisy environments. It is evaluated for speech in eight-talker babble noise. The critical sparsity constraint parameter was first tuned using objective measures and then evaluated with subjective speech perception experiments for both normal hearing and CI subjects. Results from vocoder simulations with 10 normal hearing subjects showed that the algorithm significantly enhances speech intelligibility with the selected sparsity constraints. Results from eight CI subjects showed no significant overall improvement compared with the standard advanced combination encoder algorithm, but a trend toward improvement of word identification of about 10 percentage points at +15 dB signal-to-noise ratio (SNR was observed in the eight CI subjects. Additionally, a considerable reduction of the spread of speech perception performance from 40% to 93% for advanced combination encoder to 80% to 100% for the suggested NMF coding strategy was observed.
Sparse Nonnegative Matrix Factorization Strategy for Cochlear Implants.
Hu, Hongmei; Lutman, Mark E; Ewert, Stephan D; Li, Guoping; Bleeck, Stefan
2015-12-30
Current cochlear implant (CI) strategies carry speech information via the waveform envelope in frequency subbands. CIs require efficient speech processing to maximize information transfer to the brain, especially in background noise, where the speech envelope is not robust to noise interference. In such conditions, the envelope, after decomposition into frequency bands, may be enhanced by sparse transformations, such as nonnegative matrix factorization (NMF). Here, a novel CI processing algorithm is described, which works by applying NMF to the envelope matrix (envelopogram) of 22 frequency channels in order to improve performance in noisy environments. It is evaluated for speech in eight-talker babble noise. The critical sparsity constraint parameter was first tuned using objective measures and then evaluated with subjective speech perception experiments for both normal hearing and CI subjects. Results from vocoder simulations with 10 normal hearing subjects showed that the algorithm significantly enhances speech intelligibility with the selected sparsity constraints. Results from eight CI subjects showed no significant overall improvement compared with the standard advanced combination encoder algorithm, but a trend toward improvement of word identification of about 10 percentage points at +15 dB signal-to-noise ratio (SNR) was observed in the eight CI subjects. Additionally, a considerable reduction of the spread of speech perception performance from 40% to 93% for advanced combination encoder to 80% to 100% for the suggested NMF coding strategy was observed.
Gao, Hao
2016-04-01
For the treatment planning during intensity modulated radiation therapy (IMRT) or volumetric modulated arc therapy (VMAT), beam fluence maps can be first optimized via fluence map optimization (FMO) under the given dose prescriptions and constraints to conformally deliver the radiation dose to the targets while sparing the organs-at-risk, and then segmented into deliverable MLC apertures via leaf or arc sequencing algorithms. This work is to develop an efficient algorithm for FMO based on alternating direction method of multipliers (ADMM). Here we consider FMO with the least-square cost function and non-negative fluence constraints, and its solution algorithm is based on ADMM, which is efficient and simple-to-implement. In addition, an empirical method for optimizing the ADMM parameter is developed to improve the robustness of the ADMM algorithm. The ADMM based FMO solver was benchmarked with the quadratic programming method based on the interior-point (IP) method using the CORT dataset. The comparison results suggested the ADMM solver had a similar plan quality with slightly smaller total objective function value than IP. A simple-to-implement ADMM based FMO solver with empirical parameter optimization is proposed for IMRT or VMAT.
On Quadratic Integral Equations of Urysohn Type in Fréchet Spaces
Directory of Open Access Journals (Sweden)
M. A. Darwish
2010-02-01
Full Text Available In this paper, we investigate the existence of a unique solution on a semiinfinite interval for a quadratic integral equation of Urysohn type in Fréchet spaces using a nonlinear alternative of Leray-Schauder type for contractive maps.
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2006-01-01
This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...
Linear-quadratic control and quadratic differential forms for multidimensional behaviors
Napp, D.; Trentelman, H.L.
2011-01-01
This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look
Xia, Yong; Han, Ying-Wei
2014-01-01
In this paper, we propose a mixed-binary convex quadratic programming reformulation for the box-constrained nonconvex quadratic integer program and then implement IBM ILOG CPLEX 12.6 to solve the new model. Computational results demonstrate that our approach clearly outperform the very recent state-of-the-art solvers.
Indian Academy of Sciences (India)
DEEPAK KUMAR; A G RAMAKRISHNAN
2016-03-01
Particle swarm optimization (PSO) is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The central idea is to use PSO to move in the direction towards optimal solution rather than searching the entire feasibleregion. Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or classification boundary for a data set. Our results on the Iris, Pima, Wine, Thyroid, Balance, Bupa, Haberman, and TAE datasets show that the proposed method works better than a neural network and the performance is close to that of a support vector machine
Fast approximate quadratic programming for graph matching.
Directory of Open Access Journals (Sweden)
Joshua T Vogelstein
Full Text Available Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs, we find that it efficiently achieves performance.
Fast approximate quadratic programming for graph matching.
Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance.
Quadratic Interpolation Algorithm for Minimizing Tabulated Function
Directory of Open Access Journals (Sweden)
E. A. Youness
2008-01-01
Full Text Available Problem statement: The problem of finding the minimum value of objective function, when we know only some values of it, is needed in more practical fields. Quadratic interpolation algorithms are the famous tools deal with this kind of these problems. These algorithms interested with the polynomial space in which the objective function is approximated. Approach: In this study we approximated the objective function by a one dimensional quadratic polynomial. This approach saved the time and the effort to get the best point at which the objective is minimized. Results: The quadratic polynomial in each one of the steps of the proposed algorithm, accelerate the convergent to the best value of the objective function without taking into account all points of the interpolation set. Conclusion: Any n-dimensional problem of finding a minimal value of a function, given by some values, can be converted to one dimensional problem easier in deal.
Quadratic gravity: from weak to strong
Holdom, Bob
2016-01-01
More than three decades ago quadratic gravity was found to present a perturbative, renormalizable and asymptotically free theory of quantum gravity. Unfortunately the theory appeared to have problems with a spin-2 ghost. In this essay we revisit quadratic gravity in a different light by considering the case that the asymptotically free interaction flows to a strongly interacting regime. This occurs when the coefficient of the Einstein-Hilbert term is smaller than the scale $\\Lambda_{\\mathrm{QG}}$ where the quadratic couplings grow strong. Here QCD provides some useful insights. By pushing the analogy with QCD, we conjecture that the nonperturbative effects can remove the naive spin-2 ghost and lead to the emergence of general relativity in the IR.
Functional biogeography of ocean microbes revealed through non-negative matrix factorization.
Directory of Open Access Journals (Sweden)
Xingpeng Jiang
Full Text Available The direct "metagenomic" sequencing of genomic material from complex assemblages of bacteria, archaea, viruses and microeukaryotes has yielded new insights into the structure of microbial communities. For example, analysis of metagenomic data has revealed the existence of previously unknown microbial taxa whose spatial distributions are limited by environmental conditions, ecological competition, and dispersal mechanisms. However, differences in genotypes that might lead biologists to designate two microbes as taxonomically distinct need not necessarily imply differences in ecological function. Hence, there is a growing need for large-scale analysis of the distribution of microbial function across habitats. Here, we present a framework for investigating the biogeography of microbial function by analyzing the distribution of protein families inferred from environmental sequence data across a global collection of sites. We map over 6,000,000 protein sequences from unassembled reads from the Global Ocean Survey dataset to [Formula: see text] protein families, generating a protein family relative abundance matrix that describes the distribution of each protein family across sites. We then use non-negative matrix factorization (NMF to approximate these protein family profiles as linear combinations of a small number of ecological components. Each component has a characteristic functional profile and site profile. Our approach identifies common functional signatures within several of the components. We use our method as a filter to estimate functional distance between sites, and find that an NMF-filtered measure of functional distance is more strongly correlated with environmental distance than a comparable PCA-filtered measure. We also find that functional distance is more strongly correlated with environmental distance than with geographic distance, in agreement with prior studies. We identify similar protein functions in several components and
The Wiener maximum quadratic assignment problem
Cela, Eranda; Woeginger, Gerhard J
2011-01-01
We investigate a special case of the maximum quadratic assignment problem where one matrix is a product matrix and the other matrix is the distance matrix of a one-dimensional point set. We show that this special case, which we call the Wiener maximum quadratic assignment problem, is NP-hard in the ordinary sense and solvable in pseudo-polynomial time. Our approach also yields a polynomial time solution for the following problem from chemical graph theory: Find a tree that maximizes the Wiener index among all trees with a prescribed degree sequence. This settles an open problem from the literature.
A CART extention using Quadratic Decision Borders
DEFF Research Database (Denmark)
Hartelius, Karsten
1999-01-01
In this article we put forward an extention to the hierarchical CART classification method which uses quadratic decision borders. The original CART applies univariate splits on individual variables as well as splits on combinations of variables to recursively partition the feature......-space into subsets which are successively more class-homogeneous. Guided by the fact that class-distributions in feature-space are very often hyper-elliptical shaped, we give an extension to the original CART which also uses quadratic shaped decision borders which can be modelled by a mean-vector and a dispersion...
A CART extension using Quadratic Decision Borders
DEFF Research Database (Denmark)
Hartelius, Karsten
1999-01-01
In this article we put forward an extention to the hierarchical CART classification method which uses quadratic decision borders. The original CART applies univariate splits on individual variables as well as splits on combinations of variables to recursively partition the feature......-space into subsets which are successively more class-homogeneous. Guided by the fact that class-distributions in feature-space are very often hyper-elliptical shaped, we give an extension to the original CART which also uses quadratic shaped decision borders which can be modelled by a mean-vector and a dispersion...
PSQP: Puzzle Solving by Quadratic Programming.
Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome
2017-02-01
In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.
Quintessence with quadratic coupling to dark matter
Boehmer, Christian G; Chan, Nyein; Lazkoz, Ruth; Maartens, Roy
2009-01-01
We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.
Guises and disguises of quadratic divergences
Energy Technology Data Exchange (ETDEWEB)
Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)
2014-12-15
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
Indirect quantum tomography of quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...
Lambda-lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, O.; Schultz, U.P.
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...
On orthogonality preserving quadratic stochastic operators
Energy Technology Data Exchange (ETDEWEB)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
Discrete fractional Radon transforms and quadratic forms
Pierce, Lillian B
2010-01-01
We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove sharp results for this class of discrete operators in all dimensions, providing necessary and sufficient conditions for them to extend to bounded operators from $\\ell^p$ to $\\ell^q$. The method involves an intricate spectral decomposition according to major and minor arcs, motivated by ideas from the circle method of Hardy and Littlewood. Techniques from harmonic analysis, in particular Fourier transform methods and oscillatory integrals, as well as the number theoretic structure of quadratic forms, exponential sums, and theta functions, play key roles in the proof.
Separating inequalities for nonnegative polynomials that are not sums of squares
Iliman, Sadik
2012-01-01
Ternary sextics and quaternary quartics are the smallest cases where there exist nonnegative polynomials that are not sums of squares (SOS). A complete classification of the difference between these cones was given by G. Blekherman via analyzing the corresponding dual cones. An exact computation of the extreme rays in order to separate a fixed nonnegative polynomial that is not SOS is difficult. We provide a method substantially simplifying this computation for certain classes of polynomials on the boundary of these cones. In particular, our method yields separating extreme rays for almost every nonnegative ternary sextic with at least seven zeros. As an application to further instances, we compute a rational certificate proving that the Motzkin polynomial is not SOS.
Ma, Yuanyuan; Hu, Xiaohua; He, Tingting; Jiang, Xingpeng
2017-09-26
Many datasets existed in the real world are often comprised of different representations or views which provide complementary information to each other. To integrate information from multiple views, data integration approaches such as nonnegative matrix factorization (NMF) have been developed to combine multiple heterogeneous data simultaneously to obtain a comprehensive representation. In this paper, we proposed a novel variant of symmetric nonnegative matrix factorization (SNMF), called Laplacian regularization based joint symmetric nonnegative matrix factorization (LJ-SNMF) for clustering multi-view data. We conduct extensive experiments on several realistic datasets including Human Microbiome Project data. The experimental results show that the proposed method outperforms other variants of NMF, which suggests the potential application of LJ-SNMF in clustering multi-view datasets. Additionally, we also demonstrate the capability of LJ-SNMF in community finding.
Enhanced surrogate models for statistical design exploiting space mapping technology
DEFF Research Database (Denmark)
Koziel, Slawek; Bandler, John W.; Mohamed, Achmed S.;
2005-01-01
We present advances in microwave and RF device modeling exploiting Space Mapping (SM) technology. We propose new SM modeling formulations utilizing input mappings, output mappings, frequency scaling and quadratic approximations. Our aim is to enhance circuit models for statistical analysis...
Test-assignment: a quadratic coloring problem
Duives, Jelle; Lodi, Andrea; Malaguti, Enrico
2013-01-01
We consider the problem of assigning the test variants of a written exam to the desks of a classroom in such a way that desks that are close-by receive different variants. The problem is a generalization of the Vertex Coloring and we model it as a binary quadratic problem. Exact solution methods bas
Experimental results on quadratic assignment problem
Directory of Open Access Journals (Sweden)
N.P. Nikolov
1999-08-01
Full Text Available The paper presents experimental results on quadratic assignment problem. The "scanning area" method formulated for radioelectronic equipment design is applied. For all more complex tests ours results are better or coincident with the ones known in literature. Conclusion concerning the effectiveness of method are given.
Institute of Scientific and Technical Information of China (English)
谭亚茹
2016-01-01
The quadratic Higher Algebra is an important part of this paper, the definition of quadratic forms, introduces the second type of representation, and then describes how to use the allocation method, elementary transformation, orthogonal transformation method, etc. II second type into the standard form, and the second type of normal form, finally introduced posi-tive definite quadratic form and method for determining positive definite quadratic form.%二次型是高等代数的重要组成部分，本文从二次型的定义出发，介绍了二次型的表示方法，然后介绍了如何用配方法、初等变换法、正交变换法等将二次型化为标准形，以及二次型的规范形，最后介绍了正定二次型和判定正定二次型的方法。
On Quadratic Programming with a Ratio Objective
Bhaskara, Aditya; Manokaran, Rajsekar; Vijayaraghavan, Aravindan
2011-01-01
Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \\sum_ij a_ij x_i x_j. QP captures many known combinatorial optimization problems and SDP techniques have given optimal approximation algorithms for many of these problems. We extend this body of work by initiating the study of Quadratic Programming problems where the variables take values in the domain {-1,0,1}. The specific problem we study is: QP-Ratio: max_{-1,0,1}^n (x^T A x) / (x^T x). This objective function is a natural relative of several well studied problems. Yet, it is a good testbed for both algorithms and complexity because the techniques used for quadratic problems for the {-1,1} and {0,1} domains do not seem to carry over to the {-1,0,1} domain. We give approximation algorithms and evidence for the hardness of approximating the QP-Ratio problem. We consider an SDP relaxation obtained by adding constraints to the natural SDP relaxation for this problem and obtain an O(n^{2/7}) algorithm for...
Target manifold formation using a quadratic SDF
Hester, Charles F.; Risko, Kelly K. D.
2013-05-01
Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.
The GCD property and irreduciable quadratic polynomials
Directory of Open Access Journals (Sweden)
Saroj Malik
1986-01-01
Full Text Available The proof of the following theorem is presented: If D is, respectively, a Krull domain, a Dedekind domain, or a Prüfer domain, then D is correspondingly a UFD, a PID, or a Bezout domain if and only if every irreducible quadratic polynomial in D[X] is a prime element.
Modulational instability in periodic quadratic nonlinear materials
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never complete...
Integration of the Quadratic Function and Generalization
Mitsuma, Kunio
2011-01-01
We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…
Solitons in quadratic nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families...
Range-based estimation of quadratic variation
DEFF Research Database (Denmark)
Christensen, Kim; Podolskij, Mark
In this paper, we propose using realized range-based estimation to draw inference about the quadratic variation of jump-diffusion processes. We also construct a new test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the test...
Range-based estimation of quadratic variation
DEFF Research Database (Denmark)
Christensen, Kim; Podolskij, Mark
This paper proposes using realized range-based estimators to draw inference about the quadratic variation of jump-diffusion processes. We also construct a range-based test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient...
On the Content Bound for Real Quadratic Field Extensions
Directory of Open Access Journals (Sweden)
Robert G. Underwood
2012-12-01
Full Text Available Let K be a finite extension of Q and let S = {ν} denote the collection of K normalized absolute values on K. Let V+K denote the additive group of adeles over K and let K ≥0 c : V + → R denote the content map defined as c({aν } = Q K ν ∈S ν (aν for {aν } ∈ V+K A classical result of J. W. S. Cassels states that there is a constant c > 0 depending only on the field K with the following property: if {aν } ∈ V+K with c({aν } > c, then there exists a non-zero element b ∈ K for which ν (b ≤ ν (aν , ∀ν ∈ S. Let cK be the greatest lower bound of the set of all c that satisfy this property. In the case that K is a real quadratic extension there is a known upper bound for cK due to S. Lang. The purpose of this paper is to construct a new upper bound for cK in the case that K has class number one. We compare our new bound with Lang’s bound for various real quadratic extensions and find that our new bound is better than Lang’s in many instances.
A Public Key Block Cipher Based on Multivariate Quadratic Quasigroups
Gligoroski, Danilo; Knapskog, Svein Johan
2008-01-01
We have designed a new class of public key algorithms based on quasigroup string transformations using a specific class of quasigroups called multivariate quadratic quasigroups (MQQ). Our public key algorithm is a bijective mapping, it does not perform message expansions and can be used both for encryption and signatures. The public key consist of n quadratic polynomials with n variables where n=140, 160, ... . A particular characteristic of our public key algorithm is that it is very fast and highly parallelizable. More concretely, it has the speed of a typical modern symmetric block cipher - the reason for the phrase "A Public Key Block Cipher" in the title of this paper. Namely the reference C code for the 160-bit variant of the algorithm performs decryption in less than 11,000 cycles (on Intel Core 2 Duo -- using only one processor core), and around 6,000 cycles using two CPU cores and OpenMP 2.0 library. However, implemented in Xilinx Virtex-5 FPGA that is running on 249.4 MHz it achieves decryption thro...
Quadratically constrained quadratic programs on acyclic graphs with application to power flow
Bose, Subhonmesh; Low, Steven H; Chandy, K Mani
2012-01-01
This paper proves that non-convex quadratically constrained quadratic programs have an exact semidefinite relaxation when their underlying graph is acyclic, provided the constraint set satisfies a certain technical condition. When the condition is not satisfied, we propose a heuristic to obtain a feasible point starting from a solution of the relaxed problem. These methods are then demonstrated to provide exact solutions to a richer class of optimal power flow problems than previously solved.
Geometric Approaches to Quadratic Equations from Other Times and Places.
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
Total coloring of graphs embedded in surfaces of nonnegative Euler characteristic
Institute of Scientific and Technical Information of China (English)
WANG HuiJuan; LIU Bin; WU JianLiang; WANG Bing
2014-01-01
Let G be a graph which can be embedded in a surface of nonnegative Euler characteristic.In this paper,it is proved that the total chromatic number of G is △（G）＋1 if △（G）9,where △（G）is the maximum degree of G.
Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions
Siem, A.Y.D.; de Klerk, E.; den Hertog, D.
2005-01-01
Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models.Often, it is known beforehand, that the underlying unknown function has certain properties, e.g. nonnegative or increasing on a certain region.However, the
Bayesian Nonnegative Matrix Factorization with Volume Prior for Unmixing of Hyperspectral Images
DEFF Research Database (Denmark)
Arngren, Morten; Schmidt, Mikkel Nørgaard; Larsen, Jan
2009-01-01
In hyperspectral image analysis the objective is to unmix a set of acquired pixels into pure spectral signatures (endmembers) and corresponding fractional abundances. The Non-negative Matrix Factorization (NMF) methods have received a lot of attention for this unmixing process. Many of these NMF...
Non-negative matrix analysis in x-ray spectromicroscopy: choosing regularizers
Mak, Rachel; Wild, Stefan M.; Jacobsen, Chris
2016-01-01
In x-ray spectromicroscopy, a set of images can be acquired across an absorption edge to reveal chemical speciation. We previously described the use of non-negative matrix approximation methods for improved classification and analysis of these types of data. We present here an approach to find appropriate values of regularization parameters for this optimization approach. PMID:27041779
Efficient non-negative constrained model-based inversion in optoacoustic tomography
Ding, Lu; Luís Deán-Ben, X.; Lutzweiler, Christian; Razansky, Daniel; Ntziachristos, Vasilis
2015-09-01
The inversion accuracy in optoacoustic tomography depends on a number of parameters, including the number of detectors employed, discrete sampling issues or imperfectness of the forward model. These parameters result in ambiguities on the reconstructed image. A common ambiguity is the appearance of negative values, which have no physical meaning since optical absorption can only be higher or equal than zero. We investigate herein algorithms that impose non-negative constraints in model-based optoacoustic inversion. Several state-of-the-art non-negative constrained algorithms are analyzed. Furthermore, an algorithm based on the conjugate gradient method is introduced in this work. We are particularly interested in investigating whether positive restrictions lead to accurate solutions or drive the appearance of errors and artifacts. It is shown that the computational performance of non-negative constrained inversion is higher for the introduced algorithm than for the other algorithms, while yielding equivalent results. The experimental performance of this inversion procedure is then tested in phantoms and small animals, showing an improvement in image quality and quantitativeness with respect to the unconstrained approach. The study performed validates the use of non-negative constraints for improving image accuracy compared to unconstrained methods, while maintaining computational efficiency.
Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions
Siem, A.Y.D.; de Klerk, E.; den Hertog, D.
2005-01-01
Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models.Often, it is known beforehand, that the underlying unknown function has certain properties, e.g. nonnegative or increasing on a certain region.However, the
ON THE FUNDAMENTAL GROUP OF OPEN MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE
Institute of Scientific and Technical Information of China (English)
XU SENLIN; WANG ZUOQIN; YANG FANGYUN
2003-01-01
The authors establish some uniform estimates for the distance to halfway points of minimalgeodesics in terms of the distantce to end points on some types of Riemannian manifolds, andthen prove some theorems about the finite generation of fundamental group of Riemannianmanifold with nonnegative Ricci curvature, which support the famous Milnor conjecture.
Existence of non-negative solutions for nonlinear equations in the semi-positone case
Directory of Open Access Journals (Sweden)
Naji Yebari
2006-09-01
Full Text Available Using the fibring method we prove the existence of non-negative solution of the p-Laplacian boundary value problem $-Delta_pu=lambda f(u$, for any $lambda >0$ on any regular bounded domain of $mathbb{R}^N$, in the special case $f(t=t^q-1$.
Directory of Open Access Journals (Sweden)
Shota Saito
Full Text Available Micro-blogging services, such as Twitter, offer opportunities to analyse user behaviour. Discovering and distinguishing behavioural patterns in micro-blogging services is valuable. However, it is difficult and challenging to distinguish users, and to track the temporal development of collective attention within distinct user groups in Twitter. In this paper, we formulate this problem as tracking matrices decomposed by Nonnegative Matrix Factorisation for time-sequential matrix data, and propose a novel extension of Nonnegative Matrix Factorisation, which we refer to as Time Evolving Nonnegative Matrix Factorisation (TENMF. In our method, we describe users and words posted in some time interval by a matrix, and use several matrices as time-sequential data. Subsequently, we apply Time Evolving Nonnegative Matrix Factorisation to these time-sequential matrices. TENMF can decompose time-sequential matrices, and can track the connection among decomposed matrices, whereas previous NMF decomposes a matrix into two lower dimension matrices arbitrarily, which might lose the time-sequential connection. Our proposed method has an adequately good performance on artificial data. Moreover, we present several results and insights from experiments using real data from Twitter.
Saito, Shota; Hirata, Yoshito; Sasahara, Kazutoshi; Suzuki, Hideyuki
2015-01-01
Micro-blogging services, such as Twitter, offer opportunities to analyse user behaviour. Discovering and distinguishing behavioural patterns in micro-blogging services is valuable. However, it is difficult and challenging to distinguish users, and to track the temporal development of collective attention within distinct user groups in Twitter. In this paper, we formulate this problem as tracking matrices decomposed by Nonnegative Matrix Factorisation for time-sequential matrix data, and propose a novel extension of Nonnegative Matrix Factorisation, which we refer to as Time Evolving Nonnegative Matrix Factorisation (TENMF). In our method, we describe users and words posted in some time interval by a matrix, and use several matrices as time-sequential data. Subsequently, we apply Time Evolving Nonnegative Matrix Factorisation to these time-sequential matrices. TENMF can decompose time-sequential matrices, and can track the connection among decomposed matrices, whereas previous NMF decomposes a matrix into two lower dimension matrices arbitrarily, which might lose the time-sequential connection. Our proposed method has an adequately good performance on artificial data. Moreover, we present several results and insights from experiments using real data from Twitter.
On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics
Directory of Open Access Journals (Sweden)
M. De la Sen
2014-01-01
Full Text Available This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.
