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This paper proposes new solutions for implementing wideband large switch matrices. These solutions are based on crossbar and L-shaped topologies. This paper introduces a high-performance wideband switch cell to build up scalable N x N switch matrices and gives an account of the design, fabrication, and characteristics of the switch cell and a 3 x 3 crossbar switch matrix. The chosen design procedure is seen to be appropriate since it produces valid measured results. In addition, this paper presents an RF microelectromechanical systems L-shaped switch matrix, which indicates less variation of characteristics for certain types of connectivity. It also demonstrates that for a 4 x 4 switch matrix, there is a 50% improvement in insertion loss and phase-shift variation. Index Terms--Microelectromechanical systems (MEMS), RF MEMS, switch, switch matrix and monolithic microwave integrated circuits.

In this paper, a new class of reciprocal-orthogonal parametric (ROP) transforms having 3N/2 independent parameters for a sequence length N that is a power of two is proposed. The basic idea behind the proposed transforms is to appropriately combine a new parametric kernel with that of the well-known Walsh-Hadamard transform that results in a square parametric matrix operator of order N with some very interesting properties. It is shown that the inverse matrix operator of the proposed class of transforms can be easily obtained by taking the reciprocal of each of the entries of the forward matrix and then transposing the resulting matrix. In addition, a simple method is introduced in order to facilitate the generation of the matrix operator of the proposed ROP transforms. This method is then used specifically to construct new classes of unitary and multiplication-free transforms. Many other new transforms, as well some of the existing ones, can be derived from these proposed ROP transforms. An efficient algorithm is developed for a fast computation of the proposed transforms. In view of the availability of this fast algorithm and the property of easily computable inverse transform, the proposed ROP transforms can be used in many transform-based applications, with their independent parameters providing more degrees of freedom such as affording an additional secret key in watermarking and encryption applications. Index Terms--Complex Hadamard matrices, reciprocal-orthogonal parametric (ROP) transforms and matrices, unitary transforms, Waish-Hadamard transform (WHT).

In this paper, we focus on the problem of driving a general network to a selected cluster synchronization pattern by means of a pinning control strategy. Sufficient conditions are presented to guarantee the realization of the cluster synchronization pattern for all initial values. We also show the detailed steps on how to construct the coupling matrix and to modify the control strengths. Moreover, the method of adapting the coupling strength is provided to refine the result. Index Terms--Adaptive adjustment, cluster synchronization, globally asymptotically stable, linearly coupled networks, pinning control.

The properties of first-order optical systems are described paraxially by a ray transfer matrix, also called the ABCD matrix. Here we consider the inverse problem: an ABCD matrix is given, and we look for the minimal optical system that consists of only lenses and pieces of free-space propagation. Similar decompositions have been studied before but without the restriction to these two element types or without an attempt at minimalization. As the main results of this paper, we found that general lossless one-dimensional optical systems can be synthesized with a maximum of four elements and two-dimensional optical systems can be synthesized with six elements at most. OCIS codes: 080.2720, 080.2730, 080.2740, 220.2740.

The robust state estimation problem for a class of uncertain neural networks with time-varying delay is studied in this paper. The parameter uncertainties are assumed to be norm bounded. Based on a new bounding technique, a sufficient condition is presented to guarantee the existence of the desired state estimator for the uncertain delayed neural networks. The criterion is dependent on the size of the time-varying delay and on the size of the time derivative of the time-varying delay. It is shown that the design of the robust state estimator for such neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. Finally, two simulation examples are given to demonstrate the effectiveness of the developed approach. Index Terms--Delay-dependent criteria, global asymptotical stability, linear matrix inequality (LMI), neural networks, robust state estimation, time-varying delay systems, uncertain systems.

