designing structured tight frames via an alternating projection method tight frames also known as general welch bound equality sequences generalize orthonormal systems numerous applications including communications coding and sparse approximation require finite dimensional tight frames that possess additional structural properties this paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems ieps which includes the frame design problem to apply this method one needs only to solve a matrix nearness problem that arises naturally from the design specifications therefore it is the fast and easy to develop versions of the algorithm that target new design problems alternating projection will often succeed even if algebraic constructions are unavailable to demonstrate that alternating projection is an effective tool for frame design the paper studies some important structural properties in detail first it addresses the most basic design problem constructing tight frames with prescribed vector norms then it discusses equiangular tight frames which are natural dictionaries for sparse approximation finally it examines tight frames whose individual vectors have low peak to average power ratio par which is a valuable property for code division multiple access cdma applications numerical experiments show that the proposed algorithm succeeds in each of these three cases the appendices investigate the convergence properties of the algorithm

on some matrix inequalities the arithmetic geometric mean inequality for singular values due to bhatia and kittaneh says that 2sj ab sj a a b b j 1 2 for any matrices a b we first give new proofs of this inequality and its equivalent form then we use it to prove the following trace inequality let a0 be a positive definite matrix and a1 ak be positive semidefinite matrices then tr j 1k i 0jai 2aj tra0 1

on the failure of static stability analyses of nonconservative systems in regions of divergence instability abstract the stability of perfect bifurcational discrete dissipative systems under follower loads in regions of existence non existence of adjacent equilibria is thoroughly re examined in the light of recent progress in nonlinear dynamics a general theory for such nongradient systems described by autonomous ordinary differential equations is developed conditions for the existence of adjacent equilibria the stability of precritical critical and postcritical states as well as for different types of local bifurcations are established focusing attention on the interaction of geometric nonlinearities and vanishing damping new findings contradicting widely accepted results of the classical linear analysis are discovered in a small region of adjacent equilibria near a compound branching point which is explicitly determined an interaction of two consecutive postbuckling modes occurs related to the following phenomena in case of vanishing damping loss of stability may occur via a hopf dynamic bifurcation prior to static divergence buckling moreover the critical states of divergence instability may be associated with a double zero jacobian eigenvalue satisfying also the conditions of a hopf local bifurcation besides local dynamic bifurcations global bifurcations are also found an example is used to illustrate the qualitative findings

adaptive detection of a subspace signal in signal dependent interference this paper deals with the problem of adaptive detection of subspace signals embedded in thermal noise and clutter that depends on the transmitted signal to this end at the design stage we assume that the signal dependent sd clutter shares the same subspace as the target signals as customary a set of secondary data free of signal components is also assumed available two adaptive detectors referred to as the sd rao and sd wald are proposed by resorting to the rao test and wald test design criteria unlike the classical rao and wald tests which are derived by dividing the complex parameter into the real and imaginary parts the proposed detectors treat the complex parameter as a single quantity to reduce the computational burden moreover we derive the theoretical false alarm probabilities and detection probabilities and show that both the two proposed detectors exhibit the constant false alarm rate property numerical results show that the proposed detectors achieve a detection performance improvement over the conventional multidimensional detectors

comments on the method of harmonic balance the advantages and limitations of the harmonic balance or describing function approximation scheme for solving nonlinear ordinary differential equations of oscillatory motion are discussed advantages include appicability to equations of any order and with large degrees of nonlinearity ease of determining limit cycle behavior and its stability and overall speed and efficiency the limitation rules are essentially those described by mickens 1983 it is pointed out that perturbation procedures provide better results when the degree of nonlinearity is small

a unified framework for low autocorrelation sequence design via majorization minimization in this paper we consider the low autocorrelation sequence design problem we optimize a unified metric over a general constraint set the unified metric includes the integrated sidelobe level isl and the peak sidelobe level psl as special cases and the general constraint set contains the unimodular constraint peak to average ratio par constraint and similarity constraint to name a few the optimization technique we employ is the majorization minimization mm method which is iterative and enjoys guaranteed convergence to a stationary solution we carry out the mm method in two stages in the majorization stage we propose three majorizing functions two for the unified metric and one for the isl metric in the minimization stage we give closed form solutions for algorithmic updates under different constraints the update step can be implemented with a few fast fourier transformations ffts and or inverse ffts iffts we also show the connections between the mm and gradient projection method under our algorithmic scheme numerical simulations have shown that the proposed mm based algorithms can produce sequences with low autocorrelation and converge faster than the traditional gradient projection method and the state of the art algorithms