Linear Fractional Transformations of Nevanlinna Functions Associated with a Nonnegative Operator
Behrndt, Jussi; Hassi, Seppo; de Snoo, Henk; Wietsma, Rudi; Winkler, Henrik
2013-01-01
In the present paper a subclass of scalar Nevanlinna functions is studied, which coincides with the class of Weyl functions associated to a nonnegative symmetric operator of defect one in a Hilbert space. This class consists of all Nevanlinna functions that are holomorphic on (-a, 0) and all those N
Non-negatively curved 5-manifolds with almost maximal symmetry rank
Galaz-Garcia, Fernando
2011-01-01
We show that a closed, simply-connected, non-negatively curved 5-manifold admitting an effective, isometric $T^2$ action is diffeomorphic to one of $S^5$, $S^3\\times S^2$, $S^3\\tilde{\\times} S^2$ (the non-trivial $S^3$-bundle over $S^2$) or the Wu manifold $SU(3)/SO(3)$.
Reduction of Non-stationary Noise using a Non-negative Latent Variable Decomposition
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Larsen, Jan
2008-01-01
We present a method for suppression of non-stationary noise in single channel recordings of speech. The method is based on a non-negative latent variable decomposition model for the speech and noise signals, learned directly from a noisy mixture. In non-speech regions an over complete basis...
On quadratic residue codes and hyperelliptic curves
Directory of Open Access Journals (Sweden)
David Joyner
2008-01-01
Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''
Higgsed Stueckelberg vector and Higgs quadratic divergence
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Durmuş Ali Demir
2015-01-01
Full Text Available Here we show that, a hidden vector field whose gauge invariance is ensured by a Stueckelberg scalar and whose mass is spontaneously generated by the Standard Model Higgs field contributes to quadratic divergences in the Higgs boson mass squared, and even leads to its cancellation at one-loop when Higgs coupling to gauge field is fine-tuned. In contrast to mechanisms based on hidden scalars where a complete cancellation cannot be achieved, stabilization here is complete in that the hidden vector and the accompanying Stueckelberg scalar are both free from quadratic divergences at one-loop. This stability, deriving from hidden exact gauge invariance, can have important implications for modeling dark phenomena like dark matter, dark energy, dark photon and neutrino masses. The hidden fields can be produced at the LHC.
Linear quadratic output tracking and disturbance rejection
Karimi-Ghartemani, Masoud; Khajehoddin, S. Ali; Jain, Praveen; Bakhshai, Alireza
2011-08-01
This article introduces the problem of linear quadratic tracking (LQT) where the objective is to design a closed-loop control scheme such that the output signal of the system optimally tracks a given reference signal and rejects a given disturbance. Different performance indices that have been used to address the tracking problem are discussed and an appropriate new form is introduced. It is shown that a solution to the proposed optimality index exists under very mild conditions of stabilisability and detectability of the plant state-space equations. The solution is formulated based on converting the LQT problem to a standard linear quadratic regulation problem. The method is applied to two examples, a first-order plant and a third-order plant, and their simulation results are presented and discussed.
Estimating quadratic variation using realized variance
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Shephard, N.
2002-01-01
This paper looks at some recent work on estimating quadratic variation using realized variance (RV) - that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process is a semimar......This paper looks at some recent work on estimating quadratic variation using realized variance (RV) - that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process...... have to impose some weak regularity assumptions. We illustrate the use of the limit theory on some exchange rate data and some stock data. We show that even with large values of M the RV is sometimes a quite noisy estimator of integrated variance. Copyright © 2002 John Wiley & Sons, Ltd....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2003-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, O.; Schultz, U.P.
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Quaternion orders, quadratic forms, and Shimura curves
Alsina, Montserrat
2004-01-01
Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...
A Finite Continuation Algorithm for Bound Constrained Quadratic Programming
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.
1999-01-01
The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...
Elementary Components of the Quadratic Assignment Problem
Chicano, Francisco; Alba, Enrique
2011-01-01
The Quadratic Assignment Problem (QAP) is a well-known NP-hard combinatorial optimization problem that is at the core of many real-world optimization problems. We prove that QAP can be written as the sum of three elementary landscapes when the swap neighborhood is used. We present a closed formula for each of the three elementary components and we compute bounds for the autocorrelation coefficient.
Cubic Lienard Equations with Quadratic Damping (Ⅱ)
Institute of Scientific and Technical Information of China (English)
Yu-quan Wang; Zhu-jun Jing
2002-01-01
Applying Hopf bifurcation theory and qualitative theory, we show that the general cubic Lienard equations with quadratic damping have at most three limit cycles. This implies that the guess in which the system has at most two limit cycles is false. We give the sufficient conditions for the system has at most three limit cycles or two limit cycles. We present two examples with three limit cycles or two limit cycles by using numerical simulation.
Characterization of a Quadratic Function in Rn
Xu, Conway
2010-01-01
It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.
Quadratic forms representing all odd positive integers
Rouse, Jeremy
2011-01-01
We consider the problem of classifying all positive-definite integer-valued quadratic forms that represent all positive odd integers. Kaplansky considered this problem for ternary forms, giving a list of 23 candidates, and proving that 19 of those represent all positive odds. (Jagy later dealt with a 20th candidate.) Assuming that the remaining three forms represent all positive odds, we prove that an arbitrary, positive-definite quadratic form represents all positive odds if and only if it represents the odd numbers from 1 up to 451. This result is analogous to Bhargava and Hanke's celebrated 290-theorem. In addition, we prove that these three remaining ternaries represent all positive odd integers, assuming the generalized Riemann hypothesis. This result is made possible by a new analytic method for bounding the cusp constants of integer-valued quaternary quadratic forms $Q$ with fundamental discriminant. This method is based on the analytic properties of Rankin-Selberg $L$-functions, and we use it to prove...
Optimal Approximation of Quadratic Interval Functions
Koshelev, Misha; Taillibert, Patrick
1997-01-01
Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.
Dynamics of linear maps of idempotent measures
Rozikov, U A
2012-01-01
We describe all linear operators which maps $n-1$-dimensional simplex of idempotent measures to itself. Such operators divided to two classes: the first class contains all $n\\times n$-matrices with non-negative entries which has at least one zero-row; the second class contains all $n\\times n$-matrices with non-negative entries which in each row and in each column has exactly one non-zero entry. These matrices play a role of the stochastic matrices in case of idempotent matrices. For both classes of linear maps we find fixed points. We also study the dynamical systems generated by the linear maps of the set of idempotent measures.
A note on the fundamental unit in some types of the real quadratic number fields
Özer, Ö.
2016-10-01
Let k =Q (√{d }) be a real quadratic numbefield where d > 0 is a positive square-free integer. The map d →Q (√{d }) is a bijection from the set off all square-free integers d ≠ 0, 1 to the set of all quadratic fields Q (√{d })={ x +y √{d }|x ,y ∈Q } . Furthermore, integral basis element of algebraic integer's ring in real quadratic fields is determined by either wd=√{d }=[ a0;a1,a2,⋯,aℓ (d)-1,2 a0 ¯ ] in the case of d ≡ 2,3(mod 4) or wd=1/+√{d } 2 =[ a0;a1,a2,⋯,aℓ (d)-1,2 a0-1 ¯ ] in the case of d ≡ 1(mod 4) where ℓ (d ) is the period length of continued fraction expansion. The purpose of this paper is to obtain classification of some types of real quadratic fields Q (√{d }) , which include the specific form of continued fraction expansion of integral basis element wd, for which has all partial quotient elements are equal to each other and written as ξs (except the last digit of the period) for ξ positive even integer where period length is ℓ =ℓ (d ) and d ≡ 2,3(mod 4) is a square free positive integer. Moreover, the present paper deals with determining new certain parametric formula of fundamental unit ɛd=t/d+ud√{d } 2 >1 with norm N (ɛd)=(-1) ℓ (d ) for such types of real quadratic fields. Besides, Yokoi's d-invariants nd and md in the relation to continued fraction expansion of wd are calculated by using coefficients of fundamental unit. All supported results are given in numerical tables. These new results and tables are not known in the literature of real quadratic fields.
The Unique Existence of Additive Selection Maps for a Weak Subadditive Set-valued Map
Institute of Scientific and Technical Information of China (English)
PIAO Yong-jie; SHI Ren-shu
2013-01-01
In this paper,we discuss the unique existent problems of a additive selection map for the following map F:X → Po(Y):F(r∑i=1αixi) (∈)r∑i-αiFF(xi),(V)xi ∈ K,i ＝ 1,...,r,where αi and (-α)i (i =1,...,r) are all non-negative real numbers.
具有非负Ricci曲率的完备开流形%Complete Open Manifolds with Nonnegative Ricci Curvature
Institute of Scientific and Technical Information of China (English)
徐森林; 薛琼
2006-01-01
In this paper, we study complete open manifolds with nonnegative Ricci curvature and injectivity radius bounded from below. We find that this kind of manifolds are diffeomorphic to a Euclidean space when certain distance functions satisfy a reasonable condition.
complex numbers;quadratic equations with a negtive discriminant
Institute of Scientific and Technical Information of China (English)
王雷
2008-01-01
<正>One property of a real number is that its square is nonnegative.For example,there is no rea number x for which x~2=-1.To remedy this situation we introduce a number called the imaginary unit,which we denote by i and whose square is -1.Thus,
Constrained neural approaches to quadratic assignment problems.
Ishii, S; Sato, M
1998-08-01
In this paper, we discuss analog neural approaches to the quadratic assignment problem (QAP). These approaches employ a hard constraints scheme to restrict the domain space, and are able to obtain much improved solutions over conventional neural approaches. Since only a few strong heuristics for QAP have been known to date, our approaches are good alternatives, capable of obtaining fairly good solutions in a short period of time. Some of them can also be applied to large-scale problems, say of size N>/=300.
Automatic differentiation for reduced sequential quadratic programming
Institute of Scientific and Technical Information of China (English)
Liao Liangcai; Li Jin; Tan Yuejin
2007-01-01
In order to slove the large-scale nonlinear programming (NLP) problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming (rSQP) and automatic differentiation (AD) is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.
Bianchi I solutions of effective quadratic gravity
Müller, Daniel
2012-01-01
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "flat" model $E^3$ for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity. This work is a generalization for non diagonal spatial metrics of a previous result obtained by one of us and a collaborator for Bianchi $I$ spaces.
Linear Stability Analysis of Dynamical Quadratic Gravity
Ayzenberg, Dimitry; Yunes, Nicolas
2013-01-01
We perform a linear stability analysis of dynamical, quadratic gravity in the high-frequency, geometric optics approximation. This analysis is based on a study of gravitational and scalar modes propagating on spherically-symmetric and axially-symmetric, vacuum solutions of the theory. We find dispersion relations that do no lead to exponential growth of the propagating modes, suggesting the theory is linearly stable on these backgrounds. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes' direction relative to the background geometry, just as in dynamical Chern-Simons gravity.
Range-based estimation of quadratic variation
DEFF Research Database (Denmark)
Christensen, Kim; Podolskij, Mark
In this paper, we propose using realized range-based estimation to draw inference about the quadratic variation of jump-diffusion processes. We also construct a new test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the te...... is well-sized and more powerful than a return-based t-statistic for sampling frequencies normally used in empirical work. Applied to equity data, we find that the intensity of the jump process is not as high as previously reported....
Range-based estimation of quadratic variation
DEFF Research Database (Denmark)
Christensen, Kim; Podolskij, Mark
This paper proposes using realized range-based estimators to draw inference about the quadratic variation of jump-diffusion processes. We also construct a range-based test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the ......, the test is well-sized and more powerful than a return-based t-statistic for sampling frequencies normally used in empirical work. Applied to equity data, we show that the intensity of the jump process is not as high as previously reported....
Gillis, Nicolas
2011-01-01
Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational biology, and clustering. In this paper, we consider two well-known algorithms designed to solve NMF problems, namely the multiplicative updates of Lee and Seung and the hierarchical alternating least squares of Cichocki et al. We propose a simple way to significantly accelerate their convergence, based on a careful analysis of the computational cost needed at each iteration. This acceleration technique can also be applied to other algorithms, which we illustrate on the projected gradient method of Lin. The efficiency of the accelerated algorithms is empirically demonstrated on image and text datasets, and compares favorably with a state-of-the-art alternating nonnegative least squares algorithm. Finally, we provide a theoretical argument based on the properties of NMF and its solutions that explains in particular the very ...
A Conjugate Gradient Type Method for the Nonnegative Constraints Optimization Problems
Directory of Open Access Journals (Sweden)
Can Li
2013-01-01
Full Text Available We are concerned with the nonnegative constraints optimization problems. It is well known that the conjugate gradient methods are efficient methods for solving large-scale unconstrained optimization problems due to their simplicity and low storage. Combining the modified Polak-Ribière-Polyak method proposed by Zhang, Zhou, and Li with the Zoutendijk feasible direction method, we proposed a conjugate gradient type method for solving the nonnegative constraints optimization problems. If the current iteration is a feasible point, the direction generated by the proposed method is always a feasible descent direction at the current iteration. Under appropriate conditions, we show that the proposed method is globally convergent. We also present some numerical results to show the efficiency of the proposed method.
Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves
Goodearl, K R; Lenagan, T H
2009-01-01
The algebra of quantum matrices of a given size supports a rational torus action by automorphisms. It follows from work of Letzter and the first named author that to understand the prime and primitive spectra of this algebra, the first step is to understand the prime ideals that are invariant under the torus action. In this paper, we prove that a family of quantum minors is the set of all quantum minors that belong to a given torus-invariant prime ideal of a quantum matrix algebra if and only if the corresponding family of minors defines a non-empty totally nonnegative cell in the space of totally nonnegative real matrices of the appropriate size. As a corollary, we obtain explicit generating sets of quantum minors for the torus-invariant prime ideals of quantum matrices in the case where the quantisation parameter $q$ is transcendental over $\\mathbb{Q}$.
Nonnegative Matrix Factor 2-D Deconvolution for Blind Single Channel Source Separation
DEFF Research Database (Denmark)
Schmidt, Mikkel N.; Mørup, Morten
2006-01-01
We present a novel method for blind separation of instruments in polyphonic music based on a non-negative matrix factor 2-D deconvolution algorithm. Using a model which is convolutive in both time and frequency we factorize a spectrogram representation of music into components corresponding to in...... to individual instruments. Based on this factorization we separate the instruments using spectrogram masking. The proposed algorithm has applications in computational auditory scene analysis, music information retrieval, and automatic music transcription.......We present a novel method for blind separation of instruments in polyphonic music based on a non-negative matrix factor 2-D deconvolution algorithm. Using a model which is convolutive in both time and frequency we factorize a spectrogram representation of music into components corresponding...
Technique for computing the PDFs and CDFs of non-negative infinitely divisible random variables
Veillette, Mark S
2010-01-01
We present a method for computing the PDF and CDF of a non-negative infinitely divisible random variable $X$. Our method uses the L\\'{e}vy-Khintchine representation of the Laplace transform $\\mathbb{E} e^{-\\lambda X} = e^{-\\phi(\\lambda)}$, where $\\phi$ is the Laplace exponent. We apply the Post-Widder method for Laplace transform inversion combined with a sequence convergence accelerator to obtain accurate results. We demonstrate this technique on several examples including the stable distribution, mixtures thereof, and integrals with respect to non-negative L\\'{e}vy processes. Software to implement this method is available from the authors and we illustrate its use at the end of the paper.
Jiang, Jonathan Q
2011-01-01
We show here that the problem of maximizing a family of quantitative functions, encompassing both the modularity (Q-measure) and modularity density (D-measure), for community detection can be uniformly understood as a combinatoric optimization involving the trace of a matrix called modularity Laplacian. Instead of using traditional spectral relaxation, we apply additional nonnegative constraint into this graph clustering problem and design efficient algorithms to optimize the new objective. With the explicit nonnegative constraint, our solutions are very close to the ideal community indicator matrix and can directly assign nodes into communities. The near-orthogonal columns of the solution can be reformulated as the posterior probability of corresponding node belonging to each community. Therefore, the proposed method can be exploited to identify the fuzzy or overlapping communities and thus facilitates the understanding of the intrinsic structure of networks. Experimental results show that our new algorithm ...
Single-channel source separation using non-negative matrix factorization
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard
, in which a number of methods for single-channel source separation based on non-negative matrix factorization are presented. In the papers, the methods are applied to separating audio signals such as speech and musical instruments and separating different types of tissue in chemical shift imaging.......Single-channel source separation problems occur when a number of sources emit signals that are mixed and recorded by a single sensor, and we are interested in estimating the original source signals based on the recorded mixture. This problem, which occurs in many sciences, is inherently under......-determined and its solution relies on making appropriate assumptions concerning the sources. This dissertation is concerned with model-based probabilistic single-channel source separation based on non-negative matrix factorization, and consists of two parts: i) three introductory chapters and ii) five published...
Instability of elliptic equations on compact Riemannian manifolds with non-negative Ricci curvature
Directory of Open Access Journals (Sweden)
Arnaldo S. Nascimento
2010-05-01
Full Text Available We prove the nonexistence of nonconstant local minimizers for a class of functionals, which typically appear in scalar two-phase field models, over smooth N-dimensional Riemannian manifolds without boundary and non-negative Ricci curvature. Conversely, for a class of surfaces possessing a simple closed geodesic along which the Gauss curvature is negative, we prove the existence of nonconstant local minimizers for the same class of functionals.
Expanding solitons with non-negative curvature operator coming out of cones
Schulze, Felix
2010-01-01
We show that a Ricci flow of any complete Riemannian manifold without boundary with bounded non-negative curvature operator and non-zero asymptotic volume ratio exists for all time and has constant asymptotic volume ratio. We show that there is a limit solution, obtained by scaling down this solution at a fixed point in space, which is an expanding soliton coming out of the asymptotic cone at infinity.
Non-negative submodular stochastic probing via stochastic contention resolution schemes
Adamczyk, Marek
2015-01-01
The abstract model of stochastic probing was presented by Gupta and Nagarajan (IPCO'13), and provides a unified view of a number of problems. Adamczyk, Sviridenko, Ward (STACS'14) gave better approximation for matroid environments and linear objectives. At the same time this method was easily extendable to settings, where the objective function was monotone submodular. However, the case of non-negative submodular function could not be handled by previous techniques. In this paper we address t...
Real-time detection of overlapping sound events with non-negative matrix factorization
Dessein, Arnaud; Cont, Arshia; Lemaitre, Guillaume
2013-01-01
International audience; In this paper, we investigate the problem of real-time detection of overlapping sound events by employing non-negative matrix factorization techniques. We consider a setup where audio streams arrive in real-time to the system and are decomposed onto a dictionary of event templates learned off-line prior to the decomposition. An important drawback of existing approaches in this context is the lack of controls on the decomposition. We propose and compare two provably con...
Supervised non-negative matrix factorization based latent semantic image indexing
Institute of Scientific and Technical Information of China (English)
Dong Liang; Jie Yang; Yuchou Chang
2006-01-01
@@ A novel latent semantic indexing (LSI) approach for content-based image retrieval is presented in this paper. Firstly, an extension of non-negative matrix factorization (NMF) to supervised initialization isdiscussed. Then, supervised NMF is used in LSI to find the relationships between low-level features and high-level semantics. The retrieved results are compared with other approaches and a good performance is obtained.
(3, 1)*-Choosability of graphs of nonnegative characteristic without intersecting short cycles
Indian Academy of Sciences (India)
Haihui Zhang
2016-05-01
A graph is called (, )*-choosable if for every list assignment satisfying $|L(v)|\\geq k$ for all $v \\in V (G)$, there is an -coloring of such that each vertex of has at most neighbors colored with the same color as itself. In this paper, it is proved that every graph of nonnegative characteristic without intersecting -cycles for all = 3, 4, 5 is (3, 1)*-choosable.
A Sharp upper bound for the spectral radius of a nonnegative matrix and applications
You, Lihua; Shu, Yujie; Zhang, Xiao-Dong
2016-01-01
In this paper, we obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance Laplacian spectral radius, the distance signless Laplacian spectral radius of a graph or a digraph. These results are new or generalize some known results.
An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions
Directory of Open Access Journals (Sweden)
Tilak Bhattacharya
2001-06-01
Full Text Available We present an elementary proof of the Harnack inequality for non-negative viscosity supersolutions of $Delta_{infty}u=0$. This was originally proven by Lindqvist and Manfredi using sequences of solutions of the $p$-Laplacian. We work directly with the $Delta_{infty}$ operator using the distance function as a test function. We also provide simple proofs of the Liouville property, Hopf boundary point lemma and Lipschitz continuity.
Nonnegative Matrix Factorization Numerical Method for Integrated Photonic Cavity Based Spectroscopy
Directory of Open Access Journals (Sweden)
Zhengyu Huang
2014-01-01
Full Text Available Nonnegative matrix factorization numerical method has been used to improve the spectral resolution of integrated photonic cavity based spectroscopy. Based on the experimental results for integrated photonic cavity device on Optics Letters 32, 632 (2007, the theoretical results show that the spectral resolution can be improved more than 3 times from 5.5 nm to 1.8 nm. It is a promising way to release the difficulty of fabricating high-resolution devices.
Generalized Synchronization of Different Chaotic Systems Based on Nonnegative Off-Diagonal Structure
Directory of Open Access Journals (Sweden)
Ling Guo
2013-01-01
Full Text Available The generalized synchronization problem is studied in this paper for different chaotic systems with the aid of the direct design method. Based on Lyapunov stability theory and matrix theory, some sufficient conditions guaranteeing the stability of a nonlinear system with nonnegative off-diagonal structure are obtained. Then the control scheme is designed from the stable system by the direct design method. Finally, two numerical simulations are provided to verify the effectiveness and feasibility of the proposed method.
Quadratic forms for Feynman-Kac semigroups
Energy Technology Data Exchange (ETDEWEB)
Hibey, Joseph L. [Department of Electrical Engineering, University of Colorado at Denver, Campus Box 110, Denver, CO 80217 (United States)]. E-mail: joseph.hibey@cudenver.edu; Charalambous, Charalambos D. [Electrical and Computer Engineering Department, University of Cyprus, 75 Kallipoleos Avenue, Nicosia (Cyprus)]. E-mail: chadcha@ucy.ac.cy
2006-05-15
Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions.
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2004-01-01
A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...
Robust ear recognition via nonnegative sparse representation of Gabor orientation information.
Zhang, Baoqing; Mu, Zhichun; Zeng, Hui; Luo, Shuang
2014-01-01
Orientation information is critical to the accuracy of ear recognition systems. In this paper, a new feature extraction approach is investigated for ear recognition by using orientation information of Gabor wavelets. The proposed Gabor orientation feature can not only avoid too much redundancy in conventional Gabor feature but also tend to extract more precise orientation information of the ear shape contours. Then, Gabor orientation feature based nonnegative sparse representation classification (Gabor orientation + NSRC) is proposed for ear recognition. Compared with SRC in which the sparse coding coefficients can be negative, the nonnegativity of NSRC conforms to the intuitive notion of combining parts to form a whole and therefore is more consistent with the biological modeling of visual data. Additionally, the use of Gabor orientation features increases the discriminative power of NSRC. Extensive experimental results show that the proposed Gabor orientation feature based nonnegative sparse representation classification paradigm achieves much better recognition performance and is found to be more robust to challenging problems such as pose changes, illumination variations, and ear partial occlusion in real-world applications.
Directory of Open Access Journals (Sweden)
R. Ezzati
2014-09-01
Full Text Available We propose an approach for computing an approximate nonnegative symmetric solution of some fully fuzzy linear system of equations, where the components of the coefficient matrix and the right hand side vector are nonnegative fuzzy numbers, considering equality of the median intervals of the left and right hand sides of the system. We convert the m×n fully fuzzy linear system to two m×n real linear systems, one being related to the cores and the other being concerned with spreads of the solution. We propose an approach for solving the real systems using the modified Huang method of the Abaffy-Broyden-Spedicato (ABS class of algorithms. An appropriate constrained least squares problem is solved when the solution does not satisfy nonnegative fuzziness conditions, that is, when the obtained solution vector for the core system includes a negative component, or the solution of the spread system has at least one negative component, or there exists an index for which the component of the spread is greater than the corresponding component of the core. As a special case, we discuss fuzzy systems with the components of the coefficient matrix as real crisp numbers. We finally present two computational algorithms and illustrate their effectiveness by solving some randomly generated consistent as well as inconsistent systems.
Institute of Scientific and Technical Information of China (English)
夏春明; 郑建荣; J.Howell
2007-01-01
Constrained spectral non-negative matrix factorization (NMF) analysis of perturbed oscillatory process control loop variable data is performed for the isolation of multiple plant-wide oscillatory sources.The technique is described and demonstrated by analyzing data from both simulated and real plant data of a chemical process plant.Results show that the proposed approach can map multiple oscillatory sources onto the most appropriate control loops, and has superior performance in terms of reconstruction accuracy and intuitive understanding compared with spectral independent component analysis (ICA).
