Realization Of Matrix Research Articles

Penalized weighted low-rank approximation for robust recovery of recurrent copy number variations.

BackgroundCopy number variation (CNV) analysis has become one of the most important research areas for understanding complex disease. With increasing resolution of array-based comparative genomic hybridization (aCGH) arrays, more and more raw copy number data are collected for multiple arrays. It is natural to realize the co-existence of both recurrent and individual-specific CNVs, together with the possible data contamination during the data generation process. Therefore, there is a great need for an efficient and robust statistical model for simultaneous recovery of both recurrent and individual-specific CNVs.ResultWe develop a penalized weighted low-rank approximation method (WPLA) for robust recovery of recurrent CNVs. In particular, we formulate multiple aCGH arrays into a realization of a hidden low-rank matrix with some random noises and let an additional weight matrix account for those individual-specific effects. Thus, we do not restrict the random noise to be normally distributed, or even homogeneous. We show its performance through three real datasets and twelve synthetic datasets from different types of recurrent CNV regions associated with either normal random errors or heavily contaminated errors.ConclusionOur numerical experiments have demonstrated that the WPLA can successfully recover the recurrent CNV patterns from raw data under different scenarios. Compared with two other recent methods, it performs the best regarding its ability to simultaneously detect both recurrent and individual-specific CNVs under normal random errors. More importantly, the WPLA is the only method which can effectively recover the recurrent CNVs region when the data is heavily contaminated.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0835-2) contains supplementary material, which is available to authorized users.

Kalman–Yakubovič–Popov lemma for descriptor systems

For a given descriptor realization of para-hermitian rational matrix Π(s), we present a generalization of Kalman–Yakubovič–Popov lemma, i.e. necessary and sufficient conditions for Π≥0 on the imaginary axis, in terms of an inequality with constant matrices. The result is quite general, since Π can have poles and zeros on the extended imaginary axis, hence the nonstrict inequality Π(jω)≥0, ω∈R can hold, instead of the strict inequality. Π can be singular. The descriptor realization is required to be only impulse controllable and controllable (or stabilizable and detΠ≠0). A spectral factorization of Π is given, by the above mentioned constant matrices. Three consequences of the generalized KYP lemma, and an illustrative numerical example are given.

One-parameter Neutrino Mass Matrix and Symmetry Realization

We investigate the Majorana neutrino mass matrix Mn with one real parameter in the context of two texture zeros and its symmetry realization by non-Abelian discrete symmetry. From numerical calculation, first we show the correlations between non-zero elements of Mn under assumptions of (Mn)11,12(13) = 0 and find simple examples of Mn with one real mass parameter. Next we discuss symmetry realization of the mass matrix by the type-II seesaw mechanism based on the binary icosahedral symmetry A5. Finally we give a prediction of LFV processes in our model, G(t ! μee)/G(μ ! eee)' (mt/mμ), which is determined by the flavor symmetry.

Realization and elimination in rational representations of behaviors

This article deals with the relationship between rational representations of linear differential systems and their state representations. In particular we study the relationship between rational representations on the one hand, and output nulling and driving variable representations on the other. In the input–output framework it is well-known that every controllable and observable realization of the transfer matrix of the system yields a minimal input/state/output representation. If a proper rational matrix is used for a rational kernel or image representation of the system, then the question arises under what conditions realizations of this rational matrix give rise to state representations. We will establish conditions under which realizations of the proper rational matrix appearing in a rational image representation yield minimal driving variable representations of the system. Likewise, we find conditions under which realization leads from rational kernel representations to minimal output nulling representations. We also study the converse problem, namely state elimination from driving variable and output nulling representations. We will establish closed form expressions for kernel and image representations of the external behaviors associated with these particular state representations.

Influence of the carbonaceous conductive network on the electrochemical performance of ZnFe2O4 nanoparticles

Herein, the influence of the carbon precursor used for the realization of carbonaceous percolating network incorporating ZnFe2O4 is investigated. Three different precursors, namely sucrose (Suc), citric acid (CA), and oleic acid (OLEA) were used for the realization of such carbonaceous matrix. The composite materials were characterized by means of thermogravimetric analysis (TGA), gas adsorption using the BET isotherm, Raman spectroscopy, X-ray diffraction (XRD), and scanning electron microscopy (SEM). Electrodes based on the resulting composite materials were investigated, performing electrochemical impedance spectroscopy and galvanostatic cycling. The results showed that the homogeneity of the carbon coating rather than the absolute amount of carbon enhanced the electrochemical performance of ZnFe2O4 nanoparticles. The most advantageous coating properties were obtained with sucrose as carbon precursor, obtaining a highly stable specific capacity higher than 1000 mAh g−1 for more than 60 cycles.

