an improved algorithm for reprojecting rays through pixel images it is often desired to calculate line integrals through a field of reconstructed ct density pixels for the purpose of improving ct image quality two algorithms widely published and discussed in the past are known to either degrade spatial resolution or generate errors in the results due to the discontinuous square pixel modeling of the reconstructed image an algorithm is described based on linear interpolation between pixels which provides superior accuracy without unnecessary loss of resolution it was tested on simulated data for a head section and on a narrow gaussian density distribution the experimental results demonstrated improved performance the method is expected to prove useful for many types of post reconstruction processing including beam hardening missing data and noise supression algorithms

universal approximation capability of cascade correlation for structures cascade correlation cc constitutes a training method for neural networks that determines the weights as well as the neural architecture during training various extensions of cc to structured data have been proposed recurrent cascade correlation rcc for sequences recursive cascade correlation reccc for tree structures with limited fan out and contextual recursive cascade correlation creccc for rooted directed positional acyclic graphs dpags with limited fan in and fan out we show that these models possess the universal approximation property in the following sense given a probability measure p on the input set every measurable function from sequences into a real vector space can be approximated by a sigmoidal rcc up to any desired degree of accuracy up to inputs of arbitrary small probability every measurable function from tree structures with limited fan out into a real vector space can be approximated by a sigmoidal reccc with multiplicative neurons up to any desired degree of accuracy up to inputs of arbitrary small probability for sigmoidal creccc networks with multiplicative neurons we show the universal approximation capability for functions on an important subset of all dpags with limited fan in and fan out for which a specific linear representation yields unique codes we give one sufficient structural condition for the latter property which can easily be tested the enumeration of ingoing and outgoing edges should be compatible this property can be fulfilled for every dpag with fan in and fan out two via reenumeration of children and parents and for larger fan in and fan out via an expansion of the fan in and fan out and reenumeration of children and parents in addition the result can be generalized to the case of input output isomorphic transductions of structures thus creccc networks constitute the first neural models for which the universal approximation capability of functions involving fairly general acyclic graph structures is proved

dynamic multi source x ray tomography using a spacetime level set method a novel variant of the level set method is introduced for dynamic x ray tomography the target is allowed to change in time while being imaged by one or several source detector pairs at a relatively high frame rate the algorithmic approach is motivated by the results in 22 showing that the modified level set method can tolerate highly incomplete projection data in stationary tomography furthermore defining the level set function in spacetime enforces temporal continuity in the dynamic tomography context considered here the tomographic reconstruction is found as a minimizer of a nonlinear functional the functional contains a regularization term penalizing the l 2 norms of up to n derivatives of the reconstruction the case n 1 is shown to be equivalent to a convex tikhonov problem that has a unique minimizer for n 2 the existence of a minimizer is proved under certain assumptions on the signal to noise ratio and the size of the regularization parameter numerical examples with both simulated and measured dynamic x ray data are included and the proposed method is found to yield reconstructions superior to standard methods such as fbp or non negativity constrained tikhonov regularization and favorably comparable to those of total variation regularization furthermore the methodology can be adapted to a wide range of measurement arrangements with one or more x ray sources

wavelet based multiresolution local tomography we develop an algorithm to reconstruct the wavelet coefficients of an image from the radon transform data the proposed method uses the properties of wavelets to localize the radon transform and can be used to reconstruct a local region of the cross section of a body using almost completely local data that significantly reduces the amount of exposure and computations in x ray tomography the property that distinguishes our algorithm from the previous algorithms is based on the observation that for some wavelet bases with sufficiently many vanishing moments the ramp filtered version of the scaling function as well as the wavelet function has extremely rapid decay we show that the variance of the elements of the null space is negligible in the locally reconstructed image also we find an upper bound for the reconstruction error in terms of the amount of data used in the algorithm to reconstruct a local region 16 pixels in radius in a 256 spl times 256 image we require 22 of full exposure data

convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections solving a convex set theoretic image recovery problem amounts to finding a point in the intersection of closed and convex sets in a hilbert space the projection onto convex sets pocs algorithm in which an initial estimate is sequentially projected onto the individual sets according to a periodic schedule has been the most prevalent tool to solve such problems nonetheless pocs has several shortcomings it converges slowly it is ill suited for implementation on parallel processors and it requires the computation of exact projections at each iteration we propose a general parallel projection method emopsp that overcomes these shortcomings at each iteration of emopsp a convex combination of subgradient projections onto some of the sets is formed and the update is obtained via relaxation the relaxation parameter may vary over an iteration dependent extrapolated range that extends beyond the interval 0 2 used in conventional projection methods emopsp not only generalizes existing projection based schemes but it also converges very efficiently thanks to its extrapolated relaxations theoretical convergence results are presented as well as numerical simulations

c1approximations of inertial manifolds for dissipative nonlinear equations abstract in this paper we study a class of nonlinear dissipative partial differential equations that have inertial manifolds this means that the long time behavior is equivalent to a certain finite system of ordinary differential equations we investigate ways in which these finite systems can be approximated in thec1sense geometrically this may be interpreted as constructing manifolds in phase space that arec1close to the inertial manifold of the partial differential equation under such approximations the invariant hyperbolic sets of the global attractor persist

the weighted distance scheme a globally optimizing projection ordering method for art the order in which the projections are applied in the algebraic reconstruction technique art has a great effect on speed of convergence accuracy and the amount of noise like artifacts in the reconstructed image in this paper a new projection ordering scheme for art is presented the weighted distance scheme wds it heuristically optimizes the angular distance of a newly selected projection with respect to an extended sequence of previously applied projections this sequence of influential projections may incorporate the complete set of all previously applied projections or any limited time interval subset thereof the selection algorithm results in uniform sampling of the projection access space minimizing correlation in the projection sequence this produces more accurate images with less noise like artifacts than previously suggested projection ordering schemes

improving generalization capabilities of dynamic neural networks this work addresses the problem of improving the generalization capabilities of continuous recurrent neural networks the learning task is transformed into an optimal control framework in which the weights and the initial network state are treated as unknown controls a new learning algorithm based on a variational formulation of pontrayagin s maximum principle is proposed under reasonable assumptions its convergence is discussed numerical examples are given that demonstrate an essential improvement of generalization capabilities after the learning process of a dynamic network

monotonically equivalent entropies and solution of additivity equation generalized entropies are studied as lyapunov functions for the master equation markov chains three basic properties of these lyapunov functions are taken into consideration universality independence of the kinetic coefficients trace form the form of sum over the states and additivity for composition of independent subsystems all the entropies which have all three properties simultaneously and are defined for positive probabilities are found they form a one parametric family we consider also pairs of entropies s1 s2 which are connected by the monotonous transformation s2 f s1 equivalent entropies all classes of pairs of universal equivalent entropies one of which has a trace form and another is additive these entropies can be different one from another were found these classes consist of two one parametric families the family of entropies which are equivalent to the additive trace form entropies and the family of renyi tsallis entropies