In this paper, the precise time-step integration method by step-response and impulsive-response matrices is further developed by expanding the dimension of the matrices so as to avoid computing the particular solutions separately. Two new precise time-step integration algorithms with excitations described by second-order and first-order differential equations are proposed. The first method is a direct extension of the existing algorithms. However, the extended system matrices are not symmetrical. In the second method, the Duhamel integrals are used as the particular solutions. As a result, the responses can be expressed in terms of the given initial conditions and the step-response matrix, the impulsive-response matrix and a newly derived Duhamel-response matrix. The symmetry property of the system matrices can be used in the computation. However, it will first require a calculation of the Duhamel-response matrix and its derivative. To reduce the computational effort, the relation between the Duhamel-response matrix and its derivative is established. A special computational procedure for periodic excitation is also discussed. Numerical examples are given to illustrate the present highly efficient algorithms.

We present a new type of phase-shifting interferometer, which utilizes a polarizing prism to form quadrature phase-shifted fringe patterns onto a single imaging sensor. By changing the direction of linear polarization of the incident light orthogonally, four phase-shined fringe patterns in quadrature are obtained by taking images twice; thus it is possible to reduce phase errors caused by mechanical vibrations and air turbulence that occur in temporal phase-shifting interferometers. We present the principle of this interferometer with its theoretical analysis, using the Jones matrix, along with experimental results. OCIS codes: 120.3180, 120.5050, 120.2650, 120.4820, 120.6660.

A strategy combining autocorrelation matrices and ultrahigh resolution mass spectrometry (MS) was developed to optimize the characterization of discriminating ions highlighted by metabolomics. As an example, urine samples from rats treated with phenobarbital (PB) were analyzed by ultrahigh-pressure chromatography with two different eluting conditions coupled to time-of-flight mass spectrometric detection in both the positive and negative electrospray ionization modes. Multivariate data analyses were performed to highlight discriminating variables from several thousand detected signals: a few hundred signals were found to be affected by PB, whereas a few tenths of them were linked to its metabolism. Autocorrelation matrices were then applied to eliminate adduct and fragment ions. Finally, the characterization of the ions of interest was performed with ultrahigh-resolution mass spectrometry and sequential [MS.sup.n] experiments, by using a LC-LTQ-Orbitrap system. The use of different eluting conditions was shown to drastically impact on the chromatographic retention and ionization of compounds, thus providing a way to obtain more exhaustive metabolic fingerprints, whereas autocorrelation matrices allowed one to focus the identification work on the most relevant ions. By using such an approach, 14 PB metabolites were characterized in rat urines, some of which have not been reported in the literature.

We derive an analytic expression for the local field intensity in an aggregate of particles illuminated by diffuse light (T matrix formalism). To be precise, the diffuse light average is obtained by averaging the electromagnetic response from plane waves over all possible incident field direction polarizations. We applied this new averaging formula to analyze variations in the electromagnetic couplings between two isotropic spheres as a function of their separation distance. The numerical calculations were performed with the recursive centered T matrix algorithm (RCTMA), one of the known analytical solutions of the multiple scattering equation of light. Illustrative calculations clearly demonstrate that diffuse averaging has a large smoothing effect on the strong angular and local variations in the field intensities that are omnipresent in orientation fixed calculations. We believe that this formalism can be a valuable tool in the analysis of electromagnetic couplings in dense random heterogeneous media, in which light propagation is dominated by a scalar diffusion behavior. OCIS codes: 260.2110, 290.4210, 290.5825, 290.5850.