commutators and accretive operators abstract in this paper singular values of commutators of hilbert space operators are estimated to this aim the accretivity of a transform of the operators is applied some recent results of kittaneh f kittaneh singular value inequalities for commutators of hilbert space operators linear algebra appl 430 2009 2362 2367 are extended

more results on singular value inequalities of matrices abstract the arithmetic geometric mean inequality for singular values due to bhatia and kittaneh says that 2 s j ab s j a a b b j 1 2 for any matrices a b we give a new equivalent form and some relevant generalizations of this inequality in particular we show that s j a 1 4 b 3 4 a 3 4 b 1 4 s j a b j 1 n for any n n positive semidefinite matrices a b which proves a special case of zhan s conjecture posed in 2000

doubly constrained robust capon beamformer the standard capon beamformer scb is known to have better resolution and much better interference rejection capability than the standard data independent beamformer when the array steering vector is accurately known however the major problem of the scb is that it lacks robustness in the presence of array steering vector errors in this paper we will first provide a complete analysis of a norm constrained capon beamforming nccb approach which uses a norm constraint on the weight vector to improve the robustness against array steering vector errors and noise our analysis of nccb is thorough and sheds more light on the choice of the norm constraint than what was commonly known we also provide a natural extension of the scb which has been obtained via covariance matrix fitting to the case of uncertain steering vectors by enforcing a double constraint on the array steering vector viz a constant norm constraint and a spherical uncertainty set constraint which we refer to as the doubly constrained robust capon beamformer dcrcb nccb and dcrcb can both be efficiently computed at a comparable cost with that of the scb performance comparisons of nccb dcrcb and several other adaptive beamformers via a number of numerical examples are also presented

the frobenius norm and the commutator in an earlier paper we conjectured an inequality for the frobenius norm of the commutator of two matrices this conjecture was recently proved by seak weng vong and xiao qing jin and independently also by zhiqin lu we here give a completely different proof of this inequality prove some related results and embark on the corresponding question for unitarily invariant norms

commutator inequalities for hilbert space operators we prove singular value inequalities for positive operators some of these inequalities generalize recent results for commutators due to bhatia kitttaneh kittaneh and wang du applications of our results are given

singular value inequalities for commutators of hilbert space operators abstract we prove several singular value inequalities for commutators of hilbert space operators it is shown among other inequalities that if a b and x are operators on a complex separable hilbert space such that a and b are positive and x is compact then the singular values of ax xb are dominated by those of max a b x x where is the usual operator norm

on the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues we derive some basic results on the geometry of semidefinite programming sdp and eigenvalue optimization i e the minimization of the sum of the k largest eigenvalues of a smooth matrix valued function we provide upper bounds on the rank of extreme matrices in sdps and the first theoretically solid explanation of a phenomenon of intrinsic interest in eigenvalue optimization in the spectrum of an optimal matrix the kth and k 1 st largest eigenvalues tend to be equal and frequently have multiplicity greater than two this clustering is intuitively plausible and has been observed as early as 1975 when the matrix valued function is affine we prove that clustering must occur at extreme points of the set of optimal solutions if the number of variables is sufficiently large we also give a lower bound on the multiplicity of the critical eigenvalue these results generalize to the case of a general matrix valued function under appropriate conditions

a coordinate descent framework to design low psl isl sequences this paper is focused on the design of phase sequences with good aperiodic autocorrelation properties in terms of peak sidelobe level and integrated sidelobe level the problem is formulated as a biobjective pareto optimization forcing either a continuous or a discrete phase constraint at the design stage an iterative procedure based on the coordinate descent method is introduced to deal with the resulting optimization problems that are nonconvex and np hard in general each iteration of the devised method requires the solution of a nonconvex min max problem it is handled either through a novel bisection or an fft based method respectively for the continuous and the discrete phase constraint additionally a heuristic approach to initialize the procedures employing the l p norm minimization technique is proposed simulation results illustrate that the proposed methodologies can outperform some counterparts providing sequences with good autocorrelation features especially in the discrete phase binary case