canonical distribution functions in polymer dynamics ii liquid crystalline polymers the quasi equilibrium approximation is employed as a systematic tool for solving the problem of deriving constitutive equations from kinetic models of liquid crystalline polymers it is demonstrated how kinetic models of liquid crystalline polymers can be approximated in a systematic way how canonical distribution functions can be derived from the maximum entropy principle and how constitutive equations are derived therefrom the numerical implementation of the constitutive equations based on the intrinsic dual structure of the quasi equilibrium manifold thus derived is developed and illustrated for a particular example finally a measure of the accuracy of the quasi equilibrium approximation is proposed that can be implemented into the numerical integration of the constitutive equation

eit imaging regularization based on spectral graph wavelets the objective of electrical impedance tomographic reconstruction is to identify the distribution of tissue conductivity from electrical boundary conditions this is an ill posed inverse problem usually solved under the finite element method framework in previous studies standard sparse regularization was used for difference electrical impedance tomography to achieve a sparse solution however regarding elementwise sparsity standard sparse regularization interferes with the smoothness of conductivity distribution between neighboring elements and is sensitive to noise as an effect the reconstructed images are spiky and depict a lack of smoothness such unexpected artifacts are not realistic and may lead to misinterpretation in clinical applications to eliminate such artifacts we present a novel sparse regularization method that uses spectral graph wavelet transforms single scale or multiscale graph wavelet transforms are employed to introduce local smoothness on different scales into the reconstructed images the proposed approach relies on viewing finite element meshes as undirected graphs and applying wavelet transforms derived from spectral graph theory reconstruction results from simulations a phantom experiment and patient data suggest that our algorithm is more robust to noise and produces more reliable images

wavelet localization of the radon transform the authors develop an algorithm which significantly reduces radiation exposure in x ray tomography when a local region of the body is to be imaged the algorithm uses the properties of wavelets to essentially localize the radon transform this algorithm differs from previous algorithms for doing local tomography because it recovers an approximation to the original image not the image module the nullspace of the local tomography operator or the lambda transform of the image this is possible because the authors do not truly invert the interior radon transform but rather sample the radon transform sparsely away from the local region of interest much attention in the field has been directed towards localized tomography the authors believe that this technique represents a significant contribution towards this effort

fast implementations of algebraic methods for three dimensional reconstruction from cone beam data the prime motivation of this work is to devise techniques that make the algebraic reconstruction technique art and related methods more efficient for routine clinical use while not compromising their accuracy since most of the computational effort of art is spent for projection backprojection operations the authors first seek to optimize the projection algorithm existing projection algorithms are surveyed and it is found that these algorithms either lack accuracy or speed or are not suitable for cone beam reconstruction the authors hence devise a new and more accurate extension to the splatting algorithm a well known voxel driven projection method they also describe a new three dimensional 3 d ray driven projector that is considerably faster than the voxel driven projector and at the same time more accurate and perfectly suited for the demands of cone beam the authors then devise caching schemes for both art and simultaneous art sart which minimize the number of redundant computations for projection and backprojection and at the same time are very memory conscious they find that with caching the cost for an art projection backprojection operation can be reduced to the equivalent cost of 1 12 projections they also find that sart due to its image based volume correction scheme is considerably harder to accelerate with caching implementations of the algorithms yield runtime ratios t sub sart t sub art between 1 5 and 1 15 depending on the amount of caching used

amorphous surface growth via a level set approach abstract we construct an equation for amorphous surface growth due to some deposition process within the level set approach and derive a unique viscosity solution to this equation from a source particles deposit on the initial hypersurface 0 in any direction and diffuse on the hypersurface for each time t we define thereby a hypersurface t

the foundations of informational statistical thermodynamics revisited abstract the aim of this paper is to review the fundamental ideas of the underlying method behind informational statistical thermodynamics this method is set forth to deal with phenomena that occur in nonequilibrium systems the most significant aspects of this analysis are 1 i to show that abel s theorem guarantees that in the asymptotic limit the nonequilibrium statistical operator nso obtained by maxent generates a stationary solution of the liouville equation this fact is consistent with the experimental behavior of an equilibrium system 2 ii further it is also shown how a liouville equation with sources can be obtained by the nso determined by maxent whose formal solution proves that the general interpretation of abel s theorem leading to memory effects is incorrect rather this theorem introduces a time smoothing function in a time interval t 0 t t 1 t 1 initial time of an observation which is to be understood as one that connects an adiabatic perturbation for t t 1 in fact the memory effects appear in the evolution equations for the average values of the dynamical variables obtained by the nso when these evolution equations are calculated up to second order in the perturbation hamiltonian 3 iii also some criticisms that have been presented against maxent formalism are discussed and it is shown that they are inapplicable such criticisms are related to the memory effects and with the inconsistency of evolution equations for macrovariables with respect to the total energy conservation equation

asymptotic analysis of two reduction methods for systems of chemical reactions abstract this paper concerns two methods for reducing large systems of chemical kinetics equations namely the method of intrinsic low dimensional manifolds ildms due to maas and pope combust flame 88 1992 239 and an iterative method due to fraser j chem phys 88 1988 4732 and further developed by roussel and fraser j chem phys 93 1990 1072 both methods exploit the separation of fast and slow reaction time scales to find low dimensional manifolds in the space of species concentrations where the long term dynamics are played out the asymptotic expansions of these manifolds e 0 where e measures the ratio of the reaction time scales are compared with the asymptotic expansion of m e the slow manifold given by geometric singular perturbation theory it is shown that the expansions of the ildm and m e agree up to and including terms of o e the former has an error at o e 2 that is proportional to the local curvature of m 0 the error vanishes if and only if the curvature is zero everywhere the iterative method generates term by term the asymptotic expansion of m e starting from m 0 the ith application of the algorithm yields the correct expansion coefficient at o e i while leaving the lower order coefficients invariant thus after l applications the expansion is accurate up to and including the terms of o e l the analytical results are illustrated on a planar system from enzyme kinetics michaelis menten henri and a model planar system due to davis and skodje

nonlinear reciprocity and the maximum entropy formalism abstract the maximum entropy formalism calculates a phase space distribution p x which maximizes the information theoretic entropy subject to specified values of internal energy and state variables i and i i 1 n the latter are averages calculated from p of dynamical functions ai and ai ilai respectively where l is the liouville operator from p one extracts a fluctuation distribution g a v for the values of the a and a a kinetic equation for the fluctuation distribution has been derived by grabert using projection operators appropriate to a system in thermal contact with its surroundings and g is proposed as an ansatz for its solution from the first moments of the kinetic equation after introduction therein of g one extracts phenomenological equations for ai and hi whose terms can be grouped to exhibit onsager symmetry even when nonlinear terms are included the groupings can be affected exactly but not uniquely

renormalization of the chapman enskog expansion isothermal fluid flow and rosenau saturation this paper continues the author s study of procedures for rewriting the well known chapman enskog expansion used in the kinetic theory of gases the usual chapman enskog expansion when used in isothermal fluid motion will introduce nonlinear instability at super burnett order o e3 truncation the procedure given here eliminates the truncation instability and produces the desired dissipation inequality

