theory and lattice structure of complex paraunitary filterbanks with filters of hermitian symmetry antisymmetry properties the theory of the real coefficient linear phase filterbank lpfb is extended to the complex case in two ways leading to two generalized classes of m channel filterbanks one is the symmetric antisymmetric filterbank safb where all filters are symmetric or antisymmetric the other is the complex linear phase filterbank clpfb where all filters are hermitian symmetric or hermitian antisymmetric and hence have the linear phase property necessary conditions on the filter symmetry polarity and lengths for the existence of permissible solutions are investigated complete and minimal lattice structures are developed for the paraunitary safb and paraunitary clpfb where the channel number m is arbitrary even or odd and the subband filters could have different lengths with the elementary unitary matrices in the structure of the paraunitary safb constrained to be real and orthogonal the structure covers the most general real coefficient paraunitary lpfbs compared with the existing results the number of parameters is reduced significantly

the calderon problem with partial data in this paper we improve an earlier result by bukhgeim and uhlmann 1 by showing that in dimension n 3 the knowledge of the cauchy data for the schr nodinger equation measured on possibly very small subsets of the boundary determines uniquely the potential we follow the general strategy of 1 but use a richer set of solutions to the dirichlet problem this implies a similar result for the problem of electrical impedance tomography which consists in determining the conductivity of a body by making voltage and current measurements at the boundary

boundary filter optimization for segmentation based subband coding this paper presents boundary optimization techniques for the nonexpansive decomposition of arbitrary length signals with multirate filterbanks both biorthogonal and paraunitary filterbanks are considered the paper shows how matching moments and orthonormality can be imposed as additional conditions during the boundary filter optimization process it provides direct solutions to the problem of finding good boundary filters for the following cases a biorthogonal boundary filters with exactly matching moments and b orthonormal boundary filters with almost matching moments with the proposed methods numerical optimization is only needed if orthonormality and exactly matching moments are demanded the proposed direct solutions are applicable to systems with a large number of subbands and or very long filter impulse responses design examples show that the methods allow the design of boundary filters with good frequency selectivity

an electromagnetic inverse problem in chiral media we consider the inverse boundary value problem for maxwell s equations that takes into account the chirality of a body in r3 more precisely we show that knowledge of a boundary map for the electromagnetic fields determines the electromagnetic parameters namely the conductivity electric permittivity magnetic permeability and chirality in the interior we rewrite maxwell s equations as a first order perturbation of the laplacian and construct exponentially growing solutions and obtain the result in the spirit of complex geometrical optics

perfect reconstruction fir filter banks some properties and factorizations perfect reconstruction finite impulse response fir filter banks are analyzed both in the z transform and time domains showing the alternatives between designs in the two domains various classes of perfect reconstruction schemes are indicated and relations between previously known systems are given windowed modulated filter banks with low computational complexity and perfect reconstruction are shown new factorizations of polyphase filter matrices leading in particular to linear phase filters are given the computational complexity and the architecture of the new structures are indicated

improving the precision of noisy oscillators abstract we consider how the period of an oscillator is affected by white noise with special attention given to the cases of additive noise and parameter fluctuations our treatment is based upon the concepts of isochrons which extend the notion of the phase of a stable periodic orbit to the basin of attraction of the periodic orbit and phase response curves which can be used to understand the geometry of isochrons near the periodic orbit this includes a derivation of the leading order effect of noise on the statistics of an oscillator s period several examples are considered in detail which illustrate the use and validity of the theory and demonstrate how to improve a noisy oscillator s precision by appropriately tuning system parameters or operating away from a bifurcation point it is also shown that appropriately timed impulsive kicks can give further improvements to oscillator precision

analysis synthesis techniques for subband image coding analysis synthesis systems designed for low bit rate image coding their impact on overall system quality and their computational complexity are discussed the investigation focuses on the design of analysis synthesis systems for image coding and the perceptual impact of these systems at low bit rates two objectives are emphasized in developing these systems confining the total size of the subband images to be equal to the original image size and designing the filters so that perceptual distortion is not introduced by the analysis synthesis system methods based on circular convolution and symmetric extensions are developed and discussed in detail the theory design and implementation of both recursive and nonrecursive filtering systems are discussed methods are introduced which display advantages over conventional quadrature mirror filter based approaches