unified optimization framework for multi static radar code design using information theoretic criteria in this paper we study the problem of code design to improve the detection performance of multi static radar in the presence of clutter i e a signal dependent interference to this end we briefly present a discrete time formulation of the problem as well as the optimal detector in the presence of gaussian clutter due to the lack of analytical expression for receiver operation characteristic roc code design based on roc is not feasible therefore we consider several popular information theoretic criteria including bhattacharyya distance kullback leibler kl divergence j divergence and mutual information mi as design metrics the code optimization problems associated with different information theoretic criteria are obtained and cast under a unified framework we propose two general methods based on majorization minimization to tackle the optimization problems in the framework the first method provides optimal solutions via successive majorizations whereas the second one consists of a majorization step a relaxation and a synthesis stage moreover derivations of the proposed methods are extended to tackle the code design problems with a peak to average ratio power par constraint using numerical investigations a general analysis of the coded system performance computational efficiency of the proposed methods and the behavior of the information theoretic criteria is provided

a perturbation analysis of interactive static and dynamic bifurcations the instability behavior of a nonlinear autonomous system in the vicinity of a coincident critical point which leads to interactions between static and dynamic bifurcations is studied the critical point considered is characterized by a simple zero and a pair of pure imaginary eigenvalues of the jacobian and the system contains two independent parameters the static and dynamic bifurcations and quasiperiodic motions resulting from the interaction of the bifurcation modes and the associated invariant tori are analyzed by a novel unification technique that is based on an intrinsic perturbation procedure divergence boundary dynamic bifurcation boundary secondary bifurcations and invariant tori are determined explicitly two illustrative examples concerning control systems are presented

information theoretic bounds on target recognition performance based on degraded image data this paper derives bounds on the performance of statistical object recognition systems wherein an image of a target is observed by a remote sensor detection and recognition problems are modeled as composite hypothesis testing problems involving nuisance parameters we develop information theoretic performance bounds on target recognition based on statistical models for sensors and data and examine conditions under which these bounds are tight in particular we examine the validity of asymptotic approximations to probability of error in such imaging problems problems involving gaussian poisson and multiplicative noise and random pixel deletions are considered as well as least favorable gaussian clutter a sixth application involving compressed sensor image data is considered in some detail this study provides a systematic and computationally attractive framework for analytically characterizing target recognition performance under complicated non gaussian models and optimizing system parameters

proof of bottcher and wenzel s conjecture on commutator norms for 3 by 3 matrices abstract bottcher and wenzel conjectured that the frobenius norm of the commutator of two real matrices of frobenius norm 1 is at most 2 and proved this for 2 by 2 matrices in this paper the conjecture is proved for 3 by 3 matrices

a high frequency boundary element method for scattering by a class of nonconvex obstacles in this paper we propose and analyse a hybrid numerical asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound soft nonconvex polygons the approximation space is enriched with carefully chosen oscillatory basis functions these are selected via a study of the high frequency asymptotic behaviour of the solution we demonstrate via a rigorous error analysis supported by numerical examples that to achieve any desired accuracy it is sufficient for the number of degrees of freedom to grow only in proportion to the logarithm of the frequency as the frequency increases in contrast to the at least linear growth required by conventional methods this appears to be the first such numerical analysis result for any problem of scattering by a nonconvex obstacle our analysis is based on new frequency explicit bounds on the normal derivative of the solution on the boundary and on its analytic continuation into the complex plane

center manifolds normal forms and bifurcations of vector fields with application to coupling between periodic and steady motions abstract we study the instabilities known to aeronautical engineers as flutter and divergence mathematically these states correspond to bifurcations to limit cycles and multiple equilibrium points in a differential equation making use of the center manifold and normal form theorems we concentrate on the situation in which flutter and divergence become coupled and show that there are essentially two ways in which this is likely to occur in the first case the system can be reduced to an essential model which takes the form of a single degree of freedom nonlinear oscillator this system which may be analyzed by conventional phase plane techniques captures all the qualitative features of the full system we discuss the reduction and show how the nonlinear terms may be simplified and put into normal form invariant manifold theory and the normal form theorem play a major role in this work and this paper serves as an introduction to their application in mechanics repeating the approach in the second case we show that the essential model is now three dimensional and that far more complex behavior is possible including nonperiodic and chaotic motions throughout we take a two degree of freedom system as an example but the general methods are applicable to multi and even infinite degree of freedom problems

