two extragradient methods for generalized mixed equilibrium problems nonexpansive mappings and monotone mappings in this paper we introduce iterative schemes based on the extragradient method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of an infinite a finite family of nonexpansive mappings and the set of solutions of a variational inequality problem for a monotone lipschitz continuous mapping we obtain some weak convergence theorems for the sequences generated by these processes in hilbert spaces the results in this paper generalize extend and unify some well known weak convergence theorems in the literature

perturbation analysis of orthogonal canonical forms abstract we present a complete perturbation analysis of orthogonal canonical forms ocfs of linear multivariable systems both local linear and nonlocal nonlinear perturbation bounds are derived in particular the conditioning of ocfs is determined

a computational algorithm for pole assignment of linear single input systems an efficient computational algorithm for pole assignment of linear multiinput systems is proposed a preliminary stage of the algorithm is a reduction of the system matrices into orthogonal canonical form the gain matrix elements are then found by orthogonal transformation of the closed loop system matrix into upper quasi triangular form whose diagonal blocks correspond to the desired poles the algorithm is numerically stable the computed gain matrix being exact for a system with slightly perturbed matrices it works equally well with real and complex distinct and multiple poles and is applicable to ill conditioned and high order problems

on zwicker tones and musical pitch in the likely absence of phase locking corresponding to the pitcha it was assessed whether zwicker tones zts an auditory afterimage produced by a band stop noise have a musical pitch first stage i musically trained subjects adjusted the frequency level and decay time of an exponentially decaying diotic sinusoid to sound similar to the zt they perceived following the presentation of diotic broadband noise for various band stop positions next stage ii subjects adjusted a sinusoid in frequency and level so that its pitch was a specified musical interval below that of either a preceding zt or a preceding sinusoid and so that it was equally loud for each subject the reference sinusoid corresponded to their adjusted sinusoid from stage i subjects selected appropriate frequency ratios for zts although the standard deviations of the adjustments were larger for the zts than for the equally salient sinusoids by a factor of 1 0 2 2 experiments with monaural stimuli led to similar results although the pitch of the zts could differ for monaural and diotic presentation of the zt exciting noise the results suggest that a weak musical pitch may exist in the absence of phase locking in the auditory nerve to the frequency corresponding to the pitch or harmonics thereof at the time of the percept

a unitary model of pitch perception a model of the mechanism of residue pitch perception is revisited it is evaluated in the context of some new empirical results and it is proposed that the model is able to reconcile a number of differing approaches in the history of theories of pitch perception the model consists of four sequential processing stages peripheral frequency selectivity within channel half wave rectification and low pass filtering within channel periodicity extraction and cross channel aggregation of the output the pitch percept is represented by the aggregated periodicity function using autocorrelation as the periodicity extraction method and the summary autocorrelation function sacf as the method for representing pitch information it is shown that the model can simulate new experimental results that show how the quality of the pitch percept is influenced by the resolvability of the harmonic components of the stimulus complex these include i the pitch of harmonic stimuli whose components alternate in phase ii the increased frequency difference limen of tones consisting of higher harmonics and iii the influence of a mistuned harmonic on the pitch of the complex as a function of its harmonic number to accommodate these paradigms it was necessary to compare stimuli along the length of the sacf rather than relying upon the highest peak alone these new results demonstrate that the model responds differently to complexes consisting of low and high harmonics as a consequence it is not necessary to postulate two separate mechanisms to explain different pitch percepts associated with resolved and unresolved harmonics

on the application of orthogonal transformation for the design and analysis of feedforward networks orthogonal transformation which can lead to compaction of information has been used in two ways to optimize on the size of feedforward networks 1 through the selection of optimum set of time domain inputs and the optimum set of links and nodes within a neural network nn and 2 through the orthogonalization of the data to be used in nn s in case of processes with periodicity the proposed methods are efficient and are also extremely robust numerically the singular value decomposition svd and qr with column pivoting factorization qrcp are the transformations used svd mainly serves as the null space detector qrcp coupled with svd is used for subset selection which is one of the main operations on which the design of the optimal network is based svd has also been used to devise a new approach for the assessment of the convergence of the nn s which is an alternative to the conventional output error analysis