on m channel linear phase fir filter banks and application in image compression this paper investigates the theory and structure of a large subclass of m channel linear phase perfect reconstruction fir filter banks systems with analysis and synthesis filters of length l sub i k sub i m spl beta where spl beta is an arbitrary integer 0 spl les spl beta m and k sub i is any positive integer for this subclass of systems we first investigate the necessary conditions for the existence of linear phase perfect reconstruction filter banks lpprfbs next we develop a complete and minimal factorization for all even channel linear phase paraunitary systems the most general lapped orthogonal transforms to date finally several design examples as well as comparisons with previous generalized lapped orthogonal transforms genlots in image compression are presented to confirm the validity of the theory

filters for distortion free two band multirate filter banks in this paper conditions are given for a two band multi rate filter bank to be alias free and to have a unity frequency response it is shown that the class of quadrature mirror filters qmf s that satisfies these conditions is quite limited a class of filters which does satisfy these conditions is given and a simple procedure for designing filters from this class is presented with an example

control and synchronization of neuron ensembles synchronization of oscillations is a phenomenon prevalent in natural social and engineering systems controlling synchronization of oscillating systems is motivated by a wide range of applications from surgical treatment of neurological diseases to the design of neurocomputers in this paper we study the control of an ensemble of uncoupled neuron oscillators described by phase models we examine controllability of such a neuron ensemble for various phase models and furthermore study the related optimal control problems in particular by employing pontryagin s maximum principle we analytically derive optimal controls for spiking single and two neuron systems and analyze the applicability of the latter to an ensemble system finally we present a robust computational method for optimal control of spiking neurons based on pseudospectral approximations the methodology developed here is universal to the control of general nonlinear phase oscillators

numerical resolution of an electromagnetic inverse medium problem at fixed frequency the aim of this paper is to solve numerically the inverse problem of determining the complex refractive index of an electromagnetic medium from partial boundary field measurements at a fixed frequency the governing equations are the time harmonic maxwell equations formulated in electric field in a two dimensional bounded domain we express the inverse problem as the minimization of a cost function representing the difference between the measured and predicted fields our numerical reconstruction algorithm combines the bfgs method and an iterative process called the adaptive eigenspace inversion the unknown complex coefficient is expanded in terms of eigenfunctions of an elliptic operator both the eigenspace and the mesh are iteratively adapted during the minimization procedure numerical experiments illustrate the performance of the reconstruction for various configurations

type i membranes phase resetting curves and synchrony type i membrane oscillators such as the connor model connor et al 1977 and the morris lecar model morris and lecar 1981 admit very low frequency oscillations near the critical applied current hansel et al 1995 have numerically shown that synchrony is difficult to achieve with these models and that the phase resetting curve is strictly positive we use singular perturbation methods and averaging to show that this is a general property of type i membrane models we show in a limited sense that so called type ii resetting occurs with models that obtain rhythmicity via a hopf bifurcation we also show the differences between synapses that act rapidly and those that act slowly and derive a canonical form for the phase interactions

scale free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations we consider elliptic differential operators on either the entire euclidean space rd or subsets consisting of a cube l of integer length l for eigenfunctions of the operator and more general solutions of elliptic differential equations we derive several quantitative unique continuation results the first result is of local nature and estimates the vanishing order of a solution the second is a sampling result and compares the l2 norm of a solution over a union of equidistributed balls in space with the l2 norm on the entire space in the case where the space rd is replaced by a finite cube l we derive similar estimates particular features of our bound are that they are uniform as long as the coefficients of the operator are chosen from an appropriate ensemble they are quantitative and explicit with respect to the radius and they are l independent and stable under small shifts of the balls our proof applies to second order terms which have slowly varying coefficients on the relevant length s

generalized unequal length lapped orthogonal transform for subband image coding generalized linear phase lapped orthogonal transforms with unequal length basis functions gullots are considered the length of each basis of the proposed gullot can be different from each other whereas all the bases of the conventional genlot are of equal length in general for image coding application the long basis for a low frequency band and the short basis for a high frequency one are desirable to reduce the blocking and the ringing artifact simultaneously therefore the gullot is suitable especially for a subband image coding in order to apply the gullot to a subband image coding we also investigate the size limited structure to process the finite length signal which is important in practice finally some design and image coding examples are shown to confirm the validity of the proposed gullot