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

anti aliased three dimensional cone beam reconstruction of low contrast objects with algebraic methods examines the use of the algebraic reconstruction technique art and related techniques to reconstruct 3 d objects from a relatively sparse set of cone beam projections although art has been widely used for cone beam reconstruction of high contrast objects e g in computed angiography the work presented here explores the more challenging low contrast case which represents a little investigated scenario for art preliminary experiments indicate that for cone angles greater than 20 spl deg traditional art produces reconstructions with strong aliasing artifacts these artifacts are in addition to the usual off midplane inaccuracies of cone beam tomography with planar orbits the authors find that the source of these artifacts is the nonuniform reconstruction grid sampling and correction by the cone beam rays during the art projection backprojection procedure a new method to compute the weights of the reconstruction matrix is devised which replaces the usual constant size interpolation filter by one whose size and amplitude is dependent on the source voxel distance this enables the generation of reconstructions free of cone beam aliasing artifacts at only little extra cost an alternative analysis reveals that simultaneous art sart also produces reconstructions without aliasing artifacts however at greater computational cost finally the authors thoroughly investigate the influence of various art parameters such as volume initialization relaxation coefficient spl lambda correction scheme number of iterations and noise in the projection data on reconstruction quality the authors find that art typically requires only 3 iterations to render satisfactory reconstruction results

invariant grids for reaction kinetics abstract in this paper we construct low dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold mim mim is based on a formulation of the condition of invariance as an equation and its solution by newton iterations a grid based version of mim is developed the method of invariant grids we describe the newton method and the relaxation method for the invariant grids construction the problem of the grid correction is fully decomposed into the problems of the grid s nodes correction the edges between the nodes appear only in the calculation of the tangent spaces this fact determines high computational efficiency of the method of invariant grids the method is illustrated by two examples the simplest catalytic reaction michaelis menten mechanism and the hydrogen oxidation the algorithm of analytical continuation of the approximate invariant manifold from the discrete grid is proposed generalizations to open systems are suggested the set of methods covered makes it possible to effectively reduce description in chemical kinetics

limited data x ray tomography using nonlinear evolution equations a novel approach to the x ray tomography problem with sparse projection data is proposed nonnegativity of the x ray attenuation coefficient is enforced by modelling it as max phi x 0 where phi is a smooth function the function phi is computed as the equilibrium solution of a nonlinear evolution equation analogous to the equations used in level set methods the reconstruction algorithm is applied to a simulated full and limited angle projection data of the shepp logan phantom with sparse angular sampling and b measured limited angle projection data of in vitro dental specimens the results are significantly better than those given by traditional backprojection based approaches and similar in quality but faster to compute compared to the algebraic reconstruction technique

iterative deblurring for ct metal artifact reduction iterative deblurring methods using the expectation maximization em formulation and the algebraic reconstruction technique art respectively are adapted for metal artifact reduction in medical computed tomography ct in experiments with synthetic noise free and additive noisy projection data of dental phantoms it is found that both simultaneous iterative algorithms produce superior image quality as compared to filtered backprojection after linearly fitting projection gaps furthermore the em type algorithm converges faster than the art type algorithm in terms of either the i divergence or euclidean distance between ideal and reprojected data in the authors simulation also for a given iteration number the em type deblurring method produces better image clarity but stronger noise than the art type reconstruction the computational complexity of em and art based iterative deblurring is essentially the same dominated by reprojection and backprojection relevant practical and theoretical issues are discussed

approximation of slow and fast dynamics in multiscale dynamical systems by the linearized relaxation redistribution method in this paper we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation ode system towards a stable low dimensional invariant manifold in the phase space slow invariant manifold sim as a result the demanding problem of constructing sim of any dimensions is recast into the remarkably simpler task of solving a properly devised ode system by stiff numerical schemes available in the literature in the same spirit a set of equations is elaborated for local construction of the fast subspace and possible initialization procedures for the above equations are discussed the implementation to a detailed mechanism for combustion of hydrogen and air has been carried out while a model with the exact chapman enskog solution of the invariance equation is utilized as a benchmark

a characteristic condition for convergence of steepest descent approximation to accretive operator equations in the present paper a sufficient and necessary condition for convergence of steepest descent approximation to accretive operator equations is established and for the sufficiency part a specific error estimation is also given

a binary level set model and some applications to mumford shah image segmentation in this paper we propose a pde based level set method traditionally interfaces are represented by the zero level set of continuous level set functions instead we let the interfaces be represented by discontinuities of piecewise constant level set functions each level set function can at convergence only take two values i e it can only be 1 or 1 thus our method is related to phase field methods some of the properties of standard level set methods are preserved in the proposed method while others are not using this new method for interface problems we need to minimize a smooth convex functional under a quadratic constraint the level set functions are discontinuous at convergence but the minimization functional is smooth we show numerical results using the method for segmentation of digital images

a multiresolution approach to iterative reconstruction algorithms in x ray computed tomography in computed tomography the application of iterative reconstruction methods in practical situations is impeded by their high computational demands especially in high resolution x ray computed tomography where reconstruction volumes contain a high number of volume elements several giga voxels this computational burden prevents their actual breakthrough besides the large amount of calculations iterative algorithms require the entire volume to be kept in memory during reconstruction which quickly becomes cumbersome for large data sets to overcome this obstacle we present a novel multiresolution reconstruction which greatly reduces the required amount of memory without significantly affecting the reconstructed image quality it is shown that combined with an efficient implementation on a graphical processing unit the multiresolution approach enables the application of iterative algorithms in the reconstruction of large volumes at an acceptable speed using only limited resources

learning in feedforward layered networks the tiling algorithm the authors propose a new algorithm which builds a feedforward layered network in order to learn any boolean function of n boolean units the number of layers and the number of hidden units in each layer are not prescribed in advance they are outputs of the algorithm it is an algorithm for growth of the network which adds layers and units inside a layer at will until convergence the convergence is guaranteed and numerical tests of this strategy look promising

errors in reprojection methods in computenzed tomography iterative tomographic reconstruction methods have been developed which can enforce various physical constraints on the reconstructed image an integral part of most of these methods is the repro jection of the reconstructed image these estimated projections are compared to the original projection data and modified according to some criteria based on a priori constraints in this paper the errors generated by such reprojection schemes are investigated bounds for these errors are derived under simple signal energy assumptions and using probabilistic assumptions on the distribution of discontinuities these bounds can be used in the enforcement of constraints in the determination of convergence of the iterative methods and in the detection of artifacts