parallel and large scale matrix computations in control some ideas abstract the design and analysis of time invariant linear control systems give rise to a variety of interesting linear algebra problems numerically effective methods now exist for several of these problems however algorithms for large scale computations and efficient parallel algorithms for these problems are virtually nonexistent in this paper we propose several efficient general purpose parallel algorithms for single input and multiinput eigenvalue assignment problems a desirable feature of these algorithms is that they are composed of simple linear algebraic operations such as matrix vector multiplication solution of a linear system and computations of the eigensystem and singular values of a symmetric matrix for which efficient parallel algorithms have already been developed and parallel software libraries are being built based on these algorithms the proposed algorithms thus have potential for implementations on some existing and future parallel processors we also propose a numerical method for the sylvester matrix equation arising in the construction of a luenberger observer the method does not need reduction to condensed forms and is thus suitable for large and sparse matrices the method also exhibits a certain parallelism

an algorithm for pole assignment in high order multivariable systems an efficient computational method is presented for solving the problem of pole assignment by state feedback in linear multivariable systems with large dimensions a given multiinput system is first transformed to an upper block hessenberg form by means of orthogonal state coordinate transformations the state feedback problem is then reformulated in terms of the sylvester equation the transformed system matrices along with certain assumed block forms for unknown matrices enable the sylvester equation to be decomposed and solved effectively a distinct point of the proposed algorithm is that the solution procedure can be tailored to parallel implementation and is therefore fast computational aspects of the algorithm are discussed and numerical examples are provided

modeling the identification of concurrent vowels with different fundamental frequencies human listeners are better able to identify two simultaneous vowels if the fundamental frequencies of the vowels are different a computational model is presented which for the first time is able to simulate this phenomenon at least qualitatively the first stage of the model is based upon a bank of bandpass filters and inner hair cell simulators that simulate approximately the most relevant characteristics of the human auditory periphery the output of each filter hair cell channel is then autocorrelated to extract pitch and timbre information the pooled autocorrelation function acf based on all channels is used to derive a pitch estimate for one of the component vowels from a signal composed of two vowels individual channel acfs showing a pitch peak at this value are combined and used to identify the first vowel using a template matching procedure the acfs in the remaining channels are then combined and used to identify the second vowel model recognition performance shows a rapid improvement in

strong convergence theorems for finitely many nonexpansive mappings and applications abstract let e be a uniformly convex banach space which satisfies opial s condition or whose norm is frechet differentiable recently takahashi and shimoji w takahashi k shimoji convergence theorems for nonexpansive mappings and feasibility problems math comput modelling 32 2000 1463 1471 introduced an iterative scheme given by finitely many nonexpansive mappings in e and proved weak convergence theorems which are connected with the problem of image recovery in this paper we introduce a new iterative scheme which includes their iterative scheme as a special case under the assumption that e is a reflexive banach space whose norm is uniformly g teaux differentiable and which has a weakly continuous duality mapping we prove strong convergence theorems which are connected with the problem of image recovery using the established results we consider the problem of finding a common fixed point of finitely many nonexpansive mappings

computational methods for linear matrix equations given the square matrices a b d e and the matrix c of conforming dimensions we consider the linear matrix equation a mathbf x e d mathbf x b c in the unknown matrix mathbf x our aim is to provide an overview of the major algorithmic developments that have taken place over the past few decades in the numerical solution of this and related problems which are producing reliable numerical tools in the formulation and solution of advanced mathematical models in engineering and scientific computing

feedback design for regularizing descriptor systems this paper surveys numerical techniques for the regularization of descriptor generalized state space systems by proportional and derivative feedback we review generalizations of controllability and observability to descriptor systems along with definitions of regularity and index in terms of the weierstras canonical form three condensed forms display the controllability and observability properties of a descriptor system the condensed forms are obtained through orthogonal equivalence transformations and rank decisions so they may be computed by numerically stable algorithms in addition the condensed forms display whether a descriptor system is regularizable i e when the system pencil can be made to be regular by derivative and or proportional output feedback and if so what index can be achieved also included is a a new characterization of descriptor systems that can be made to be regular with index 1 by proportional and derivative output feedback

the frequency range applicable to pitch identification based upon the auto correlation function model abstract pitch identification experiments were conducted to determine the upper boundary of the frequency range within which the autocorrelation function acf model described by ando see reference 16 is applicable to the phenomenon of the missing fundamental of a complex tone pitch matching tests were conducted using 1 complex tones consisting of 2 f 3 f and 4 f where f denotes the fundamental frequencies of 0 5 1 0 1 2 1 6 2 0 or 3 0 khz and 2 complex tones consisting of 2 f and 3 f these tests showed that for both kinds of complex tones the acf model can account for the perception of pitch when the fundamental frequency is below 1200 hz