linear phase paraunitary filter banks theory factorizations and designs m channel maximally decimated filter banks have been used in the past to decompose signals into subbands the theory of perfect reconstruction filter banks has also been studied extensively nonparaunitary systems with linear phase filters have also been designed the authors study paraunitary systems in which each individual filter in the analysis synthesis banks has linear phase specific instances of this problem have been addressed by other authors and linear phase paraunitary systems have been shown to exist this property is often desirable for several applications particularly in image processing they begin by answering several theoretical questions pertaining to linear phase paraunitary systems next they develop a minimal factorization for a large class of such systems this factorization will be proved to be complete for even m further they structurally impose the additional condition that the filters satisfy pairwise mirror image symmetry in the frequency domain this significantly reduces the number of parameters to be optimized in the design process they then demonstrate the use of these filter banks in the generation of m band orthonormal wavelets several design examples are also given to validate the theory

a quantitative carleman estimate for second order elliptic operators we prove a carleman estimate for elliptic second order partial differential expressions with lipschitz continuous coefficients the carleman estimate is valid for any complex valued function u w2 2 with support in a punctured ball of arbitrary radius the novelty of this carleman estimate is that we establish an explicit dependence on the lipschitz and ellipticity constants the dimension of the space and the radius of the ball in particular we provide a uniform and quantitative bound on the weight function for a class of elliptic operators given explicitly in terms of ellipticity and lipschitz constant

a development of symmetric extension method for subband image coding describes the development of a technique for subband image coding called the symmetric extension method which utilizes the nature of a symmetrically extended image to achieve high quality coding there are however some restrictions on the usable subband coding system the development is done based on the property of a symmetrically extended signal in the analysis process to remove the restriction the behavior of the sequence after two processes filtering and decimation is examined and formulated the development extends the application area of the technique

the mean field theory of a q state neural network model the mean field equations of a q state clock neural network model are derived in the replica symmetric approximation using the replica method these equations are studied for the cases q 2 3 4 and q to infinity it is shown that an infinite number of patterns can be stored in the network even in the limit q to infinity the phase diagram and storage capacity of the network are calculated and the information content considered although the overlap achieved with a nominated pattern is shown to decrease as q increases the information stored in the network is shown to increase

inverse problems for the anisotropic maxwell equations we prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time harmonic maxwell equations in certain anisotropic settings we give a uniqueness result in the inverse problem for maxwell equations on an admissible riemannian manifold and a uniqueness result for maxwell equations in euclidean space with admissible matrix coefficients the proofs are based on a new fourier analytic construction of complex geometrical optics solutions on admissible manifolds and involve a proper notion of uniqueness for such solutions

class ii neurons display a higher degree of stochastic synchronization than class i neurons we describe the relationship between the shape of the phase resetting curve prc and the degree of stochastic synchronization observed between a pair of uncoupled general oscillators receiving partially correlated poisson inputs in addition to inputs from independent sources we use perturbation methods to derive an expression relating the shape of the prc to the probability density function pdf of the phase difference between the oscillators we compute various measures of the degree of synchrony and cross correlation from the pdf s and use the same to compare and contrast differently shaped prcs with respect to their ability to undergo stochastic synchronization since the shape of the prc depends on underlying dynamical details of the oscillator system we utilize the results obtained from the analysis of general oscillator systems to study specific models of neuronal oscillators it is shown that the degree of stochastic synchronization is controlled both by the firing rate of the neuron and the membership of the prc type i or type ii it is also shown that the circular variance for the integrate and fire neuron and the generalized order parameter for a hippocampal interneuron model have a nonlinear relationship to the input correlation

lattice structure for regular paraunitary linear phase filterbanks and m band orthogonal symmetric wavelets parauninary linear phase pulp m channel uniform filterbanks which are also known as the generalized lapped orthogonal transforms genlots can be designed and implemented using lattice structures this paper discusses how to impose regularity constraints onto the lattice structure of pulp filterbanks these conditions are expressed in term of the rotation angles of the lattice components by which the resulting filterbanks are guaranteed to have one or two degrees of regularity iterating these new regular filterbanks on the lowpass subband generates a large family of symmetric m band orthonormal wavelets design procedures with many design examples are presented smooth interpolation using regular pulp filterbanks is illustrated through image coding experiments where the novel m band wavelets consistently yield smoother reconstructed images and better perceptual quality