level set methods for optimization problems involving geometry and constraints i frequencies of a two density inhomogeneous drum many problems in engineering design involve optimizing the geometry to maximize a certain design objective geometrical constraints are often imposed in this paper we use the level set method devised in osher and sethian j comput phys 79 12 1988 the variational level set calculus presented in zhao et al j comput phys 127 179 1996 and the projected gradient method as in rudin et al physica d 60 259 1992 to construct a simple numerical approach for problems of this type we apply this technique to a model problem involving a vibrating system whose resonant frequency or whose spectral gap is to be optimized subject to constraints on geometry our numerical results are quite promising we expect to use this approach to deal with a wide class of optimal design problems in the future

induction of finite state languages using second order recurrent networks second order recurrent networks that recognize simple finite state languages over 0 1 are induced from positive and negative examples using the complete gradient of the recurrent network and sufficient training examples to constrain the definition of the language to be induced solutions are obtained that correctly recognize strings of arbitrary length

quasi equilibrium closure hierarchies for the boltzmann equation abstract after boltzmann and gibbs the notion of disorder in statistical physics relates to ensembles not to individual states this disorder is measured by the logarithm of ensemble volume the entropy but recent results about measure concentration effects in analysis and geometry allow us to return from the ensemble based point of view to a state based one at least partially in this paper the order disorder problem is represented as a problem of relation between distance and measure the effect of strong order disorder separation for multiparticle systems is described the phase space could be divided into two subsets one of them set of disordered states has almost zero diameter the second one has almost zero measure the symmetry with respect to permutations of particles is responsible for this type of concentration dynamics of systems with strong order disorder separation has high average acceleration squared which can be interpreted as evolution through a series of collisions acceleration dominated dynamics the time arrow direction from order to disorder follows from the strong order disorder separation but inverse for systems in space of symmetric configurations with sticky boundaries the way back from disorder to order is typical natural selection recommendations for mining of molecular dynamics results are also presented

reconstruction from limited angle projections based on delta u spectrum analysis this paper proposes a sparse representation of an image using discrete u functions a u function is defined as the product of a kronecker delta function and a step function based on the sparse representation we have developed a novel and effective method for reconstructing an image from limited angle projections the method first estimates the parameters of the sparse representation from the incomplete projection data and then directly calculates the image to be reconstructed experiments have shown that the proposed method can effectively recover the missing data and reconstruct images more accurately than the total variation tv regularized reconstruction method

limited angle reconstruction in tomography via squashing we give a new algorithm for reconstructing a density f in the plane from its projections along those lines making an angle greater than a fixed 0 with the x axis of course the performance of the algorithm depends on and on the smoothness of f but it appears to give a practical and simple solution to the problem whenever one exists the basic idea which seems to be new is to make an affine squashing scale change of f to g for which the projections are then known at n equally spaced angles so that we know how to find g and then we obtainf from g by inverting the scale change

adaptive simplification of complex multiscale systems a fully adaptive methodology is developed for reducing the complexity of large dissipative systems this represents a significant step toward extracting essential physical knowledge from complex systems by addressing the challenging problem of a minimal number of variables needed to exactly capture the system dynamics accurate reduced description is achieved by construction of a hierarchy of slow invariant manifolds with an embarrassingly simple implementation in any dimension the method is validated with the autoignition of the hydrogen air mixture where a reduction to a cascade of slow invariant manifolds is observed

adart an adaptive algebraic reconstruction algorithm for discrete tomography in this paper we suggest an algorithm based on the discrete algebraic reconstruction technique dart which is capable of computing high quality reconstructions from substantially fewer projections than required for conventional continuous tomography adaptive dart adart goes a step further than dart on the reduction of the number of unknowns of the associated linear system achieving a significant reduction in the pixel error rate of reconstructed objects the proposed methodology automatically adapts the border definition criterion at each iteration resulting in a reduction of the number of pixels belonging to the border and consequently of the number of unknowns in the general algebraic reconstruction linear system to be solved being this reduction specially important at the final stage of the iterative process experimental results show that reconstruction errors are considerably reduced using adart when compared to original dart both in clean and noisy environments

microscopic origins of irreversible macroscopic behavior time asymmetric behavior as embodied in the second law of thermodynamics is observed in individual macroscopic systems it can be understood as arising naturally from time symmetric microscopic laws in accord with the ideas of thompson maxwell and boltzmann alternative explanations based on equating irreversible macroscopic behavior with the mixing type of behavior already present in the time evolution of ensembles probability distributions of certain systems having only a few degrees of freedom are in my opinion unnecessary misguided and misleading

image compression via joint statistical characterization in the wavelet domain we develop a probability model for natural images based on empirical observation of their statistics in the wavelet transform domain pairs of wavelet coefficients corresponding to basis functions at adjacent spatial locations orientations and scales are found to be non gaussian in both their marginal and joint statistical properties specifically their marginals are heavy tailed and although they are typically decorrelated their magnitudes are highly correlated we propose a markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties and show that it accounts for the statistics of a wide variety of images including photographic images graphical images and medical images in order to directly demonstrate the power of the model we construct an image coder called epwic embedded predictive wavelet image coder in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model bitplanes are ordered using a greedy algorithm that considers the mse reduction per encoded bit the decoder uses the statistical model to predict coefficient values based on the bits it has received despite the simplicity of the model the rate distortion performance of the coder is roughly comparable to the best image coders in the literature

projection space iteration reconstruction reprojection recently an iterative reconstruction reprojection irr algorithm has been suggested for application to limited view computed tomography ct in the irr the interpolation operation is performed in the object space during backprojection reprojection the errors associated with the interpolation degrade the reconstructed image and may cause divergence unless a large number of rays is used in this paper we propose a projection space iterative reconstruction reprojection psirr algorithm based on backprojection reprojection in the projection space in the process of the backprojection reprojection iteration is performed with a single equation instead of multiple equations and interpolation is eliminated computer simulation results are presented and image quality of the psirr algorithm shows a substantial improvement compared to the original irr algorithm in addition the new algorithm was applied to ultrasonic attenuation ct using a sponge phantom

wavelet based reconstruction for limited angle x ray tomography the aim of x ray tomography is to reconstruct an unknown physical body from a collection of projection images when the projection images are only available from a limited angle of view the reconstruction problem is a severely ill posed inverse problem statistical inversion allows stable solution of the limited angle tomography problem by complementing the measurement data by a priori information in this work the unknown attenuation distribution inside the body is represented as a wavelet expansion and a besov space prior distribution together with positivity constraint is used the wavelet expansion is thresholded before reconstruction to reduce the dimension of the computational problem feasibility of the method is demonstrated by numerical examples using in vitro data from mammography and dental radiology