For electrically large complex electromagnetic (EM) scattering problems, huge memory is often required for most EM solvers, which is too difficult to be handled by a personal computer (PC) even a workstation. Although the multilevel fast multipole algorithm (MLFMA) effectively deals with electrically large problems to some extent, it is still time and memory consuming for very large objects. In order to further reduce the CPU time and the memory requirement, a hybrid algorithm, based on the overlapped domain decomposition method for integral equations (IE-ODDM), MLFMA and block-diagonal, incomplete lower and upper triangular matrices (DILU) preconditioner, is proposed for the analysis of electrically large problems. The dominant memory requirement for plane wave expansions in the three processes of aggregation, translation and disaggregation in the MLFMA is drastically reduced by the first two techniques. The iterative procedure for each overlapped subdomain solved by the MLFMA is effectively sped up by the DILU preconditioner. After integrating these techniques, the proposed hybrid algorithm is more efficient in computing time and memory requirement compared to the conventional MLFMA and is more suitable for analyzing very large EM scattering problems. Enough accurate solution can be obtained within quite a few outer iterations, where an outer iteration means a complete sweep for all the subdomains. Some numerical examples are presented to demonstrate its validity and efficiency. Index Terms--Block-diagonal, incomplete lower and upper triangular matrices (DILU) preconditioner, electromagnetic (EM) scattering, integral equations (IE), multilevel fast multipole algorithm (MLFMA), overlapped domain decomposition method (ODDM).

A depolarization scalar metric for Mueller matrices, named Q(M), is derived from the degree of polarization. Q(M) has been recently reported, and it has been deduced from the nine bilinear constraints between the sixteen elements of the Mueller-Jones matrix. We discuss the relations between Q(M) and the depolarization index. OCIS codes: 120.2130, 260.5430.

In this paper, we propose and study a general array model of coupled delayed neural networks with hybrid coupling, which is composed of constant coupling, discrete-delay coupling, and distributed-delay coupling. Based on the Lyapunov functional method and Kronecker product properties, several sufficient conditions are established to ensure global exponential synchronization based on the design of the coupling matrices, the inner linking matrices, and/or some free matrices representing the relationships between the system matrices. The conditions are expressed within the framework of linear matrix inequalities, which can be easily computed by the interior-point method. In addition, a typical chaotic cellular neural network is used as the node in the array to illustrate the effectiveness and advantages of the theoretical results. Index Terms--Delayed neural network, distributed-delay coupling, global exponential synchronization, hybrid coupling, Kronecker product, Lyapunov-Krasovskii functional.

A hybrid method is developed to solve the vector radiative transfer equation (VRTE) in a three-dimensional atmosphere-ocean system (AOS). The system is divided into three parts: the atmosphere, the dielectric interface, and the ocean. The Monte Carlo method is employed to calculate the impulse response functions (Green functions) for the atmosphere and ocean. The impulse response function of the dielectric interface is calculated by the Fresnel formulas. The matrix operator method is then used to couple these impulse response functions to obtain the vector radiation field for the AOS. The primary advantage of this hybrid method is that it solves the VRTE efficiently in an AOS with different dielectric interfaces while keeping the same atmospheric and oceanic conditions. For the first time, we present the downward radiance field in an ocean with a sinusoidal ocean wave. OCIS codes: 010.5620, 290.4210, 290.7050, 010.1290, 010.4450.

This paper analyzes MIMO systems with multichannel beamforming in Ricean fading. Our results apply to a wide class of multichannel systems which transmit on the eigenmodes of the MIMO channel. We first present new closedform expressions for the marginal ordered eigenvalue distributions of complex noncentral Wishart matrices. These are used to characterize the statistics of the signal to noise ratio (SNR) on each eigenmode. Based on this, we present exact symbol error rate (SER) expressions. We also derive closed-form expressions for the diversity order, array gain, and outage probability. We show that the global SER performance is dominated by the subchannel corresponding to the minimum channel singular value. We also show that, at low outage levels, the outage probability varies inversely with the Ricean K-factor for cases where transmission is only on the most dominant subchannel (i.e. a singlechannel beamforming system). Numerical results are presented to validate the theoretical analysis. Index Terms--Multiple-input multiple-output systems, Ricean fading, Wishart matrices, multichannel beamforming.