generalized symmetric extension for size limited multirate filter banks a multirate mr filter bank is called size limited if the total number of output samples equals the number of input samples a method called symmetric extension improved performance in subband image compression systems compared to the earlier method of circular convolution however the symmetric extension method was developed only for two band uniform filter banks and required even length linear phase analysis filters the authors generalize the symmetric extension method to the m band possibly nonuniform filter banks where m spl ges 2 the length restriction on the analysis filters is relaxed

boundary operation of 2 d nonseparable linear phase paraunitary filter banks this paper proposes a boundary operation technique of 2 d nonseparable linear phase paraunitary filter banks ns lppufbs for size limitation the proposed technique is based on a lattice structure consisting of the 2 d separable block discrete cosine transform and nonseparable support extension processes the bases are allowed to be anisotropic with the fixed critically subsampling overlapping orthogonal symmetric real valued and compact support properties first the blockwise implementation is developed so that the basis images can be locally controlled the local control of basis images is shown to maintain orthogonality this property leads a basis termination bt technique as a boundary operation the technique overcomes the drawback of ns lppufbs that the popular symmetric extension method is invalid through some experimental results of diagonal texture coding the significance of the bt is verified

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

corrigendum self dual instantons and holomorphic curves we correct two mistakes in 1 the first concerns the exponential decay in the proof of theorem 7 4 and the second concerns the bubbling argument in the proof of theorem 9 1

limiting carleman weights and anisotropic inverse problems in this article we consider the anisotropic calderon problem and related inverse problems the approach is based on limiting carleman weights introduced in kenig et al ann math 165 567 591 2007 in the euclidean case we characterize those riemannian manifolds which admit limiting carleman weights and give a complex geometrical optics construction for a class of such manifolds this is used to prove uniqueness results for anisotropic inverse problems via the attenuated geodesic ray transform earlier results in dimension n 3 were restricted to real analytic metrics

measurement of infinitesimal phase response curves from noisy real neurons we sought to measure infinitesimal phase response curves iprcs from rat hippocampal ca1 pyramidal neurons it is difficult to measure iprcs from noisy neurons because of the dilemma that either the linearity or the signal to noise ratio of responses to external perturbations must be sacrificed to overcome this difficulty we used an iprc measurement model formulated as the langevin phase equation lpe to extract iprcs in the bayesian scheme we then simultaneously verified the effectiveness of the measurement model and the reliability of the estimated iprcs by demonstrating that lpes with the estimated iprcs could predict the stochastic behaviors of the same neurons whose iprcs had been measured when they were perturbed by periodic stimulus currents our results suggest that the lpe is an effective model for real oscillating neurons and that many theoretical frameworks based on it may be applicable to real nerve systems

m channel nonlinear phase filter banks in image compression structure design and signal extension this paper describes a transform coding technique based on m channel perfect reconstruction filter banks with a nonlinear phase in contrast with linear phase filter banks the nonlinearity provides an extra degree of freedom that can be used to design a more efficient transform we present new lattice structures of paraunitary and perfect reconstruction biorthogonal filter banks which can be implemented with a lower computational complexity and or represented by a few free parameters through the decomposition of the lattice blocks and the displacement across the delay block we further discuss a smooth extension method for nonlinear phase filter banks to obtain a nonexpansive transform the promise of our proposed approaches is demonstrated through several design examples extended signals and compression results

symmetric extension methods for m channel linear phase perfect reconstruction filter banks the symmetric extension method has been shown to he an efficient way for subband processing of finite length sequences this paper presents an extension of this method to general linear phase perfect reconstruction filter banks we derive constraints on the length and symmetry polarity of the permissible filter banks and propose a new design algorithm in the algorithm different symmetric sequences are formulated in a unified form based on the circular symmetry framework the length constraints in symmetrically extending the input sequence and windowing the subband sequences are investigated the effect of shifting the input sequence is included when the algorithm is applied to equal length filter banks we explicitly show that symmetric extension methods can always be constructed to replace the circular convolution approach

electromagnetic inverse problems and generalized sommerfeld potentials in this article we study the inverse boundary value problem for maxwell s equation that is we determine the scalar permeability permissibility and conductivity of a body from electromagnetic field measurements outside the body in this paper the problem is approached by using certain generalized sommerfeld potentials that are shown to satisfy a vector valued schrodinger equation by using these potentials the inverse boundary value problem is reduced to the problem of determining the potential of this second order operator further it is shown that the electromagnetic material parameters can be determined by using electric or magnetic dipole point sources only