On a general class of quadratic hopping sequences
Institute of Scientific and Technical Information of China (English)
JIA HuaDing; YUAN Ding; PENG DaiYuan; GUO Ling
2008-01-01
Based upon quadratic polynomials over the finite field, a new class of frequency hopping sequences with large family size suitable for applications in time/frequency hopping CDMA systems, multi-user radar and sonar systems is proposed and investigated. It is shown that the new time/frequency hopping sequences have at most one hit in their autocorrelation functions and at most two hits in their crosscorrelation functions except for a special case, and their family size is much larger than the conventional quadratic hopping sequences. The percentage of full collisions for the new quadratic hopping sequences is discussed. In addition, the average number of hits for the new quadratic hopping sequences, quadratic congruence sequences, extended quadratic congruence sequences and the general linear hopping sequences are also derived.
Quadratic residues and non-residues selected topics
Wright, Steve
2016-01-01
This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.
On Quadratic BSDEs with Final Condition in L2
Yang, Hanlin
2015-01-01
This thesis consists of three parts. In the first part, we study $\\mathbb{L}^p$ solutions of a large class of BSDEs. Existence, comparison theorem, uniqueness and a stability result are proved. In the second part, we establish the solvability of quadratic semimartingale BSDEs. In contrast to current literature, we use Lipschitz-quadratic regularization and obtain the existence and uniqueness results with minimal assumptions. The third part is a brief summary of quadratic semimartingales and t...
Quadratic forms and Clifford algebras on derived stacks
Vezzosi, Gabriele
2013-01-01
In this paper we present an approach to quadratic structures in derived algebraic geometry. We define derived n-shifted quadratic complexes, over derived affine stacks and over general derived stacks, and give several examples of those. We define the associated notion of derived Clifford algebra, in all these contexts, and compare it with its classical version, when they both apply. Finally, we prove three main existence results for derived shifted quadratic forms over derived stacks, define ...
Robust Solutions of Uncertain Complex-valued Quadratically Constrained Programs
Institute of Scientific and Technical Information of China (English)
Da Chuan XU; Zheng Hai HUANG
2008-01-01
In this paper,we discuss complex convex quadratically constrained optimization with uncertain data.Using S-Lemma,we show that the robust counterpart of complex convex quadratically constrained optimization with ellipsoidal or intersection-of-two-ellipsoids uncertainty set leads to a complex semidefinite program.By exploring the approximate S-Lemma,we give a complex semidefinite program which approximates the NP-hard robust counterpart of complex convex quadratic optimization with intersection-of-ellipsoids uncertainty set.
Some Aspects of Quadratic Generalized White Noise Functionals
Si, Si; Hida, Takeyuki
2009-02-01
We shall discuss some particular roles of quadratic generalized white noise functionals. First observation is made from the viewpoint of the so-called "la passage du fini à l'infini". We then come to a dual pairing of spaces formed by quadratic generalized white noise functionals. In this line, we can further discuss quadratic forms of differential operators acting on the space of white noise functionals.
Quadratic dynamical decoupling with nonuniform error suppression
Energy Technology Data Exchange (ETDEWEB)
Quiroz, Gregory; Lidar, Daniel A. [Department of Physics and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States); Departments of Electrical Engineering, Chemistry, and Physics, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States)
2011-10-15
We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N{sub 1} and N{sub 2} pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N{sub 1} and N{sub 2}, and near-optimal performance is achieved for general single-qubit interactions when N{sub 1}=N{sub 2}.
The Quadratic Selective Travelling Salesman Problem
DEFF Research Database (Denmark)
Thomadsen, Tommy; Stidsen, Thomas K.
2003-01-01
complication that each pair of nodes have an associated profit which can be gained only if both nodes are visited. The QSTSP is a subproblem when constructing hierarchical ring networks. We describe an integer linear programming model for the QSTSP. The QSTSP is solved by two construction heuristics...... solutions at a cost of much higher running time. All problems with up to 50 nodes are solved within one hour.......A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...
Compact stars with quadratic equation of state
Ngubelanga, Sifiso A; Ray, Subharthi
2015-01-01
We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.
Low-rank quadratic semidefinite programming
Yuan, Ganzhao
2013-04-01
Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.
Directed animals, quadratic and rewriting systems
Marckert, Jean-François
2011-01-01
A directed animal is a percolation cluster in the directed site percolation model. The aim of this paper is to exhibit a strong relation between in one hand, the problem of computing the generating function $\\G$ of directed animals on the square lattice, counted according to the area and the perimeter, and on the other hand, the problem to find a solution to a system of quadratic equations involving unknown matrices. The matrices solution of this problem can be finite or infinite. We were unable to find finite solutions. We present some solid clues that some infinite explicit matrices, fix points of a rewriting like system are the natural solutions of this system of equations: some strong evidences are given that the problem of finding $\\G$ reduces then to the problem of finding an eigenvector to an explicit infinite matrix. Similar properties are shown for other combinatorial questions concerning directed animals, and for different lattices.
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation used in compilers and in partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one for each...... local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters that yields the cubic factor in the traditional formulation of lambda-lifting, which...... is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity of lambda-lifting from O(n 3 log n)toO(n2 log n), where n is the size of the program. Since a lambda-lifter can output...
A SPLITTING METHOD FOR QUADRATIC PROGRAMMING PROBLEM
Institute of Scientific and Technical Information of China (English)
魏紫銮
2001-01-01
A matrix splitting method is presented for minimizing a quadratic programming (QP)problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate, and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region, and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.
Linear ultrasonic motor using quadrate plate transducer
Institute of Scientific and Technical Information of China (English)
Jiamei JIN; Chunsheng ZHAO
2009-01-01
A linear ultrasonic motor using a quadrate plate transducer was developed for precision positioning. This motor consists of two pairs of Pb(Zr, Ti)O3 piezo-electric ceramic elements, which are piezoelectrically excited into the second-bending mode of the motor stator's neutral surface in two orthogonal directions, on which the tops of four projections move along an elliptical trajectory, which in turn drives a contacted slider into linear motion via frictional forces. The coincident frequency of the stator is easily obtained for its coincident characteristic dimen-sion in two orthogonal directions. The performance characteristics achieved by the motor are: 1) a maximum linear speed of more than 60 mm/s; 2) a stroke of more than 150 mm; 3) a driving force of more than 5.0 N; and 4) a response time of about 2 ms.
Large-scale sequential quadratic programming algorithms
Energy Technology Data Exchange (ETDEWEB)
Eldersveld, S.K.
1992-09-01
The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.
Linearly and Quadratically Separable Classifiers Using Adaptive Approach
Institute of Scientific and Technical Information of China (English)
Mohamed Abdel-Kawy Mohamed Ali Soliman; Rasha M. Abo-Bakr
2011-01-01
This paper presents a fast adaptive iterative algorithm to solve linearly separable classification problems in Rn.In each iteration,a subset of the sampling data (n-points,where n is the number of features) is adaptively chosen and a hyperplane is constructed such that it separates the chosen n-points at a margin e and best classifies the remaining points.The classification problem is formulated and the details of the algorithm are presented.Further,the algorithm is extended to solving quadratically separable classification problems.The basic idea is based on mapping the physical space to another larger one where the problem becomes linearly separable.Numerical illustrations show that few iteration steps are sufficient for convergence when classes are linearly separable.For nonlinearly separable data,given a specified maximum number of iteration steps,the algorithm returns the best hyperplane that minimizes the number of misclassified points occurring through these steps.Comparisons with other machine learning algorithms on practical and benchmark datasets are also presented,showing the performance of the proposed algorithm.
New Heuristic Rounding Approaches to the Quadratic Assignment Problem
Gharibi, Wajeb
2011-01-01
Quadratic assignment problem is one of the great challenges in combinatorial optimization. It has many applications in Operations research and Computer Science. In this paper, the author extends the most-used rounding approach to a one-parametric optimization model for the quadratic assignment problems. A near-optimum parameter is also predestinated. The numerical experiments confirm the efficiency.
Quadratic elongation: A quantitative measure of distortion in coordination polyhedra
Robinson, Kelly F.; Gibbs, G.V.; Ribbe, P.H.
1971-01-01
Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elonga tion is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.
Binary GCD like Algorithms for Some Complex Quadratic Rings
DEFF Research Database (Denmark)
Agarwal, Saurabh; Frandsen, Gudmund Skovbjerg
2004-01-01
binary gcd like algorithms for the ring of integers in and , one now has binary gcd like algorithms for all complex quadratic Euclidean domains. The running time of our algorithms is O(n 2) in each ring. While there exists an O(n 2) algorithm for computing the gcd in quadratic number rings by Erich...
Quadratic Twists of Rigid Calabi–Yau Threefolds Over
DEFF Research Database (Denmark)
Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko
2013-01-01
We consider rigid Calabi–Yau threefolds defined over Q and the question of whether they admit quadratic twists. We give a precise geometric definition of the notion of a quadratic twists in this setting. Every rigid Calabi–Yau threefold over Q is modular so there is attached to it a certain newfo...
Immunizing Conic Quadratic Optimization Problems Against Implementation Errors
Ben-Tal, A.; den Hertog, D.
2011-01-01
We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonali
A Constructive Transition from Linear to Quadratic Functions.
Movshovitz-Hadar, Nitsa
1993-01-01
Presents an approach to quadratic functions that draws upon knowledge of linear functions by looking at the product of two linear functions. Then considers the quadratic function as the sum of three monomials. Potential advantages of each approach are discussed. (Contains 17 references.) (MDH)
Approximate *-derivations and approximate quadratic *-derivations on C*-algebras
Directory of Open Access Journals (Sweden)
Park Choonkil
2011-01-01
Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.
AdS Waves as Exact Solutions to Quadratic Gravity
Gullu, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram
2011-01-01
We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity.
QUADRATIC ADMISSIBLE ESTIMATE OF COVARIANCE IN PSEUDO-ELLIPTICAL CONTOURED DISTRIBUTION
Institute of Scientific and Technical Information of China (English)
Hengjian CUI; Xiuhong GAO
2006-01-01
This article mainly discusses the admissibility of quadratic estimate of covariance in pseudoelliptical distribution. Under the quadratic loss function, the necessary and sufficient conditions that a quadratic estimator is an admissible estimator of covariance in the class of quadratic estimators are obtained. A complete class of the quadratic estimator class is also given.
Directory of Open Access Journals (Sweden)
Rocío Meza-Moreno
2015-01-01
Full Text Available Let p=4k+1 be a prime number and Fp the finite field with p elements. For x∈1,n, Nx will denote the set of quadratic nonresidues less than or equal to x. In this work we calculate the number of quadratic nonresidues in the shifted set N(p-1/2+a.
Ascent sequences and upper triangular matrices containing non-negative integers
Dukes, Mark
2009-01-01
This paper presents a bijection between ascent sequences and upper triangular matrices whose non-negative entries are such that all rows and columns contain at least one non-zero entry. We show the equivalence of several natural statistics on these structures under this bijection and prove that some of these statistics are equidistributed. Several special classes of matrices are shown to have simple formulations in terms of ascent sequences. Binary matrices are shown to correspond to ascent sequences with no two adjacent entries the same. Bidiagonal matrices are shown to be related to order-consecutive set partitions and a simple condition on the ascent sequences generate this class.
Institute of Scientific and Technical Information of China (English)
Zheng Zhonglong; Yang Jie
2005-01-01
Many problems in image representation and classification involve some form of dimensionality reduction. Non-negative matrix factorization (NMF) is a recently proposed unsupervised procedure for learning spatially localized, parts-based subspace representation of objects. An improvement of the classical NMF by combining with Log-Gabor wavelets to enhance its part-based learning ability is presented. The new method with principal component analysis (PCA) and locally linear embedding (LLE) proposed recently in Science are compared. Finally, the new method to several real world datasets and achieve good performance in representation and classification is applied.
Fast Bayesian Non-Negative Matrix Factorisation and Tri-Factorisation
DEFF Research Database (Denmark)
Brouwer, Thomas; Frellsen, Jes; Liò, Pietro
We present a fast variational Bayesian algorithm for performing non-negative matrix factorisation and tri-factorisation. We show that our approach achieves faster convergence per iteration and timestep (wall-clock) than Gibbs sampling and non-probabilistic approaches, and do not require additional...... samples to estimate the posterior. We show that in particular for matrix tri-factorisation convergence is difficult, but our variational Bayesian approach offers a fast solution, allowing the tri-factorisation approach to be used more effectively....
On the Equivalence of Nonnegative Matrix Factorization and K-means- Spectral Clustering
Energy Technology Data Exchange (ETDEWEB)
Ding, Chris; He, Xiaofeng; Simon, Horst D.; Jin, Rong
2005-12-04
We provide a systematic analysis of nonnegative matrix factorization (NMF) relating to data clustering. We generalize the usual X = FG{sup T} decomposition to the symmetric W = HH{sup T} and W = HSH{sup T} decompositions. We show that (1) W = HH{sup T} is equivalent to Kernel K-means clustering and the Laplacian-based spectral clustering. (2) X = FG{sup T} is equivalent to simultaneous clustering of rows and columns of a bipartite graph. We emphasizes the importance of orthogonality in NMF and soft clustering nature of NMF. These results are verified with experiments on face images and newsgroups.
Non-negative Ricci curvature on closed manifolds under Ricci flow
Maximo, Davi
2009-01-01
In this short note we show that non-negative Ricci curvature is not preserved under Ricci flow for closed manifolds of dimensions four and above, strengthening a previous result of Knopf in \\cite{K} for complete non-compact manifolds of bounded curvature. This brings down to four dimensions a similar result B\\"ohm and Wilking have for dimensions twelve and above, \\cite{BW}. Moreover, the manifolds constructed here are \\Kahler manifolds and relate to a question raised by Xiuxiong Chen in \\cite{XC}, \\cite{XCL}.
Single-Channel Speech Separation using Sparse Non-Negative Matrix Factorization
DEFF Research Database (Denmark)
Schmidt, Mikkel N.; Olsson, Rasmus Kongsgaard
2007-01-01
We apply machine learning techniques to the problem of separating multiple speech sources from a single microphone recording. The method of choice is a sparse non-negative matrix factorization algorithm, which in an unsupervised manner can learn sparse representations of the data. This is applied...... to the learning of personalized dictionaries from a speech corpus, which in turn are used to separate the audio stream into its components. We show that computational savings can be achieved by segmenting the training data on a phoneme level. To split the data, a conventional speech recognizer is used...
Approximate Graph Edit Distance in Quadratic Time.
Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst
2015-09-14
Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.
A Quadratic Closure for Compressible Turbulence
Energy Technology Data Exchange (ETDEWEB)
Futterman, J A
2008-09-16
We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.
Optimal power flow using sequential quadratic programming
Nejdawi, Imad M.
1999-11-01
Optimal power flow (OPF) is an operational as well as a planning tool used by electric utilities to help them operate their network in the most economic and secure mode of operation. Various algorithms to solve the OPF problem evolved over the past three decades; linear programming (LP) techniques were among the major mathematical programming methods utilized. The linear models of the objective function and the linearization of the constraints are the main features of these techniques. The main advantages of the LP approach are simplicity and speed. Nonlinear programming techniques have been applied to OPF solution. The major drawback is the expensive solution of large sparse systems of equations. This research is concerned with the development of a new OPF solution algorithm using sequential quadratic programming (SQP). In this formulation, a small dense system the size of which is equal to the number of control variables is solved in an inner loop. The Jacobian and Hessian terms are calculated in an outer loop. The total number of outer loop iterations is comparable to those in an ordinary load flow in contrast to 20--30 iterations in other nonlinear methods. In addition, the total number of floating point operations is less than that encountered in direct methods by two orders of magnitude. We also model dispatch over a twenty four-hour time horizon in a transmission constrained power network that includes price-responsive loads where large energy customers can operate their loads in time intervals with lowest spot prices.
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard
2015-05-04
In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport).
Linear quadratic regulator for laser beam shaping
Escárate, Pedro; Agüero, Juan C.; Zúñiga, Sebastián; Castro, Mario; Garcés, Javier
2017-07-01
The performance of an adaptive optics system depends on multiple factors, including the quality of the laser beam before being projected to the mesosphere. In general, cumbersome procedures are required to optimize the laser beam in terms of amplitude and phase. However, aberrations produced by the optics of the laser beam system are still detected during the operations due to, for example, uncertainty in the utilized models. In this paper we propose the use of feedback to overcome the presence of model uncertainty and disturbances. In particular we use a Linear Quadratic Regulator (LQR) for closed loop laser beam shaping using a setup of two deformable mirrors. The proposed method is studied and simulated to provide an automatic optimization of the Amplitude of the laser beam. The performance of the LQR control algorithm is evaluated via numerical simulations using the root mean square error (RMSE). The results show an effective amplitude correction of the laser system aberrations after 20 iterations of the algorithm, a RMSE less than 0.7 was obtained, with about 140 actuators per mirror and a separation of z=3 [m] among the mirrors.
Slawski, Martin
2012-01-01
Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a paradigm according to which sparsity-promoting regularization is regarded as a necessity in such setting. Deviating from this paradigm, we show that non-negativity constraints on the regression coefficients may be similarly effective as explicit regularization. For a broad range of designs with Gram matrix having non-negative entries, we establish bounds on the $\\ell_2$-prediction error of non-negative least squares (NNLS) whose form qualitatively matches corresponding results for $\\ell_1$-regularization. Under slightly stronger conditions, it is established that NNLS followed by hard thresholding performs excellently in terms of support recovery of an (approximately) sparse target, in some cases improving over $\\ell_1$-regularization. A substantial advantage of NNLS over r...
On nondecomposable positive definite Hermitian forms over imaginary quadratic fields
Institute of Scientific and Technical Information of China (English)
ZHU; Fuzu
2001-01-01
［1］Mordell, L. J., The representation of a definite quadratic form as a sum of two others, Ann. of Math., 937, 38: 75.［2］Erds, P., Ko Chao, On definite quadratic forms, which are not the sum of two definite or semidefinite forms, Acta Arith., 939, 3: 02.［3］Erds, P., Ko Chao, Some results on definite quadratic forms, J. London Math. Soc., 938, 3: 27.［4］Zhu Fu-zu, Construction of nondecomposable positive definite quadratic forms, Sci. Sinica, Ser. A, 987, 30(): 9.［5］Zhu Fuzu, On nondecomposability and indecomposability of quadratic forms, Sci. Sinica, Ser. A, 988, 3(3): 265.［6］Pleskin, W., Additively indecomposable positive integral quadratic forms, J. Number Theory, 994, 47: 273.［7］Zhu Fuzu, An existence theorem on positive definite unimodular even Hermitian forms, Chinese Ann. of Math., Ser. A, 984, 5: 33.［8］Zhu Fu-Zu, On the construction of positive definite indecomposable unimodular even Hermitian forms, J. Number Theory, 995, 30: 38.［9］O'Meara, O. T., Introduction to Quadratic Forms, Berlin, New York: Springer-Verlag, 973.［10］Zhu Fuzu, Construction of indecomposable definite Hermitian forms, Chinese Ann. of Math., Ser. B, 994, 5: 349.［11］Zhu Fuzu, On nondecomposable Hermitian forms over Gaussian domain, Acta Math. Sinica, New Ser., 998, 4: 447.
Zhang, Ruoqiao; Thibault, Jean-Baptiste; Bouman, Charles A; Sauer, Ken D; Hsieh, Jiang
2014-01-01
Dual-energy X-ray CT (DECT) has the potential to improve contrast and reduce artifacts as compared to traditional CT. Moreover, by applying model-based iterative reconstruction (MBIR) to dual-energy data, one might also expect to reduce noise and improve resolution. However, the direct implementation of dual-energy MBIR requires the use of a nonlinear forward model, which increases both complexity and computation. Alternatively, simplified forward models have been used which treat the material-decomposed channels separately, but these approaches do not fully account for the statistical dependencies in the channels. In this paper, we present a method for joint dual-energy MBIR (JDE-MBIR), which simplifies the forward model while still accounting for the complete statistical dependency in the material-decomposed sinogram components. The JDE-MBIR approach works by using a quadratic approximation to the polychromatic log-likelihood and a simple but exact nonnegativity constraint in the image domain. We demonstrate that our method is particularly effective when the DECT system uses fast kVp switching, since in this case the model accounts for the inaccuracy of interpolated sinogram entries. Both phantom and clinical results show that the proposed model produces images that compare favorably in quality to previous decomposition-based methods, including FBP and other statistical iterative approaches.
The Cyclicity of the Period Annulus Around the Quadratic Isochronous Center
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The number of the limit cycles bifurcating in small quadratic perturbations of quadratic systems with an isochronous center is studied, it turns out that the cyclicity of the period annulus around one kind of quadratic isochronous center is two.
A Finite Continuation Algorithm for Bound Constrained Quadratic Programming
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.
1999-01-01
The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems. The u....... The unique path generated by the minimizers of these problems yields the solution to the original problem for finite values of the approximation parameter. Thus, a finite continuation algorithm is designed. Results of extensive computational experiments are reported....
Online multi-modal robust non-negative dictionary learning for visual tracking.
Zhang, Xiang; Guan, Naiyang; Tao, Dacheng; Qiu, Xiaogang; Luo, Zhigang
2015-01-01
Dictionary learning is a method of acquiring a collection of atoms for subsequent signal representation. Due to its excellent representation ability, dictionary learning has been widely applied in multimedia and computer vision. However, conventional dictionary learning algorithms fail to deal with multi-modal datasets. In this paper, we propose an online multi-modal robust non-negative dictionary learning (OMRNDL) algorithm to overcome this deficiency. Notably, OMRNDL casts visual tracking as a dictionary learning problem under the particle filter framework and captures the intrinsic knowledge about the target from multiple visual modalities, e.g., pixel intensity and texture information. To this end, OMRNDL adaptively learns an individual dictionary, i.e., template, for each modality from available frames, and then represents new particles over all the learned dictionaries by minimizing the fitting loss of data based on M-estimation. The resultant representation coefficient can be viewed as the common semantic representation of particles across multiple modalities, and can be utilized to track the target. OMRNDL incrementally learns the dictionary and the coefficient of each particle by using multiplicative update rules to respectively guarantee their non-negativity constraints. Experimental results on a popular challenging video benchmark validate the effectiveness of OMRNDL for visual tracking in both quantity and quality.
Online multi-modal robust non-negative dictionary learning for visual tracking.
Directory of Open Access Journals (Sweden)
Xiang Zhang
Full Text Available Dictionary learning is a method of acquiring a collection of atoms for subsequent signal representation. Due to its excellent representation ability, dictionary learning has been widely applied in multimedia and computer vision. However, conventional dictionary learning algorithms fail to deal with multi-modal datasets. In this paper, we propose an online multi-modal robust non-negative dictionary learning (OMRNDL algorithm to overcome this deficiency. Notably, OMRNDL casts visual tracking as a dictionary learning problem under the particle filter framework and captures the intrinsic knowledge about the target from multiple visual modalities, e.g., pixel intensity and texture information. To this end, OMRNDL adaptively learns an individual dictionary, i.e., template, for each modality from available frames, and then represents new particles over all the learned dictionaries by minimizing the fitting loss of data based on M-estimation. The resultant representation coefficient can be viewed as the common semantic representation of particles across multiple modalities, and can be utilized to track the target. OMRNDL incrementally learns the dictionary and the coefficient of each particle by using multiplicative update rules to respectively guarantee their non-negativity constraints. Experimental results on a popular challenging video benchmark validate the effectiveness of OMRNDL for visual tracking in both quantity and quality.
Hyperspectral Image Super-Resolution via Non-Negative Structured Sparse Representation.
Dong, Weisheng; Fu, Fazuo; Shi, Guangming; Cao, Xun; Wu, Jinjian; Li, Guangyu; Li, Guangyu
2016-05-01
Hyperspectral imaging has many applications from agriculture and astronomy to surveillance and mineralogy. However, it is often challenging to obtain high-resolution (HR) hyperspectral images using existing hyperspectral imaging techniques due to various hardware limitations. In this paper, we propose a new hyperspectral image super-resolution method from a low-resolution (LR) image and a HR reference image of the same scene. The estimation of the HR hyperspectral image is formulated as a joint estimation of the hyperspectral dictionary and the sparse codes based on the prior knowledge of the spatial-spectral sparsity of the hyperspectral image. The hyperspectral dictionary representing prototype reflectance spectra vectors of the scene is first learned from the input LR image. Specifically, an efficient non-negative dictionary learning algorithm using the block-coordinate descent optimization technique is proposed. Then, the sparse codes of the desired HR hyperspectral image with respect to learned hyperspectral basis are estimated from the pair of LR and HR reference images. To improve the accuracy of non-negative sparse coding, a clustering-based structured sparse coding method is proposed to exploit the spatial correlation among the learned sparse codes. The experimental results on both public datasets and real LR hypspectral images suggest that the proposed method substantially outperforms several existing HR hyperspectral image recovery techniques in the literature in terms of both objective quality metrics and computational efficiency.
