system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

a new kernel based approach for linear system identification this paper describes a new kernel based approach for linear system identification of stable systems we model the impulse response as the realization of a gaussian process whose statistics differently from previously adopted priors include information not only on smoothness but also on bibo stability the associated autocovariance defines what we call a stable spline kernel the corresponding minimum variance estimate belongs to a reproducing kernel hilbert space which is spectrally characterized compared to parametric identification techniques the impulse response of the system is searched for within an infinite dimensional space dense in the space of continuous functions overparametrization is avoided by tuning few hyperparameters via marginal likelihood maximization the proposed approach may prove particularly useful in the context of robust identification in order to obtain reduced order models by exploiting a two step procedure that projects the nonparametric estimate onto the space of nominal models the continuous time derivation immediately extends to the discrete time case on several continuous and discrete time benchmarks taken from the literature the proposed approach compares very favorably with the existing parametric and nonparametric techniques

an interior point constrained trust region method for a special class of nonlinear semidefinite programming problems in this paper an interior point trust region algorithm for the solution of a class of nonlinear semidefinite programming sdp problems is described and analyzed such nonlinear and nonconvex programs arise e g in the design of optimal static or reduced order output feedback control laws and have the structure of abstract optimal control problems in a finite dimensional hilbert space the algorithm treats the abstract states and controls as independent variables in particular an algorithm for minimizing a nonlinear matrix objective functional subject to a nonlinear sdp condition a positive definiteness condition and a nonlinear matrix equation is considered the algorithm is designed to take advantage of the structure of the problem it is an extension of an interior point trust region method to nonlinear and nonconvex sdps with a special structure which applies sequential quadratic programming techniques to a sequence of barrier problems and uses trust regions to ensure robustness of the iteration some convergence results are given and finally several numerical examples demonstrate the applicability of the considered algorithm

continuous time quantum walk on integer lattices and homogeneous trees this paper is concerned with the continuous time quantum walk on d and infinite homogeneous trees by using the generating function method we compute the limit of the average probability distribution for the general isotropic walk on and for nearest neighbor walks on d and infinite homogeneous trees in addition we compute the asymptotic approximation for the probability of the return to zero at time t in all these cases

a trust region spectral bundle method for nonconvex eigenvalue optimization we present a nonsmooth optimization technique for nonconvex maximum eigenvalue functions and for nonsmooth functions which are infinite maxima of eigenvalue functions we prove global convergence of our method in the sense that for an arbitrary starting point every accumulation point of the sequence of iterates is critical the method is tested on several problems in feedback control synthesis

a global algorithm for nonlinear semidefinite programming in this paper we propose a global algorithm for solving nonlinear semidefinite programming problems this algorithm inspired by the classic sqp sequentially quadratic programming method modifies the s sdp sequentially semidefinite programming local method by using a nondifferentiable merit function combined with a line search strategy

a spatio temporal deconvolution method to improve perfusion ct quantification perfusion imaging is a useful adjunct to anatomic imaging in numerous diagnostic and therapy monitoring settings one approach to perfusion imaging is to assume a convolution relationship between a local arterial input function and the tissue enhancement profile of the region of interest via a residue function and subsequently solve for this residue function this ill posed problem is generally solved using singular value decomposition based approaches and the hemodynamic parameters are solved for each voxel independently in this paper we present a formulation which incorporates both spatial and temporal correlations and show through simulations that this new formulation yields higher accuracy and greater robustness with respect to image noise we also show using rectal cancer tumor images that this new formulation results in better segregation of normal and cancerous voxels

bayesian methods for pharmacokinetic models in dynamic contrast enhanced magnetic resonance imaging this paper proposes a new method for estimating kinetic parameters of dynamic contrast enhanced magnetic resonance imaging dce mri based on adaptive gaussian markov random fields kinetic parameter estimates using neighboring voxels reduce the observed variability in local tumor regions while preserving sharp transitions between heterogeneous tissue boundaries asymptotic results for standard errors from likelihood based nonlinear regression are compared with those derived from the posterior distribution using bayesian estimation with and without neighborhood information application of the method to the analysis of breast tumors based on kinetic parameters has shown that the use of bayesian analysis combined with adaptive gaussian markov random fields provides improved convergence behavior and more consistent morphological and functional statistics

second order optimality conditions in nonlinear programming obtained by way of epi derivatives dedicated to the memory of robin w chaney second order optimality conditions for finite dimensional smooth and nonsmooth nonlinear programming are obtained by a new method that emphasizes a close connection with geometrical approximation of the essential objective function the approximation is secured by the use of certain epi derivatives defined by epiconvergence the optimality conditions are expressed in a form that covers general interval constraints and their possible representation through penalties or an augmented lagrangian an abstract constraint involving restriction to a convex polyhedron is incorporated

from quantum cellular automata to quantum lattice gases a natural architecture for nanoscale quantum computation is that of a quantum cellular automaton motivated by this observation we begin an investigation of exactly unitary cellular automata after proving that there can be no nontrivial homogeneous local unitary scalar cellular automaton in one dimension we weaken the homogeneity condition and show that there are nontrivial exactly unitary partitioning cellular automata we find a one parameter family of evolution rules which are best interpreted as those for a one particle quantum automaton this model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the dirac equation we describe two generalizations of this automaton the second of which to multiple interacting particles is the correct definition of a quantum lattice gas