Bayes multiple decision functions.

This paper deals with the problem of simultaneously making many (M) binary decisions based on one realization of a random data matrix X. M is typically large and X will usually have M rows associated with each of the M decisions to make, but for each row the data may be low dimensional. Such problems arise in many practical areas such as the biological and medical sciences, where the available dataset is from microarrays or other high-throughput technology and with the goal being to decide which among of many genes are relevant with respect to some phenotype of interest; in the engineering and reliability sciences; in astronomy; in education; and in business. A Bayesian decision-theoretic approach to this problem is implemented with the overall loss function being a cost-weighted linear combination of Type I and Type II loss functions. The class of loss functions considered allows for use of the false discovery rate (FDR), false nondiscovery rate (FNR), and missed discovery rate (MDR) in assessing the quality of decision. Through this Bayesian paradigm, the Bayes multiple decision function (BMDF) is derived and an efficient algorithm to obtain the optimal Bayes action is described. In contrast to many works in the literature where the rows of the matrix X are assumed to be stochastically independent, we allow a dependent data structure with the associations obtained through a class of frailty-induced Archimedean copulas. In particular, non-Gaussian dependent data structure, which is typical with failure-time data, can be entertained. The numerical implementation of the determination of the Bayes optimal action is facilitated through sequential Monte Carlo techniques. The theory developed could also be extended to the problem of multiple hypotheses testing, multiple classification and prediction, and high-dimensional variable selection. The proposed procedure is illustrated for the simple versus simple hypotheses setting and for the composite hypotheses setting through simulation studies. The procedure is also applied to a subset of a microarray data set from a colon cancer study.

동일한 전달 행렬을 가지는 안정화 가능한 이종 시스템들의 출력 일치

This paper studies the output consensus problem for a class of heterogeneous linear multi-agent systems under a fixed directed communication network. The dynamics, as well as its dimension, of each agent can widely differ from the others, but all the agents are assumed to have the same transfer matrix. In addition, only the system outputs are constrained to be delivered through the network. Under these conditions, we show that the output consensus is reached by a group of identical controllers, which is designed to achieve the state consensus for the homogeneous multi-agent system obtained from the minimal realization of the transfer matrix. Finally, an example is given to demonstrate the proposed result.

A new realization of shared resource matrix transitive closure computation algorithm

A new realization of shared resource matrix transitive closure computation algorithm

Unboundedness of Adjacency Matrices of Locally Finite Graphs

Given a locally finite simple graph so that its degree is not bounded, every self-adjoint realization of the adjacency matrix is unbounded from above. In this note, we give an optimal condition to ensure it is also unbounded from below. We also consider the case of weighted graphs. We discuss the question of self-adjoint extensions and prove an optimal criterium.

Nonintersecting Brownian interfaces and Wishart random matrices

We study a system of N nonintersecting (1+1)-dimensional fluctuating elastic interfaces ("vicious bridges") at thermal equilibrium, each subject to periodic boundary condition in the longitudinal direction and in presence of a substrate that induces an external confining potential for each interface. We show that, for a large system and with an appropriate choice of the external confining potential, the joint distribution of the heights of the N nonintersecting interfaces at a fixed point on the substrate can be mapped to the joint distribution of the eigenvalues of a Wishart matrix of size N with complex entries (Dyson index beta=2), thus providing a physical realization of the Wishart matrix. Exploiting this analogy to random matrix, we calculate analytically (i) the average density of states of the interfaces, (ii) the height distribution of the uppermost and lowermost interfaces (extrema), and (iii) the asymptotic (large-N) distribution of the center of mass of the interfaces. In the last case, we show that the probability density of the center of mass has an essential singularity around its peak, which is shown to be a direct consequence of a phase transition in an associated Coulomb gas problem.

On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space Systems

On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space SystemsWe review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space system models. The concept of anirreducible-at-infinitygeneralized state space realization of a polynomial matrix is defined and the mechanism of the "cancellations" of "decoupling zeros at infinity" is closely examined. The difference between the concepts ofirreducibilityandminimalityof generalized state space realizations of polynomial (transfer function) matrices is pointed out and the associated concepts ofdynamicandnon-dynamicvariables appearing in generalized state space realizations are also examined.