Non-negative constraint for image-based breathing gating in ultrasound hepatic perfusion data
Wu, Kaizhi; Ding, Mingyue; Chen, Xi; Deng, Wenjie; Zhang, Zhijun
2015-12-01
Images acquired during free breathing using contrast enhanced ultrasound hepatic perfusion imaging exhibits a periodic motion pattern. It needs to be compensated for if a further accurate quantification of the hepatic perfusion analysis is to be executed. To reduce the impact of respiratory motion, image-based breathing gating algorithm was used to compensate the respiratory motion in contrast enhanced ultrasound. The algorithm contains three steps of which respiratory kinetics extracted, image subsequences determined and image subsequences registered. The basic performance of the algorithm was to extract the respiratory kinetics of the ultrasound hepatic perfusion image sequences accurately. In this paper, we treated the kinetics extracted model as a non-negative matrix factorization (NMF) problem. We extracted the respiratory kinetics of the ultrasound hepatic perfusion image sequences by non-negative matrix factorization (NMF). The technique involves using the NMF objective function to accurately extract respiratory kinetics. It was tested on simulative phantom and used to analyze 6 liver CEUS hepatic perfusion image sequences. The experimental results show the effectiveness of our proposed method in quantitative and qualitative.
Online Multi-Modal Robust Non-Negative Dictionary Learning for Visual Tracking
Zhang, Xiang; Guan, Naiyang; Tao, Dacheng; Qiu, Xiaogang; Luo, Zhigang
2015-01-01
Dictionary learning is a method of acquiring a collection of atoms for subsequent signal representation. Due to its excellent representation ability, dictionary learning has been widely applied in multimedia and computer vision. However, conventional dictionary learning algorithms fail to deal with multi-modal datasets. In this paper, we propose an online multi-modal robust non-negative dictionary learning (OMRNDL) algorithm to overcome this deficiency. Notably, OMRNDL casts visual tracking as a dictionary learning problem under the particle filter framework and captures the intrinsic knowledge about the target from multiple visual modalities, e.g., pixel intensity and texture information. To this end, OMRNDL adaptively learns an individual dictionary, i.e., template, for each modality from available frames, and then represents new particles over all the learned dictionaries by minimizing the fitting loss of data based on M-estimation. The resultant representation coefficient can be viewed as the common semantic representation of particles across multiple modalities, and can be utilized to track the target. OMRNDL incrementally learns the dictionary and the coefficient of each particle by using multiplicative update rules to respectively guarantee their non-negativity constraints. Experimental results on a popular challenging video benchmark validate the effectiveness of OMRNDL for visual tracking in both quantity and quality. PMID:25961715
Pavement crack detection combining non-negative feature with fast LoG in complex scene
Wang, Wanli; Zhang, Xiuhua; Hong, Hanyu
2015-12-01
Pavement crack detection is affected by much interference in the realistic situation, such as the shadow, road sign, oil stain, salt and pepper noise etc. Due to these unfavorable factors, the exist crack detection methods are difficult to distinguish the crack from background correctly. How to extract crack information effectively is the key problem to the road crack detection system. To solve this problem, a novel method for pavement crack detection based on combining non-negative feature with fast LoG is proposed. The two key novelties and benefits of this new approach are that 1) using image pixel gray value compensation to acquisit uniform image, and 2) combining non-negative feature with fast LoG to extract crack information. The image preprocessing results demonstrate that the method is indeed able to homogenize the crack image with more accurately compared to existing methods. A large number of experimental results demonstrate the proposed approach can detect the crack regions more correctly compared with traditional methods.
Directory of Open Access Journals (Sweden)
Chen Yidong
2011-10-01
Full Text Available Abstract Background Transcriptional regulation by transcription factor (TF controls the time and abundance of mRNA transcription. Due to the limitation of current proteomics technologies, large scale measurements of protein level activities of TFs is usually infeasible, making computational reconstruction of transcriptional regulatory network a difficult task. Results We proposed here a novel Bayesian non-negative factor model for TF mediated regulatory networks. Particularly, the non-negative TF activities and sample clustering effect are modeled as the factors from a Dirichlet process mixture of rectified Gaussian distributions, and the sparse regulatory coefficients are modeled as the loadings from a sparse distribution that constrains its sparsity using knowledge from database; meantime, a Gibbs sampling solution was developed to infer the underlying network structure and the unknown TF activities simultaneously. The developed approach has been applied to simulated system and breast cancer gene expression data. Result shows that, the proposed method was able to systematically uncover TF mediated transcriptional regulatory network structure, the regulatory coefficients, the TF protein level activities and the sample clustering effect. The regulation target prediction result is highly coordinated with the prior knowledge, and sample clustering result shows superior performance over previous molecular based clustering method. Conclusions The results demonstrated the validity and effectiveness of the proposed approach in reconstructing transcriptional networks mediated by TFs through simulated systems and real data.
Sharp maximal inequalities for the moments of martingales and non-negative submartingales
Osȩkowski, Adam
2012-01-01
In the paper we study sharp maximal inequalities for martingales and non-negative submartingales: if $f$, $g$ are martingales satisfying \\[|\\mathrm{d}g_n|\\leq|\\mathrm{d}f_n|,\\qquad n=0,1,2,...,\\] almost surely, then \\[\\Bigl\\|\\sup_{n\\geq0}|g_n|\\Bigr\\|_p\\leq p\\|f\\|_p,\\qquad p\\geq2,\\] and the inequality is sharp. Furthermore, if $\\alpha\\in[0,1]$, $f$ is a non-negative submartingale and $g$ satisfies \\[|\\mathrm{d}g_n|\\leq|\\mathrm{d}f_n|\\quad and\\quad |\\mathbb{E}(\\mathrm{d}g_{n+1}|\\mathcal {F}_n)|\\leq\\alpha\\mathbb{E}(\\mathrm{d}f_{n+1}|\\mathcal{F}_n),\\qquad n=0,1,2,...,\\] almost surely, then \\[\\Bigl\\|\\sup_{n\\geq0}|g_n|\\Bigr\\|_p\\leq(\\alpha+1)p\\|f\\|_p,\\qquad p\\geq2,\\] and the inequality is sharp. As an application, we establish related estimates for stochastic integrals and It\\^{o} processes. The inequalities strengthen the earlier classical results of Burkholder and Choi.
Yang, Haixuan; Seoighe, Cathal
2016-01-01
Nonnegative Matrix Factorization (NMF) has proved to be an effective method for unsupervised clustering analysis of gene expression data. By the nonnegativity constraint, NMF provides a decomposition of the data matrix into two matrices that have been used for clustering analysis. However, the decomposition is not unique. This allows different clustering results to be obtained, resulting in different interpretations of the decomposition. To alleviate this problem, some existing methods directly enforce uniqueness to some extent by adding regularization terms in the NMF objective function. Alternatively, various normalization methods have been applied to the factor matrices; however, the effects of the choice of normalization have not been carefully investigated. Here we investigate the performance of NMF for the task of cancer class discovery, under a wide range of normalization choices. After extensive evaluations, we observe that the maximum norm showed the best performance, although the maximum norm has not previously been used for NMF. Matlab codes are freely available from: http://maths.nuigalway.ie/~haixuanyang/pNMF/pNMF.htm. PMID:27741311
A novel edge-preserving nonnegative matrix factorization method for spectral unmixing
Bao, Wenxing; Ma, Ruishi
2015-12-01
Spectral unmixing technique is one of the key techniques to identify and classify the material in the hyperspectral image processing. A novel robust spectral unmixing method based on nonnegative matrix factorization(NMF) is presented in this paper. This paper used an edge-preserving function as hypersurface cost function to minimize the nonnegative matrix factorization. To minimize the hypersurface cost function, we constructed the updating functions for signature matrix of end-members and abundance fraction respectively. The two functions are updated alternatively. For evaluation purpose, synthetic data and real data have been used in this paper. Synthetic data is used based on end-members from USGS digital spectral library. AVIRIS Cuprite dataset have been used as real data. The spectral angle distance (SAD) and abundance angle distance(AAD) have been used in this research for assessment the performance of proposed method. The experimental results show that this method can obtain more ideal results and good accuracy for spectral unmixing than present methods.
Ma, Yehao; Li, Xian; Huang, Pingjie; Hou, Dibo; Wang, Qiang; Zhang, Guangxin
2017-04-01
In many situations the THz spectroscopic data observed from complex samples represent the integrated result of several interrelated variables or feature components acting together. The actual information contained in the original data might be overlapping and there is a necessity to investigate various approaches for model reduction and data unmixing. The development and use of low-rank approximate nonnegative matrix factorization (NMF) and smooth constraint NMF (CNMF) algorithms for feature components extraction and identification in the fields of terahertz time domain spectroscopy (THz-TDS) data analysis are presented. The evolution and convergence properties of NMF and CNMF methods based on sparseness, independence and smoothness constraints for the resulting nonnegative matrix factors are discussed. For general NMF, its cost function is nonconvex and the result is usually susceptible to initialization and noise corruption, and may fall into local minima and lead to unstable decomposition. To reduce these drawbacks, smoothness constraint is introduced to enhance the performance of NMF. The proposed algorithms are evaluated by several THz-TDS data decomposition experiments including a binary system and a ternary system simulating some applications such as medicine tablet inspection. Results show that CNMF is more capable of finding optimal solutions and more robust for random initialization in contrast to NMF. The investigated method is promising for THz data resolution contributing to unknown mixture identification.
Aspect-Aided Dynamic Non-Negative Sparse Representation-Based Microwave Image Classification
Directory of Open Access Journals (Sweden)
Xinzheng Zhang
2016-09-01
Full Text Available Classification of target microwave images is an important application in much areas such as security, surveillance, etc. With respect to the task of microwave image classification, a recognition algorithm based on aspect-aided dynamic non-negative least square (ADNNLS sparse representation is proposed. Firstly, an aspect sector is determined, the center of which is the estimated aspect angle of the testing sample. The training samples in the aspect sector are divided into active atoms and inactive atoms by smooth self-representative learning. Secondly, for each testing sample, the corresponding active atoms are selected dynamically, thereby establishing dynamic dictionary. Thirdly, the testing sample is represented with ℓ 1 -regularized non-negative sparse representation under the corresponding dynamic dictionary. Finally, the class label of the testing sample is identified by use of the minimum reconstruction error. Verification of the proposed algorithm was conducted using the Moving and Stationary Target Acquisition and Recognition (MSTAR database which was acquired by synthetic aperture radar. Experiment results validated that the proposed approach was able to capture the local aspect characteristics of microwave images effectively, thereby improving the classification performance.
Non-negative matrix factorization by maximizing correntropy for cancer clustering
Wang, Jim Jing-Yan
2013-03-24
Background: Non-negative matrix factorization (NMF) has been shown to be a powerful tool for clustering gene expression data, which are widely used to classify cancers. NMF aims to find two non-negative matrices whose product closely approximates the original matrix. Traditional NMF methods minimize either the l2 norm or the Kullback-Leibler distance between the product of the two matrices and the original matrix. Correntropy was recently shown to be an effective similarity measurement due to its stability to outliers or noise.Results: We propose a maximum correntropy criterion (MCC)-based NMF method (NMF-MCC) for gene expression data-based cancer clustering. Instead of minimizing the l2 norm or the Kullback-Leibler distance, NMF-MCC maximizes the correntropy between the product of the two matrices and the original matrix. The optimization problem can be solved by an expectation conditional maximization algorithm.Conclusions: Extensive experiments on six cancer benchmark sets demonstrate that the proposed method is significantly more accurate than the state-of-the-art methods in cancer clustering. 2013 Wang et al.; licensee BioMed Central Ltd.
Semi-Supervised Projective Non-Negative Matrix Factorization for Cancer Classification.
Directory of Open Access Journals (Sweden)
Xiang Zhang
Full Text Available Advances in DNA microarray technologies have made gene expression profiles a significant candidate in identifying different types of cancers. Traditional learning-based cancer identification methods utilize labeled samples to train a classifier, but they are inconvenient for practical application because labels are quite expensive in the clinical cancer research community. This paper proposes a semi-supervised projective non-negative matrix factorization method (Semi-PNMF to learn an effective classifier from both labeled and unlabeled samples, thus boosting subsequent cancer classification performance. In particular, Semi-PNMF jointly learns a non-negative subspace from concatenated labeled and unlabeled samples and indicates classes by the positions of the maximum entries of their coefficients. Because Semi-PNMF incorporates statistical information from the large volume of unlabeled samples in the learned subspace, it can learn more representative subspaces and boost classification performance. We developed a multiplicative update rule (MUR to optimize Semi-PNMF and proved its convergence. The experimental results of cancer classification for two multiclass cancer gene expression profile datasets show that Semi-PNMF outperforms the representative methods.
Modulational stability and dark solitons in periodic quadratic nonlinear media
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We show that stable dark solitons exist in quadratic nonlinear media with periodic linear and nonlinear susceptibilities. We investigate the modulational stability of plane waves in such systems, a necessary condition for stable dark solitons....
Reconsideration on Homogeneous Quadratic Riemann Boundary Value Problem
Institute of Scientific and Technical Information of China (English)
Lu Jian-ke
2004-01-01
The homogeneous quadratic Riemann boundary value problem (1) with Hǒlder continuous coefficients for the normal case was considered by the author in 1997. But the solutions obtained there are incomplete. Here its general method of solution is obtained.
A Trust-region-based Sequential Quadratic Programming Algorithm
DEFF Research Database (Denmark)
Henriksen, Lars Christian; Poulsen, Niels Kjølstad
This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....
Geometric structure of pseudo-plane quadratic flows
Sun, Che
2017-03-01
Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous applications focused on two-dimensional homogeneous fluid, this study examines the geometric structure of three-dimensional quadratic flows in stratified fluid by solving a steady-state pseudo-plane flow model. The complete set of exact solutions reveals that steady quadratic flows have an invariant conic type in the non-rotating frame and a non-rotatory vertical structure in the rotating frame. Three baroclinic solutions with vertically non-aligned formulation disprove an earlier conjecture. All elliptic and hyperbolic solutions, except for the inertial ones, exhibit vertical concentricity. The rich geometry of quadratic flows stands in contrast to the depleted geometry of high-degree polynomial flows. A paradox in the steady solutions of shallow-water reduced-gravity models is also explained.
Finite dimensional semigroup quadratic algebras with minimal number of relations
Iyudu, Natalia
2011-01-01
A quadratic semigroup algebra is an algebra over a field given by the generators $x_1,...,x_n$ and a finite set of quadratic relations each of which either has the shape $x_jx_k=0$ or the shape $x_jx_k=x_lx_m$. We prove that a quadratic semigroup algebra given by $n$ generators and $d\\leq \\frac{n^2+n}{4}$ relations is always infinite dimensional. This strengthens the Golod--Shafarevich estimate for the above class of algebras. Our main result however is that for every $n$, there is a finite dimensional quadratic semigroup algebra with $n$ generators and $\\delta_n$ generators, where $\\delta_n$ is the first integer greater than $\\frac{n^2+n}{4}$. This shows that the above Golod-Shafarevich type estimate for semigroup algebras is sharp.
Quadratic measurement and conditional state preparation in an optomechanical system
DEFF Research Database (Denmark)
A. Brawley, George; Vanner, Michael A.; Bowen, Warwick P.;
2014-01-01
We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator.......We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator....
An Interval Maximum Entropy Method for Quadratic Programming Problem
Institute of Scientific and Technical Information of China (English)
RUI Wen-juan; CAO De-xin; SONG Xie-wu
2005-01-01
With the idea of maximum entropy function and penalty function methods, we transform the quadratic programming problem into an unconstrained differentiable optimization problem, discuss the interval extension of the maximum entropy function, provide the region deletion test rules and design an interval maximum entropy algorithm for quadratic programming problem. The convergence of the method is proved and numerical results are presented. Both theoretical and numerical results show that the method is reliable and efficient.
On wave-packet dynamics in a decaying quadratic potential
DEFF Research Database (Denmark)
Møller, Klaus Braagaard; Henriksen, Niels Engholm
1997-01-01
We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics.......We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics....
DERIVATIVES OF EIGENPAIRS OF SYMMETRIC QUADRATIC EIGENVALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Derivatives of eigenvalues and eigenvectors with respect to parameters in symmetric quadratic eigenvalue problem are studied. The first and second order derivatives of eigenpairs are given. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the quadratic eigenvalue problem, and the use of state space representation is avoided, hence the cost of computation is greatly reduced. The efficiency of the presented method is demonstrated by considering a spring-mass-damper system.
Scale-Invariant Rotating Black Holes in Quadratic Gravity
Directory of Open Access Journals (Sweden)
Guido Cognola
2015-07-01
Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.
Ideal Class Groups and Subgroups of Real Quadratic Function Fields
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper, we study the real quadratic function fields K=k(D), given a necessary and sufficient condition for the ideal class group H(K) of any real quadratic function field K to have a cyclic subgroup of order n, and obtained eight series of such fields. The ideal class numbers h(OK) of K in the series all have a factor n.
Burgers' turbulence problem with linear or quadratic external potential
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.
2005-01-01
We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....
On Integers, Primes and UniqueFactorization in Quadratic Fields
Hedenlund, Alice
2013-01-01
Abstract. This thesis will deal with quadratic elds. The prob- lem is to study such elds and their properties including, but not limited to, determining integers, nding primes and deciding which quadratic elds have unique factorization. The goal is to get famil- iar with these concepts and to provide a starting point for students with an interest in algebra to explore eld extensions and inte- gral closures in relation to elementary number theory. The reader will be assumed to have a basic kn...
Stability of a Generalized Quadratic Functional Equation in Schwartz Distributions
Institute of Scientific and Technical Information of China (English)
Jae-Young CHUNG
2009-01-01
We consider the Hyers-Ulam stability problem of the generalized quadratic functional equation u(o)A+v(o)B-2w(o)P1-2k(o)P2=0, which is a distributional version of the classical generalized quadratic functional equation f(x + y) + g(x - y) - 2h(x) - 2k(y) = 0.
Quadratic function approaching method for magnetotelluric soundingdata inversion
Energy Technology Data Exchange (ETDEWEB)
Liangjun, Yan; Wenbao, Hu; Zhang, Keni
2004-04-05
The quadratic function approaching method (QFAM) is introduced for magnetotelluric sounding (MT) data inversion. The method takes the advantage of that quadratic function has single extreme value, which avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of an objective function. The method does not need calculation of sensitivity matrix and not require a strict initial earth model. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.
On the use of simplex methods in constructing quadratic models
Institute of Scientific and Technical Information of China (English)
Qing-hua ZHOU
2007-01-01
In this paper, we investigate the quadratic approximation methods. After studying the basic idea of simplex methods, we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces. And the quadratic model is solved in the new subspaces. The motivation is to use the information disclosed by the former steps to construct more promising directions. For most tested problems, the number of function evaluations have been reduced obviously through our algorithms.
Devarajan, Karthik; Cheung, Vincent C.K.
2017-01-01
Non-negative matrix factorization (NMF) by the multiplicative updates algorithm is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into two nonnegative matrices, W and H where V ~ WH. It has been successfully applied in the analysis and interpretation of large-scale data arising in neuroscience, computational biology and natural language processing, among other areas. A distinctive feature of NMF is its nonnegativity constraints that allow only additive linear combinations of the data, thus enabling it to learn parts that have distinct physical representations in reality. In this paper, we describe an information-theoretic approach to NMF for signal-dependent noise based on the generalized inverse Gaussian model. Specifically, we propose three novel algorithms in this setting, each based on multiplicative updates and prove monotonicity of updates using the EM algorithm. In addition, we develop algorithm-specific measures to evaluate their goodness-of-fit on data. Our methods are demonstrated using experimental data from electromyography studies as well as simulated data in the extraction of muscle synergies, and compared with existing algorithms for signal-dependent noise. PMID:24684448
A hybrid-optimization method for large-scale non-negative full regualarization in image restoration
Guerrero, J.; Raydan, M.; Rojas, M.
2011-01-01
We describe a new hybrid-optimization method for solving the full-regularization problem of comput- ing both the regularization parameter and the corresponding regularized solution in 1-norm and 2-norm Tikhonov regularization with additional non-negativity constraints. The approach combines the simu
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper investigates the existence and multiplicity of nonnegative solutions to a singular nonlinear boundary value problem of second order differential equations with integral boundary conditions in a Banach space. The arguments are based on the construction of a nonempty bounded open convex set and fixed point index theory. Our nonlinearity possesses singularity and first derivative which makes it different with that in [10].
Detecting cells using non-negative matrix factorization on calcium imaging data.
Maruyama, Ryuichi; Maeda, Kazuma; Moroda, Hajime; Kato, Ichiro; Inoue, Masashi; Miyakawa, Hiroyoshi; Aonishi, Toru
2014-07-01
We propose a cell detection algorithm using non-negative matrix factorization (NMF) on Ca2+ imaging data. To apply NMF to Ca2+ imaging data, we use the bleaching line of the background fluorescence intensity as an a priori background constraint to make the NMF uniquely dissociate the background component from the image data. This constraint helps us to incorporate the effect of dye-bleaching and reduce the non-uniqueness of the solution. We demonstrate that in the case of noisy data, the NMF algorithm can detect cells more accurately than Mukamel's independent component analysis algorithm, a state-of-art method. We then apply the NMF algorithm to Ca2+ imaging data recorded on the local activities of subcellular structures of multiple cells in a wide area. We show that our method can decompose rapid transient components corresponding to somas and dendrites of many neurons, and furthermore, that it can decompose slow transient components probably corresponding to glial cells.
Cao, Xiaochun; Wang, Xiao; Jin, Di; Cao, Yixin; He, Dongxiao
2013-10-21
Community detection is important for understanding networks. Previous studies observed that communities are not necessarily disjoint and might overlap. It is also agreed that some outlier vertices participate in no community, and some hubs in a community might take more important roles than others. Each of these facts has been independently addressed in previous work. But there is no algorithm, to our knowledge, that can identify these three structures altogether. To overcome this limitation, we propose a novel model where vertices are measured by their centrality in communities, and define the identification of overlapping communities, hubs, and outliers as an optimization problem, calculated by nonnegative matrix factorization. We test this method on various real networks, and compare it with several competing algorithms. The experimental results not only demonstrate its ability of identifying overlapping communities, hubs, and outliers, but also validate its superior performance in terms of clustering quality.
Convergence, Non-negativity and Stability of a New Milstein Scheme with Applications to Finance
Higham, Desmond J; Szpruch, Lukasz
2012-01-01
We propose and analyse a new Milstein type scheme for simulating stochastic differential equations (SDEs) with highly nonlinear coefficients. Our work is motivated by the need to justify multi-level Monte Carlo simulations for mean-reverting financial models with polynomial growth in the diffusion term. We introduce a double implicit Milstein scheme and show that it possesses desirable properties. It converges strongly and preserves non-negativity for a rich family of financial models and can reproduce linear and nonlinear stability behaviour of the underlying SDE without severe restriction on the time step. Although the scheme is implicit, we point out examples of financial models where an explicit formula for the solution to the scheme can be found.
Zhou, Guoxu; Yang, Zuyuan; Xie, Shengli; Yang, Jun-Mei
2011-04-01
Online blind source separation (BSS) is proposed to overcome the high computational cost problem, which limits the practical applications of traditional batch BSS algorithms. However, the existing online BSS methods are mainly used to separate independent or uncorrelated sources. Recently, nonnegative matrix factorization (NMF) shows great potential to separate the correlative sources, where some constraints are often imposed to overcome the non-uniqueness of the factorization. In this paper, an incremental NMF with volume constraint is derived and utilized for solving online BSS. The volume constraint to the mixing matrix enhances the identifiability of the sources, while the incremental learning mode reduces the computational cost. The proposed method takes advantage of the natural gradient based multiplication updating rule, and it performs especially well in the recovery of dependent sources. Simulations in BSS for dual-energy X-ray images, online encrypted speech signals, and high correlative face images show the validity of the proposed method.
Facial Expression Recognition via Non-Negative Least-Squares Sparse Coding
Directory of Open Access Journals (Sweden)
Ying Chen
2014-05-01
Full Text Available Sparse coding is an active research subject in signal processing, computer vision, and pattern recognition. A novel method of facial expression recognition via non-negative least squares (NNLS sparse coding is presented in this paper. The NNLS sparse coding is used to form a facial expression classifier. To testify the performance of the presented method, local binary patterns (LBP and the raw pixels are extracted for facial feature representation. Facial expression recognition experiments are conducted on the Japanese Female Facial Expression (JAFFE database. Compared with other widely used methods such as linear support vector machines (SVM, sparse representation-based classifier (SRC, nearest subspace classifier (NSC, K-nearest neighbor (KNN and radial basis function neural networks (RBFNN, the experiment results indicate that the presented NNLS method performs better than other used methods on facial expression recognition tasks.