solution of inverse problems in image processing by wavelet expansion we describe a wavelet based approach to linear inverse problems in image processing in this approach both the images and the linear operator to be inverted are represented by wavelet expansions leading to a multiresolution sparse matrix representation of the inverse problem the constraints for a regularized solution are enforced through wavelet expansion coefficients a unique feature of the wavelet approach is a general and consistent scheme for representing an operator in different resolutions an important problem in multigrid multiresolution processing this and the sparseness of the representation induce a multigrid algorithm the proposed approach was tested on image restoration problems and produced good results

edge preserving tomographic reconstruction with nonlocal regularization tomographic image reconstruction using statistical methods can provide more accurate system modeling statistical models and physical constraints than the conventional filtered backprojection fbp method because of the ill posedness of the reconstruction problem a roughness penalty is often imposed on the solution to control noise to avoid smoothing of edges which are important image attributes various edge preserving regularization methods have been proposed most of these schemes rely on information from local neighborhoods to determine the presence of edges in this paper we propose a cost function that incorporates nonlocal boundary information into the regularization method we use an alternating minimization algorithm with deterministic annealing to minimize the proposed cost function jointly estimating region boundaries and object pixel values we apply variational techniques implemented using level sets methods to update the boundary estimates then using the most recent boundary estimate we minimize a space variant quadratic cost function to update the image estimate for the positron emission tomography transmission reconstruction application we compare the bias variance tradeoff of this method with that of a conventional penalized likelihood algorithm with local huber roughness penalty

ehrenfest s argument extended to a formalism of nonequilibrium thermodynamics a general method of constructing dissipative equations is developed following ehrenfest s idea of coarse graining the approach resolves the major issue of discrete time coarse graining versus continuous time macroscopic equations proof of the h theorem for macroscopic equations is given several examples supporting the construction are presented and generalizations are suggested

multiresolution tomographic reconstruction using wavelets shows how the separable two dimensional wavelet representation leads naturally to an efficient multiresolution tomographic reconstruction algorithm this algorithm is similar to the conventional filtered backprojection algorithm except that the filters are now angle dependent and the backprojection gives the wavelet coefficients of the reconstruction which are then used to synthesize the reconstruction at various resolution levels by reconstructing only a small localized region at high resolution the authors show how radiation exposure and computation can be significantly reduced compared to a standard reconstruction

wavelet sampling and localization schemes for the radon transform in two dimensions two theorems are presented for wavelet decompositions of the two dimensional radon transform the rst theorem establishes an upper error bound in l 2 norm between the radon transform and its wavelet approximation whose coecients at dierent scales are estimated from radon data acquired at corresponding sampling rates the second theorem gives an estimate of the accuracy of a local image reconstructed from localized radon data at multiple levels these results show how to design a multilevel sampling and localization strategy for parallel beam scanning by using wavelet regularity and vanishing moment characteristics clarify the interaction between the wavelet structure and the essential bandwidth of an object image and provide guidelines for wavelet local tomography

a generalized gaussian image model for edge preserving map estimation the authors present a markov random field model which allows realistic edge modeling while providing stable maximum a posterior map solutions the model referred to as a generalized gaussian markov random field ggmrf is named for its similarity to the generalized gaussian distribution used in robust detection and estimation the model satisfies several desirable analytical and computational properties for map estimation including continuous dependence of the estimate on the data invariance of the character of solutions to scaling of data and a solution which lies at the unique global minimum of the a posteriori log likelihood function the ggmrf is demonstrated to be useful for image reconstruction in low dosage transmission tomography

the barzilai and borwein gradient method for the large scale unconstrained minimization problem the barzilai and borwein gradient method for the solution of large scale unconstrained minimization problems is considered this method requires few storage locations and very inexpensive computations furthermore it does not guarantee descent in the objective function and no line search is required recently the global convergence for the convex quadratic case has been established however for the nonquadratic case the method needs to be incorporated in a globalization scheme in this work a nonmonotone line search strategy that guarantees global convergence is combined with the barzilai and borwein method this strategy is based on the nonmonotone line search technique proposed by grippo lampariello and lucidi siam j numer anal 23 1986 pp 707 716 numerical results to compare the behavior of this method with recent implementations of the conjugate gradient method are presented these results indicate that the global barzilai and borwein method may allow some significant reduction in the number of line searches and also in the number of gradient evaluations

finite dimensional control of parabolic pde systems using approximate inertial manifolds abstract this paper introduces a methodology for the synthesis of nonlinear finite dimensional output feedback controllers for systems of quasi linear parabolic partial differential equations pdes for which the eigenspectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement combination of galerkin s method with a novel procedure for the construction of approximate inertial manifolds for the pde system is employed for the derivation of ordinary differential equation ode systems whose dimension is equal to the number of slow modes that yield solutions which are close up to a desired accuracy to the ones of the pde system for almost all times these ode systems are used as the basis for the synthesis of nonlinear output feedback controllers that guarantee stability and enforce the output of the closed loop system to follow up to a desired accuracy a prespecified response for almost all times

efficient simulation of finite automata by neural nets let k m denote the smallest number with the property that every m state finite automaton can be built as a neural net using k m or fewer neurons a counting argument shows that k m is at least o m log m 1 3 and a construction shows that k m is at most o m 3 4 the counting argument and the construction allow neural nets with arbitrarily complex local structure and thus may require neurons that themselves amount to complicated networks mild and in practical situations almost necessary constraints on the local structure of the network give again by a counting argument and a construction lower and upper bounds for k m that are both linear in m

convergence of the simultaneous algebraic reconstruction technique sart computed tomography ct has been extensively studied for years and widely used in the modern society although the filtered back projection algorithm is the method of choice by manufacturers efforts are being made to revisit iterative methods due to their unique advantages such as superior performance with incomplete noisy data in 1984 the simultaneous algebraic reconstruction technique sart was developed as a major refinement of the algebraic reconstruction technique art however the convergence of the sart has never been established since then in this paper the convergence is proved under the condition that coefficients of the linear imaging system are nonnegative it is shown that from any initial guess the sequence generated by the sart converges to a weighted least square solution