space time code design for mimo detection based on kullback leibler divergence the focus of the paper is on the design of space time codes for a general multiple input multiple output detection problem when multiple observations are available at the receiver the figure of merit used for optimization purposes is the convex combination of the kullback leibler divergences between the densities of the observations under the two hypotheses and different system constraints are considered this approach permits to control the average sample number i e the time for taking a decision in a sequential probability ratio test and to asymptotically minimize the probability of miss in a likelihood ratio test the solutions offer an interesting insight in the optimal transmit policies encapsulated in the rank of the code matrix which rules the amount of diversity to be generated as well as in the power allocation policy along the active eigenmodes a study of the region of achievable divergence pairs whose availability permits optimization of a wide range of merit figures is also undertaken a set of numerical results is finally given in order to analyze and discuss the performance and validate the theoretical results

norm estimates related to self commulators abstract for a given self adjoint matrix h with h 1 and tr h 0 we consider the number h which is defined to be the minimum of t 2 for those t satisfying t t h we show that 1 h 2 and that h is close to 2 if h is suitably chosen

choices in the harmonic balance technique we apply the harmonic balance technique in low orders to three types of oscillator model for three equations of the van der pol type with rational nonlinear terms used to model electronic oscillators we examine the choice between a rationalizing before expanding in harmonics and b obtaining fourier coefficients of nonlinear terms alternative b is shown to be more accurate in first order for the models of scott murata and of walker and connelly which apply to circuits with an inverse tangent nonlinear component for these equations in the case of alternative a we find acceptable dependence of the second order corrections on the bifurcation parameter when the harmonic balance method is used to set up a semi classical quantization treatment of a nonlinear conservative oscillator values of energies are slightly improved by the use of alternative b for conservative oscillators with cubic or fifth power forces we compare the standard method using the acceleration equation with an alternative using the energy equation the first is shown to be more accurate in low order

modeling cell to cell spread of hiv 1 with logistic target cell growth abstract in this paper we consider a model containing two modes for hiv 1 infection and spread one is the diffusion limited cell free virus transmission and the other is the direct cell to cell transfer of viral particles we show that the basic reproduction number is underestimated in the existing models that consider only the cell free virus transmission or the cell to cell infection ignoring the other assuming logistic growth for target cells we find that if the basic reproduction number is greater than one the infection can persist and the hopf bifurcation can occur from the positive equilibrium within certain parameter ranges

inequalities for commutators of positive operators abstract it is shown that if a b and x are operators on a complex separable hilbert space such that a and b are compact and positive then the singular values of the generalized commutator a x x b are dominated by those of x a b where is the usual operator norm consequently for every unitarily invariant norm we have a x x b x a b it is also shown that if a and b are positive and x is compact then a x x b max a b x for every unitarily invariant norm moreover if x is positive then the singular values of the commutator a x x a are dominated by those of 1 2 a x x consequently a x x a 1 2 a x x for every unitarily invariant norm for the usual operator norm these norm inequalities hold without the compactness conditions and in this case the first two norm inequalities are the same our inequalities include and improve upon earlier inequalities proved in this context and they seem natural enough and applicable to be widely useful

inequalities for sums and direct sums of hilbert space operators abstract we prove several singular value inequalities and norm inequalities involving sums and direct sums of hilbert space operators it is shown among other inequalities that if x and y are compact operators then the singular values of x y 2 are dominated by those of x y applications of these inequalities are also given