Song Recommendation with Non-Negative Matrix Factorization and Graph Total Variation
Benzi, Kirell; Bresson, Xavier; Vandergheynst, Pierre
2016-01-01
This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode both playlist proximity information and song similarity, using a rich combination of audio, meta-data and social features. As we demonstrate, our hybrid recommendation system is very versatile and incorporates several well-known methods while outperforming them. Particularly, we show on real-world data that our model overcomes w.r.t. two evaluation metrics the recommendation of models solely based on low-rank information, graph-based information or a combination of both.
Community Detection in Political Twitter Networks using Nonnegative Matrix Factorization Methods
Ozer, Mert; Davulcu, Hasan
2016-01-01
Community detection is a fundamental task in social network analysis. In this paper, first we develop an endorsement filtered user connectivity network by utilizing Heider's structural balance theory and certain Twitter triad patterns. Next, we develop three Nonnegative Matrix Factorization frameworks to investigate the contributions of different types of user connectivity and content information in community detection. We show that user content and endorsement filtered connectivity information are complementary to each other in clustering politically motivated users into pure political communities. Word usage is the strongest indicator of users' political orientation among all content categories. Incorporating user-word matrix and word similarity regularizer provides the missing link in connectivity only methods which suffer from detection of artificially large number of clusters for Twitter networks.
Deep learning and non-negative matrix factorization in recognition of mammograms
Swiderski, Bartosz; Kurek, Jaroslaw; Osowski, Stanislaw; Kruk, Michal; Barhoumi, Walid
2017-02-01
This paper presents novel approach to the recognition of mammograms. The analyzed mammograms represent the normal and breast cancer (benign and malignant) cases. The solution applies the deep learning technique in image recognition. To obtain increased accuracy of classification the nonnegative matrix factorization and statistical self-similarity of images are applied. The images reconstructed by using these two approaches enrich the data base and thanks to this improve of quality measures of mammogram recognition (increase of accuracy, sensitivity and specificity). The results of numerical experiments performed on large DDSM data base containing more than 10000 mammograms have confirmed good accuracy of class recognition, exceeding the best results reported in the actual publications for this data base.
Joint cluster and non-negative least squares analysis for aerosol mass spectrum data
Energy Technology Data Exchange (ETDEWEB)
Zhang, T; Zhu, W [Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600 (United States); McGraw, R [Environmental Sciences Department, Brookhaven National Laboratory, Upton, NY 11973-5000 (United States)], E-mail: zhu@ams.sunysb.edu
2008-07-15
Aerosol mass spectrum (AMS) data contain hundreds of mass to charge ratios and their corresponding intensities from air collected through the mass spectrometer. The observations are usually taken sequentially in time to monitor the air composition, quality and temporal change in an area of interest. An important goal of AMS data analysis is to reduce the dimensionality of the original data yielding a small set of representing tracers for various atmospheric and climatic models. In this work, we present an approach to jointly apply the cluster analysis and the non-negative least squares method towards this goal. Application to a relevant study demonstrates the effectiveness of this new approach. Comparisons are made to other relevant multivariate statistical techniques including the principal component analysis and the positive matrix factorization method, and guidelines are provided.
Chang, Hsuan T; Shui, J-W; Lin, K-P
2017-02-01
In this paper, a joint multiple-image encryption and multiplexing system, which utilizes both the nonnegative matrix factorization (NMF) scheme and digital holography, is proposed. A number of images are transformed into noise-like digital holograms, which are then decomposed into a defined number of basis images and a corresponding weighting matrix using the NMF scheme. The determined basis images are similar to the digital holograms and appear as noise-like patterns, which are then stored as encrypted data and serve as the lock in an encryption system. On the other hand, the column vectors in the weighting matrix serve as the keys for the corresponding plain images or the addresses of the multiplexed images. Both the increased uniformity of the column weighting factors and the parameters used in the digital holography enhance the security of the distributed keys. The experimental results show that the proposed method can successfully perform multiple-image encryption with high-level security.
Categorical dimensions of human odor descriptor space revealed by non-negative matrix factorization
Energy Technology Data Exchange (ETDEWEB)
Chennubhotla, Chakra [University of Pittsburgh School of Medicine, Pittsburgh PA; Castro, Jason [Bates College
2013-01-01
In contrast to most other sensory modalities, the basic perceptual dimensions of olfaction remain un- clear. Here, we use non-negative matrix factorization (NMF) - a dimensionality reduction technique - to uncover structure in a panel of odor profiles, with each odor defined as a point in multi-dimensional descriptor space. The properties of NMF are favorable for the analysis of such lexical and perceptual data, and lead to a high-dimensional account of odor space. We further provide evidence that odor di- mensions apply categorically. That is, odor space is not occupied homogenously, but rather in a discrete and intrinsically clustered manner. We discuss the potential implications of these results for the neural coding of odors, as well as for developing classifiers on larger datasets that may be useful for predicting perceptual qualities from chemical structures.
Park, Sang Ha; Lee, Seokjin; Sung, Koeng-Mo
Non-negative matrix factorization (NMF) is widely used for monaural musical sound source separation because of its efficiency and good performance. However, an additional clustering process is required because the musical sound mixture is separated into more signals than the number of musical tracks during NMF separation. In the conventional method, manual clustering or training-based clustering is performed with an additional learning process. Recently, a clustering algorithm based on the mel-frequency cepstrum coefficient (MFCC) was proposed for unsupervised clustering. However, MFCC clustering supplies limited information for clustering. In this paper, we propose various timbre features for unsupervised clustering and a clustering algorithm with these features. Simulation experiments are carried out using various musical sound mixtures. The results indicate that the proposed method improves clustering performance, as compared to conventional MFCC-based clustering.
Montcuquet, Anne-Sophie; Hervé, Lionel; Navarro, Fabrice; Dinten, Jean-Marc; Mars, Jérôme I
2011-09-01
Fluorescence imaging locates fluorescent markers that specifically bind to targets; like tumors, markers are injected to a patient, optimally excited with near-infrared light, and located thanks to backward-emitted fluorescence analysis. To investigate thick and diffusive media, as the fluorescence signal decreases exponentially with the light travel distance, the autofluorescence of biological tissues comes to be a limiting factor. To remove autofluorescence and isolate specific fluorescence, a spectroscopic approach, based on nonnegative matrix factorization (NMF), is explored. To improve results on spatially sparse markers detection, we suggest a new constrained NMF algorithm that takes sparsity constraints into account. A comparative study between both algorithms is proposed on simulated and in vivo data.
Montcuquet, Anne-Sophie; Hervé, Lionel; Navarro, Fabrice; Dinten, Jean-Marc; Mars, Jérôme I
2010-01-01
Fluorescence imaging in diffusive media is an emerging imaging modality for medical applications that uses injected fluorescent markers that bind to specific targets, e.g., carcinoma. The region of interest is illuminated with near-IR light and the emitted back fluorescence is analyzed to localize the fluorescence sources. To investigate a thick medium, as the fluorescence signal decreases with the light travel distance, any disturbing signal, such as biological tissues intrinsic fluorescence (called autofluorescence) is a limiting factor. Several specific markers may also be simultaneously injected to bind to different molecules, and one may want to isolate each specific fluorescent signal from the others. To remove the unwanted fluorescence contributions or separate different specific markers, a spectroscopic approach is explored. The nonnegative matrix factorization (NMF) is the blind positive source separation method we chose. We run an original regularized NMF algorithm we developed on experimental data, and successfully obtain separated in vivo fluorescence spectra.
Linear coloring of graphs embeddable in a surface of nonnegative characteristic
Institute of Scientific and Technical Information of China (English)
2009-01-01
A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of the graph G is the smallest number of colors in a linear coloring of G. In this paper, we prove that every graph G with girth g(G) and maximum degree Δ(G) that can be embedded in a surface of nonnegative characteristic has lc(G) = Δ(2G )+ 1 if there is a pair (Δ, g) ∈ {(13, 7), (9, 8), (7, 9), (5, 10), (3, 13)} such that G satisfies Δ(G) Δ and g(G) g.
Linear coloring of graphs embeddable in a surface of nonnegative characteristic
Institute of Scientific and Technical Information of China (English)
WANG WeiFan; LI Chao
2009-01-01
A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of the graph G is the smallest number of colors in a linear coloring of G. In this paper, we prove that every graph G with girth g(G) and maximum degree △(G) that can be embedded in a surface of nonnegative characteristic has lc(G) = 「△(G)/2」+ 1 if there is a pair (△,g) ∈ {(13, 7), (9, 8), (7, 9), (5, 10), (3, 13)} such that G satisfies △(G) ≥ △ and g(G) ≥ g.
HPC-NMF: A High-Performance Parallel Algorithm for Nonnegative Matrix Factorization
Energy Technology Data Exchange (ETDEWEB)
2016-08-22
NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient distributed algorithms to solve the problem for big data sets. We propose a high-performance distributed-memory parallel algorithm that computes the factorization by iteratively solving alternating non-negative least squares (NLS) subproblems for $\\WW$ and $\\HH$. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). As opposed to previous implementation, our algorithm is also flexible: It performs well for both dense and sparse matrices, and allows the user to choose any one of the multiple algorithms for solving the updates to low rank factors $\\WW$ and $\\HH$ within the alternating iterations.
A transient, quadratic nodal method for triangular-Z geometry
Energy Technology Data Exchange (ETDEWEB)
DeLorey, T.F.
1993-06-01
Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.
Quadratic 0-1 programming: Geometric methods and duality analysis
Liu, Chunli
The unconstraint quadratic binary problem (UBQP), as a classical combinatorial problem, finds wide applications in broad field and human activities including engineering, science, finance, etc. The NP-hardness of the combinatorial problems makes a great challenge to solve the ( UBQP). The main purpose of this research is to develop high performance solution method for solving (UBQP) via the geometric properties of the objective ellipse contour and the optimal solution. This research makes several contributions to advance the state-of-the-art of geometric approach of (UBQP). These contributions include both theoretical and numerical aspects as stated below. In part I of this dissertation, certain rich geometric properties hidden behind quadratic 0-1 programming are investigated. Especially, we derive new lower bounding methods and variable fixation techniques for quadratic 0-1 optimization problems by investigating geometric features of the ellipse contour of a (perturbed) convex quadratic function. These findings further lead to some new optimality conditions for quadratic 0-1 programming. Integrating these novel solution schemes into a proposed solution algorithm of a branch-and-bound type, we obtain promising preliminary computational results. In part II of this dissertation, we present new results of the duality gap between the binary quadratic optimization problem and its Lagrangian dual. We first derive a necessary and sufficient condition for the zero duality gap and discuss its relationship with the polynomial solvability of the problem. We then characterize the zeroness of duality gap by the distance, delta, between the binary set and certain affine space C. Finally, we discuss a computational procedure of the distance delta. These results provide new insights into the duality gap and polynomial solvability of binary quadratic optimization problems.
Institute of Scientific and Technical Information of China (English)
Xiuxiong CHEN; Haozhao LI
2008-01-01
The authors show that the 2-non-negative traceless bisectional curvature is preserved along the K(a)hler-Ricci flow.The positivity of Ricci curvature is also preserved along the K(a)hler-Ricci flow with 2-non-negative traceless bisectional curvature.As a corollary,the K(a)hler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a K(a)hler-Ricci soliton in the sense of Cheeger-Gromov-Hausdorff topology if complex dimension n≥3.
Directory of Open Access Journals (Sweden)
Pavel Matei
2007-06-01
Full Text Available Let $a:mathbb{R}o mathbb{R}$ be a strictly increasing odd continuous function with $lim_{to +infty }a(t=+infty $ and $A(t=int_{0}^{t}a(s,ds$, $tin mathbb{R}$, the $N$-function generated by $a$. Let $Omega $ be a bounded open subset of $mathbb{R}^{N}$, $Ngeq 2$, $T[u,u]$ a nonnegative quadratic form involving the only generalized derivatives of order $m$ of the function $uin W_{0}^{m}E_{A}(Omega $ and $g_{alpha }:Omegaimesmathbb{R}omathbb{R}$, $| alpha |
The generalized quadratic knapsack problem. A neuronal network approach.
Talaván, Pedro M; Yáñez, Javier
2006-05-01
The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.
Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
Energy Technology Data Exchange (ETDEWEB)
Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar
2016-06-15
We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.
The quadratic reciprocity law a collection of classical proofs
Baumgart, Oswald
2015-01-01
This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.
Parametric localized modes in quadratic nonlinear photonic structures
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole;
2001-01-01
We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi2) nonlinear interfaces embedded in a linear layered structure-a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear...... interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi2 equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface...... in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media....
On Volterra quadratic stochastic operators with continual state space
Energy Technology Data Exchange (ETDEWEB)
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar [Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University, Jalan Sultan Ahmad Shah, Bandar Indera Mahkota, 25200 Kuantan, Pahang (Malaysia)
2015-05-15
Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.
Amalgamated Products of Ore and Quadratic Extensions of Rings
Johnson, Garrett
2012-01-01
We study the ideal theory of amalgamated products of Ore and quadratic extensions over a base ring R. We prove an analogue of the Hilbert Basis theorem for an amalgamated product Q of quadratic extensions and determine conditions for when the one-sided ideals of Q are principal or doubly-generated. We also determine conditions that make Q a principal ideal ring. Finally, we show that the double affine Hecke algebra $H_{q,t}$ associated to the general linear group GL_2(k) (here, k is a field with characteristic not 2) is an amalgamated product of quadratic extensions over a three-dimensional quantum torus and give an explicit isomorphism. In this case, it follows that $H_{q,t}$ is a noetherian ring.
A Projection Neural Network for Constrained Quadratic Minimax Optimization.
Liu, Qingshan; Wang, Jun
2015-11-01
This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.
Wang, T.; Zhang, H.; Lin, H.
2017-09-01
surfaces has increasingly roused widely interests of researchers in monitoring urban development and determining the overall environmental health of a watershed. However, studies on the impervious surface using multi-spectral imageries is insufficient and inaccurate due to the complexity of urban infrastructures base on the need to further recognize these impervious surface materials in a finer scale. Hyperspectral imageries have been proved to be sensitive to subtle spectral differences thus capable to exquisitely discriminate these similar materials while limited to the low spatial resolution. Coupled nonnegative matrix factorization (CNMF) unmixing method is one of the most physically straightforward and easily complemented hyperspectral pan-sharpening methods that could produce fused data with both high spectral and spatial resolution. This paper aimed to exploit the latent capacity and tentative validation of CNMF on the killer application of mapping urban impervious surfaces in complexed metropolitan environments like Hong Kong. Experiments showed that the fusion of high spectral and spatial resolution image could provide more accurate and comprehensive information on urban impervious surface estimation.
Convergence properties of the softassign quadratic assignment algorithm.
Rangarajan, A; Vuille, A; Mjolsness, E
1999-08-15
The softassign quadratic assignment algorithm is a discrete-time, continuous-state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching, and graph partitioning in thousands of simulations, its convergence properties have not been studied. Here, we construct discrete-time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction, which show convergence to a fixed point. The combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization.
Robust quadratic assignment problem with budgeted uncertain flows
Directory of Open Access Journals (Sweden)
Mohammad Javad Feizollahi
2015-12-01
Full Text Available We consider a generalization of the classical quadratic assignment problem, where material flows between facilities are uncertain, and belong to a budgeted uncertainty set. The objective is to find a robust solution under all possible scenarios in the given uncertainty set. We present an exact quadratic formulation as a robust counterpart and develop an equivalent mixed integer programming model for it. To solve the proposed model for large-scale instances, we also develop two different heuristics based on 2-Opt local search and tabu search algorithms. We discuss performance of these methods and the quality of robust solutions through extensive computational experiments.
Selectable linear or quadratic coupling in an optomechanical system
Xuereb, André
2012-01-01
There has been much interest recently in the analysis of optomechanical systems incorporating dielectric nano- or microspheres inside a cavity field. We analyse here the situation when one of the mirrors of the cavity itself is also allowed to move. We reveal that the interplay between the two oscillators yields a cross-coupling that results in, e.g., appreciable cooling and squeezing of the motion of the sphere, despite its nominal quadratic coupling. We also discuss a simple modification that would allow this cross-coupling to be removed at will, thereby yielding a purely quadratic coupling for the sphere.
On the use of simplex methods in constructing quadratic models
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper,we investigate the quadratic approximation methods.After studying the basic idea of simplex methods,we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces.And the quadratic model is solved in the new subspaces.The motivation is to use the information disclosed by the former steps to construct more promising directions.For most tested problems,the number of function evaluations have been reduced obviously through our algorithms.
New robust chaotic system with exponential quadratic term
Institute of Scientific and Technical Information of China (English)
Bao Bo-Cheng; Li Chun-Biao; Xu Jian-Peing; Liu Zhong
2008-01-01
This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term.This system can display a double-scroll chaotic attractor with only two equilibria,and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent.Some basic dynamical properties and chaotic behaviour of novel attractor are studied.By numerical simulation,this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviottrs by a constant controller.
Approximation algorithms for indefinite complex quadratic maximization problems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper,we consider the following indefinite complex quadratic maximization problem: maximize zHQz,subject to zk ∈ C and zkm = 1,k = 1,...,n,where Q is a Hermitian matrix with trQ = 0,z ∈ Cn is the decision vector,and m 3.An (1/log n) approximation algorithm is presented for such problem.Furthermore,we consider the above problem where the objective matrix Q is in bilinear form,in which case a 0.7118 cos mπ 2approximation algorithm can be constructed.In the context of quadratic optimization,various extensions and connections of the model are discussed.
Simultaneous quadratic performance stabilization for linear time-delay systems
Institute of Scientific and Technical Information of China (English)
Chen Yuepeng; Zhou Zude; Liu Huanbin; Zhang Qingling
2006-01-01
A newly designed approach of simultaneous stabilization is given for linear discrete time-delay systems. The problem of stabilization for a collection of systems is discussed initially. Adequate condition are obtained in terms of linear matrix inequalities (LMIs) which are independent of time delays such that the resultant collection of discrete time-delay systems are stable with an upper bound of the quadratic performance index. Subsequently, controllers are designed such that the resultant closed-loop discrete time-delay systems are simultaneously stabilized with the upper bound of the quadratic performance index. Finally,a numerical example is given to illustrate the design method.
PORTAL SUPPLY TO CAUDATE LOBE AND QUADRATE LOBE OF LIVER
Directory of Open Access Journals (Sweden)
Maheswari
2015-09-01
Full Text Available The precise knowledge of intra hepatic branching pattern of portal vein to caudate lobe and quadrate lobe is important for Gastroenterologist during hepatic segmental and subsegmental resection. The study was done in 47 adult human liver specimens. In this study methods like Manual dissection and Contrast study were used. During this study the portal branches to caudate l obe, Quadrate lobe and accessory branches to segment IV in addition to its branches were observed. The results were compared with previous studies
Sparse Signal Recovery from Quadratic Measurements via Convex Programming
Li, Xiaodong; Voroninski, Vladislav
2012-01-01
In this paper we consider a system of quadratic equations ||^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurements b_j in R are known. The system is assumed to be underdetermined, i.e., m < n. We prove that if there exists a sparse solution x, i.e., at most k components of x are non-zero, then by solving a convex optimization program, we can solve for x up to a multiplicative constant with high probability, provided that k
Exact solutions to quadratic gravity generated by a conformal method
Pravda, Vojtech; Podolsky, Jiri; Svarc, Robert
2016-01-01
We study the role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one non-linear partial differential equation for the conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. We show that all spacetimes conformal to Kundt are either Kundt or Robinson--Trautmann, and we provide explicit Kundt and Robinson--Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.
DEFF Research Database (Denmark)
Nielsen, Søren Føns Vind; Mørup, Morten
2014-01-01
of the component matrices. We examine three gene expression prediction scenarios based on data missing at random, whole genes missing and whole areas missing within a subject. We find that the column-wise updating approach also known as HALS performs the most efficient when fitting the model. We further observe...... that the non-negativity constrained CP model is able to predict gene expressions better than predicting by the subject average when data is missing at random. When whole genes and whole areas are missing it is in general better to predict by subject averages. However, we find that when whole genes are missing...... missing in our problem. Our analysis is based on the non-negativity constrained Canonical Polyadic (CP) decomposition where we handle the missing data using marginalization considering three prominent alternating least squares procedures; multiplicative updates, column-wise, and row-wise updating...
Lu, Qieni; Han, Jinxin; Dai, Haitao; Ge, Baozhen; Zhao, Shuang
2015-08-01
We measure temperature dependence on Kerr coefficient and quadratic polarized optical coefficient of a paraelectric Mn:Fe:KTN crystal simultaneously in this work, based on digital holographic interferometry (DHI). And the spatial distribution of the field-induced refractive index change can also be visualized and estimated by numerically retrieving sequential phase maps of Mn:Fe:KTN crystal from recording digital holograms in different states. The refractive indices decrease with increasing temperature and quadratic polarized optical coefficient is insensitive to temperature. The experimental results suggest that the DHI method presented here is highly applicable in both visualizing the temporal and spatial behavior of the internal electric field and accurately measuring electro-optic coefficient for electrooptical media.
DEFF Research Database (Denmark)
Shah, Ghafoor; Koch, Peter; Papadias, Constantinos B.
2014-01-01
. A novel method based on hierarchical decomposition of the single channel mixture using various nonnegative matrix factorization techniques is proposed, which provides unsupervised clustering of the underlying component signals. HRV is determined over the recovered normal cardiac acoustic signals....... This novel decomposition technique is compared against the state-of-the-art techniques; experiments are performed using real-world clinical data, which show the potential significance of the proposed technique....
Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.
Wang, Di; Kleinberg, Robert D
2009-11-28
Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.
A new heuristic for the quadratic assignment problem
Zvi Drezner
2002-01-01
We propose a new heuristic for the solution of the quadratic assignment problem. The heuristic combines ideas from tabu search and genetic algorithms. Run times are very short compared with other heuristic procedures. The heuristic performed very well on a set of test problems.
HOMOCLINIC CYCLES OF A QUADRATIC SYSTEM DESCRIBED BY QUARTIC CURVES
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
This paper is devoted to discussing the topological classification of the quartic invariant algebraic curves for a quadratic system. We obtain sufficient and necessary conditions which ensure that the homoclinic cycle of the system is defined by the quartic invariant algebraic curve. Finally, the corresponding global phase diagrams are drawn.
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
DEFF Research Database (Denmark)
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
Positivity and storage functions for quadratic differential forms
Trentelman, Hendrikus; Willems, Jan C.
1996-01-01
Differential equations and one-variable polynomial matrices play an essential role in describing dynamics of systems. When studying functions of the dynamical variables or specifying performance criteria in optimal control, we invariably encounter quadratic expressions in the variables and their der
Canonical realization of Bondi-Metzner-Sachs symmetry: Quadratic Casimir
Gomis, Joaquim; Longhi, Giorgio
2016-01-01
We study the canonical realization of Bondi-Metzner-Sacks symmetry for a massive scalar field introduced by Longhi and Materassi [J. Math. Phys. 40, 480 (1999)]. We construct an invariant scalar product for the generalized momenta. As a consequence we introduce a quadratic Casimir with the supertranslations.
A Unified Approach to Teaching Quadratic and Cubic Equations.
Ward, A. J. B.
2003-01-01
Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)
Second Order Backward Stochastic Differential Equations with Quadratic Growth
Dylan, Possamai
2012-01-01
We prove the existence and uniqueness of a solution for one-dimensionnal second order backward stochastic differential equations introduced by Soner, Touzi and Zhang (2010), with a bounded terminal condition and a generator which is continuous with quadratic growth in z. We also prove a Feyman-Kac formula and a probabilistic representation for fully nonlinear PDEs in this setting.
Quantum electroweak symmetry breaking through loop quadratic contributions
Directory of Open Access Journals (Sweden)
Dong Bai
2015-06-01
Full Text Available Based on two postulations that (i the Higgs boson has a large bare mass mH≫mh≃125 GeV at the characteristic energy scale Mc which defines the Standard Model (SM in the ultraviolet region, and (ii quadratic contributions of Feynman loop diagrams in quantum field theories are physically meaningful, we show that the SM electroweak symmetry breaking is induced by the quadratic contributions from loop effects. As the quadratic running of Higgs mass parameter leads to an additive renormalization, which distinguishes from the logarithmic running with a multiplicative renormalization, the symmetry breaking occurs once the sliding energy scale μ moves from Mc down to a transition scale μ=ΛEW at which the additive renormalized Higgs mass parameter mH2(Mc/μ gets to change the sign. With the input of current experimental data, this symmetry breaking energy scale is found to be ΛEW≃760 GeV, which provides another basic energy scale for the SM besides Mc. Studying such a symmetry breaking mechanism could play an important role in understanding both the hierarchy problem and naturalness problem. It also provides a possible way to explore the experimental implications of the quadratic contributions as ΛEW lies within the probing reach of the LHC and the future Great Collider.