Screw System Approach to Physical Realization of Stiffness Matrix With Arbitrary Rank

It is possible to realize the desired compliance characteristics of a robot in a form of a passive compliance device, which demands the synthesis technique of a stiffness matrix by parallel connections of line and/or torsional springs. In this paper, the stiffness matrix is expressed in terms of the screw coordinates with respect to the basis consisting of its eigenvectors, thereby the synthesis equation is derived. Examination of the numbers of free design parameters involved in the synthesis suggests that a line or free vector for a spring can be freely selected from the induced wrench space depending on the rank of the stiffness matrix. The recursive synthesis method that allows one to select the positions or directions of the springs from the screw system spanned by the induced wrenches of the given stiffness matrix is proposed.

Dynamics of the Density Matrix in Contact with a Thermal Bath and the Quantum Master Equation

We study the structure of the time evolution of the density matrix in contact with a thermal bath in a standard projection operator sheme. The reduced density matrix of the system in the steady state is obtained by tracing out the degree of freedom of the thermal bath from the equilibrium density matrix of the total system. This reduced density matrix is modified by the interaction, and is different from that of the equilibrium of the system alone. We explicitly calculate the contribution of each term in quantum master equation to the realization of the steady state density matrix, and make clear roles of each term. By making use of the role of each term, the properties of the commonly used quantum master equation are examined.

Numerical [formula omitted]-spectral factorization of general para-hermitian matrices

A numerical algorithm for J -spectral factorization of para-hermitian rational matrices is presented, based on a generalization of the notion of separated realization of a para-hermitian matrix. The transformations used preserve the para-hermitian matrix pencil structure.

Topological realizability conditions and their interpretation for admittance matrices of an MTL system with mode delays

In a previous study by the authors regarding passive multiconductor transmission line (MTL) system quasi-TEM mode delay, we encounter longitudinal immittance matrix functions (LIMFs) whose behavior initially appears problematic, yet they are shown to be passive. This paper addresses the constraints on the realization of the admittance matrix and the physical interpretation of the realized circuits in the passive, common-ground microstrip system.

Canonical State Representations and Hilbert Functions of Multidimensional Systems

A basic and substantial theorem of one-dimensional systems theory, due to R. Kalman, says that an arbitrary input/output behavior with proper transfer matrix admits an observable state representation which, in particular, is a realization of the transfer matrix. The state equations have the characteristic property that any local, better temporal, state at time zero and any input give rise to a unique global state or trajectory of the system or, in other terms, that the global state is the unique solution of a suitable Cauchy problem. With an adaption of this state property to the multidimensional situation or rather its algebraic counter-part we prove that any behavior governed by a linear system of partial differential or difference equations with constant coefficients is isomorphic to a canonical state behavior which is constructed by means of Gröbner bases. In contrast to the one-dimensional situation, to J.C. Willems’ multidimensional state space models and and to J.F. Pommaret’s modified Spencer form the canonical state behavior is not necessarily a first order system. Further first order models are due E. Zerz. As a by-product of the state space construction we derive a new variant of the algorithms for the computation of the Hilbert function of finitely generated polynomial modules or behaviors. J.F. Pommaret, J. Wood and P. Rocha discussed the Hilbert polynomial in the systems theoretic context. The theorems of this paper are constructive and have been implemented in MAPLE in the two-dimensional case and demonstrated in a simple, but instructive example. A two-page example also gives the complete proof of Kalman’s one-dimensional theorem mentioned above. We believe that for this standard case the algorithms of the present paper compare well with their various competitors from the literature.

Lumped-element analysis and design of CMOS distributed amplifiers with image impedance termination

This paper presents a systematic matrix-based lumped-element analysis of CMOS distributed amplifiers (DAs). Since transmission lines (TLs) of the DAs are artificially constructed from a ladder of a finite number of inductors and capacitors, the conventional TL-based analysis of microwave DAs can not be accurately applied to CMOS DAs. The proposed lumped-analysis method is also more intuitive for analog circuit designers than the TL analysis adapted from microwave amplifiers analysis because it provides the performance characteristics of the amplifiers as functions of circuit elements values, and not the TL characteristics. The image impedance technique is used for the design of input/output terminating networks. A new image impudence matrix is defined to accommodate the extension of the theory from two- to four-port networks, and a practical realization of the image impedance matrix is presented using the available circuit elements in CMOS technology. The simulation results clearly indicate an improved voltage gain and a better gain uniformity over the bandwidth of the proposed DA design terminated at its image impedance compared with the amplifier terminated at its nominal TL characteristics impedance.

