brief paper some new results for system decoupling and pole assignment problems in a related article we derived a canonical decomposition of the right invertible system c a b and applied this canonical decomposition to study the smith form of the matrix pencil p s a sibc0 and findout the finite zeros and infinite zeros of p s the range of the ranks of p s for email protected c and the controllability of the right invertible system in this paper we will apply this canonical decomposition of the right invertible system c a b to deduce the triangular decouple upon to row permutation provide some new results of the row by row decoupling and associated pole assignment problems

fractals from genomes exact solutions of a biology inspired problem abstract this is a review of a few recent papers with some new results added after a brief biological introduction a visualization scheme of the string composition of long dna sequences in particular of bacterial complete genomes will be described this scheme leads to a class of self similar and self overlapping fractals in the limit of infinitely long constituent strings the calculation of their exact dimensions and the counting of true and redundant avoided strings at different string lengths turn out to be one and the same problem we give exact solution of the problem using two independent methods the goulden jackson cluster method in combinatorics and the method of formal language theory

higher order correlations of tchebyscheff maps we determine the higher order correlation functions of iterates of tchebyscheff polynomials of arbitrary order n the non vanishing correlations can be described by suitable sets of graphs these graphs allow for a perturbative evaluation of invariant densities for langevin like systems that are driven by deterministic chaotic forces generated by tchebyscheff maps rather than gaussian white noise

is the dimension of chaotic attractors invariant under coordinate changes several different dimensionlike quantities which have been suggested as being relevant to the study of chaotic attractors are examined in particular we discuss whether these quantities are invariant under changes of variables that are differentiable except at a finite number of points it is found that some are and some are not it is suggested that the word dimension be reversed only for those quantities have this invariance property

disturbance decoupling for linear time invariant systems a matrix pencil approach we give a new systematic analysis of disturbance decoupling problems for standard linear time invariant systems based on the theory of matrix pencils this approach is based on the computation of condensed forms under orthogonal equivalence transformations from these forms which can be computed in a numerically stable way we obtain new necessary and sufficient conditions that are numerically verifiable and furthermore we immediately obtain numerically stable algorithms to compute the desired compensators we present a numerical example that demonstrates the properties of the new approach

multifractal analysis of dna sequences using a novel chaos game representation abstract we present a generalization of the standard chaos game representation method introduced by jeffrey to this aim a dna symbolic sequence is mapped onto a singular measure on the attractor of a particular ifs model which is a perfect statistical representation of the sequence a multifractal analysis of the resulting measure is introduced and an interpretation of singularities in terms of mutual information and redundancy statistical dependence among subsequence symbols within the dna sequence is provided the multifractal spectrum is also shown to be more sensitive for detecting dependence structures within the dna sequence than the averaged contribution given by redundancy this method presents several advantages with respect to other representations such as walks or interfaces which may introduce spurious effects in contrast with the results obtained by other standard methods here we note that no general statement can be made on the influence of coding and non coding content on the correlation length of a given sequence

vibration of annular sector plates from three dimensional analysis accurate three dimensional elasticity solutions are presented for the free vibration analysis of annular sector plates with arbitrary but continuous boundary conditions the ritz procedure is used to minimize the integral energy functional which is formulated in a cylindrical polar coordinate system in the derivation of the governing eigenvalue equation the vibratory characteristics of annular sector plates with variations in boundary condition sector angle and thickness are examined the accuracy of the method is validated through appropriate convergence and comparison studies the first known results presented here provide a basis for understanding the physics of vibrations of annular sector plates and can be used to assess numerical results obtained from various refined two dimensional theories

multifractal analysis of thermal denaturation based on the peyrard bishop dauxois model the theory of dna dynamics is exceedingly complex and not easily explained in the past two decades by adapting methods of statistical physics the dynamics of dna in contact with a thermal bath is widely studied in this paper the thermal denaturation of dna in the framework of the peyrard bishop dauxois pbd model through the renyi dimension is investigated as a result the renyi dimension spectrum of the melting transition process reveals the multifractal nature of the dynamics of the peyrard bishop dauxois model also it can be concluded that the renyi dimension d q at negative values of q is the characteristic signature of pre melting and thermal denaturation of dna furthermore this approach is in excellent agreement with previous experimental studies