Bandit-Inspired Memetic Algorithms for Solving Quadratic Assignment Problems
Puglierin, Francesco; Drugan, Madalina M.; Wiering, Marco
2013-01-01
In this paper we propose a novel algorithm called the Bandit-Inspired Memetic Algorithm (BIMA) and we have applied it to solve different large instances of the Quadratic Assignment Problem (QAP). Like other memetic algorithms, BIMA makes use of local search and a population of solutions. The novelty
The Quadratic Assignment Problem is Easy for Robinsonian Matrices
Laurent, M.; Seminaroti, M.
2014-01-01
We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form QAP(A;B), by showing that the identity permutation is optimal when A and B are respectively a Robinson similarity and dissimilarity matrix and one of A or B is a Toeplitz matrix. A Robinson (dis)
A bilinear programming solution to the quadratic assignment problem
J.F. Kaashoek (Johan); J.H.P. Paelinck (Jean)
1999-01-01
textabstractThe quadratic assignment problem (QAP) or maximum acyclical graph problem is well documented (see e.g. Pardalos and Wolkowicz, 1994). One of the authors has published some material, in which it was tried, by structuring the problem additionally, to bring it as closely as possible in the
The quadratic assignment problem is easy for robinsonian matrices
Laurent, M.; Seminaroti, M.
2015-01-01
We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans–Beckman form QAP(A,B), by showing that the identity permutation is optimal when AA and BB are respectively a Robinson similarity and dissimilarity matrix and one of AA or BB is a Toeplitz matrix. A Robinson (
Solving quadratic programming problems by delayed projection neural network.
Yang, Yongqing; Cao, Jinde
2006-11-01
In this letter, the delayed projection neural network for solving convex quadratic programming problems is proposed. The neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem. Three examples show the effectiveness of the proposed network.
A Result on Output Feedback Linear Quadratic Control
Engwerda, J.C.; Weeren, A.J.T.M.
2006-01-01
In this note we consider the static output feedback linear quadratic control problem.We present both necessary and sufficient conditions under which this problem has a solution in case the involved cost depend only on the output and control variables.This result is used to present both necessary and
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
ON WEIGHTED GENERALIZED FUNCTIONS ASSOCIATED WITH QUADRATIC FORMS
Directory of Open Access Journals (Sweden)
E. L. Shishkina
2016-12-01
Full Text Available In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with the Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with the Bessel operator.
Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales
Institute of Scientific and Technical Information of China (English)
ZHANG JI; LIU ZHEN-XIN
2011-01-01
In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△ ＝ A(t)x on time scales.Moreover, for the nonlinear perturbed equation x△ ＝ A(t)x + f(t,x) we give the instability of the zero solution when f is sufficiently small.
Radar Rainfall Estimation using a Quadratic Z-R equation
Hall, Will; Rico-Ramirez, Miguel Angel; Kramer, Stefan
2016-04-01
The aim of this work is to test a method that enables the input of event based drop size distributions to alter a quadratic reflectivity (Z) to rainfall (R) equation that is limited by fixed upper and lower points. Results will be compared to the Marshall-Palmer Z-R relation outputs and validated by a network of gauges and a single polarisation weather radar located close to Essen, Germany. The time window over which the drop size distribution measurements will be collected is varied to note any effect on the generated quadratic Z-R relation. The new quadratic algorithm shows some distinct improvement over the Marshall-Palmer relationship through multiple events. The inclusion of a minimum number of Z-R points helped to decrease the associated error by defaulting back to the Marshall-Palmer equation if the limit was not reached. More research will be done to discover why the quadratic performs poorly in some events as there appears to be little correlation between number of drops or mean rainfall amount and the associated error. In some cases it seems the spatial distribution of the disdrometers has a significant effect as a large percentage of the rain bands pass to the north of two of the three disdrometers, frequently in a slightly north-easterly direction. However during widespread precipitation events the new algorithm works very well with reductions compared to the Marshall-Palmer relation.
ANOTHER LOOK AT LINEAR-QUADRATIC OPTIMIZATION PROBLEMS OVER TIME
NIEUWENHUIS, JW
1995-01-01
We will study deterministic quadratic optimization problems over time with linear constraints by means of the behavioral approach of linear systems as developed by Willems (1986, 1989). We will start with a simple example from economics and embed this in a general framework. Then we will develop the
Entanglement entropy of fermionic quadratic band touching model
Chen, Xiao; Cho, Gil Young; Fradkin, Eduardo
2014-03-01
The entanglement entropy has been proven to be a useful tool to diagnose and characterize strongly correlated systems such as topologically ordered phases and some critical points. Motivated by the successes, we study the entanglement entropy (EE) of a fermionic quadratic band touching model in (2 + 1) dimension. This is a fermionic ``spinor'' model with a finite DOS at k=0 and infinitesimal instabilities. The calculation on two-point correlation functions shows that a Dirac fermion model and the quadratic band touching model both have the asymptotically identical behavior in the long distance limit. This implies that EE for the quadratic band touching model also has an area law as the Dirac fermion. This is in contradiction with the expectation that dense fermi systems with a finite DOS should exhibit LlogL violations to the area law of entanglement entropy (L is the length of the boundary of the sub-region) by analogy with the Fermi surface. We performed numerical calculations of entanglement entropies on a torus of the lattice models for the quadratic band touching point and the Dirac fermion to confirm this. The numerical calculation shows that EE for both cases satisfy the area law. We further verify this result by the analytic calculation on the torus geometry. This work was supported in part by the NSF grant DMR-1064319.
Finding the Best Quadratic Approximation of a Function
Yang, Yajun; Gordon, Sheldon P.
2011-01-01
This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…
Kronecker limit formula for real quadratic number fields(III)
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
For a kind of L-function of the real quadratic number fields, we prove a Kronecker limit formula which generalized a result of Hecke. And taking an example we give an interesting identity on a fundamental unit of such a field.
A realised volatility measurement using quadratic variation and ...
African Journals Online (AJOL)
the instantaneous volatility does not change too much as a result of a weighted average ... method is also based on quadratic variation theory, but the underlying return model is ..... [3] Barndorff-Nielsen OE & Shepard N, 2001, Non-Gaussian ...
The strong law of large numbers for random quadratic forms
Mikosch, T
1996-01-01
The paper establishes strong laws of large numbers for the quadratic forms [GRAPHICS] and the bilinear forms [GRAPHICS] where X = (X(n)) is a sequence of independent random variables and Y = (Y-n) is an independent copy of it. In the case of independent identically distributed symmetric p-stable ran
Confidence set interference with a prior quadratic bound. [in geophysics
Backus, George E.
1989-01-01
Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.
Optimization with quadratic support functions in nonconvex smooth optimization
Khamisov, O. V.
2016-10-01
Problem of global minimization of twice continuously differentiable function with Lipschitz second derivatives over a polytope is considered. We suggest a branch and bound method with polytopes as partition elements. Due to the Lipschitz property of the objective function we can construct a quadratic support minorant at each point of the feasible set. Global minimum of of this minorant provides a lower bound of the objective over given partition subset. The main advantage of the suggested method consists in the following. First quadratic minorants usually are nonconvex and we have to solve auxiliary global optimization problem. This problem is reduced to a mixed 0-1 linear programming problem and can be solved by an advanced 0-1 solver. Then we show that the quadratic minorants are getting convex as soon as partition elements are getting smaller in diameter. Hence, at the final steps of the branch and bound method we solve convex auxiliary quadratic problems. Therefore, the method accelerates when we are close to the global minimum of the initial problem.
Stochastic level-value approximation for quadratic integer convex programming
Institute of Scientific and Technical Information of China (English)
PENG Zheng; WU Dong-hua
2008-01-01
We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and re-port some numerical results to illuminate its effectiveness.
Semismooth Newton method for quadratic programs with bound constraints
Daryina, A. N.; Izmailov, A. F.
2009-10-01
Convex quadratic programs with bound constraints are proposed to be solved by applying a semismooth Newton method to the corresponding variational inequality. Computational experiments demonstrate that, for strongly convex problems, this approach can be considerably more efficient than more traditional approaches.
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
DEFF Research Database (Denmark)
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
Sub-quadratic decoding of one-point hermitian codes
DEFF Research Database (Denmark)
Nielsen, Johan Sebastian Rosenkilde; Beelen, Peter
2015-01-01
We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power...
Cosmological Vorticity in a Gravity with Quadratic Order Curvature Couplings
Hwang, J
1998-01-01
We analyse the evolution of the rotational type cosmological perturbation in a gravity with general quadratic order gravitational coupling terms. The result is expressed independently of the generalized nature of the gravity theory, and is simply interpreted as a conservation of the angular momentum.
The strong law of large numbers for random quadratic forms
Mikosch, T
1996-01-01
The paper establishes strong laws of large numbers for the quadratic forms [GRAPHICS] and the bilinear forms [GRAPHICS] where X = (X(n)) is a sequence of independent random variables and Y = (Y-n) is an independent copy of it. In the case of independent identically distributed symmetric p-stable
Institute of Scientific and Technical Information of China (English)
Xiu-rui GENG; Lu-yan JI; Kang SUN
2016-01-01
Non-negative matrix factorization (NMF) has been widely used in mixture analysis for hyperspectral remote sensing. When used for spectral unmixing analysis, however, it has two main shortcomings: (1) since the dimensionality of hyperspectral data is usually very large, NMF tends to suffer from large computational complexity for the popular multiplicative iteration rule;(2) NMF is sensitive to noise (outliers), and thus the corrupted data will make the results of NMF meaningless. Although principal component analysis (PCA) can be used to mitigate these two problems, the transformed data will contain negative numbers, hindering the direct use of the multiplicative iteration rule of NMF. In this paper, we analyze the impact of PCA on NMF, and fi nd that multiplicative NMF can also be applicable to data after principal component transformation. Based on this conclusion, we present a method to perform NMF in the principal component space, named ‘principal component NMF’ (PCNMF). Experimental results show that PCNMF is both accurate and time-saving.
Fast Nonnegative Deconvolution for Spike Train Inference From Population Calcium Imaging
Packer, Adam M.; Machado, Timothy A.; Sippy, Tanya; Babadi, Baktash; Yuste, Rafael; Paninski, Liam
2010-01-01
Fluorescent calcium indicators are becoming increasingly popular as a means for observing the spiking activity of large neuronal populations. Unfortunately, extracting the spike train of each neuron from a raw fluorescence movie is a nontrivial problem. This work presents a fast nonnegative deconvolution filter to infer the approximately most likely spike train of each neuron, given the fluorescence observations. This algorithm outperforms optimal linear deconvolution (Wiener filtering) on both simulated and biological data. The performance gains come from restricting the inferred spike trains to be positive (using an interior-point method), unlike the Wiener filter. The algorithm runs in linear time, and is fast enough that even when simultaneously imaging >100 neurons, inference can be performed on the set of all observed traces faster than real time. Performing optimal spatial filtering on the images further refines the inferred spike train estimates. Importantly, all the parameters required to perform the inference can be estimated using only the fluorescence data, obviating the need to perform joint electrophysiological and imaging calibration experiments. PMID:20554834
Wang, Jim Jing-Yan
2014-09-20
Nonnegative matrix factorization (NMF), a popular part-based representation technique, does not capture the intrinsic local geometric structure of the data space. Graph regularized NMF (GNMF) was recently proposed to avoid this limitation by regularizing NMF with a nearest neighbor graph constructed from the input data set. However, GNMF has two main bottlenecks. First, using the original feature space directly to construct the graph is not necessarily optimal because of the noisy and irrelevant features and nonlinear distributions of data samples. Second, one possible way to handle the nonlinear distribution of data samples is by kernel embedding. However, it is often difficult to choose the most suitable kernel. To solve these bottlenecks, we propose two novel graph-regularized NMF methods, AGNMFFS and AGNMFMK, by introducing feature selection and multiple-kernel learning to the graph regularized NMF, respectively. Instead of using a fixed graph as in GNMF, the two proposed methods learn the nearest neighbor graph that is adaptive to the selected features and learned multiple kernels, respectively. For each method, we propose a unified objective function to conduct feature selection/multi-kernel learning, NMF and adaptive graph regularization simultaneously. We further develop two iterative algorithms to solve the two optimization problems. Experimental results on two challenging pattern classification tasks demonstrate that the proposed methods significantly outperform state-of-the-art data representation methods.
Directory of Open Access Journals (Sweden)
Qunyi Xie
2016-01-01
Full Text Available Content-based image retrieval has recently become an important research topic and has been widely used for managing images from repertories. In this article, we address an efficient technique, called MNGS, which integrates multiview constrained nonnegative matrix factorization (NMF and Gaussian mixture model- (GMM- based spectral clustering for image retrieval. In the proposed methodology, the multiview NMF scheme provides competitive sparse representations of underlying images through decomposition of a similarity-preserving matrix that is formed by fusing multiple features from different visual aspects. In particular, the proposed method merges manifold constraints into the standard NMF objective function to impose an orthogonality constraint on the basis matrix and satisfy the structure preservation requirement of the coefficient matrix. To manipulate the clustering method on sparse representations, this paper has developed a GMM-based spectral clustering method in which the Gaussian components are regrouped in spectral space, which significantly improves the retrieval effectiveness. In this way, image retrieval of the whole database translates to a nearest-neighbour search in the cluster containing the query image. Simultaneously, this study investigates the proof of convergence of the objective function and the analysis of the computational complexity. Experimental results on three standard image datasets reveal the advantages that can be achieved with the proposed retrieval scheme.
Naik, Ganesh R; Nguyen, Hung T
2015-03-01
Surface electromyography (sEMG) is widely used in evaluating the functional status of the hand to assist in hand gesture recognition, prosthetics and rehabilitation applications. The sEMG is a noninvasive, easy to record signal of superficial muscles from the skin surface. Considering the nonstationary characteristics of sEMG, recent feature selection of hand gesture recognition using sEMG signals necessitate designers to use nonnegative matrix factorization (NMF)-based methods. This method exploits both the additive and sparse nature of signals by extracting accurate and reliable measurements of sEMG features using a minimum number of sensors. The testing has been conducted for simple and complex finger flexions using several experiments with artificial neural network classification scheme. It is shown, both by simulation and experimental studies, that the proposed algorithm is able to classify ten finger flexions (five simple and five complex finger flexions) recorded from two sEMG sensors up to 92% (95% for simple and 87% for complex flexions) accuracy. The recognition performances of simple and complex finger flexions are also validated with NMF permutation matrix analysis.
EEG source imaging with spatio-temporal tomographic nonnegative independent component analysis.
Valdés-Sosa, Pedro A; Vega-Hernández, Mayrim; Sánchez-Bornot, José Miguel; Martínez-Montes, Eduardo; Bobes, María Antonieta
2009-06-01
This article describes a spatio-temporal EEG/MEG source imaging (ESI) that extracts a parsimonious set of "atoms" or components, each the outer product of both a spatial and a temporal signature. The sources estimated are localized as smooth, minimally overlapping patches of cortical activation that are obtained by constraining spatial signatures to be nonnegative (NN), orthogonal, sparse, and smooth-in effect integrating ESI with NN-ICA. This constitutes a generalization of work by this group on the use of multiple penalties for ESI. A multiplicative update algorithm is derived being stable, fast and converging within seconds near the optimal solution. This procedure, spatio-temporal tomographic NN ICA (STTONNICA), is equally able to recover superficial or deep sources without additional weighting constraints as tested with simulations. STTONNICA analysis of ERPs to familiar and unfamiliar faces yields an occipital-fusiform atom activated by all faces and a more frontal atom that only is active with familiar faces. The temporal signatures are at present unconstrained but can be required to be smooth, complex, or following a multivariate autoregressive model.
Assessing instantaneous energy in the EEG: a non-negative, frequency-weighted energy operator.
O'Toole, John M; Temko, Andriy; Stevenson, Nathan
2014-01-01
Signal processing measures of instantaneous energy typically include only amplitude information. But measures that include both amplitude and frequency do better at assessing the energy required by the system to generate the signal, making them more sensitive measures to include in electroencephalogram (EEG) analysis. The Teager-Kaiser operator is a frequency-weighted measure that is frequently used in EEG analysis, although the operator is poorly defined in terms of common signal processing concepts. We propose an alternative frequency-weighted energy measure that uses the envelope of the derivative of the signal. This simple envelope- derivative operator has the advantage of being nonnegative, which when applied to a detection application in newborn EEG improves performance over the Teager-Kaiser operator: without post-processing filters, area-under the receiver-operating characteristic curve (AUC) is 0.57 for the Teager-Kaiser operator and 0.80 for the envelope-derivative operator. The envelope-derivative operator also satisfies important properties, similar to the Teager-Kaiser operator, such as tracking instantaneous amplitude and frequency.
Robust and Non-Negative Collective Matrix Factorization for Text-to-Image Transfer Learning.
Yang, Liu; Jing, Liping; Ng, Michael K
2015-12-01
Heterogeneous transfer learning has recently gained much attention as a new machine learning paradigm in which the knowledge can be transferred from source domains to target domains in different feature spaces. Existing works usually assume that source domains can provide accurate and useful knowledge to be transferred to target domains for learning. In practice, there may be noise appearing in given source (text) and target (image) domains data, and thus, the performance of transfer learning can be seriously degraded. In this paper, we propose a robust and non-negative collective matrix factorization model to handle noise in text-to-image transfer learning, and make a reliable bridge to transfer accurate and useful knowledge from the text domain to the image domain. The proposed matrix factorization model can be solved by an efficient iterative method, and the convergence of the iterative method can be shown. Extensive experiments on real data sets suggest that the proposed model is able to effectively perform transfer learning in noisy text and image domains, and it is superior to the popular existing methods for text-to-image transfer learning.
Exploring Mixed Membership Stochastic Block Models via Non-negative Matrix Factorization
Peng, Chengbin
2014-12-01
Many real-world phenomena can be modeled by networks in which entities and connections are represented by nodes and edges respectively. When certain nodes are highly connected with each other, those nodes forms a cluster, which is called community in our context. It is usually assumed that each node belongs to one community only, but evidences in biology and social networks reveal that the communities often overlap with each other. In other words, one node can probably belong to multiple communities. In light of that, mixed membership stochastic block models (MMB) have been developed to model those networks with overlapping communities. Such a model contains three matrices: two incidence matrices indicating in and out connections and one probability matrix. When the probability of connections for nodes between communities are significantly small, the parameter inference problem to this model can be solved by a constrained non-negative matrix factorization (NMF) algorithm. In this paper, we explore the connection between the two models and propose an algorithm based on NMF to infer the parameters of MMB. The proposed algorithms can detect overlapping communities regardless of knowing or not the number of communities. Experiments show that our algorithm can achieve a better community detection performance than the traditional NMF algorithm. © 2014 IEEE.
Xi, Jianing; Li, Ao
2016-01-01
Recurrent copy number aberrations (RCNAs) in multiple cancer samples are strongly associated with tumorigenesis, and RCNA discovery is helpful to cancer research and treatment. Despite the emergence of numerous RCNA discovering methods, most of them are unable to detect RCNAs in complex patterns that are influenced by complicating factors including aberration in partial samples, co-existing of gains and losses and normal-like tumor samples. Here, we propose a novel computational method, called non-negative sparse singular value decomposition (NN-SSVD), to address the RCNA discovering problem in complex patterns. In NN-SSVD, the measurement of RCNA is based on the aberration frequency in a part of samples rather than all samples, which can circumvent the complexity of different RCNA patterns. We evaluate NN-SSVD on synthetic dataset by comparison on detection scores and Receiver Operating Characteristics curves, and the results show that NN-SSVD outperforms existing methods in RCNA discovery and demonstrate more robustness to RCNA complicating factors. Applying our approach on a breast cancer dataset, we successfully identify a number of genomic regions that are strongly correlated with previous studies, which harbor a bunch of known breast cancer associated genes.
UTOPIAN: user-driven topic modeling based on interactive nonnegative matrix factorization.
Choo, Jaegul; Lee, Changhyun; Reddy, Chandan K; Park, Haesun
2013-12-01
Topic modeling has been widely used for analyzing text document collections. Recently, there have been significant advancements in various topic modeling techniques, particularly in the form of probabilistic graphical modeling. State-of-the-art techniques such as Latent Dirichlet Allocation (LDA) have been successfully applied in visual text analytics. However, most of the widely-used methods based on probabilistic modeling have drawbacks in terms of consistency from multiple runs and empirical convergence. Furthermore, due to the complicatedness in the formulation and the algorithm, LDA cannot easily incorporate various types of user feedback. To tackle this problem, we propose a reliable and flexible visual analytics system for topic modeling called UTOPIAN (User-driven Topic modeling based on Interactive Nonnegative Matrix Factorization). Centered around its semi-supervised formulation, UTOPIAN enables users to interact with the topic modeling method and steer the result in a user-driven manner. We demonstrate the capability of UTOPIAN via several usage scenarios with real-world document corpuses such as InfoVis/VAST paper data set and product review data sets.
Moschidis, Georgios
2016-01-01
The wave equation $\\square_{g_{M,a}}\\psi=0$ on subextremal Kerr spacetimes $(\\mathcal{M}_{M,a},g_{M,a})$, $0<|a|
Detecting heterogeneity in single-cell RNA-Seq data by non-negative matrix factorization
Zhu, Xun; Ching, Travers; Pan, Xinghua; Weissman, Sherman M.
2017-01-01
Single-cell RNA-Sequencing (scRNA-Seq) is a fast-evolving technology that enables the understanding of biological processes at an unprecedentedly high resolution. However, well-suited bioinformatics tools to analyze the data generated from this new technology are still lacking. Here we investigate the performance of non-negative matrix factorization (NMF) method to analyze a wide variety of scRNA-Seq datasets, ranging from mouse hematopoietic stem cells to human glioblastoma data. In comparison to other unsupervised clustering methods including K-means and hierarchical clustering, NMF has higher accuracy in separating similar groups in various datasets. We ranked genes by their importance scores (D-scores) in separating these groups, and discovered that NMF uniquely identifies genes expressed at intermediate levels as top-ranked genes. Finally, we show that in conjugation with the modularity detection method FEM, NMF reveals meaningful protein-protein interaction modules. In summary, we propose that NMF is a desirable method to analyze heterogeneous single-cell RNA-Seq data. The NMF based subpopulation detection package is available at: https://github.com/lanagarmire/NMFEM. PMID:28133571
A perturbation-based framework for link prediction via non-negative matrix factorization
Wang, Wenjun; Cai, Fei; Jiao, Pengfei; Pan, Lin
2016-12-01
Many link prediction methods have been developed to infer unobserved links or predict latent links based on the observed network structure. However, due to network noises and irregular links in real network, the performances of existed methods are usually limited. Considering random noises and irregular links, we propose a perturbation-based framework based on Non-negative Matrix Factorization to predict missing links. We first automatically determine the suitable number of latent features, which is inner rank in NMF, by Colibri method. Then, we perturb training set of a network by perturbation sets many times and get a series of perturbed networks. Finally, the common basis matrix and coefficients matrix of these perturbed networks are obtained via NMF and form similarity matrix of the network for link prediction. Experimental results on fifteen real networks show that the proposed framework has competitive performances compared with state-of-the-art link prediction methods. Correlations between the performances of different methods and the statistics of networks show that those methods with good precisions have similar consistence.
Nonnegative Matrix Factorization-Based Spatial-Temporal Clustering for Multiple Sensor Data Streams
Directory of Open Access Journals (Sweden)
Di-Hua Sun
2014-01-01
Full Text Available Cyber physical systems have grown exponentially and have been attracting a lot of attention over the last few years. To retrieve and mine the useful information from massive amounts of sensor data streams with spatial, temporal, and other multidimensional information has become an active research area. Moreover, recent research has shown that clusters of streams change with a comprehensive spatial-temporal viewpoint in real applications. In this paper, we propose a spatial-temporal clustering algorithm (STClu based on nonnegative matrix trifactorization by utilizing time-series observational data streams and geospatial relationship for clustering multiple sensor data streams. Instead of directly clustering multiple data streams periodically, STClu incorporates the spatial relationship between two sensors in proximity and integrates the historical information into consideration. Furthermore, we develop an iterative updating optimization algorithm STClu. The effectiveness and efficiency of the algorithm STClu are both demonstrated in experiments on real and synthetic data sets. The results show that the proposed STClu algorithm outperforms existing methods for clustering sensor data streams.
Beyond cross-domain learning: Multiple-domain nonnegative matrix factorization
Wang, Jim Jing-Yan
2014-02-01
Traditional cross-domain learning methods transfer learning from a source domain to a target domain. In this paper, we propose the multiple-domain learning problem for several equally treated domains. The multiple-domain learning problem assumes that samples from different domains have different distributions, but share the same feature and class label spaces. Each domain could be a target domain, while also be a source domain for other domains. A novel multiple-domain representation method is proposed for the multiple-domain learning problem. This method is based on nonnegative matrix factorization (NMF), and tries to learn a basis matrix and coding vectors for samples, so that the domain distribution mismatch among different domains will be reduced under an extended variation of the maximum mean discrepancy (MMD) criterion. The novel algorithm - multiple-domain NMF (MDNMF) - was evaluated on two challenging multiple-domain learning problems - multiple user spam email detection and multiple-domain glioma diagnosis. The effectiveness of the proposed algorithm is experimentally verified. © 2013 Elsevier Ltd. All rights reserved.