novel matrix singular value inequalities and their applications to uncertain mimo channels novel matrix singular value inequalities are established for a sum product of three matrices their application to the uncertain compound multiple input multiple output mimo channel subject to normed additive uncertainty establishes the saddle point property for a wide range of performance metrics monotonic in the channel singular values including among others the mutual information mmse error exponent and pairwise error probability this in turn implies that the transmission on the eigenmodes of the nominal or worst case channel is also optimal for the whole set of channels under a general power constraint and hence achieves the compound channel capacity the worst case channel turns out to be antiparallel of the nominal one for all these performance metrics an application of these results to beamforming over compound mimo channels is discussed an optimal robust precoder for the uncertain mimo channel is obtained in a closed form under the sum mse criterion and the total power constraint the saddle point property is shown to hold and the optimal strategy is to diagonalize the nominal or worst case channel

optimal transmit receiver design in the presence of signal dependent interference and channel noise optimal detection of a target return contaminated by signal dependent interference as well as additive channel noise requires the design of a transmit pulse f t and a receiver impulse response h t jointly maximizing the output signal to interference plus noise ratio sinr despite the highly nonlinear nature of this problem it has been possible to show that f t may always be chosen minimum phase a full analysis concludes with the construction of an effective numerical procedure for the determination of optimal pairs f h that appears to converge satisfactorily for most values of input sinr extensive simulation reveals that the shape of f t can be a critical factor in particular the performance of a chirp like pulse is often unacceptable especially when clutter and channel noise are low pass dominant and comparable

design of optimized radar codes with a peak to average power ratio constraint this paper considers the problem of radar waveform design in the presence of colored gaussian disturbance under a peak to average power ratio par and an energy constraint first of all we focus on the selection of the radar signal optimizing the signal to noise ratio snr in correspondence of a given expected target doppler frequency algorithm 1 then through a max min approach we make robust the technique with respect to the received doppler algorithm 2 namely we optimize the worst case snr under the same constraints as in the previous problem since algorithms 1 and 2 do not impose any condition on the waveform phase we also devise their phase quantized versions algorithms 3 and 4 respectively which force the waveform phase to lie within a finite alphabet all the problems are formulated in terms of nonconvex quadratic optimization programs with either a finite or an infinite number of quadratic constraints we prove that these problems are np hard and hence introduce design techniques relying on semidefinite programming sdp relaxation and randomization as well as on the theory of trigonometric polynomials providing high quality suboptimal solutions with a polynomial time computational complexity finally we analyze the performance of the new waveform design algorithms in terms of detection performance and robustness with respect to doppler shifts

relative entropy based waveform design for mimo radar detection in the presence of clutter and interference this paper considers the waveform design problem for multiple input multiple output mimo radars in order to improve the detection performance of the systems we assume that target echoes are embedded in signal dependent clutter as well as colored interference considering the optimal neyman pearson detector obtaining waveforms which maximize the detection probability for a fixed value of the probability of false alarm is intractable therefore we employ relative entropy associated with the detection problem as the figure of merit for the waveform design we devise an iterative method based on minorization maximization mm technique to tackle the nonconvex design problem this method also includes a novel trick for replacing a nonconvex constraint set associated with an equivalent form of the design problem with a convex one iteratively the proposed method increases the design metric monotonically and is guaranteed to converge we extend the devised method for using in design with peak to average power ratio par and similarity constraints the method can be applied to both statistical and colocated mimo radars several numerical examples are included to demonstrate the effectiveness of the proposed method

norm inequalities for commutators of positive operators and applications let x y and z be operators on a hilbert space such that x and z are positive it is shown that left xy yz right leqslant rm max left left x right left z right right left y right applications of this commutator inequality are given

singular values norms and commutators abstract let a i b i and x i i 1 n be bounded linear operators on a separable hilbert space such that x i is compact for i 1 n it is shown that the singular values of i 1 n a i x i b i are dominated by those of i 1 n a i b i i 1 n x i where is the usual operator norm among other applications of this inequality we prove that if a and b are self adjoint operators such that a 1 a a 2 and b 1 b b 2 for some real numbers a 1 a 2 b 1 and b 2 and if x is compact then the singular values of the generalized commutator ax xb are dominated by those of max b 2 a 1 a 2 b 1 x x this inequality proves a recent conjecture concerning the singular values of commutators several inequalities for norms of commutators are also given