solution to morgan s problem a necessary and sufficient condition is presented for the solution of the row by row decoupling problem known as morgan s problem in the general case that is without any restrictive assumption added to the system to the feedback law u fx gy g may be noninvertible this is a structural condition in terms of invariant lists of integers which are easily computable from a given state realization of the system these integers are the infinite zero orders morse s list i sub 4 and the essential orders of the system which only depend on the input output behavior and morse s list i sub 2 of the system which depends on the choice of a particular state realization

accurate computing of higher vibration modes of thin flexible structures motivated by the need for high fidelity modeling and accurate control of future hypersonic vehicles subjected to complex aerothermomechanical loads and many other such applications a novel scheme is proposed to accurately compute higher modes of vibration for one dimensional structures by coupling the classic ritz method as a predictor and the linear two point boundary value problem solver supore as a corrector the ritz method is used to compute a preliminary estimate of the natural frequencies for the desired modes these estimates are then used as initial guesses by supore which employs superposition and reorthonormalization to accurately solve the governing boundary value problem compared to a high fidelity ritz approximation or a highly refined finite element modeling procedure this is a simple computationally less expensive and yet highly accurate method to compute mode shapes for applications that require higher modes this scheme is used to compute mode shapes within an absolute and relative

spectrum and symbol distribution of nucleotide sequences this paper explores the connection between the size of the spectral coefficients of a nucleotide or any other symbolic sequence and the distribution of nucleotides along certain subsequences it explains the connection between the nucleotide distribution and the size of the spectral coefficients and gives a necessary and sufficient condition for a coefficient to have a prescribed magnitude furthermore it gives a fast algorithm for computing the value of a given spectral coefficient of a nucleotide sequence discussing periods 3 and 4 as examples finally it shows that the spectrum of a symbolic sequence is redundant in the sense that there exists a linear recursion that determines the values of all the coefficients from those of a subset

solution of the static state feedback decoupling problem for linear systems with two outputs we give for linear systems with two outputs a necessary and sufficient condition for the solvability of the restricted decoupling problem rdp in terms of some structural invariants a geometric characterization is also given which provides the least dynamical extension needed when rdp is not solvable

the row by row decoupling problem with stability a structural approach the row by row decoupling problem with stability via regular static state feedback is revisited here for linear systems a new geometric characterization is provided which easily lends to a nice structural solution expressed in terms of infinite and unstable contents

decomposition of dna sequence complexity profiles of sequence compositional complexity provide a view of the spatial heterogeneity of symbolic sequences at different levels of detail sequence compositional complexity profiles are here decomposed into partial profiles using the branching property of the shannon entropy this decomposition shows the complexity contributed by each individual symbol or group of symbols in particular we apply this method to the mapping rules symbol groupings commonly used in dna sequence analysis we find that strong weak bindings are remarkable homogeneously distributed as compared to purine pyrimidine and that a and t are the most heterogeneous distributed bases

multifractal fourier spectra and power law decay of correlations in random substitution sequences binary symbolic sequences produced by randomly alternating substitution rules are considered exact expressions for the characteristics of autocorrelations and power spectra are derived the decay of autocorrelation function obeys the power law the fourier spectral measure is either absolutely continuous or a mixture of the absolutely continuous and singular continuous components for the latter case the multifractal characteristics of this measure are computed

on the structure at infinity of linear square decoupled systems the purpose of this note is to demonstrate that a square invertible linear system c a b is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the infinite zero orders of the subsystems c i a b where c i denotes the i th row of c until now only the necessity of this condition has been established 1