uniqueness of thermodynamic projector and kinetic basis of molecular individualism three results are presented first we solve the problem of persistence of dissipation for reduction of kinetic models kinetic equations with thermodynamic lyapunov functions are studied uniqueness of the thermodynamic projector is proven there exists only one projector which transforms any vector field equipped with the given lyapunov function into a vector field with the same lyapunov function for a given anzatz manifold which is not tangent to the lyapunov function levels second we use the thermodynamic projector for developing the short memory approximation and coarse graining for general nonlinear dynamic systems we prove that in this approximation the entropy production increases the theorem about entropy overproduction in example we apply the thermodynamic projector to derive the equations of reduced kinetics for the fokker planck equation a new class of closures is developed the kinetic multipeak polyhedra distributions of this type are expected in kinetic models with multidimensional instability as universally as the gaussian distribution appears for stable systems the number of possible relatively stable states of a nonequilibrium system grows as 2m and the number of macroscopic parameters is in order mn where n is the dimension of configuration space and m is the number of independent unstable directions in this space the elaborated class of closures and equations pretends to describe the effects of molecular individualism this is the third result

a recurrent self organizing neural fuzzy inference network a recurrent self organizing neural fuzzy inference network rsonfin is proposed the rsonfin is inherently a recurrent multilayered connectionist network for realizing the basic elements and functions of dynamic fuzzy inference and may be considered to be constructed from a series of dynamic fuzzy rules the temporal relations embedded in the network are built by adding some feedback connections representing the memory elements to a feedforward neural fuzzy network each weight as well as node in the rsonfin has its own meaning and represents a special element in a fuzzy rule there are no hidden nodes initially in the rsonfin they are created online via concurrent structure identification and parameter identification the structure learning together with the parameter learning forms a fast learning algorithm for building a small yet powerful dynamic neural fuzzy network two major characteristics of the rsonfin can thus be seen 1 the recurrent property of the rsonfin makes it suitable for dealing with temporal problems and 2 no predetermination like the number of hidden nodes must be given since the rsonfin can find its optimal structure and parameters automatically and quickly moreover to reduce the number of fuzzy rules generated a flexible input partition method the aligned clustering based algorithm is proposed various simulations on temporal problems are done and performance comparisons with some existing recurrent networks are also made efficiency of the rsonfin is verified from these results

validity of a macroscopic description in dilute polymeric solutions derivation of macroscopic equations from the simplest dumbbell models is revisited it is demonstrated that the onset of the macroscopic description is sensitive to the flows for peterlin s approximation makromol chem 338 44 1961 to warner s finitely extensible nonlinear elastic spring force model ind eng chem fundam 11 379 1972 fene p small deviations from the gaussian solution undergo a slow relaxation before the macroscopic description sets on some consequences of these observations are discussed

moment closure hierarchies for kinetic theories this paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory the first member of the hierarchy is the euler system which is based on maxwellian velocity distributions while the second member is based on nonisotropic gaussian velocity distributions the closure proceeds in two steps the first ensures that every member of the hierarchy is hyperbolic has an entropy and formally recovers the euler limit the second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct navier stokes behavior this is achieved through the introduction of a generalization of the bgk collision operator the simplest such system in three spatial dimensions is a 14 moment closure which also recovers the behavior of the grad 13 moment system when the velocity distributions lie near local maxwellians the closure procedure can be applied to a general class of kinetic theories

family of additive entropy functions out of thermodynamic limit we derive a one parametric family of entropy functions that respect the additivity condition and which describe effects of finiteness of statistical systems in particular distribution functions with long tails this one parametric family is different from the tsallis entropies and is a convex combination of the boltzmann gibbs shannon entropy and the entropy function proposed by burg an example of how longer tails are described within the present approach is worked out for the canonical ensemble we also discuss a possible origin of a hidden statistical dependence and give explicit recipes on how to construct corresponding generalizations of the master equation

constructive learning of recurrent neural networks limitations of recurrent cascade correlation and a simple solution it is often difficult to predict the optimal neural network size for a particular application constructive or destructive methods that add or subtract neurons layers connections etc might offer a solution to this problem we prove that one method recurrent cascade correlation due to its topology has fundamental limitations in representation and thus in its learning capabilities it cannot represent with monotone i e sigmoid and hard threshold activation functions certain finite state automata we give a preliminary approach on how to get around these limitations by devising a simple constructive training method that adds neurons during training while still preserving the powerful fully recurrent structure we illustrate this approach by simulations which learn many examples of regular grammars that the recurrent cascade correlation method is unable to learn

function approximation fast convergence neural approach based on spectral analysis we propose a constructive approach to building single hidden layer neural networks for nonlinear function approximation using frequency domain analysis we introduce a spectrum based learning procedure that minimizes the difference between the spectrum of the training data and the spectrum of the network s estimates the network is built up incrementally during training and automatically determines the appropriate number of hidden units this technique achieves similar or better approximation with faster convergence times than traditional techniques such as backpropagation

the universal limit in dynamics of dilute polymeric solutions the method of invariant manifold is developed for a derivation of reduced description in kinetic equations of dilute polymeric solutions it is demonstrated that this reduced description becomes universal in the limit of small deborah and weissenberg numbers and it is represented by the revised oldroyd 8 constants constitutive equation for the polymeric stress tensor coefficients of this constitutive equation are expressed in terms of the microscopic parameters a systematic procedure of corrections to the revised oldroyd 8 constants equations is developed results are tested with simple flows c 2000 elsevier science b v all rights reserved

finite state automata and simple recurrent networks we explore a network architecture introduced by elman 1988 for predicting successive elements of a sequence the network uses the pattern of activation over a set of hidden units from time step t1 together with element t to predict element t 1 when the network is trained with strings from a particular finite state grammar it can learn to be a perfect finite state recognizer for the grammar when the network has a minimal number of hidden units patterns on the hidden units come to correspond to the nodes of the grammar although this correspondence is not necessary for the network to act as a perfect finite state recognizer we explore the conditions under which the network can carry information about distant sequential contingencies across intervening elements such information is maintained with relative ease if it is relevant at each intermediate step it tends to be lost when intervening elements do not depend on it at first glance this may suggest that such networks are not relevant to natural language in which dependencies may span indefinite distances however embeddings in natural language are not completely independent of earlier information the final simulation shows that long distance sequential contingencies can be encoded by the network even if only subtle statistical properties of embedded strings depend on the early information

a parametric level set approach to simultaneous object identification and background reconstruction for dual energy computed tomography dual energy computerized tomography has gained great interest because of its ability to characterize the chemical composition of a material rather than simply providing relative attenuation images as in conventional tomography the purpose of this paper is to introduce a novel polychromatic dual energy processing algorithm with an emphasis on detection and characterization of piecewise constant objects embedded in an unknown cluttered background physical properties of the objects particularly the compton scattering and photoelectric absorption coefficients are assumed to be known with some level of uncertainty our approach is based on a level set representation of the characteristic function of the object and encompasses a number of regularization techniques for addressing both the prior information we have concerning the physical properties of the object and the fundamental physics based limitations associated with our ability to jointly recover the compton scattering and photoelectric absorption properties of the scene in the absence of an object with appropriate physical properties our approach returns a null characteristic function and thus can be viewed as simultaneously solving the detection and characterization problems unlike the vast majority of methods that define the level set function nonparametrically i e as a dense set of pixel values we define our level set parametrically via radial basis functions and employ a gauss newton type algorithm for cost minimization numerical results show that the algorithm successfully detects objects of interest finds their shape and location and gives an adequate reconstruction of the background