an information theoretic approach to robust constrained code design for mimo radars the problem of transmit code design in multiple input multiple output mimo radar systems is addressed in this paper the problem is considered in both colocated and widely separated antenna radars in the presence of signal dependent interference and target mobility due to complexity of exact expressions of the optimal detector in the mimo radars information theoretic criteria are employed as design metrics which results in a general form of nonconvex optimization problems in order to tackle the problem a novel technique based on the minorization maximization algorithm is proposed and solutions are presented under practical constraints on the transmit code namely energy constraint peak to average power ratio constraint and similarity constraint furthermore the devised method is extended to be robust against uncertainties of the clutter and interference statistics finally numerical examples are used to show the performance of the proposed technique in different situations

sequence design to minimize the weighted integrated and peak sidelobe levels sequences with low aperiodic autocorrelation sidelobes are well known to have extensive applications in active sensing and communication systems in this paper we first consider the problem of minimizing the weighted integrated sidelobe level wisl which can be used to design sequences with impulse like autocorrelation and a zero or low correlation zone two algorithms based on the general majorization minimization method are developed to tackle the wisl minimization problem with guaranteed convergence to a stationary point the proposed methods are then extended to optimize the ell p norm of the autocorrelation sidelobes which leads to a way to minimize the peak sidelobe level psl criterion all the proposed algorithms can be implemented via the fast fourier transform fft and thus are computationally efficient an acceleration scheme is considered to further accelerate the algorithms numerical experiments show that the proposed algorithms can efficiently generate sequences with virtually zero autocorrelation sidelobes in a specified lag interval and can also produce very long sequences with much smaller psl compared with some well known analytical sequences

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

mimo radar waveform design in colored noise based on information theory in this paper we consider multiple input multiple output mimo radar waveform design in colored noise two information theoretic measures are used as criterions for optimal waveform design under transmitted power constraint the first one is by maximizing the mutual information between target impulse response and target echoes the second one is by maximizing the relative entropy between two hypotheses in the first hypothesis we assume the target is not present in the echoes while in the second hypothesis we assume the target exists in the echoes we derive optimal solutions for both cases interestingly both optimal solutions require that transmitted waveform should match with the target and noise however the optimal solutions of the two problems lead to different power allocation strategies

norm inequalities for sums and differences of positive operators abstract it is shown that if a and b are positive operators on a separable complex hilbert space and if is any unitarily invariant norm then 2 a b 0 0 a b a b 0 0 a a b b a 1 2 b 1 2 a 1 2 b 1 2 a 1 2 b 1 2 a 1 2 b 1 2 when specialized to the usual operator norm this inequality reduces to max a b a 1 2 b 1 2 a b related inequalities for sums and differences of positive operators are obtained and applications of these inequalities to norms of self commutators are also considered

a generalization of the method of harmonic balance a procedure is provided for generalizing the method of harmonic balance to obtain higher order approximations to the periodic solutions of differential equations for two systems one a conservative system and the other nonconservative the procedure is currently being applied to investigate the possible solution behaviors of singular nonlinear oscillators where the usual perturbation methods do not work

cartesian decompositions and schatten norms abstract let t be a hilbert space operator with t a i b where a and b are hermitian we prove sharp inequalities comparing the norms t p with a 2 b 2 1 2 p and a 2 p b 2 p 1 2

an intrinsic method of harmonic analysis for non linear oscillations a perturbation technique abstract an intrinsic method of harmonic analysis for application to problems concerning non linear periodic oscillations is presented the method is designed to overcome the observed shortcomings of the conventional method of harmonic balance and it is described with the aid of an example which was used earlier to demonstrate the inconsistency of the results obtained through the method of harmonic balance the new technique is a perturbation method and it eliminates the danger of omitting any possible contributions of various harmonics to a particular approximation by engaging all the necessary harmonics and excluding the others automatically thefore the new approach yields ordered forms of consistent approximations for the non linear problem without requiring knowledge about the number of harmonics a priori in contrast to the conventional technique

on the practical implication of mutual information for statistical decisionmaking a basic mathematical function that conjoins the two key conceptions of mutual information and bayes risk is defined based on that function some asymptotic theorems that verify an important implication of mutual information in the context of practical bayesian decisionmaking are proven