Source coding theorems and Shannon rate-distortion functions were studied for the discrete-time Wiener process by Berger and generalized to nonstationary Gaussian autoregressive processes by Gray and by Hashimoto and Arimoto. Hashimoto and Arimoto provided an example apparently contradicting the methods used in Gray, implied that Gray's rate-distortion evaluation was not correct in the nonstationary case, and derived a new formula that agreed with previous results for the stationary case and held in the nonstationary case. In this correspondence it is shown that the rate-distortion formulas of Gray and Hashimoto and Arimoto are in fact consistent and that the example of Hashimoto and Arimoto does not form a counterexample to the methods or results of the earlier paper. Their results do provide an alternative, but equivalent, formula for the rate-distortion function in the nonstationary case and they provide a concrete example that the classic Kolmogorov formula differs from the autoregressive formula when the autoregressive source is not stationary. Some observations are offered on the equality of the asymptotic distributions of the eigenvalues of the sequence of inverse autocorrelation matrices of possibly nonstationary autoregressive processes and of their Toeplitz approximations. Index Terms--Nonstationary Gaussian autoregressive sources, rate-distortion functions, Toeplitz matrices.

This paper is a tutorial on Grobner bases and a survey on the applications of Grobner bases in the broad field of signals and systems. A reasonably detailed review is given of several fundamental theoretical issues that occur in the use of Grobner bases in multidimensional signals and systems applications. These topics include the primeness of multivariate polynomial matrices, multivariate unimodular polynomial matrix completion, and prime factorization of multivariate polynomial matrices. A brief review is also presented on the wide-ranging applications of Griibner bases in multidimensional as well as one-dimensional circuits, networks, control, coding, signals, and systems and other related areas like robotics and applied mechanics. The impact and scope of Grobner bases in signals and systems are highlighted with respect to what has already been accomplished as a stepping stone to expanding future research. Index Terms--Circuits and systems, Grobner bases, matrix factorization, multidimensional systems, multivariate polynomial, signal processing.

In the simplest case, the matrix inversion lemma gives an explicit formula of the inverse of a positive-definite matrix A added to a rank-one matrix [bb.sup.H] as follows:[(A + [bb.sup.H]).sup.-1] = [A.sup.-1] - [A.sup.-1]b[(1 + [b.sup.H][A.sup.-1]b).sup.-1] [b.sup.H[ [A.sup.-1]. It is well known in the literature that this formula is very useful to develop a recursive least-squares algorithm for the recursive identification of linear systems or the design of adaptive filters. We extend this result to the case when the matrix A is singular and present a matrix pseudo-inversion lemma along with some illustrative examples. Such a singular case may occur in a situation where a given problem is overdetermined in the sense that it has more equations than unknowns. This iemma is important in its own right, but in order to show the usefulness of the lemma, we apply it to develop an adaptive super-exponential algorithm for the blind deconvolution of multi-input multi-output systems. Index Terms--Adaptive super-exponential algorithm (SEA), matrix pseudo-inversion lemma, recursive algorithms.

A constructive procedure for factoring a polynomial paraunitary matrix as a product of atomic paraunitary matrices is considered. The generic form of the paraunitary factors results from the use of projection matrices. In the univariate case, the factorization carried out in the z-transform domain collapses to other univariate paraunitary matrix factorization methods. In the multivariate case, the generic factor is constructed based on the assumption of its existence. Nontrivial examples for multiband univariate, bivariate, and trivariate cases are given to illustrate the simple and straightforward algorithmic implementation. Index Terms--Multivariate polynomial paraunitary matrix factorization, projection operators.

This paper proposes a new algorithm to simplify the multiple valued logic (MVL) decision diagrams. This algorithm is based on a new level coupling rule. By changing the designer's perspective towards the design, this rule can make further simplification possible. In most of state of the art designs, the decision diagram plays a serious role in the implementation of the logical functions. The proposed algorithm uses the new level coupling rule and combines it with the existing ones, presenting a new method in simplifying and implementing the basic decision diagram. Keywords: Multiple-Valued Logic (MVL), Matrix Computation, Directed Acyclic Graph, Free Decision Diagram (FDD), Ordered Decision Diagram (ODD) Design Automation., INTERODUCTION Using the decision diagram is a very efficient and common method to illustrate the switching functions. Additionally using this method compared to the other methods has many advantages such [...]