hierarchical multifractal representation of symbolic sequences and application to human chromosomes the two dimensional density correlation matrix is constructed for symbolic sequences using contiguous segments of arbitrary size the multifractal spectrum obtained from this matrix motif is shown to characterize the correlations in the symbolic sequences this method is applied to entire human chromosomes shuffled human chromosomes reconstructed human genomic sequences and to artificial random sequences it is shown that all human chromosomes have common characteristics in their multifractal spectrum and deviate substantially from random and uncorrelated sequences of the same size small deviations are observed between the longer and the shorter chromosomes especially for the higher in absolute values statistical moments the correlations are crucial for the form of the multifractal spectrum surrogate shuffled chromosomes present randomlike spectrum distinctly different from the actual chromosomes analytical approaches based on hierarchical superposition of tensor products show that retaining pair correlations in the sequences leads to a closer representation of the genomic multifractal spectra especially in the region of negative exponents due to the underrepresentation of various functional units such as the cytosine guanine cg combination and its complementary gc complex retaining higher order correlations in the construction of the tensor products is a way to approach closer the structure of the multifractal spectra of the actual genomic sequences this hierarchical approach is generic and is applicable to other correlated symbolic sequences

stable synchronised states of coupled tchebyscheff maps abstract coupled tchebyscheff maps have recently been introduced to explain parameters in the standard model of particle physics using the stochastic quantisation of parisi and wu this paper studies dynamical properties of these maps finding analytic expressions for a number of periodic states and determining their linear stability numerical evidence is given for nonlinear stability of some of these states and also the presence of exponentially slow dynamics for some ranges of the parameter these results indicate that a theory of particle physics based on coupled map lattices must specify strong physical arguments for any choice of initial conditions and explain how stochastic quantisation is obtained in the many stable parameter regions

pole assignment in the regular row by row decoupling problem by applying the canonical decomposition of the right invertible system c a b obtained in wei cheng and wang 2010 in this paper we derive a general formula of all solutions to the regular row by row decoupling problem based on this formula we characterize all attainable transfer function matrices for the decoupling and pole assignment problem in general cases the results obtained in this paper extend those in the literature

multifractal analysis of nonhyperbolic coupled map lattices application to genomic sequences symbolic sequences generated by coupled map lattices cmls can be used to model the chaotic like structure of genomic sequences in this study it is shown that diffusively coupled chebyshev maps of order 4 corresponding to a shift of four symbols very closely reproduce the multifractal spectrum d q of human genomic sequences for coupling constant 0 35 0 01 if q 0 the presence of rare configurations causes deviations for q 0 which disappear if the rare event statistics of the cml is modified such rare configurations are known to play specific functional roles in genomic sequences serving as promoters or regulatory elements

scaling behavior of nonhyperbolic coupled map lattices coupled map lattices of nonhyperbolic local maps arise naturally in many physical situations described by discretized reaction diffusion equations or discretized scalar field theories as a prototype for these types of lattice dynamical systems we study diffusively coupled tchebyscheff maps of nth order which exhibit strongest possible chaotic behavior for small coupling constants a we prove that the expectations of arbitrary observables scale with sqrt of a in the low coupling limit contrasting the hyperbolic case which is known to scale with a moreover we prove that there are log periodic oscillations of period ln n2 modulating the sqrt of a dependence of a given expectation value we develop a general 1st order perturbation theory to analytically calculate the invariant one point density show that the density exhibits log periodic oscillations in phase space and obtain excellent agreement with numerical results

nature of stationarity of the natural frequencies at the natural modes in the rayleigh ritz method abstract a variational formulation of the rayleigh ritz method to obtain approximate natural frequencies and natural modes is presented the stationarity of the natural frequencies with respect to the arbitrary coefficients in the linear combination of the assumed deflection shapes and also at the natural modes is investigated it is concluded that the natural frequencies are stationary and need not always be minimum with respect to the arbitrary coefficients however they are minimum with respect to the natural modes this may provide a means of checking the accuracy of the computed natural frequencies obtained by using energy techniques such as the rayleigh ritz galerkin and finite element methods