structures for m channel perfect reconstruction fir qmf banks which yield linear phase analysis filters the authors develop structures for fir finite impulse response perfect reconstruction qmf quadrature mirror filter banks which cover a subclass of systems that yield linear phase analysis filters for arbitrary m the parameters of these structures can be optimized to design analysis filters with minimum stopband energy which at the same time have linear phase and satisfy the perfect reconstruction property if there are m subbands then depending on whether the coefficients h sub k n of each analysis filter are symmetric or antisymmetric several combinations of filter banks are possible some of these permit perfect reconstruction and some do not for a given m the authors develop a formula for the number of combinations for a subclass of linear phase perfect reconstruction structures as an example they elaborate on a perfect reconstruction linear phase lattice structure for three channels the lattice structure is such that regardless of the parameter values the qmf bank enjoys the perfect reconstruction property while at the same time the analysis filters have linear phase a design example is presented along with tables of impulse response coefficients

synchronization in networks of excitatory and inhibitory neurons with sparse random connectivity in model networks of e cells and i cells excitatory and inhibitory neurons respectively synchronous rhythmic spiking often comes about from the interplay between the two cell groups the e cells synchronize the i cells and vice versa under ideal conditions homogeneity in relevant network parameters and all to all connectivity for instance this mechanism can yield perfect synchronization we find that approximate imperfect synchronization is possible even with very sparse random connectivity the crucial quantity is the expected number of inputs per cell as long as it is large enough more precisely as long as the variance of the total number of synaptic inputs per cell is small enough tight synchronization is possible the desynchronizing effect of random connectivity can be reduced by strengthening the e i synapses more surprising it cannot be reduced by strengthening the i e synapses however the decay time constant of inhibition plays an important role faster decay yields tighter synchrony in particular in models in which the inhibitory synapses are assumed to be instantaneous the effects of sparse random connectivity cannot be seen

generalization of coupled spiking models and effects of the width of an action potential on synchronization phenomena the integrate and fire if neuron model and the piecewise linear version of fitzhugh nagumo pl neuron model with a time scale parameter mu are frequently being used in the study of synchronization phenomena although the two models are regarded to be different type we show a certain equivalence between them by deriving the coupled if model of an improved version with a firing duration from the recovery variable coupled system of the pl model under taking the limit of mu 0 without a loss of any coupling properties in the coupled if model with the duration time the synchronization behavior of a pair of neurons with excitatory or inhibitory synaptic coupling can be systematically explored in terms of three parameters in the model synaptic strength decaying relaxation rate of the synaptic coupling and the parameter exhibiting the firing duration we find some irregularly synchronous behavior with or without constant firing order alternations we show that the duration of an impulse plays an important role in synchronization phenomena

increasing inhibitory input increases neuronal firing rate why and when diffusion process cases increasing inhibitory input to single neuronal models such as the fitzhugh nagumo model and the hodgkin huxley model can sometimes increase their firing rates a phenomenon which we term inhibition boosted firing ibf here we consider neuronal models with diffusion approximation inputs i e they share the identical first and second order statistics of the corresponding poisson process inputs using the integrate and fire model and the if fhn model we explore theoretically how and when ibf can happen for both models it is shown that there is a critical input frequency at which the efferent firing rate is identical when the neuron receives purely excitatory inputs or exactly balanced inhibitory and excitatory inputs when the input frequency is lower than the critical frequency ibf occurs

an initial boundary value problem for the maxwell equations abstract in this paper by using methods from complex analysis and quaternionic analysis we investigate an initial boundary value problem for the maxwell equations and obtain the general solutions and solvable conditions of the problem respectively in different cases in addition by using a similar method we also discuss an initial boundary value problem for a hyperbolic complex system of first order equations in r 3

a linearized inverse boundary value problem for maxwell s equations abstract in this paper we consider the problem of determining the electromagnetic state of a body from measurements made on the surface of the body we study the full set of maxwell s equations that govern time harmonic electric and magnetic fields we seek to reconstruct the magnetic permeability the electric permitivity and the electric conductivity in the interior of the body from measurements made on the surface we exhibit appropriate boundary measurements in the form of a boundary mapping specifically the mapping from the tangential components of the electric field to the tangential components of the magnetic field this data can be used to reconstruct and approximately provided they deviate only slightly from known constants we also estimate the reconstruction errors