detection filter design spectral theory and algorithms a new formulation of the detection filter problem is generated by assignment of the closed loop eigenstructure under certain constraints detection filters which are actually a specific class of observers fix the output error direction of the system so that it can be associated with a particular failure mode and its known design failure direction the derivation of detection filters from an eigensystem assignment approach permits a very transparent theory the detection filter gains and closed loop eigenvectors are obtained from a set of simultaneous equations necessary and sufficient conditions for the solution of these algebraic equations are determined which produce a complete theory for detection filters

principal pivot transforms properties and applications the principal pivot transform ppt is a transformation of the matrix of a linear system tantamount to exchanging unknowns with the corresponding entries of the right hand side of the system the notion of the ppt is encountered in mathematical programming statistics and numerical analysis among other areas the purpose of this paper is to draw attention to the main properties and uses of ppts make some new observations and motivate further applications of ppts in matrix theory special consideration is given to ppts of matrices whose principal minors are positive 2000 elsevier science inc all rights reserved

an autocorrelation model with place dependence to account for the effect of harmonic number on fundamental frequency discrimination fundamental frequency f0 difference limens dls were measured as a function of f0 for sine and random phase harmonic complexes bandpass filtered with 3 db cutoff frequencies of 2 5 and 3 5 khz low region or 5 and 7 khz high region and presented at an average 15 db sensation level approximately 48 db spl per component in a wideband background noise fundamental frequencies ranged from 50 to 300 hz and 100 to 600 hz in the low and high spectral regions respectively in each spectral region f0 dls improved dramatically with increasing f0 as approximately the tenth harmonic appeared in the passband generally f0 dls for complexes with similar harmonic numbers were similar in the two spectral regions the dependence of f0 discrimination on harmonic number presents a significant challenge to autocorrelation ac models of pitch in which predictions generally depend more on spectral region than harmonic number a modification involving a lag window is proposed and tested restricting the ac repr

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

matrix bidiagonal form the matrix bidiagonal form is analysed and some applications to linear system theory are shown in the first part it is shown that the reduction of a given matrix a to the mbf is immediate in the very common situation in which a vector b such that a b is controllable is known in the second part some applications are presented such as the evaluation of a function of a matrix and the solution of the lyapunov equation

a gametheoretic approach for non uniform pole shifting and pole homothety this paper investigates the problems of non uniform pole shifting or pole homothety in multivariable linear systems by using a gametheoretic approach and more specifically a particular nash strategy with an open loop information structure for a game including a time preference rate in the quadratic criteria such a result is possible due to properties of non symmetric algebraic riccati equations associated with an open loop nash strategy numerical examples allow to illustrate the efficiency of the proposed approach

the case of the missing delay lines synthetic delays obtained by cross channel phase interaction temporal models of pitch and harmonic segregation call for delays of up to 30ms to cover the full range of existence of musical pitch to date there is little anatomical or physiological evidence for delays that long we propose a mechanism by which delays may be synthesized from cross channel phase interaction phases of adjacent cochlear filter channels are shifted by an amount proportional to frequency and then combined as a weighted sum to approximate a delay synthetic delays may be used by pitch perception models such as autocorrelation segregation models such as harmonic cancellation and binaural processing models to explain sensitivity to large interaural delays the maximum duration of synthetic delays is limited by the duration of the impulse responses of cochlear filters itself inversely proportional to cochlear filter bandwidth maximum delay is thus frequency dependent this may explain the fact puzzling for temporal pitch models such as autocorrelation that pitch is more salient and eas

cancellation model of pitch perception a model of pitch perception is presented involving an array of delay lines and inhibitory gating neurons in response to a periodic sound a minimum appears in the pattern of outputs of the inhibitory neurons at a lag equal to the period of the sound the position of this minimum is the cue to pitch the model is similar to the autocorrelation model of pitch multiplication being replaced by an operation similar to subtraction and maxima by minima the two models account for a wide class of pitch phenomena in very much the same way the principal goal of this paper is to demonstrate this fact several features of the cancellation model may be to its advantage it is closely related to the operation of harmonic cancellation that can account for segregation of concurrent harmonic stimuli it can be generalized to explain the perception of multiple pitches and it shows a greater degree of sensitivity to phase than autocorrelation which may allow it to explain certain phenomena that autocorrelation cannot account for