global stabilty analysis of a classical non conservative system under a follower load abstract the bifurcations critical conditions and global stability of the classical two degree of freedom ziegler s dissipative model under a partial follower load are thoroughly discussed with the aid of a complete non linear dynamic analysis attention is mainly focused on the range of values of the non conservativeness loading parameter for which adjacent equilibria do not exist various characteristic findings are established by studying the nature of the jacobian matrix eigenvalues associated with the above non linear autonomous dissipative system it is found that the system exhibits stable hopf bifurcations global stability for the entire region of non adjacent equilibria while the classical linear stability analysis leads to flutter instability local instability moreover in an explicit general form the significant effect of damping on the critical dynamic bifurcation load is established on the basis of the latter the critical loads for the case of vanishing damping are found to be completely different from those of the classical local stability analysis all findings of this analysis are checked against numerical solution of the equations of motion

diversity integration tradeoffs in mimo detection in this paper a multiple input multiple output mimo detection problem is considered at first we derive the generalized likelihood ratio test glrt for arbitrary transmitted signals and arbitrary time correlation of the disturbance then we investigate design criteria for the transmitted waveforms in both power unlimited and power limited systems and we derive closed form formulas for the probability of false alarm and the detection probability finally we study the interplay among the rank of the optimized space time code i e the number of linearly independent transmitted waveforms the number of transmit diversity paths generated in the signal space and the amount of energy integrated along each path the results confirm that there is an inherent tradeoff between diversity and integration and that no uniformly optimum waveform design strategy exists

comments on the method of harmonic balance in which jacobi elliptic functions are used abstract a harmonic balance method is presented in which jacobi elliptic functions are used in the trial solution instead of circular functions to obtain approximate periodic solutions of the oscillator x f x dot x 0 conditions for the method to work well are the usual ones of the current method of harmonic balance and that x t must pass through zero the procedure for obtaining a higher order approximation is described and in particular two criteria for chosing the elliptic function parameter m are discussed illustrative examples are presented with f being diverse polynomials of x

analytical analysis of the gavrilov guckenheimer bifurcation unfolding in the case of a proportional integral controlled cstr in the field of reactor modeling a single ideal nonisothermal continuous stirred tank reactor is considered as an example of a proportional integral controlled dynamic system the aim is to analyze the normal form theory in the case of a nongeneric gavrilov guckenheimer bifurcation and to make a validity check at least in the related unfolding the observed nongeneric nature of the considered bifurcation is strictly dependent upon the integral controller mode introduction infinitesimal analysis coupled with the study of implicitly defined functions is required to successfully handle such a bifurcation special attention has also been paid to the study of complex dynamic phenomena that may typically originate in the neighborhood of the present bifurcation the presence and the asymptotical stability properties of the rising family of invariant tori have been analytically proved last the quoted analysis is generalized to any three dimensional pi controlled dynamic system thereby showing the intrinsi

how big can the commutator of two matrices be and how big is it typically abstract numerical experiments show that the frobenius norm of the commutator of two large matrices typically clusters sharply around a certain value which moreover is much smaller than one would predict the purpose of this paper is to give a rigorous foundation of this phenomenon we also discuss the question how big the frobenius norm of commutator of the two matrices can actually be

the mimo radar and jammer games the interaction between a smart target and a smart mimo radar is investigated from a game theory perspective since the target and the radar form an adversarial system their interaction is modeled as a two person zero sum game the mutual information criterion is used in formulating the utility functions the unilateral hierarchical and symmetric games are studied and the equilibria solutions are derived

bifurcations associated with a double zero and a pair of pure imaginary eigenvalues interactive static and dynamic bifurcations associated with a nonlinear autonomous system and the stability properties of various solutions are explored attention is focused on the vicinity of a compound critical point where the jacobian of the system exhibits a double zero eigenvalue of index one and a pair of pure imaginary eigenvalues the system under consideration has three independent parameters and depending on the route followed in the parameter space the system may exhibit static bifurcations hopf bifurcations secondary hopf bifurcations and bifurcations into two or three dimensional tori the general analysis is based on a perturbation method which combines an intrinsic harmonic balancing technique with a certain unification procedure this approach leads to bifurcation equations and simplified differential equations governing the local dynamics in the vicinity of the compound critical point a control system is analyzed for illustration