On Quadratic Scalarization of One Class of Vector Optimization Problems in Banach Spaces
Directory of Open Access Journals (Sweden)
V. M. Bogomaz
2012-01-01
Full Text Available We study vector optimization problems in partially ordered Banach Spaces. We suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We discuss the ”classical” scalarization of vector optimization problems in the form of weighted sum and also we propose other type of scalarization for vector optimization problem, the socalled adaptive scalarization, which inherits some ideas of Pascoletti-Serafini approach. As a result, we show that the scalar nonlinear optimization problems can byturn approximated by the quadratic minimization problems. The advantage of such regularization is especially interesting from a numerical point of view because it gives a possibility to apply rather simple computational methods for the approximation of the whole set of efficient solutions.
MODIFIED BERNOULLI ITERATION METHODS FOR QUADRATIC MATRIX EQUATION
Institute of Scientific and Technical Information of China (English)
Zhong-Zhi Bai; Yong-Hua Gao
2007-01-01
We construct a modified Bernoulli iteration method for solving the quadratic matrix equation AX2+BX+C=0,where A,B and C are square matrices.This method is motivated from the Gauss-Seidel iteration for solving linear systems and the ShermanMorrison-Woodbury formula for updating matrices.Under suitable conditions, we prove the local linear convergence of the Dew method.An algorithm is presented to find the solution of the quadratic matrix equation and some numerical results are given to show the feasibility and the effectiveness of the algorithm.In addition,we also describe and analyze the block version of the modified Bernoulli iteration method.
Gravitomagnetic effects in quadratic gravity with a scalar field
Finch, Andrew
2016-01-01
The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.
Induced motion of domain walls in multiferroics with quadratic interaction
Energy Technology Data Exchange (ETDEWEB)
Gerasimchuk, Victor S., E-mail: viktor.gera@gmail.com [National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremohy Avenue 37, 03056 Kiev (Ukraine); Shitov, Anatoliy A., E-mail: shitov@mail.ru [Donbass National Academy of Civil Engineering, Derzhavina Street 2, 86123 Makeevka, Donetsk Region (Ukraine)
2013-10-15
We theoretically study the dynamics of 180-degree domain wall of the ab-type in magnetic materials with quadratic magnetoelectric interaction in external alternating magnetic and electric fields. The features of the oscillatory and translational motions of the domain walls and stripe structures depending on the parameters of external fields and characteristics of the multiferroics are discussed. The possibility of the domain walls drift in a purely electric field is established. - Highlights: • We study DW and stripe DS in multiferroics with quadratic magnetoelectric interaction. • We build up the theory of oscillatory and translational (drift) DW and DS motion. • DW motion can be caused by crossed alternating electric and magnetic fields. • DW motion can be caused by alternating “pure” electric field. • DW drift velocity is formed by the AFM and Dzyaloshinskii interaction terms.
Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates
Rand, Alexander; Bajaj, Chandrajit
2011-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon satisfying simple geometric criteria, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n+1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called `serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2014-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.
Quadratic differentials in low genus: exceptional and non-varying
Chen, Dawei
2012-01-01
We give an algebraic way of distinguishing the components of the exceptional strata of quadratic differentials in genus three and four. The complete list of these strata is (9, -1), (6,3,-1), (3,3,3, -1) in genus three and (12), (9,3), (6,6), (6,3,3) and (3,3,3,3) in genus four. This result is part of a more general investigation of disjointness of Teichmueller curves with divisors of Brill-Noether type on the moduli space of curves. As a result we show that for many strata of quadratic differentials in low genus the sum of Lyapunov exponents for the Teichmueller geodesic flow is the same for all Teichmueller curves in that stratum.
QUADRATIC INVARIANTS AND SYMPLECTIC STRUCTURE OF GENERAL LINEAR METHODS
Institute of Scientific and Technical Information of China (English)
Ai-guo Xiao; Shou-fu Li; Min Yang
2001-01-01
In this paper, we present some invariants and conservation laws of general linear methods applied to differential equation systems. We show that the quadratic invariants and symplecticity of the systems can be extended to general linear methods by a tensor product, and show that general linear methods with the matrix M=0 inherit in an extended sense the quadratic invariants possessed by the differential equation systems being integrated and preserve in an extended sense the symplectic structure of the phase space in the integration of Hamiltonian systems. These unify and extend existing relevant results on Runge-Kutta methods, linear multistep methods and one-leg methods. Finally, as special cases of general linear methods, we examine multistep Runge-Kutta methods, one-leg methods and linear two-step methods in detail.
On Jannsen's conjecture for Hecke characters of imaginary quadratic fields
Bars, Francesc
2007-01-01
We present a collection of results on a conjecture of Jannsen about the $p$-adic realizations associated to Hecke characters over an imaginary quadratic field $K$ of class number 1. The conjecture is easy to check for Galois groups purely of local type. We prove the conjecture under a geometric regularity condition for the imaginary quadratic field $K$ at $p$, which is related to the property that a global Galois group is purely of local type. Without this regularity assumption at $p$, we present a review of the known situations in the critical case and in the non-critical case for the realizations associated to Hecke characters over $K$. We relate the conjecture to the non-vanishing of some concrete non-critical values of the associated $p$-adic $L$-function of the Hecke character. Finally, we prove that the conjecture follows from a general conjecture on Iwasawa theory for almost all Tate twists.
Identity-based signature scheme based on quadratic residues
Institute of Scientific and Technical Information of China (English)
CHAI ZhenChuan; CAO ZhenFu; DONG XiaoLei
2007-01-01
Identity-based (ID-based) cryptography has drawn great concerns in recent years, and most of ID-based schemes are constructed from bilinear parings. Therefore, ID-based scheme without pairing is of great interest in the field of cryptography. Up to now,there still remains a challenge to construct ID-based signature scheme from quadratic residues. Thus, we aim to meet this challenge by proposing a concrete scheme. In this paper, we first introduce the technique of how to calculate a 2lth root of a quadratic residue, and then give a concrete ID-based signature scheme using such technique.We also prove that our scheme is chosen message and ID secure in the random oracle model, assuming the hardness of factoring.
Time-Inconsistent Stochastic Linear--Quadratic Control
Hu, Ying; Zhou, Xun Yu
2011-01-01
In this paper, we formulate a general time-inconsistent stochastic linear--quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we find an explicit equilibrium control. As an application, we then consider a mean-variance portfolio selection model in a complete financial market where the risk-free rate is a deterministic function of time but all the other market parameters are possibly stochastic processes. Applying the general sufficient condition, we obtain explicit equilibrium strategies when the risk premium is both deterministic and stochastic.
Institute of Scientific and Technical Information of China (English)
易称福; 陈宇环; 张小红
2011-01-01
针对不同于传统基于梯度法的递归神经网络定义一种基于标量范数取值的非负能量函数,通过定义一种基于向量取值的不定无界的误差函数,构建了一种能实时求解具有线性等式约束的凸二次规划问题.基于Simulink仿真平台的计算机实验结果表明,该新型神经网络模型能够准确有效地求解此类二次规划问题.%Differing from the conventional gradient-based recurrent neural networks, which associated with scalar-valued norm-based nonnegative energy function, by defining an indefinite error function based on the vector-valued, presented a new neural network for the online solution of the convex quadratic programming problem with equality constrains. Computer simulation results based on the Simulink show that the new neural networks can solve such quadratic programming with effectiveness and accuracy.
A Special Role of Boolean Quadratic Polytopes among Other Combinatorial Polytopes
Directory of Open Access Journals (Sweden)
A. N. Maksimenko
2016-01-01
Full Text Available We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set, 3-assignment. For comparing two families of polytopes we use the following method. We say that a family
de Klerk, E.; Sotirov, R.; Truetsch, U.
2015-01-01
Recent progress in solving quadratic assignment problems (QAPs) from the QAPLIB (Quadratic Assignment Problem Library) test set has come from mixed-integer linear or quadratic programming models that are solved in a branch-and-bound framework. Semidefinite programming (SDP) bounds for QAPs have also
UNIFORM SUPERAPPROXIMATION OF THE DERIVATIVE OF TETRAHEDRAL QUADRATIC FINITE ELEMENT APPROXIMATION
Institute of Scientific and Technical Information of China (English)
Jing-hong Liu; Qi-ding Zhu
2005-01-01
In this paper,we will prove the derivative of tetrahedral quadratic finite element approximation is superapproximate to the derivative of the quadratic Lagrange interpolant of the exact solution in the L∞-norm, which can be used to enhance the accuracy of the derivative of tetrahedral quadratic finite element approximation to the derivative of the exact solution.
A Hamiltonian-based solution to the linear quadratic consensus control problem
Weiss, M.
2012-01-01
The Linear Quadratic Consensus Control (LQCC) problem is a relaxation of the classical Linear Quadratic Regulation (LQR) problem, that consists of asymptotically driving the state of the system to a "consensus" point in which all coordinates are equal, in such a way that a quadratic cost function on
Rivera, Mariano; Bizuet, Rocky; Martinez, Amalia; Rayas, Juan A
2006-04-17
We present a phase shifting robust method for irregular and unknown phase steps. The method is formulated as the minimization of a half-quadratic (robust) regularized cost function for simultaneously computing phase maps and arbitrary phase shifts. The convergence to, at least, a local minimum is guaranteed. The algorithm can be understood as a phase refinement strategy that uses as initial guess a coarsely computed phase and coarsely estimated phase shifts. Such a coarse phase is assumed to be corrupted with artifacts produced by the use of a phase shifting algorithm but with imprecise phase steps. The refinement is achieved by iterating alternated minimization of the cost function for computing the phase map correction, an outliers rejection map and the phase shifts correction, respectively. The method performance is demonstrated by comparison with standard filtering and arbitrary phase steps detecting algorithms.
Quadratic and Cubic Nonlinear Oscillators with Damping and Their Applications
Li, Jibin; Feng, Zhaosheng
We apply the qualitative theory of dynamical systems to study exact solutions and the dynamics of quadratic and cubic nonlinear oscillators with damping. Under certain parametric conditions, we also consider the van der Waals normal form, Chaffee-Infante equation, compound Burgers-KdV equation and Burgers-KdV equation for explicit representations of kink-profile wave solutions and unbounded traveling wave solutions.
Solving the Quadratic Assignment Problem by a Hybrid Algorithm
Directory of Open Access Journals (Sweden)
Aldy Gunawan
2011-01-01
Full Text Available This paper presents a hybrid algorithm to solve the Quadratic Assignment Problem (QAP. The proposed algorithm involves using the Greedy Randomized Adaptive Search Procedure (GRASP to obtain an initial solution, and then using a combined Simulated Annealing (SA and Tabu Search (TS algorithm to improve the solution. Experimental results indicate that the hybrid algorithm is able to obtain good quality solutions for QAPLIB test problems within reasonable computation time.
Developing A Combined Strategy For Solving Quadratic Assignment Problem
Directory of Open Access Journals (Sweden)
Faiz Ahyaningsih
2015-08-01
Full Text Available Abstract The quadratic assigment problem QAP is one of the most interesting and most challenging combinatorial optimization problems in existence. In this paper we propose a random point strategy to get a starting point and then we use a combination methods to get optimal solution. As a computational experience weve solved QAP 30 x 30 adopted from Nugent and backboard wiring problem 42 amp61620 42 adopted from Skorin-Kapov.
A new genetic representation for quadratic assignment problem
Directory of Open Access Journals (Sweden)
Kratica Jozef
2011-01-01
Full Text Available In this paper, we propose a new genetic encoding for well known Quadratic Assignment Problem (QAP. The new encoding schemes are implemented with appropriate objective function and modified genetic operators. The numerical experiments were carried out on the standard QAPLIB data sets known from the literature. The presented results show that in all cases proposed genetic algorithm reached known optimal solutions in reasonable time.
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
A Riccati approach for constrained linear quadratic optimal control
Sideris, Athanasios; Rodriguez, Luis A.
2011-02-01
An active-set method is proposed for solving linear quadratic optimal control problems subject to general linear inequality path constraints including mixed state-control and state-only constraints. A Riccati-based approach is developed for efficiently solving the equality constrained optimal control subproblems generated during the procedure. The solution of each subproblem requires computations that scale linearly with the horizon length. The algorithm is illustrated with numerical examples.
Linear Quadratic Controller with Fault Detection in Compact Disk Players
DEFF Research Database (Denmark)
Vidal, Enrique Sanchez; Hansen, K.G.; Andersen, R.S.
2001-01-01
The design of the positioning controllers in Optical Disk Drives are today subjected to a trade off between an acceptable suppression of external disturbances and an acceptable immunity against surfaces defects. In this paper an algorithm is suggested to detect defects of the disk surface combined...... with an observer and a Linear Quadratic Regulator. As a result, the mentioned trade off is minimized and the playability of the tested compact disk player is considerably enhanced....
On a linear-quadratic problem with Caputo derivative
Directory of Open Access Journals (Sweden)
Dariusz Idczak
2016-01-01
Full Text Available In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.
Information sets as permutation cycles for quadratic residue codes
Directory of Open Access Journals (Sweden)
Richard A. Jenson
1982-01-01
Full Text Available The two cases p=7 and p=23 are the only known cases where the automorphism group of the [p+1, (p+1/2] extended binary quadratic residue code, O(p, properly contains PSL(2,p. These codes have some of their information sets represented as permutation cycles from Aut(Q(p. Analysis proves that all information sets of Q(7 are so represented but those of Q(23 are not.
Adomian solution of a nonlinear quadratic integral equation
Directory of Open Access Journals (Sweden)
E.A.A. Ziada
2013-04-01
Full Text Available We are concerned here with a nonlinear quadratic integral equation (QIE. The existence of a unique solution will be proved. Convergence analysis of Adomian decomposition method (ADM applied to these type of equations is discussed. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of Adomian’s series solution. Two methods are used to solve these type of equations; ADM and repeated trapezoidal method. The obtained results are compared.
Zimmermann, Karl-Heinz; Achtziger, Wolfgang
2001-09-01
The size of a systolic array synthesized from a uniform recurrence equation, whose computations are mapped by a linear function to the processors, matches the problem size. In practice, however, there exist several limiting factors on the array size. There are two dual schemes available to derive arrays of smaller size from large-size systolic arrays based on the partitioning of the large-size arrays into subarrays. In LSGP, the subarrays are clustered one-to-one into the processors of a small-size array, while in LPGS, the subarrays are serially assigned to a reduced-size array. In this paper, we propose a common methodology for both LSGP and LPGS based on polyhedral partitionings of large-size k-dimensional systolic arrays which are synthesized from n-dimensional uniform recurrences by linear mappings for allocation and timing. In particular, we address the optimization problem of finding optimal piecewise linear timing functions for small-size arrays. These are mappings composed of linear timing functions for the computations of the subarrays. We study a continuous approximation of this problem by passing from piecewise linear to piecewise quasi-linear timing functions. The resultant problem formulation is then a quadratic programming problem which can be solved by standard algorithms for nonlinear optimization problems.
New sequential quadratic programming algorithm with consistent subproblems
Institute of Scientific and Technical Information of China (English)
贺国平; 高自友; 赖炎连
1997-01-01
One of the most interesting topics related to sequential quadratic programming algorithms is how to guarantee the consistence of all quadratic programming subproblems. In this decade, much work trying to change the form of constraints to obtain the consistence of the subproblems has been done The method proposed by De O. Panto-ja J F A and coworkers solves the consistent problem of SQP method, and is the best to the authors’ knowledge. However, the scale and complexity of the subproblems in De O. Pantoja’s work will be increased greatly since all equality constraints have to be changed into absolute form A new sequential quadratic programming type algorithm is presented by means of a special ε-active set scheme and a special penalty function. Subproblems of the new algorithm are all consistent, and the form of constraints of the subproblems is as simple as one of the general SQP type algorithms. It can be proved that the new method keeps global convergence and local superhnear convergence.
Measurement of quadratic electrogyration effect in castor oil
Izdebski, Marek; Ledzion, Rafał; Górski, Piotr
2015-07-01
This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.
Parameter Optimization of Linear Quadratic Controller Based on Genetic Algorithm
Institute of Scientific and Technical Information of China (English)
LI Jimin; SHANG Chaoxuan; ZOU Minghu
2007-01-01
The selection of weighting matrix in design of the linear quadratic optimal controller is an important topic in the control theory. In this paper, an approach based on genetic algorithm is presented for selecting the weighting matrix for the optimal controller. Genetic algorithm is adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection and genetic. In this algorithm, the fitness function is used to evaluate individuals and reproductive success varies with fitness. In the design of the linear quadratic optimal controller, the fitness function has relation to the anticipated step response of the system. Not only can the controller designed by this approach meet the demand of the performance indexes of linear quadratic controller, but also satisfy the anticipated step response of close-loop system. The method possesses a higher calculating efficiency and provides technical support for the optimal controller in engineering application. The simulation of a three-order single-input single-output (SISO) system has demonstrated the feasibility and validity of the approach.
Gene Ranking of RNA-Seq Data via Discriminant Non-Negative Matrix Factorization.
Jia, Zhilong; Zhang, Xiang; Guan, Naiyang; Bo, Xiaochen; Barnes, Michael R; Luo, Zhigang
2015-01-01
RNA-sequencing is rapidly becoming the method of choice for studying the full complexity of transcriptomes, however with increasing dimensionality, accurate gene ranking is becoming increasingly challenging. This paper proposes an accurate and sensitive gene ranking method that implements discriminant non-negative matrix factorization (DNMF) for RNA-seq data. To the best of our knowledge, this is the first work to explore the utility of DNMF for gene ranking. When incorporating Fisher's discriminant criteria and setting the reduced dimension as two, DNMF learns two factors to approximate the original gene expression data, abstracting the up-regulated or down-regulated metagene by using the sample label information. The first factor denotes all the genes' weights of two metagenes as the additive combination of all genes, while the second learned factor represents the expression values of two metagenes. In the gene ranking stage, all the genes are ranked as a descending sequence according to the differential values of the metagene weights. Leveraging the nature of NMF and Fisher's criterion, DNMF can robustly boost the gene ranking performance. The Area Under the Curve analysis of differential expression analysis on two benchmarking tests of four RNA-seq data sets with similar phenotypes showed that our proposed DNMF-based gene ranking method outperforms other widely used methods. Moreover, the Gene Set Enrichment Analysis also showed DNMF outweighs others. DNMF is also computationally efficient, substantially outperforming all other benchmarked methods. Consequently, we suggest DNMF is an effective method for the analysis of differential gene expression and gene ranking for RNA-seq data.
Finding Imaging Patterns of Structural Covariance via Non-Negative Matrix Factorization
Sotiras, Aristeidis; Resnick, Susan M.; Davatzikos, Christos
2015-01-01
In this paper, we investigate the use of Non-Negative Matrix Factorization (NNMF) for the analysis of structural neuroimaging data. The goal is to identify the brain regions that co-vary across individuals in a consistent way, hence potentially being part of underlying brain networks or otherwise influenced by underlying common mechanisms such as genetics and pathologies. NNMF offers a directly data-driven way of extracting relatively localized co-varying structural regions, thereby transcending limitations of Principal Component Analysis (PCA), Independent Component Analysis (ICA) and other related methods that tend to produce dispersed components of positive and negative loadings. In particular, leveraging upon the well known ability of NNMF to produce parts-based representations of image data, we derive decompositions that partition the brain into regions that vary in consistent ways across individuals. Importantly, these decompositions achieve dimensionality reduction via highly interpretable ways and generalize well to new data as shown via split-sample experiments. We empirically validate NNMF in two data sets: i) a Diffusion Tensor (DT) mouse brain development study, and ii) a structural Magnetic Resonance (sMR) study of human brain aging. We demonstrate the ability of NNMF to produce sparse parts-based representations of the data at various resolutions. These representations seem to follow what we know about the underlying functional organization of the brain and also capture some pathological processes. Moreover, we show that these low dimensional representations favorably compare to descriptions obtained with more commonly used matrix factorization methods like PCA and ICA. PMID:25497684
Non-negative Matrix Factorization as a Method for Studying Coronal Heating
Barnes, Will; Bradshaw, Stephen
2015-04-01
Many theoretical efforts have been made to model the response of coronal loops to nanoflare heating, but the theory has long suffered from a lack of direct observations. Nanoflares, originally proposed by Parker (1988), heat the corona through short, impulsive bursts of energy. Because of their short duration and comparatively low amplitude, emission signatures from nanoflare heating events are often difficult to detect. Past algorithms (e.g. Ugarte-Urra and Warren, 2014) for measuring the frequency of transient brightenings in active region cores have provided only a lower bound for such measurements. We present the use of non-negative matrix factorization (NMF) to analyze spectral data in active region cores in order to provide more accurate determinations of nanoflare heating properties. NMF, a matrix deconvolution technique, has a variety of applications , ranging from Raman spectroscopy to face recognition, but, to our knowledge, has not been applied in the field of solar physics. The strength of NMF lies in its ability to estimate sources (heating events) from measurements (observed spectral emission) without any knowledge of the mixing process (Cichocki et al., 2009). We apply our NMF algorithm to forward-modeled emission representative of that produced by nanoflare heating events in an active region core. The heating events are modeled using a state-of-the-art hydrodynamics code (Bradshaw and Cargill, 2013) and the emission and active regions are synthesized using advanced forward modeling and visualization software (Bradshaw and Klimchuk, 2011; Reep et al., 2013). From these active region visualizations, our NMF algorithm is then able to predict the heating event frequency and amplitudes. Improved methods of nanoflare detection will help to answer fundamental questions regarding the frequency of energy release in the solar corona and how the corona responds to such impulsive heating. Additionally, development of reliable, automated nanoflare detection
Lu, Na; Li, Tengfei; Pan, Jinjin; Ren, Xiaodong; Feng, Zuren; Miao, Hongyu
2015-05-01
Electroencephalogram (EEG) provides a non-invasive approach to measure the electrical activities of brain neurons and has long been employed for the development of brain-computer interface (BCI). For this purpose, various patterns/features of EEG data need to be extracted and associated with specific events like cue-paced motor imagery. However, this is a challenging task since EEG data are usually non-stationary time series with a low signal-to-noise ratio. In this study, we propose a novel method, called structure constrained semi-nonnegative matrix factorization (SCS-NMF), to extract the key patterns of EEG data in time domain by imposing the mean envelopes of event-related potentials (ERPs) as constraints on the semi-NMF procedure. The proposed method is applicable to general EEG time series, and the extracted temporal features by SCS-NMF can also be combined with other features in frequency domain to improve the performance of motor imagery classification. Real data experiments have been performed using the SCS-NMF approach for motor imagery classification, and the results clearly suggest the superiority of the proposed method. Comparison experiments have also been conducted. The compared methods include ICA, PCA, Semi-NMF, Wavelets, EMD and CSP, which further verified the effectivity of SCS-NMF. The SCS-NMF method could obtain better or competitive performance over the state of the art methods, which provides a novel solution for brain pattern analysis from the perspective of structure constraint. Copyright © 2015 Elsevier Ltd. All rights reserved.
Blind source separation for groundwater pressure analysis based on nonnegative matrix factorization
Alexandrov, Boian S.; Vesselinov, Velimir V.
2014-09-01
The identification of the physical sources causing spatial and temporal fluctuations of aquifer water levels is a challenging, yet a very important hydrogeological task. The fluctuations can be caused by variations in natural and anthropogenic sources such as pumping, recharge, barometric pressures, etc. The source identification can be crucial for conceptualization of the hydrogeological conditions and characterization of aquifer properties. We propose a new computational framework for model-free inverse analysis of pressure transients based on Nonnegative Matrix Factorization (NMF) method for Blind Source Separation (BSS) coupled with k-means clustering algorithm, which we call NMFk. NMFk is capable of identifying a set of unique sources from a set of experimentally measured mixed signals, without any information about the sources, their transients, and the physical mechanisms and properties controlling the signal propagation through the subsurface flow medium. Our analysis only requires information about pressure transients at a number of observation points, m, where m≥r, and r is the number of unknown unique sources causing the observed fluctuations. We apply this new analysis on a data set from the Los Alamos National Laboratory site. We demonstrate that the sources identified by NMFk have real physical origins: barometric pressure and water-supply pumping effects. We also estimate the barometric pressure efficiency of the monitoring wells. The possible applications of the NMFk algorithm are not limited to hydrogeology problems; NMFk can be applied to any problem where temporal system behavior is observed at multiple locations and an unknown number of physical sources are causing these fluctuations.
Matrix Representation in Quantum Mechanics with Non-Negative QDF in the Case of a Hydrogen-Like Atom
Zhidkov, E P; Lovetsky, K P; Tretiakov, N P
2002-01-01
The correspondence rules A(q,p)\\mapsto\\hat{A} of the orthodoxal quantum mechanics do not allow one to introduce into the theory the non-negative quantum distribution function F(q,p). The correspondence rules A(q,p)\\mapsto\\hat{O}(A) of Kuryshkin's quantum mechanics (QMK) do allow one to do it. Besides, the operators \\hat{O}(A) turn out to be \\hat{A} bounded and \\hat{A} small at infinity for all systems of auxiliary functions {\\varphi_k}. This allows one to realise canonical matrix representation of QMK to investigate its dependence on the systems of functions {\\varphi_k}.