coupled intermittent maps modeling the statistics of genomic sequences a network approach the dynamics of coupled intermittent maps is used to model the correlated structure of genomic sequences the use of intermittent maps as opposed to other simple chaotic maps is particularly suited for the production of long range correlation features which are observed in the genomic sequences of higher eucaryotes a weighted network approach to symbolic sequences is introduced and it is shown that coupled intermittent polynomial maps produce degree and link size distributions with power law exponents similar to the ones observed in real genomes the proposed network approach to symbolic sequences is generic and can be applied to any symbol sequence artificial or natural

on the lateral vibration of thin annular and circular composite plates subject to certain complicating effects abstract series comprising orthogonally generated polynomial functions are used in the rayleigh ritz method to obtain an eigenvalue equation for the flexural vibration of thin flat annular and circular plates the plates may be of isotropic or polar orthotropic material of uniform or radially varying thickness and may pass over intermediate concentric ring supports numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

the pole assignment for the regular triangular decoupling problem in this paper by applying the canonical decomposition of the right invertible system c a b obtained in wei cheng and wang 2010 we derive all explicit solutions of the regular triangular decoupling problem and then characterize all attainable transfer function matrices for the decoupling and pole assignment problem

a numerical solution for the simultaneous disturbance decoupling and row by row decoupling problem the numerical computation of the simultaneous disturbance decoupling and row by row decoupling problem is considered based on a condensed form for the system matrices the solvability of the simultaneous disturbance decoupling and row by row decoupling problem is reduced to the verification of an integer equality and the nonsingularity of a lower dimensional constant matrix the condensed form we use is computed using only orthogonal transformations which can be implemented in a numerically stable way hence it leads directly to an effective numerical method for solving the disturbance decoupling and row by row decoupling problem using existing tools such as lapack and matlab our result complements existing geometric and structural approaches which are of a theoretical nature and are not suitable for numerical computation

measure representation and multifractal analysis of complete genomes this paper introduces the notion of measure representation of dna sequences spectral analysis and multifractal analysis are then performed on the measure representations of a large number of complete genomes the main aim of this paper is to discuss the multifractal property of the measure representation and the classification of bacteria from the measure representations and the values of the dq spectra and related cq curves it is concluded that these complete genomes are not random sequences in fact spectral analyses performed indicate that these measure representations considered as time series exhibit strong long range correlation here the long range correlation is for the k strings with dictionary ordering and it is different from the base pair correlations introduced by other people for substrings with length k58 the dq spectra of all organisms studied are multifractal like and sufficiently smooth for the cq curves to be meaningful with the decreasing value of k the multifractality lessens the cq curves of all bacteria resemble a classical phase transition at a critical point but the analogous phase transitions of chromosomes of nonbacteria organisms are different apart from chromosome 1 of c elegans they exhibit the shape of double peaked specific heat function a classification of genomes of bacteria by assigning to each sequence a point in two dimensional space d21 d1 and in three dimensional space d21 d1 d22 was given bacteria that are close phylogenetically are almost close in the spaces d21 d1 and d21 d1 d22

power law exponents characterizing human dna the size distributions of all known coding and noncoding dna sequences are studied in all human chromosomes in a unified approach both introns and intergenic regions are treated as noncoding regions the distributions of noncoding segments p mathit nc s of size s present long tails p mathit nc s ensuremath sim s ensuremath 1 ensuremath ensuremath mu mathit nc with exponents ensuremath mu mathit nc ranging between 0 71 for chromosome 13 and 1 2 for chromosome 19 on the contrary the exponential short range decay terms dominate in the distributions of coding exon segments p c s in all chromosomes aiming to address the emergence of these statistical features minimal stochastic mean field models are proposed based on randomly aggregating dna strings with duplication influx and outflux of genomic segments these minimal models produce both the short range statistics in the coding and the observed power law and fractal statistics in the noncoding dna the minimal models also demonstrate that although the two systems coding and noncoding coexist alternating on the same linear chain they act independently the coding as a closed equilibrium system and the noncoding as an open out of equilibrium one