on modified iterative method for nonexpansive mappings and monotone mappings abstract in this paper we introduce a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for inverse strongly monotone mappings we show that the sequence converges strongly to a common element of the above two sets under some parameters controlling conditions

psychophysical evidence against the autocorrelation theory of auditory temporal processing nowadays it is widely believed that the temporal structure of the auditory nerve fibers response to sound stimuli plays an important role in auditory perception an influential hypothesis is that information is extracted from this temporal structure by neural operations akin to an autocorrelation algorithm the goal of the present work was to test this hypothesis the stimuli consisted of sequences of unipolar clicks that were high pass filtered and mixed with low pass noise so as to exclude spectral cues in experiment 1 interfering clicks were inserted in an otherwise periodic isochronous click sequence each click belonging to the periodic sequence was followed after a random portion of the period by one interfering click this disrupted the detection of temporal regularity even when the interfering clicks were 5 db less intense than the periodic clicks experiments 2 4 used click sequences that showed a single peak in their autocorrelation functions for some sequences this peak originated from first order temporal regularities that is from the temporal relations between consecutive clicks for other sequences the peak originated instead from second order regularities relative to nonconsecutive clicks the detection of second order regularities appeared to be much more difficult than the detection of comparable first order regularities overall these results do not tally with the current autocorrelation models of temporal processing they suggest that the extraction of temporal information from a group of closely spaced spectral components makes no use of time intervals between nonconsecutive peaks of the amplitude envelope

an algorithm for the assignment of system zeros abstract this paper presents an algorithm for assigning the locations and number of zeros to a linear system through synthesis of the system input and output space couplings the approach imposes no restrictions on the state space model can assign both real and complex zeros using only real arithmetic and is computationally efficient numerical properties of the algorithm are discussed and examples are given to illustrate its performance

orthogonal canonical forms for second order systems it is shown that a linear second order system with arbitrary damping cannot be reduced to hessenberg triangular form by means of orthogonal transformations however it is also shown that such an orthogonal reduction is always possible for the modal damping commonly assumed for models of flexible structures it is shown that modally damped models can be orthogonally reduced to a new triangular second order schur form

a schur decomposition for hamiltonian matrices abstract a schur type decomposition for hamiltonian matrices is given that relies on unitary symplectic similarity transformations these transformations preserve the hamiltonian structure and are numerically stable making them ideal for analysis and computation using this decomposition and a special singular value decomposition for unitary symplectic matrices a canonical reduction of the algebraic riccati equation is obtained which sheds light on the sensitivity of the nonnegative definite solution after presenting some real decompositions for real hamiltonian matrices we look into the possibility of an orthogonal symplectic version of the qr algorithm suitable for hamiltonian matrices a finite step initial reduction to a hessenberg type canonical form is presented however no extension of the francis implicit shift technique was found and reasons for the difficulty are given

linear and numerical linear algebra in control theory some research problems abstract this paper presents an informal survey of theoretical and computational aspects of three linear algebra problems arising in control theory namely the sylvester observer matrix equation the matrix eigenvalue assignment problem and the stability and stabilization of large second order systems difficulties are highlighted recent developments are mentioned some research problems in these areas which should be of interest to both linear algebraists and control theorists are described

an iterative method of solution for equilibrium and optimization problems abstract in this paper we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping the set of solutions of the variational inequality for an inverse strongly monotone mapping and the set of solutions of an equilibrium problem in a hilbert space we show that the iterative sequence converges strongly to a common element of the three sets the results of this paper extended and improved the results of h iiduka and w takahashi strong convergence theorems for nonexpansive mappings and inverse strongly monotone mappings nonlinear anal 61 2005 341 350 and s takahashi and w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 2007 506 515 therefore by using the above result an iterative algorithm for the solution of a optimization problem was obtained

computing the radius of controllability for state space systems abstract in this paper we discuss the problem of computing the nearest uncontrollable system to a given control system represented by a matrix pair a b in order to do so we construct a sequence of structured matrices from given system matrices a and b controllability of the pair a b is equivalent to a condition on the null space dimension of an appropriate matrix in this sequence we show that the dimension of the reachability space is also related to the above condition further it is shown that the nearest structured low rank approximation slra of this structured matrix corresponds to a nearest uncontrollable system to the pair a b

viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces abstract in this paper we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a hilbert space then we prove a strong convergence theorem which is connected with combettes and hirstoaga s result p l combettes s a hirstoaga equilibrium programming in hilbert spaces j nonlinear convex anal 6 2005 117 136 and wittmann s result r wittmann approximation of fixed points of nonexpansive mappings arch math 58 1992 486 491 using this result we obtain two corollaries which improve and extend their results

equilibrium programming using proximal like algorithms we compute constrained equilibria satisfying an optimality condition important examples include convex programming saddle problems noncooperative games and variational inequalities under a monotonicity hypothesis we show that equilibrium solutions can be found via iterative convex minimization in the main algorithm each stage of computation requires two proximal steps possibly using bregman functions one step serves to predict the next point the other helps to correct the new prediction to enhance practical applicability we tolerate numerical errors

pitch shifts of mistuned partials a time domain model mistuning one partial of a complex harmonic tone makes that partial easier to hear as a tone separate from the complex at the same time two pitch shifts may be observed first the low pitch of the complex is shifted in the direction of the mistuning as if it were pulled by the partial second the mistuning of the partial is perceptually exaggerated as if the pitch of the partial were pushed away from the harmonic series defined by the complex this paper shows how the latter effect can emerge within a hypothetical neural circuit the circuit involves a gating neuron fed by three pathways one direct and excitatory and the other two delayed and inhibitory the neuron responds to any excitatory input spike unless it is accompanied by an inhibitory input spike on either delayed input thus acting as a kind of anticoincidence counter the first delay is fixed and tuned to the period of the background harmonic complex its purpose is to weaken correlates of in tune components and allow the mistuned partial to stand out the second delay is variable and used to estimate the period of the mistuned partial by searching for a minimum output as a function of delay with an appropriate choice of parameters the estimate is subject to shifts that are of the same sign as the mistuning and that peak at about 4 mistuning and decrease beyond as observed experimentally

on hamiltonian and symplectic hessenberg forms abstract characterizations are given for the hamiltonian matrices that can be reduced to hamiltonian hessenberg form and the symplectic matrices that can be reduced to symplectic hessenberg form by orthogonal symplectic similarity transformations the reduction to these special hessenberg forms is the missing link in the solution of the open problem of constructing a stable structure preserving qr like method of complexity o n 3 for the computation of invariant subspaces of hamiltonian and symplectic matrices our considerations lead us to propose an approach to the computation of lagrangian invariant subspaces of a hamiltonian or symplectic matrix

missing data model of vowel identification vowel identity correlates well with the shape of the transfer function of the vocal tract in particular the position of the first two or three formant peaks however in voiced speech the transfer function is sampled at multiples of the fundamental frequency f0 and the short term spectrum contains peaks at those frequencies rather than at formants it is not clear how the auditory system estimates the original spectral envelope from the vowel waveform cochlear excitation patterns for example resolve harmonics in the low frequency region and their shape varies strongly with f0 the problem cannot be cured by smoothing lag domain components of the spectral envelope are aliased and cause f0 dependent distortion the problem is severe at high f0 s where the spectral envelope is severely undersampled this paper treats vowel identification as a process of pattern recognition with missing data matching is restricted to available data and missing data are ignored using an f0 dependent weighting functi

a new parameter estimate in singular perturbations abstract a new upper bound is obtained for the singular perturbation parameter of an asymptotically stable singularly perturbed system general time invariant systems with a single small parameter are considered the paper employs a riccati equation whose solution is known to facilitate the exact decoupling of fast and slow dynamics an application of the brouwer fixed point theorem to the riccati equation and of liapunov s direct method to the fast and slow subsystems results in the desired upper bound computation of the estimate requires only the solution of two liapunov matrix equations

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

on the computation of sensitivity functions of linear time invariant systems responses via diagonalization this note presents a method for computing the sensitivity functions of parametrized linear time invariant systems for the case where the system matrix a is diagonalizable the method is based on a formula derived in the note for the sensitivity of an exponential of a diagonalizable matrix

bias reduction in parameter estimation abstract the upper bound of the bias in the estimated parameters is derived in terms of the spectral norm it is then established that the bias is related to the condition of the problem as well as the noise existing in the data conventional methods such as the generalized least squares gls the instrumental variables iv and the extended matrix em method seek to minimize bias by reducing the level of noise correlation in the data the method presented in this paper approaches the bias reduction problem via the condition number which acts as a multiply factor on the bias due to noise correlation by improving the condition of the problem it can be shown that bias in the estimated parameters is significantly reduced

strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a hilbert space abstract we introduce an iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a hilbert space and then obtain that the sequence converges strongly to a common element of two sets using this result we prove three new strong convergence theorems in fixed point problems variational inequalities and equilibrium problems

generalized schur methods with condition estimators for solving the generalized sylvester equation stable algorithms are presented for solving the generalized sylvester equation they are based on orthogonal equivalence transformations of the original problem perturbation theory and rounding error analysis are included condition estimators dif sup 1 estimators are developed which when substituted into derived error bounds give accuracy estimates of a computed solution results from numerical experiments on well conditioned and ill conditioned problems are reported

decomposition and stability for multiparameter singular perturbation problems time scale separation and stability of linear time varying and time invariant multiparameter singular perturbation problems are analyzed the first problem considered in the paper is that of deriving upper bounds on the small parasitic parameters ensuring the existence of an invertible bounded transformation exactly separating fast and slow dynamics this problem is most interesting for the time varying case the analysis of this problem in the time varying case requires the two time scale setting introduced by h k khalil and p v kokotovic 16 this entails that the mutual ratios of the small parameters are bounded by known positive constants the second problem considered is to derive parameter bounds ensuring that the system in question is uniformly asymptotically stable the results on decomposition are used to facilitate the derivation of these latter bounds fortunately the analysis of decomposition and stability questions for time invariant multiparameter singular perturbation problems requires no restriction on the relative magnitudes of the small parameters a concept of strong d stability is introduced and shown to greatly simplify the stability analysis of time invariant multiparameter problems

temporal dynamics of pitch strength in regular interval noises the pitch strength of rippled noise and iterated rippled noise has recently been fitted by an exponential function of the height of the first peak in the normalized autocorrelation function j acoust soc am 100 3329 3335 1996 the current study compares the pitch strengths and autocorrelation functions of rippled noise rn and another regular interval noise aabb rn is generated by delaying a copy of a noise sample and adding it to the undelayed version aabb with the same pitch is generated by taking a sample of noise a with the same duration as the rn delay and repeating it to produce aa and then concatenating many of these once repeated sequences to produce aabbccdd the height of the first peak h1 in the normalized autocorrelation function of aabb is 0 5 identical to that of rn the current experiments show the following 1 aabb and rn can be discriminated when the pitch is less than about 250 hz 2 for these low pitches the pitch strength of aabb is greater than that for rn

a new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings abstract in this paper we introduce a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for inverse strongly monotone mappings we show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions this main theorem extends a recent result of yao and yao y yao j c yao on modified iterative method for nonexpansive mappings and monotone mappings applied mathematics and computation 186 2 2007 1551 1558

properties of numerical algorithms related to computing controllability the numerical properties of some methods for computing controllability are used in an expository way to motivate a wider understanding of numerical computations in particular the numerical rank of a matrix the numerical stability of algorithms the sensitivity of problems and the scaling of problems are discussed a numerically stable algorithm is given for computing controllability but it is pointed out that a measure of the distance of the given system from the nearest uncontrollable system would be more useful and this appears to be an open computational problem

pitch strength of iterated rippled noise two versions of a cascade add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose pitch strength relative to the noise percept can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to use pitch strength to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds the number of iterations and the attenuation in the network a description based on an exponential function of the first peak of the autocorrelation function of irn stimuli is consistent with the results the discrimination data were well fit by a function based on the difference in the exponential functions of the first peak of the autocorrelation functions a magnitude estimation experiment indicated that pitch strength was an exponential function of the height of the first peak in the autocorrelation function these results suggest that the strength of the pitch of irn stimuli is based on temporal processing as might be revealed by autocorrelation

numerical linear algebra aspects of control design computations the interplay between recent results and methodologies in numerical linear algebra and mathematical software and their application to problems arising in systems control and estimation theory is discussed the impact of finite precision finite range arithmetic including the implications of the proposed ieee floating point standard s on control design computations is illustrated with numerous examples as are pertinent remarks concerning numerical stability and conditioning basic tools from numerical linear algebra such as linear equations linear least squares eigenproblems generalized eigenproblems and singular value decomposition are then outlined a selected list of applications of the basic tools then follows including algorithms for solution of problems such as matrix exponentials frequency response system balancing and matrix riccati equations the implementation of such algorithms as robust mathematical software is then discussed a number of issues are addressed including characteristics of reliable mathematical software availability and evaluation language implications fortran ada etc and the overall role of mathematical software as a component of computer aided control system design