DEFF Research Database (Denmark)
2014-01-01
Due to applications in areas such as diagnostics and environmental safety, detection of molecules at very low concentrations has attracted recent attention. A powerful tool for this is Surface Enhanced Raman Spectroscopy (SERS) where substrates form localized areas of electromagnetic “hot spots...... a Bayesian Non-negative Matrix Factorization (NMF) approach to identify locations of target molecules. The proposed method is able to successfully analyze the spectra and extract the target spectrum. A visualization of the loadings of the basis vector is created and the results show a clear SNR enhancement...
On Linear Stability of Parametric Convex Quadratic Programming%参数凸二次规划的线性稳定性
Institute of Scientific and Technical Information of China (English)
王明征; 夏尊铨; 张立卫
2003-01-01
本文研究参数凸二次规划的最优解集的稳定性.首先给出参数数学规划的方向线性稳定的定义,然后利用集值映射的微分理论证明线性约束参数凸二次规划是线性稳定的.%We consider the optimal set mapping S(x) associated with a parametric convex quadratic programming problem depending on a parameter vector x. In this paper, we give a definition of directionally linear stability for parametric mathematical programming problems, and prove that a class of linear constrained parametric convex quadratic programming is linear stable by means of the differentiable theory, in the sense of Tyurin (1965) and Banks & Jacobs (1970), of set-valued mappings.
A kind of signature scheme based on class groups of quadratic fields
Institute of Scientific and Technical Information of China (English)
董晓蕾; 曹珍富
2004-01-01
Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic fields remained open, because of the difficulty of computing class numbers of quadratic fields. In this paper, according to our researches on quadratic fields, we construct the first digital signature scheme in ideal class groups of quadratic fields, using q as modulus, which denotes the prime divisors of ideal class numbers of quadratic fields. Security of the new signature scheme is based fully on CL-DLP. This paper also investigates realization of the scheme, and proposes the concrete technique. In addition, the technique introduced in the paper can be utilized to realize signature schemes of other kinds.
NMF-mGPU: non-negative matrix factorization on multi-GPU systems.
Mejía-Roa, Edgardo; Tabas-Madrid, Daniel; Setoain, Javier; García, Carlos; Tirado, Francisco; Pascual-Montano, Alberto
2015-02-13
In the last few years, the Non-negative Matrix Factorization ( NMF ) technique has gained a great interest among the Bioinformatics community, since it is able to extract interpretable parts from high-dimensional datasets. However, the computing time required to process large data matrices may become impractical, even for a parallel application running on a multiprocessors cluster. In this paper, we present NMF-mGPU, an efficient and easy-to-use implementation of the NMF algorithm that takes advantage of the high computing performance delivered by Graphics-Processing Units ( GPUs ). Driven by the ever-growing demands from the video-games industry, graphics cards usually provided in PCs and laptops have evolved from simple graphics-drawing platforms into high-performance programmable systems that can be used as coprocessors for linear-algebra operations. However, these devices may have a limited amount of on-board memory, which is not considered by other NMF implementations on GPU. NMF-mGPU is based on CUDA ( Compute Unified Device Architecture ), the NVIDIA's framework for GPU computing. On devices with low memory available, large input matrices are blockwise transferred from the system's main memory to the GPU's memory, and processed accordingly. In addition, NMF-mGPU has been explicitly optimized for the different CUDA architectures. Finally, platforms with multiple GPUs can be synchronized through MPI ( Message Passing Interface ). In a four-GPU system, this implementation is about 120 times faster than a single conventional processor, and more than four times faster than a single GPU device (i.e., a super-linear speedup). Applications of GPUs in Bioinformatics are getting more and more attention due to their outstanding performance when compared to traditional processors. In addition, their relatively low price represents a highly cost-effective alternative to conventional clusters. In life sciences, this results in an excellent opportunity to facilitate the
Exact solution of the classical mechanical quadratic Zeeman effect
Indian Academy of Sciences (India)
Sambhu N Datta; Anshu Pandey
2007-06-01
We address the curious problem of quadratic Zeeman effect at the classical mechanical level. The problem has been very well understood for decades, but an analytical solution of the equations of motion is still to be found. This state of affairs persists because the simultaneous presence of the Coulombic and quadratic terms lowers the dynamical symmetry. Energy and orbital angular momentum are still constants of motion. We find the exact solutions by introducing the concept of an image ellipse. The quadratic effect leads to a dilation of space–time, and a one-to-one correspondence is observed for pairs of physical quantities like energy and angular momentum, and the maximum and minimum distances from the Coulomb center for the Zeeman orbit and the corresponding pairs for the image ellipse. Thus, instead of finding additional conserved quantities, we find constants of motion for an additional dynamics, namely, the image problem. The trajectory is open, in agreement with Bertrand's theorem, but necessarily bound. A stable unbound trajectory does not exist for real values of energy and angular momentum. The radial distance, the angle covered in the plane of the orbit, and the time are uniquely determined by introducing further the concept of an image circle. While the radial distance is defined in a closed form as a transcendental function of the image-circular angle, the corresponding orbit angle and time variables are found in the form of two convergent series expansions. The latter two variables are especially contracted, thereby leading to a precession of the open cycles around the Coulomb center. It is expected that the space–time dilation effect observed here would somehow influence the solution of the quantum mechanical problem at the non-relativistic level.
Vacuum solutions of Bianchi cosmologies in quadratic gravity
Energy Technology Data Exchange (ETDEWEB)
Deus, Juliano Alves de; Muller, Daniel [Universidade de Brasilia (UnB), DF (Brazil)
2011-07-01
Full text: In this work we solve numerically the vacuum solutions of field equations of Bianchi homogeneous universes in the context of Semiclassical theory. Our interest is to study the quadratic theory of gravity with regard in the cosmological description of our universe in periods of intense fields. Bianchi cosmologies are anisotropic homogeneous cosmological models, but can include the isotropic models as particular cases (Bianchi I, VII and IX include homogeneous and isotropic Friedmann models plane, hyperbolic and spherical, respectively). Homogeneous models are good cosmological representations of our universe. With focus in solutions for intense fields, like the early universe, where isotropy is not necessarily required, the adopted scenario is the vacuum solutions, where the geometry is dominant in determining the gravitation. Still following in this way, the Semiclassical theory, which considers quantum matter fields propagating in classical geometrical background, is addressed to give the field equations. This formalism leads to fourth-order ordinary differential equations, in contrast to second-order equations from General Relativity. The Lagrangian of the theory is quadratic in the Ricci scalar and in the Ricci tensor. The equations system is highly non-linear and can be only numerically solved, except perhaps for few particular cases. We obtained numerical solutions for Bianchi V II{sub A} evolving to Minkowski and to de Sitter solutions, and also to singularities. The both first and second solutions were obtained choosing initial conditions near from respective exact vacuum solutions from Einstein theory, which are also exact solutions of the quadratic theory. Other Bianchi types are still under study. (author)
Creepers: Real quadratic orders with large class number
Patterson, Roger
2007-03-01
Shanks's sequence of quadratic fields Q(sqrt{S_{n}}) where S_{n}=(2^n+1)^2 + 2^{n+2} instances a class of quadratic fields for which the class number is large and, therefore, the continued fraction period is relatively short. Indeed, that period length increases linearly with n, that is: in arithmetic progression. The fields have regulator O(n^2). In the late nineties, these matters intrigued Irving Kaplansky, and led him to compute period length of the square root of sequences a^2x^{2n}+bx^{n}+c for integers a, b, c, and x. In brief, Kap found unsurprisingly that, generically, triples (a,b,c) are `leapers': they yield sequences with period length increasing at exponential rate. But there are triples yielding sequences with constant period length, Kap's `sleepers'. Finally, there are triples, as exemplified by the Shanks's sequence, for which the period lengths increase in arithmetic progression. Felicitously, Kaplansky called these `creepers'. It seems that the sleepers and creepers are precisely those for which one is able to detail the explicit continued fraction expansion for all n. Inter alia, this thesis noticeably extends the known classes of creepers and finds that not all are `kreepers' (of the shape identified by Kaplansky) and therefore not of the shape of examples studied by earlier authors looking for families of quadratic number fields with explicitly computable unit and of relatively large regulator. The work of this thesis includes the discovery of old and new families of hyperelliptic curves of increasing genus g and torsion divisor of order O(g^2). It follows that the apparent trichotomy leaper/sleeper/creeper coincides with the folk belief that the just-mentioned torsion is maximum possible.
Solving the quadratic assignment problem with clues from nature.
Nissen, V
1994-01-01
This paper describes a new evolutionary approach to solving quadratic assignment problems. The proposed technique is based loosely on a class of search and optimization algorithms known as evolution strategies (ES). These methods are inspired by the mechanics of biological evolution and have been applied successfully to a variety of difficult problems, particularly in continuous optimization. The combinatorial variant of ES presented here performs very well on the given test problems as compared with the standard 2-Opt heuristic and results with simulated annealing and tabu search. Extensions for practical applications in factory layout are described.
Two Reformulations for the Dynamic Quadratic Assignment Problem
Directory of Open Access Journals (Sweden)
Sirirat Muenvanichakul
2010-01-01
Full Text Available Problem statement: The Dynamic Quadratic Assignment Problem (DQAP, an NP-hard problem, is outlined and reformulated in two alternative models: Linearized model and logic-based model. Approach: The solution methods for both models based on combinatorial methods (Benders Decomposition and Approximate Dynamic Programming and constraint logic programming, respectively, are proposed. Results: Proofs of model equivalence and solution methodology are presented. Conclusion: Both proposed models are more simplified leading to possible hybrid adaptations of existing techniques for more practical approaches.
STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENTS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper studies a stochastic linear quadratic optimal control problem (LQ problem, for short), for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. The authors introduce the stochastic Riccati equation for the LQ problem. This is a backward SDE with a complicated nonlinearity and a singularity. The local solvability of such a backward SDE is established, which by no means is obvious. For the case of deterministic coefficients, some further discussions on the Riccati equations have been carried out. Finally, an illustrative example is presented.
Restart-Based Genetic Algorithm for the Quadratic Assignment Problem
Misevicius, Alfonsas
The power of genetic algorithms (GAs) has been demonstrated for various domains of the computer science, including combinatorial optimization. In this paper, we propose a new conceptual modification of the genetic algorithm entitled a "restart-based genetic algorithm" (RGA). An effective implementation of RGA for a well-known combinatorial optimization problem, the quadratic assignment problem (QAP), is discussed. The results obtained from the computational experiments on the QAP instances from the publicly available library QAPLIB show excellent performance of RGA. This is especially true for the real-life like QAPs.
Gilmore-Lawler bound of quadratic assignment problem
Institute of Scientific and Technical Information of China (English)
Yong XIA
2008-01-01
The Gilmore-Lawler bound (GLB) is one of the well-known lower bound of quadratic assignment problem (QAP). Checking whether GLB is tight is an NP-complete problem. In this article, based on Xia and Yuan linearization technique, we provide an upper bound of the complexity of this problem, which makes it pseudo-polynomial solvable. We also pseudo-polynomially solve a class of QAP whose GLB is equal to the optimal objec-tive function value, which was shown to remain NP-hard.
A Solution Proposal To Indefinite Quadratic Interval Transportation Problem
Directory of Open Access Journals (Sweden)
Hasan Dalman
2013-12-01
Full Text Available The data of real world applications generally cannot be expressed strictly. An efficient way of handling this situation is expressing the data as intervals. Thus, this paper focus on the Indefinite Quadratic Interval Transportation Problem (IQITP in which all the parameters i.e. cost and risk coefficients of the objective function, supply and demand quantities are expressed as intervals. A Taylor series approach is presented for the solution of IQITP by means of the expression of intervals with its left and right limits. Also a numerical example is executed to illustrate the procedure.
Neural network for solving convex quadratic bilevel programming problems.
He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie
2014-03-01
In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network.
Rigorous Performance Bounds for Quadratic and Nested Dynamical Decoupling
Xia, Yuhou; Lidar, Daniel A
2011-01-01
We present rigorous performance bounds for the quadratic dynamical decoupling (QDD) pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumption of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.
Analysis of electroperforated materials using the quadrat counts method
Energy Technology Data Exchange (ETDEWEB)
Miranda, E; Garzon, C; Garcia-Garcia, J [Departament d' Enginyeria Electronica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona (Spain); MartInez-Cisneros, C; Alonso, J, E-mail: enrique.miranda@uab.cat [Departament de Quimica AnalItica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona (Spain)
2011-06-23
The electroperforation distribution in thin porous materials is investigated using the quadrat counts method (QCM), a classical statistical technique aimed to evaluate the deviation from complete spatial randomness (CSR). Perforations are created by means of electrical discharges generated by needle-like tungsten electrodes. The objective of perforating a thin porous material is to enhance its air permeability, a critical issue in many industrial applications involving paper, plastics, textiles, etc. Using image analysis techniques and specialized statistical software it is shown that the perforation locations follow, beyond a certain length scale, a homogeneous 2D Poisson distribution.
Bianchi $VII_A$ solutions of quadratic gravity
de Deus, Juliano A
2011-01-01
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "open" model $H^ 3$ for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity.
Quadratic controller syntheses for the steam generator water level
Energy Technology Data Exchange (ETDEWEB)
Arzelier, D.; Daafouz, J.; Bernussou, J.; Garcia, G
1998-06-01
The steam generator water level, (SGWL), control problem in the pressurized water reactor of a nuclear power plant is considered from robust control techniques point of view. The plant is a time-varying system with a non minimum phase behavior and an unstable open-loop response. The time-varying nature of the plant due to change in operating power is taken into account by including slowly time-varying uncertainty in the model. A linear Time-Invariant, (LTI) guaranteed cost quadratic stabilizing controller is designed in order to address some of the particular issues arising for such a control problem. (author) 17 refs.
SPEECH EMOTION RECOGNITION USING MODIFIED QUADRATIC DISCRIMINATION FUNCTION
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Quadratic Discrimination Function(QDF)is commonly used in speech emotion recognition,which proceeds on the premise that the input data is normal distribution.In this Paper,we propose a transformation to normalize the emotional features,then derivate a Modified QDF(MQDF) to speech emotion recognition.Features based on prosody and voice quality are extracted and Principal Component Analysis Neural Network (PCANN) is used to reduce dimension of the feature vectors.The results show that voice quality features are effective supplement for recognition.and the method in this paper could improve the recognition ratio effectively.
FaSa: A Fast and Stable Quadratic Placement Algorithm
Institute of Scientific and Technical Information of China (English)
HOU WenTing(侯文婷); HONG XianLong(洪先龙); WU WeiMin(吴为民); CAI YiCi(蔡懿慈)
2003-01-01
Placement is a critical step in VLSI design because it dominates overall speed andquality of design flow. In this paper, a new fast and stable placement algorithm called FaSa is pro-posed. It uses quadratic programming model and Lagrange multiplier method to solve placementproblems. And an incremental LU factorization method is used to solve equations for speeding up.The experimental results show that FaSa is very stable, much faster than previous algorithms andits total wire length is comparable with other algorithms.
Quadratic growth and stability in convex programming problems
Bonnans, J. Frederic; Ioffe, Alexander D.
1994-01-01
Projet PROMATH; Given a convex program with $C^2$ functions and a convex set $S$ of solutions to the problem, we give a second order condition which guarantees that the problem does not have solutions outside of $S$. This condition is interpreted as a characterization for the quadratic growth of the cost function. The crucial role in the proofs is played by a theorem describing a certain uniform regularity property of critical cones in smooth convex programs. We apply these results to the dis...
Asymmetric Simple Exclusion Process with Open Boundaries and Quadratic Harnesses
Bryc, Włodek; Wesołowski, Jacek
2017-04-01
We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses. We use our representation to prove the large deviations principle for the total number of particles in the system. We use the generator of the Markov process to show how explicit formulas for the average occupancy of a site arise for special choices of parameters. We also give similar representations for limits of stationary measures as the number of sites tends to infinity.
Linear and quadratic in temperature resistivity from holography
Ge, Xian-Hui; Wu, Shang-Yu; Wu, Shao-Feng
2016-01-01
We present a new black hole solution in the Lifshitz spacetime with a hyperscaling violating factor. We analytically compute all of the DC thermoelectric conductivities in this theory. We find that both the linear-T and quadratic-T contributions to the resistivity can be realized, indicating that a more detailed comparison with experimental phenomenology can be performed in this scenario. At zero temperature, the Lorenz ratios are a constant, obeying the Wiedemann-Franz law, indications of a Fermi-liquid ground state.
Construction of Rational Maps on the Projective Line with Given Dynamical Structure
2016-05-11
1)2 = (x+ 1) (x− 1) we see that g(x) is in fact a linear map. Consider another map: h(x) = x2 + 1 x2 − 2x+ 1. Res(h) = ∣∣∣∣∣∣∣∣∣∣∣∣ 1 0 1 0 0 1 0 1 1...a1 = b1 + b0 12 Also note that if a2 = 0 or b0 = 0 the map will become linear . Therefore if a quadratic rational map φ has fixed points 0,1...quadratic map using algebra to show the fixed points and two-cycle hold for the map, then using the resultant to show that the map is quadratic and does not
Ding, Xiaoyu; Lee, Jong-Hwan; Lee, Seong-Whan
2013-04-01
Nonnegative matrix factorization (NMF) is a blind source separation (BSS) algorithm which is based on the distinct constraint of nonnegativity of the estimated parameters as well as on the measured data. In this study, according to the potential feasibility of NMF for fMRI data, the four most popular NMF algorithms, corresponding to the following two types of (1) least-squares based update [i.e., alternating least-squares NMF (ALSNMF) and projected gradient descent NMF] and (2) multiplicative update (i.e., NMF based on Euclidean distance and NMF based on divergence cost function), were investigated by using them to estimate task-related neuronal activities. These algorithms were applied firstly to individual data from a single subject and, subsequently, to group data sets from multiple subjects. On the single-subject level, although all four algorithms detected task-related activation from simulated data, the performance of multiplicative update NMFs was significantly deteriorated when evaluated using visuomotor task fMRI data, for which they failed in estimating any task-related neuronal activities. In group-level analysis on both simulated data and real fMRI data, ALSNMF outperformed the other three algorithms. The presented findings may suggest that ALSNMF appears to be the most promising option among the tested NMF algorithms to extract task-related neuronal activities from fMRI data.
Dai, Yimian; Wu, Yiquan; Song, Yu; Guo, Jun
2017-03-01
To further enhance the small targets and suppress the heavy clutters simultaneously, a robust non-negative infrared patch-image model via partial sum minimization of singular values is proposed. First, the intrinsic reason behind the undesirable performance of the state-of-the-art infrared patch-image (IPI) model when facing extremely complex backgrounds is analyzed. We point out that it lies in the mismatching of IPI model's implicit assumption of a large number of observations with the reality of deficient observations of strong edges. To fix this problem, instead of the nuclear norm, we adopt the partial sum of singular values to constrain the low-rank background patch-image, which could provide a more accurate background estimation and almost eliminate all the salient residuals in the decomposed target image. In addition, considering the fact that the infrared small target is always brighter than its adjacent background, we propose an additional non-negative constraint to the sparse target patch-image, which could not only wipe off more undesirable components ulteriorly but also accelerate the convergence rate. Finally, an algorithm based on inexact augmented Lagrange multiplier method is developed to solve the proposed model. A large number of experiments are conducted demonstrating that the proposed model has a significant improvement over the other nine competitive methods in terms of both clutter suppressing performance and convergence rate.
Wright, L.; Coddington, O.; Pilewskie, P.
2015-12-01
Current challenges in Earth remote sensing require improved instrument spectral resolution, spectral coverage, and radiometric accuracy. Hyperspectral instruments, deployed on both aircraft and spacecraft, are a growing class of Earth observing sensors designed to meet these challenges. They collect large amounts of spectral data, allowing thorough characterization of both atmospheric and surface properties. The higher accuracy and increased spectral and spatial resolutions of new imagers require new numerical approaches for processing imagery and separating surface and atmospheric signals. One potential approach is source separation, which allows us to determine the underlying physical causes of observed changes. Improved signal separation will allow hyperspectral instruments to better address key science questions relevant to climate change, including land-use changes, trends in clouds and atmospheric water vapor, and aerosol characteristics. In this work, we investigate a Non-negative Matrix Factorization (NMF) method for the separation of atmospheric and land surface signal sources. NMF offers marked benefits over other commonly employed techniques, including non-negativity, which avoids physically impossible results, and adaptability, which allows the method to be tailored to hyperspectral source separation. We adapt our NMF algorithm to distinguish between contributions from different physically distinct sources by introducing constraints on spectral and spatial variability and by using library spectra to inform separation. We evaluate our NMF algorithm with simulated hyperspectral images as well as hyperspectral imagery from several instruments including, the NASA Airborne Visible/Infrared Imaging Spectrometer (AVIRIS), NASA Hyperspectral Imager for the Coastal Ocean (HICO) and National Ecological Observatory Network (NEON) Imaging Spectrometer.
Electroweak vacuum stability and finite quadratic radiative corrections
Energy Technology Data Exchange (ETDEWEB)
Masina, Isabella [Ferrara Univ. (Italy). Dipt. di Fisica e Scienze della Terra; INFN, Sezione di Ferrara (Italy); Southern Denmark Univ., Odense (Denmark). CP3-Origins; Southern Denmark Univ., Odense (Denmark). DIAS; Nardini, Germano [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Quiros, Mariano [Institucio Catalana de Recerca i Estudis Avancats (ICREA), Barcelona (Spain); IFAE-IAB, Barcelona (Spain)
2015-07-15
If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale Λ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative Ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales the cutoff is not unique and each SM sector has its own UV cutoff Λ{sub i}. We have performed this calculation assuming the Minimal Supersymmetric Standard Model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs Λ{sub i}, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the Focus Point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.
Creepers: Real quadratic orders with large class number
Patterson, R
2007-01-01
Shanks's sequence of quadratic fields $\\Q(\\sqrt{S_{n}})$ where $S_{n}=(2^n+1)^2 + 2^{n+2}$ instances a class of quadratic fields for which the class number is large and, therefore, the continued fraction period is relatively short. Indeed, that period length increases linearly with $n$, that is: in arithmetic progression. The fields have regulator $O(n^2)$. In the late nineties, these matters intrigued Irving Kaplansky, and led him to compute period length of the square root of sequences $a^2x^{2n}+bx^{n}+c$ for integers $a$, $b$, $c$, and $x$. In brief, Kap found unsurprisingly that, generically, triples $(a,b,c)$ are `leapers': they yield sequences with period length increasing at exponential rate. But there are triples yielding sequences with constant period length, Kap's `sleepers'. Finally, there are triples, as exemplified by the Shanks's sequence, for which the period lengths increase in arithmetic progression. Felicitously, Kaplansky called these `creepers'. It seems that the sleepers and creepers are...
Local Points on Quadratic Twists of X_0(N)
Ozman, Ekin
2009-01-01
Let X^d(N) be the quadratic twist of the modular curve X_0(N) through the Atkin-Lehner involution w_N and a quadratic extension Q(\\sqrt{d})/Q. The points of X^d(N)(Q) are precisely the Q(\\sqrt{d})-rational points of X_0(N) that are fixed by \\sigma composition w_N, where \\sigma is the generator of Gal(Q(\\sqrt{d})/Q).Ellenberg asked the following question: For which d and N does X^d(N) have rational points over every completion of Q? Given (N,d,p) we give necessary and sufficient conditions for the existence of a Q_p-rational point on X^d(N), whenever p is not simultaneously ramified in Q(\\sqrt{d}) and Q(\\sqrt{-N}), answering Ellenberg's question for all odd primes p when (N,d)=1. The main theorem yields a population of curves which have local points everywhere but no points over Q; in several cases we show that this obstruction to the Hasse Principle is explained by the Brauer-Manin obstruction.
Analytical Solution of Projectile Motion with Quadratic Resistance and Generalisations
Ray, Shouryya
2013-01-01
The paper considers the motion of a body under the influence of gravity and drag of the surrounding fluid. Depending on the fluid mechanical regime, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body relative to the fluid. The case of quadratic drag is substantially more complex than the linear case, as it nonlinearly couples both components of the momentum equation, and no explicit analytic solution is known for a general trajectory. After a detailed account of the literature, the paper provides such a solution in form of a series expansion. This result is discussed in detail and related to other approaches previously proposed. In particular, it is shown to yield certain approximate solutions proposed in the literature as limiting cases. The solution technique employs a strategy to reduce systems of ordinary differential equations with a triangular dependence of the right-hand side on the vector of unknowns to a single equation in an auxiliary variable....