An efficient computational method for nonlinear three-dimensional wave-wave and wave-body interactions

We develop and apply a highly efficient computational method for the study of three-dimensional nonlinear wave dynamics and interactions with floating bodies and bottom topography. Similarly to the classical boundary element methods, this method is based on the boundary integral equation formulation in the context of potential flow assumptions. In solving the integral equation, however, it employs a highly efficient fast Fourier transform technique for the calculation of far-field influences of boundary source/dipole distributions without an explicit realization of the influence coefficient matrix. As a result, the computational cost associated with the boundary-value solution at each time in the simulation of nonlinear wave-wave and wave-body interactions is reduced to O( Nln N) in comparison to the requisite O( N 2 ) effort of the classical methods, where N is the total number of boundary unknowns. The focus of this paper is on the development of the method and investigation of the features and dependence of its efficiency and accuracy on physical and computational parameters.

The application of polynomial matrix factorization in active network synthesis

PurposeTo investigate the general necessary condition for synthesis of square, real rational matrices of complex frequency as admittance matrices of active multiports with resistors, inductors, capacitors and possibly multiport transformers and to prove that this condition is also sufficient for synthesis of stable, square, real rational matrices of complex frequency as admittance matrices of balanced active multiports having only resistors, capacitors and voltage‐amplifiers with sufficiently large amplifications. The main aim of the paper is to provide a new and general method for stable admittance matrices synthesis and to develop strict realization algorithm by active balanced transformerless multiport networks.Design/methodology/approachThe objectives of the paper are achieved by using factorization of regular polynomial matrices in complex frequency with certain degree as products of other regular polynomial matrices with specified degrees. A set of sufficient conditions for such a factorization is presented and derived a pertinent algorithm as the starting point for investigation and solving network synthesis problem and generation of class of equivalent realizations.FindingsTheorem 1 states that sufficient condition for factorization of Pth order, generally regular polynomial matrix P(s) in complex frequency s with degree L, whose determinant has K distinct zeros, in form P(s)=P1(s)·P2(s), where 1≤p2=P20≤L−1 is degree of polynomial matrix P2(s), reads: K>(P−1)·L+p2−1. The coefficient‐matrices of s, s2,… in P1(s) and P2(s) are real or complex depending on whether distinct zeros of det P(s) are real or complex, respectively. Theorem 2 states that: (a) for realization of Pth order matrix of real rational functions in complex frequency s (i.e. RRF matrix) as admittance matrix of active balanced RLC P‐port network with multiport transformers, or without them, P generalized controlled‐sources and P controlling‐ports are necessary, in general; and (b) P balanced voltage‐controlled voltage‐sources (VCVSs) with real and by module greater than unity controlling coefficients (“voltage amplifications”) are sufficient for realization of stable admittance RRF matrix by active, balanced, transformerless, RC P‐port network.Originality/valueThis is a research paper with the following two main contributions (original results). First, a theorem on sufficient conditions for factorization of regular polynomial matrices in complex frequency; and second, a theorem relating to sufficient conditions for synthesis of matrices of real rational functions in complex frequency by active, balanced, transformerless networks. The results may be interesting for network theorists and researchers in the field of electric circuits and systems.

Formula omitted]-spectral factorization of regular para-Hermitian transfer matrices

This paper characterizes a class of regular para-Hermitian transfer matrices and then reveals the elementary characteristics of J -spectral factorization for this class. A transfer matrix Λ in this class admits a J -spectral factorization if and only if there exists a common nonsingular matrix to similarly transform the A-matrices of Λ and Λ - 1 , resp., into 2 × 2 lower (upper, resp.) triangular block matrices with the ( 1 , 1 ) -block including all the stable modes of Λ ( Λ - 1 , resp.). For a transfer matrix in a smaller subset, this nonsingular matrix is formulated in terms of the stabilizing solutions of two algebraic Riccati equations. The J -spectral factor is formulated in terms of the original realization of the transfer matrix.