a schur method for pole assignment in this paper a new numerical algorithm for pole assignment of linear time invariant systems is presented the proposed algorithm uses reliable numerical techniques based on the schur form of the state matrix and on the use of orthogonal transformations only the bad eigenvalues of the system are modified by a sequential pole shifting procedure and the resulted gains in the feedback matrix are minimized

mistuning detection and onset asynchrony in harmonic complexes in mongolian gerbils by applying a go nogo paradigm thresholds for detecting mistuning of components of a 200 hz complex were determined in the mongolian gerbil and compared with thresholds obtained in a previous study with an 800 hz complex frequency difference limens fdls for detecting mistuning decreased with increasing harmonic frequency and harmonic number 0 5 to 0 01 weber fraction it was furthermore examined how starting and ending the mistuned component earlier than the remaining complex affects the fdl duration of all components 400 ms time shift 30 to 500 ms large fdls that are similar to pure tone fdls between 21 and 6 7 were found for onset asynchronies of 300 ms and more indicating separate processing of the mistuned component small fdls that are similar to fdls of the synchronous condition were found if the temporal overlap between the mistuned component and the remaining complex was 100 ms or more these experimental data in combination with a simulation of processing of the harmonic complexe

feedback properties of multivariable systems the role and use of the return difference matrix for linear time invariant multivariable feedback systems the feedback properties of plant disturbance attenuation sensor noise response stability margins and sensitivity to plant and sensor variation are quantitatively related to the bode magnitude versus frequency plots of the singular values of the return difference matrix i l and of the associated inverse return difference matrix i l 1 implied fundamental limits of feedback performance are quantitatively described and design tradeoffs are discussed the penalty function in the stochastic linear quadratic gaussian lqg optimal control problem is found to be a weighted sum of the singular values with the weights determined by the quadratic cost and noise intensity matrices this enables systematic tuning of lqg cost and noise matrices so that the resulting optimal return difference and inversereturn difference meet inequality constraints derived from design specifications on feedback properties the theory has been used to synthesize a multivariable automatic controller for the longitudinal dynamics of an advanced fighter aircraft

a time domain description for the pitch strength of iterated rippled noise two versions of a cascaded add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose strength relative to the noise can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds or the number of iterations n 1 2 3 4 7 and 9 performance was determined for irn stimuli generated with delays of 2 4 and 8 ms and for four bandpass filter conditions 0 2000 250 2000 500 2000 and 750 2000 hz some irn stimuli were extremely difficult to discriminate despite relatively large spectral differences while other irn stimuli produced readily discriminable changes in perception despite small spectral differences these contrasting results are inconsistent with simple spectral explanations for the perception of irn stimuli an explanation based on the first peak of the autocorrelation function of irn stimuli is consistent with the results simulations of the processing performed by the peripheral auditory system i e interval histograms and correlograms produce results which are consistent with the involvement of these temporal processes in the perception of irn stimuli

pitch discrimination of diotic and dichotic tone complexes harmonic resolvability or harmonic number three experiments investigated the relationship between harmonic number harmonic resolvability and the perception of harmonic complexes complexes with successive equal amplitude sine or random phase harmonic components of a 100 or 200 hz fundamental frequency f0 were presented dichotically with even and odd components to opposite ears or diotically with all harmonics presented to both ears experiment 1 measured performance in discriminating a 3 5 5 frequency difference between a component of a harmonic complex and a pure tone in isolation listeners achieved at least 75 correct for approximately the first 10 and 20 individual harmonics in the diotic and dichotic conditions respectively verifying that only processes before the binaural combination of information limit frequency selectivity experiment 2 measured fundamental frequency difference limens f0 dls as a function of the average lowest harmonic number similar results at both f0 s provide further evidence that harmonic number not absolute frequency underlies the order of magnitude increase observed in f0 dls when only harmonics above about the 10th are presented similar results under diotic and dichotic conditions indicate that the auditory system in performing f0 discrimination is unable to utilize the additional peripherally resolved harmonics in the dichotic case in experiment 3 dichotic complexes containing harmonics below the 12th or only above the 15th elicited pitches of the f0 and twice the f0 respectively together experiments 2 and 3 suggest that harmonic number regardless of peripheral resolvability governs the transition between two different pitch percepts one based on the frequencies of individual resolved harmonics and the other based on the periodicity of the temporal envelope