quasi equilibrium grid algorithm geometric construction for model reduction the method of invariant grid mig is an iterative procedure for model reduction in chemical kinetics which is based on the notion of slow invariant manifold sim a n gorban i v karlin method of invariant manifold for chemical kinetics chem eng sci 58 2003 4751 4768 e chiavazzo a n gorban i v karlin comparison of invariant manifolds for model reduction in chemical kinetics commun comput phys 2 5 2007 964 992 a n gorban i v karlin a y zinovyev invariant grids for reaction kinetics physica a 333 2004 106 154 a n gorban i v karlin invariant manifolds for physical and chemical kinetics lecture notes physics 660 springer berlin heidelberg 2005 doi 10 1007 b98103 important role in that method is played by the initial grid which once refined gives a description of the invariant manifold the invariant grid a convenient way to get a first approximation of the sim is given by the spectral quasi equilibrium manifold sqem a n gorban i v karlin method of invariant manifold for chemical kinetics chem eng sci 58 2003 4751 4768 e chiavazzo a n gorban i v karlin comparison of invariant manifolds for model reduction in chemical kinetics commun comput phys 2 5 2007 964 992 in the present paper a flexible numerical method to construct the discrete analog of a quasi equilibrium manifold in any dimension is presented that object is named quasi equilibrium grid qeg while the procedure quasi equilibrium grid algorithm qega extensions of the qem notion are also suggested the qega is a numerical tool which can be used to find a grid based approximation for the locus of minima of a convex function under some linear constraints the method is validated by construction of one and two dimensional grids for a model of hydrogen oxidation reaction

a wavelet based method for multiscale tomographic reconstruction the authors represent the standard ramp filter operator of the filtered back projection fbp reconstruction in different bases composed of haar and daubechies compactly supported wavelets the resulting multiscale representation of the ramp filter matrix operator is approximately diagonal the accuracy of this diagonal approximation becomes better as wavelets with larger numbers of vanishing moments are used this wavelet based representation enables the authors to formulate a multiscale tomographic reconstruction technique in which the object is reconstructed at multiple scales or resolutions a complete reconstruction is obtained by combining the reconstructions at different scales the authors multiscale reconstruction technique has the same computational complexity as the fbp reconstruction method it differs from other multiscale reconstruction techniques in that 1 the object is defined through a one dimensional multiscale transformation of the projection domain and 2 the authors explicitly account for noise in the projection data by calculating maximum a posteriori probability map multiscale reconstruction estimates based on a chosen fractal prior on the multiscale object coefficients the computational complexity of this maximum a posteriori probability map solution is also the same as that of the fbp reconstruction this result is in contrast to commonly used methods of statistical regularization which result in computationally intensive optimization algorithms

small animal in vivo x ray tomosynthesis anatomical relevance of the reconstructed images whole body x ray micro digital tomosynthesis micro dt for small animal imaging is introduced in this work such a system allows to deal with geometrical constraints that do not allow to use a micro ct system as well as to reduce the radiological dose compared to a micro ct scan data was simulated using the digimouse anatomical model of the mouse with the designed system an algebraic reconstruction algorithm regularized by total variation norm tv minimization was used to reconstruct images parameters for the reconstruction were optimized and the algorithm performance was evaluated quantitatively high contrast tissues were subsequently segmented by thresholding the image quantitative analysis of the segmented domains indicates that a relevant anatomical information can possibly be extracted from micro dt images indeed the dice s coefficient values are greater than 0 8 for the segmented high contrast tissues compared to the phantom which indicates an important overlap between the domains the volume of the segmented tissues is over estimated for the bones and skin with 1 313 and 1 113 ratios of the estimated over reference volumes respectively and under estimated in the case of the lungs with a 0 762 ratio the mean point to surface distance is inferior to the voxel size of 400 mu rm m for the three segmented tissues these results are very encouraging and let us consider micro dt as an alternative to micro ct to deal with geometrical constraints

optimization for limited angle tomography in medical image processing this paper aims to reduce the problems of incomplete data in computed tomography which happens frequently in medical image process and analysis e g when the high density region of objects can only be penetrated by x rays at a limited angular range as the projection data are available only in an angular range the incomplete data problem can be attributed to the limited angle problem which is an ill posed inverse problem image reconstruction based on total variation tv reduces the problem and gives better performance on edge preserving reconstruction however the artificial parameter can only be determined through considerable experimentation in this paper an effective tv objective function is proposed to reduce the inverse problem in the limited angle tomography this novel objective function provides a robust and effective reconstruction without any artificial parameter in the iterative processes using the tv as a multiplicative constraint the results demonstrate that this reconstruction strategy outperforms some previous ones

relaxational trajectories global approximations abstract the paper intends to fill the gap of analytic approximate methods for non linear space independent dissipative systems equipped with the entropy functional the key point of the analysis is an upper limiting state in the beginning of the relaxation extremal properties of this state are described and explicit estimations are derived this limiting state is used to construct explicit approximations of the phase trajectories special attention is paid to accomplish positivity smoothness and the entropy growth along the approximate trajectories the method is tested for the space independent boltzmann equation with various collisional mechanisms

minimal curvature trajectories riemannian geometry concepts for slow manifold computation in chemical kinetics in dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories model reduction methods exploit this for simplifying chemical kinetics via a time scale separation into fast and slow modes the aim is to approximate the system dynamics with a dimension reduced model after eliminating the fast modes by enslaving them to the slow ones via computation of a slow attracting manifold we present a novel method for computing approximations of such manifolds using trajectory based optimization we discuss riemannian geometry concepts as a basis for suitable optimization criteria characterizing trajectories near slow attracting manifolds and thus provide insight into fundamental geometric properties of multiple time scale chemical kinetics the optimization criteria correspond to a suitable mathematical formulation of minimal relaxation of chemical forces along reaction trajectories under given constraints we present various geometrically motivated criteria and the results of their application to four test case reaction mechanisms serving as examples we demonstrate that accurate numerical approximations of slow invariant manifolds can be obtained