sufficient conditions for linear control system decoupling by static state feedback sufficient conditions for solvability of linear control system decoupling by static state feedback are given in terms of integer relations it is shown that these integer relations in the generic case are very simple if the decoupling conditions are satisfied a given algorithm for decoupling based on solving systems of linear equations and spending controls can be applied

the row by row decoupling via state feedback a polynomial approach necessary and sufficient conditions for the row by row and integrator decoupling of a linear system x ax bu y cx via nonregular static state feedback are established a procedure is outlined to calculate one such gain

new results about morgan s problem some aspects of the nonsquare morgan s problem are considered in particular it is shown that the condition given by j descusse et al 1986 to solve this problem is not sufficient it is also shown that the essential orders are not necessarily preserved in the static decoupling problem a necessary and sufficient condition for static decoupling of a system without modifying the essential orders is given for the case k p 1 where p is the number of outputs and k is the rank at infinity of the proper part of the interactor

input output decoupling by output feedback with disturbance attenuation of h control for any square system the combined problem of diagonal decoupling by output feedback with disturbance attenuation performance for any square system is formulated a sufficient condition which is more general than the necessary and sufficient one of static state feedback for the existence of the controller is determined the necessary and sufficient conditions for the controller and decoupled system that are both stable are presented an analytical form and a numerical computable method for the controller are obtained for the first time when the condition is satisfied the correctness of our method is tested by simulations for an example

some new properties of the right invertible system in control theory in this paper we deduce equivalent conditions of controllability stability and observability of a right invertible system c a b by applying the canonical decomposition of c a b obtained by wei et al wei m cheng x wang q 2010 a canonical decomposition of the right invertible system with applications siam journal on matrix analysis and applications 31 4 1958 1981 we also derive three equivalent sufficient solvability conditions of the non regular row by row decoupling problem which are generalization of necessary and sufficient conditions of the regular row by row decoupling problem

what can we learn with wavelets about dna sequences we use the wavelet transform to explore the complexity of dna sequences long range correlations are clearly identified and shown to be related to the sequence gc content the significance of this observation to gene evolution is discussed

symbolic stochastic dynamical systems viewed as binary n step markov chains a theory of systems with long range correlations based on the consideration of binary n step markov chains is developed in the model the conditional probability that the ith symbol in the chain equals zero or unity is a linear function of the number of unities among the preceding n symbols the correlation and distribution functions as well as the variance of the number of symbols in the words of arbitrary length l are obtained analytically and numerically a self similarity of the studied stochastic process is revealed and the similarity group transformation of the chain parameters is presented the diffusion fokker planck equation governing the distribution function of the l words is explored if the persistent correlations are not extremely strong the distribution function is shown to be the gaussian with the variance being nonlinearly dependent on l the applicability of the developed theory to the coarse grained written and dna texts is discussed

identifying characteristic scales in the human genome received 1 june 2006 published 16 march 2007the scale free long range correlations detected in dna sequences contrast with characteristic lengths ofgenomic elements being particularly incompatible with the isochores long homogeneous dna segments bycomputing the local behavior of the scaling exponent of detrended uctuation analysis dfa we discrimi nate between sequences with and without true scaling and we nd that no single scaling exists in the humangenome instead human chromosomes show a common compositional structure with two characteristic scales the large one corresponding to the isochores and the other to small and medium scale genomic elements doi 10 1103 physreve 75 032903 pacs number s 87 15 cc 87 14 gg 87 15 aa

analysis of symbolic sequences using the jensen shannon divergence we study statistical properties of the jensen shannon divergence d which quantifies the difference between probability distributions and which has been widely applied to analyses of symbolic sequences we present three interpretations of d in the framework of statistical physics information theory and mathematical statistics and obtain approximations of the mean the variance and the probability distribution of d in random uncorrelated sequences we present a segmentation method based on d that is able to segment a nonstationary symbolic sequence into stationary subsequences and apply this method to dna sequences which are known to be nonstationary on a wide range of different length scales