The applicability of different approximate methods proposed to determine the paraxial properties of the gradient-index (GRIN) distribution resembling that of the human lens, by means of the system ABCD matrix, is tested. Thus, the parabolic-ray-path approximation has been extended to provide the ABCD matrix of a slab lens comprised of a rotationally GRIN medium. The results show that this method has good numerical stability, and it is also the easiest one in determining the Gaussian constants of the human lens GRIN profile. OCIS codes: 330.4460, 330.5370, 080.2710, 080.2730.

In medical image processing, many filters have been developed to enhance certain structures in 3-D data. In this paper, we propose to use pattern recognition techniques to design more optimal filters. The essential difference with previous approaches is that we provide a system with examples of what it should enhance and suppress. This training data is used to construct a classifier that determines the probability that a voxel in an unseen image belongs to the target structure(s). The output of a rich set of basis filters serves as input to the classifier. In a feature selection process, this set is reduced to a compact, efficient subset. We show that the output of the system can be reused to extract new features, using the same filters, that can be processed by a new classifier. Such a multistage approach further improves performance. While the approach is generally applicable, in this work the focus is on enhancing pulmonary fissures in 3-D computed tomography (CT) chest scans. A supervised fissure enhancement filter is evaluated on two data sets, one of scans with a normal clinical dose and one of ultra-low dose scans. Results are compared with those of a recently proposed conventional fissure enhancement filter. It is demonstrated that both methods are able to enhance fissures, but the supervised approach shows better performance; the areas under the receiver operating characteristic (ROC) curve are 0.98 versus 0.90, for the normal dose data and 0.97 versus 0.87 for the ultra low dose data, respectively. Index Terms--Classifier, enhancement, Hessian matrix, pulmonary fissures, supervised.

The unidirectional grating-assisted codirectional coupler (U-GACC) has recently been proposed. This unique structure permits irreversible coupling between orthogonal waveguide eigenmodes by means of simultaneous modulation of both the real and imaginary parts of the refractive index in the coupling region. Analysis of the U-GACC has until now relied on coupled mode theory, which can be restrictive in its application as a design tool. We analyze the U-GACC by the transfer matrix method, which demonstrates in a simple fashion why the device operates in a unidirectional manner. In addition, we show that for all practical designs, there is a limit to the minimum cross talk between outputs, a phenomenon that has not been previously identified. OCIS codes: 060.1810, 130.3120, 250.4480.

Shift-full-rank (SFR) matrices are matrices that have full row rank no matter how their rows are shifted. SFR matrices have been used lately as generator matrices for a family of space-time trellis codes to achieve full diversity in asynchronous cooperative communications, where the numbers of columns of the SFR matrices correspond to the memory sizes of the trellis codes. A systematic construction of SFR matrices, including the shortest (square) SFR (SSFR) matrices, has been also previously proposed. In this paper, we study a variation of SFR matrices with a relaxed condition: limited-shift-full-rank (LT-SFR) matrices, i.e., the matrices that have full row rank no matter how their rows are shifted as long as the shifts are within some range called delay tolerance. As the generator matrices for the previously proposed space-time trellis codes, LT-SFR matrices can guarantee asynchronous full diversity of the corresponding codes when the timing errors are within the delay tolerance. Therefore, due to the relaxed condition imposed on LT-SFR matrices, more eligible generator matrices than SFR matrices become available. Index Terms--Asynchronous cooperative communications, cooperative diversity, distributed space-time coding, limited-shift-full-rank (LT-SFR) matrices, relay networks, shift-full-rank (SFR) matrices.

Two methods used to retrieve Mueller matrices from intensity measurements are revisited. It is shown that with symmetry or orthogonality considerations, numerical inversions of polarimetric equations can be avoided. With the obtained analytical formulas, noise propagation can be analyzed. If the intensity noise is a Gaussian white noise, the noise of Mueller matrices features remarkable properties. Mueller components are mutually correlated according to a scheme that involves decomposition into four blocks of 2 x 2 matrices. Variances are unequally distributed: the middle 2 x 2 block has the highest variance, the element on the bottom right has the lowest. These characteristics have been validated on experimental Mueller images of the free space. OCIS codes: 110.4280, 120.5410, 260.5430.