efficient framework for model based tomographic image reconstruction using wavelet packets the use of model based algorithms in tomographic imaging offers many advantages over analytical inversion methods however the relatively high computational complexity of model based approaches often restricts their efficient implementation in practice many modern imaging modalities such as computed tomography positron emission tomography or optoacoustic tomography normally use a very large number of pixels voxels for image reconstruction consequently the size of the forward model matrix hinders the use of many inversion algorithms in this paper we present a new framework for model based tomographic reconstructions which is based on a wavelet packet representation of the imaged object and the acquired projection data the frequency localization property of the wavelet packet base leads to an approximately separable model matrix for which reconstruction at each spatial frequency band is independent and requires only a fraction of the projection data thus the large model matrix is effectively separated into a set of smaller matrices facilitating the use of inversion schemes whose complexity is highly nonlinear with respect to matrix size the performance of the new methodology is demonstrated for the case of 2 d optoacoustic tomography for both numerically generated and experimental data

general approach to constructing models of the boltzmann equation abstract the problem of thermodynamic parameterization of an arbitrary approximation of reduced description is solved on the base of this solution a new class of model kinetic equations is constructed that gives a model extension of the chosen approximation to a kinetic model model equations describe two processes rapid relaxation to the chosen approximation along the planes of rapid motions and the slow motion caused by the chosen approximation the h theorem is proved for these models it is shown that the rapid process always leads to entropy growth and also a neighborhood of the approximation is determined inside which the slow process satisfies the h theorem kinetic models for grad moment approximations and for the tamm mott smith approximation are constructed explicitly in particular the problem of concordance of the es model with the h theorem is solved

additive generalization of the boltzmann entropy there exists a unique extension of the classical boltzmann entropy functional to a one parametric family of additive trace form entropy functionals we find the analytical solution to the corresponding deformation of the classical ensembles and present an example of the deformation of the uncorrelated state caused by finiteness of the number of particles

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

a convergence result for nonautonomous subgradient evolution equations and its application to the steepest descent exponential penalty trajectory in linear programming abstract we present a new result on the asymptotic behavior of nonautonomous subgradient evolution equations of the form u t t u t where t t 0 is a family of closed proper convex functions the result is used to study the flow generated by the family t x f x r t where f x r ctx r exp aix bi r is the exponential penalty approximation of the linear program min ctx ax b and r t is a positive function tending to 0 when t we prove that the trajectory u t converges to an optimal solution u of the linear program and we give conditions for the convergence of an associated dual trajectory t toward an optimal solution of the dual program

globally convergent edge preserving regularized reconstruction an application to limited angle tomography we introduce a generalization of a deterministic relaxation algorithm for edge preserving regularization in linear inverse problems this algorithm transforms the original possibly nonconvex optimization problem into a sequence of quadratic optimization problems and has been shown to converge under certain conditions when the original cost functional being minimized is strictly convex we prove that our more general algorithm is globally convergent i e converges to a local minimum from any initialization under less restrictive conditions even when the original cost functional is nonconvex we apply this algorithm to tomographic reconstruction from limited angle data by formulating the problem as one of regularized least squares optimization the results demonstrate that the constraint of piecewise smoothness applied through the use of edge preserving regularization can provide excellent limited angle tomographic reconstructions two edge preserving regularizers one convex the other nonconvex are used in numerous simulations to demonstrate the effectiveness of the algorithm under various limited angle scenarios and to explore how factors such as the choice of error norm angular sampling rate and amount of noise affect the reconstruction quality and algorithm performance these simulation results show that for this application the nonconvex regularizer produces consistently superior results

an efficient iterative algorithm for the approximation of the fast and slow dynamics of stiff systems the relation between the iterative algorithms based on the computational singular perturbation csp and the invariance equation ie methods is examined the success of the two methods is based on the appearance of fast and slow time scales in the dynamics of stiff systems both methods can identify the low dimensional surface in the phase space slow invariant manifold sim where the state vector is attracted under the action of fast dynamics it is shown that this equivalence of the two methods can be expressed by simple algebraic relations csp can also construct the simplified non stiff system that models the slow dynamics of the state vector on the sim an extended version of ie is presented which can also perform this task this new ie version is shown to be exactly similar to a modified version of csp which results in a very efficient algorithm especially in cases where the sim dimension is small so that significant model simplifications are possible

quantum moment hydrodynamics and the entropy principle this paper presents how a non commutative version of the entropy extremalization principle allows to construct new quantum hydrodynamic models our starting point is the moment method which consists in integrating the quantum liouville equation with respect to momentum p against a given vector of monomials of p like in the classical case the so obtained moment system is not closed inspired from levermore s procedure in the classical case 26 we propose to close the moment system by a quantum wigner distribution function which minimizes the entropy subject to the constraint that its moments are given in contrast to the classical case the quantum entropy is defined globally and not locally as the trace of an operator therefore the relation between the moments and the lagrange multipliers of the constrained entropy minimization problem becomes nonlocal and the resulting moment system involves nonlocal operators instead of purely local ones in the classical case in the present paper we discuss some practical aspects and consequences of this nonlocal feature

canonical distribution functions in polymer dynamics i dilute solutions of flexible polymers abstract the quasi equilibrium or maximum entropy approximation is applied in order to derive constitutive equations from kinetic models of polymer dynamics it is shown in general and illustrated for an example how canonical distribution functions are obtained from the maximum entropy principle how macroscopic and constitutive equations are derived therefrom and how these constitutive equations can be implemented numerically in addition a measure for the accuracy of the quasi equilibrium approximation is proposed that can be evaluated while integrating the constitutive equations in the example considered it is confirmed that the accuracy of the approximation is increased by including more macroscopic variables in steady elongational flow it is found that more macroscopic variables need to be included above the coil stretch transition to achieve the same accuracy as below

algebraic reconstruction in ct from limited views the author presents an algebraic reconstruction technique art as a viable alternative in computerized tomography ct from limited views recently algorithms of iterative reconstruction reprojection irr based on the method of convolution backprojection have been proposed for application in limited view ct reprojection was used in an iterative fashion alternating with backprojection as a means of estimating projection values within the sector of missing views in algebraic methods of reconstruction for ct only those projections corresponding to known data are required reprojection along missing views would merely serve to introduce redundant equations computer simulation studies are presented which demonstrate significantly improved reconstructed images achieved by an art algorithm as compared to irr methods

wavelet thresholding via a bayesian approach we discuss a bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression a prior distribution is imposed on the wavelet coefficients of the unknown response function designed to capture the sparseness of wavelet expansion that is common to most applications for the prior specified the posterior median yields a thresholding procedure our prior model for the underlying function can be adjusted to give functions falling in any specific besov space we establish a relationship between the hyperparameters of the prior model and the parameters of those besov spaces within which realizations from the prior will fall such a relationship gives insight into the meaning of the besov space parameters moreover the relationship established makes it possible in principle to incorporate prior knowledge about the function s regularity properties into the prior model for its wavelet coefficients however prior knowledge about a function s regularity properties might be difficult to elicit with this in mind we propose a standard choice of prior hyperparameters that works well in our examples several simulated examples are used to illustrate our method and comparisons are made with other thresholding methods we also present an application to a data set that was collected in an anaesthesiological study