A criterion for the elimination of limit cycles in direct form digital filters utilizing single saturation overflow nonlinearity is presented. The criterion takes the form of linear matrix inequality and, hence, is computationally tractable. An example showing the effectiveness of the present criterion is given. Index Terms--Asymptotic stability, digital filters, finite wordlength effects, limit cycles, nonlinear systems.

Ionomeric polymers are a promising class of intelligent material which exhibit electromechanical coupling similar to that of piezoelectric bimorphs, lonomeric polymers are much more compliant than piezoelectric ceramics or polymers and have been shown to produce actuation strain on the order of 2% at operating voltages between 1 V and 3 V (Akle et al., 2004, Proceedings IMECE). Their high compliance is advantageous in low force sensing configurations because ionic polymers have a very little impact on the dynamics of the measured system. Here we present a variational approach to the dynamic modeling of structures which incorporate ionic polymer materials. To demonstrate the method a cantilever beam model is developed using this variational approach. The modeling approach requires a priori knowledge of three empirically determined material properties: elastic modulus, dielectric permittivity, and effective strain coefficient. Previous work by Newbury and Leo has demonstrated that these three parameters are strongly frequency dependent in the range between less than 1 Hz to frequencies greater than 1 kHz. Combining the frequency-dependent material parameters with the variational method produces a second-order matrix representation of the structure. The frequency dependence of the material parameters is incorporated using a complex-property approach similar to the techniques for modeling viscoelastic materials. A transducer is manufactured and the method of material characterization is applied to determine the mtaerial properties. Additional experiments are performed on this transducer and both the material and structural model are validated. Finally, the model is shown to predict sensing response very well in comparison to experimental results, which supports the use of an energy-based variational approach for modeling ionomeric polymer transducers. [DOI: 10.1115/1.2424973]

A method for free vibration of 3D space frame structures employing transfer dynamic stiffness matrix (TDSM) method based on Euler-Bernoulli beam theory is developed in this paper. The exact TDSM of each member is assembled to obtain the system matrix that is frequency dependent. All free vibration eigensolutions including coincident roots for the characteristic equation can be obtained to any desired accuracy using the algorithm developed by Wittrick and William~ (1971, 'A General Algorithm for Computing Natural Frequencies of Elastic Structures,' Q. J. Mech. Appl. Math., 24, pp. 263-284). Exact eigenfunction of structures can then be computed using the dynamic shape function and the corresponding eigenvector. The results showed good agreement with those computed by finite element method. [DOI: 10.1115/1.28273661

In this correspondence, we construct new self-dual codes over [F.sub.4], [F.sub.5], [F.sub.7] with larger minimum weights than the previously known self-dual codes, using construction methods based on circulant and negacirculant matrices. In particular, a self-dual [36, 18, 13] code over [F.sub.7] is constructed which has a larger minimum weight than the previously known [36, 18] codes. Index Terms--Circulant matrix, negacirculant matrix, nonbinary codes, self-dual codes.

We extend the Enestrom-Kakeya theorem and its refinement by Hurwitz to polynomial matrices H(z) with positive semidefinite coefficients. We determine an annular region containing the zeros of det H(z). A stability result for systems of linear difference equations is given as an application. Index Terms--Block companion matrix, Enestrom-Kakeya theorem, polynomial matrices, root location, system of difference equations, zeros of polynomials.

In this note, we point out that the results given in the paper by Wu and Cui (2007) can be obtained by using the results given in Lu et al. (2003). Moreover, the results given in the second paper are much stronger under less restrictive conditions. Index Terms--Delayed neural networks, equilibrium point, global exponential stability, linear matrix inequality (LMI).