trust region methods for solving the optimal output feedback design problem we consider the problem of designing feedback control laws when a complete set of state variables is not available for linear autonomous control systems with quadratic performance criterion the design problem consists of choosing an appropriate static output feedback sof gain matrix according to a certain objective function the corresponding non linear matrix optimization problem can be interpreted as an equality constrained minimization problem for solving this problem we propose a constrained trust region ctr algorithm which presents a new and efficient numerical approach for this problem class on the other hand based on the formulation used in the past the sof problem can be also interpreted as an unconstrained programming problem thus based on this interpretation we also develop an unconstrained trust region utr method finally several numerical examples for optimal sof problems demonstrate the applicability of the considered algorithm

controller design via nonsmooth multidirectional search we propose an algorithm which combines multidirectional search mds with nonsmooth optimization techniques to solve difficult problems in automatic control applications include static and fixed order output feedback controller design simultaneous stabilization h 2 h infty synthesis and much else we show how to combine direct search techniques with nonsmooth descent steps in order to obtain convergence certificates in the presence of nonsmoothness our technique is efficient when small and medium size controllers for plants with large state dimension are sought our numerical testing includes several benchmark examples for instance our algorithm needs 0 41 s to compute a static output feedback stabilizing controller for the boeing 767 flutter benchmark problem e e j davison ifac technical committee reports pergamon press oxford 1990 a system with 55 states the first static controller without performance specifications for this system was obtained in j burke a lewis and m overton siam j optim 15 2003 pp 751 779

on the relationship between continuous and discrete time quantum walk quantum walk is one of the main tools for quantum algorithms defined by analogy to classical random walk a quantum walk is a time homogeneous quantum process on a graph both random and quantum walks can be defined either in continuous or discrete time but whereas a continuous time random walk can be obtained as the limit of a sequence of discrete time random walks the two types of quantum walk appear fundamentally different owing to the need for extra degrees of freedom in the discrete time case

a partially augmented lagrangian method for low order rm h infinity controller synthesis using rational constraints this technical note proposes a method for low order h infinity synthesis where the constraint on the order of the controller is formulated as a rational equation the resulting nonconvex optimization problem is then solved by applying a partially augmented lagrangian method the proposed method is evaluated together with two well known methods from the literature the results indicate that the proposed method has comparable performance and speed

dynamics of continuous time quantum walks in restricted geometries we study quantum transport on finite discrete structures and we model the process by means of continuous time quantum walks a direct and effective comparison between quantum and classical walks can be attained based on the average displacement of the walker as a function of time indeed a fast growth of the average displacement can be advantageously exploited to build up efficient search algorithms by means of analytical and numerical investigations we show that the finiteness and the inhomogeneity of the substrate jointly weaken the quantum walk performance we further highlight the interplay between the quantum walk dynamics and the underlying topology by studying the temporal evolution of the transfer probability distribution and the lower bound of long time averages

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

first and second order analysis of nonlinear semidefinite programs in this paper we study nonlinear semidefinite programming problems convexity duality and first order optimality conditions for such problems are presented a second order analysis is also given second order necessary and sufficient optimality conditions are derived finally sensitivity analysis of such programs is discussed

robust low dose ct perfusion deconvolution via tensor total variation regularization acute brain diseases such as acute strokes and transit ischemic attacks are the leading causes of mortality and morbidity worldwide responsible for 9 of total death every year time is brain is a widely accepted concept in acute cerebrovascular disease treatment efficient and accurate computational framework for hemodynamic parameters estimation can save critical time for thrombolytic therapy meanwhile the high level of accumulated radiation dosage due to continuous image acquisition in ct perfusion ctp raised concerns on patient safety and public health however low radiation leads to increased noise and artifacts which require more sophisticated and time consuming algorithms for robust estimation in this paper we focus on developing a robust and efficient framework to accurately estimate the perfusion parameters at low radiation dosage specifically we present a tensor total variation ttv technique which fuses the spatial correlation of the vascular structure and the temporal continuation of the blood signal flow an efficient algorithm is proposed to find the solution with fast convergence and reduced computational complexity extensive evaluations are carried out in terms of sensitivity to noise levels estimation accuracy contrast preservation and performed on digital perfusion phantom estimation as well as in vivo clinical subjects our framework reduces the necessary radiation dose to only 8 of the original level and outperforms the state of art algorithms with peak signal to noise ratio improved by 32 it reduces the oscillation in the residue functions corrects over estimation of cerebral blood flow cbf and under estimation of mean transit time mtt and maintains the distinction between the deficit and normal regions

convergence of continuous time quantum walks on the line the position density of a particle performing a continuous time quantum walk on the integer lattice viewed on length scales inversely proportional to the time t converges as t tends to infinity to a probability distribution that depends on the initial state of the particle this convergence behavior has recently been demonstrated for the simplest continuous time random walk n konno phys rev e 72 026113 2005 in this brief report we use a different technique to establish the same convergence for a very large class of continuous time quantum walks and we identify the limit distribution in the general case

spectral bundle methods for non convex maximum eigenvalue functions second order methods we study constrained and unconstrained optimization programs for nonconvex maximum eigenvalue functions we show how second order techniques may be introduced as soon as it is possible to reliably guess the multiplicity of the maximum eigenvalue at a limit point we examine in which way standard and projected newton steps may be combined with a nonsmooth first order method to obtain a globally convergent algorithm with a fair chance to local superlinear or quadratic convergence

two numerical methods for optimizing matrix stability consider the affine matrix family a x a0 m 1 xkak mapping a design vector x r m into the space of n n real matrices we are interested in the question of how to choose x to optimize the stability of the matrix a x a typical motivation is that one wishes to control the stability of the dynamical system a x z a classic example is stabilization by output feedback we take two approaches let x denote the spectral abscissa the largest real part of the eigenvalues of a matrix x as is well known this quantity bounds the asymptotic decay rate of the trajectories of the associated dynamical system z xz our first approach to optimizing stability is to directly minimize the function a x the spectral abscissa x is a continuous but non smooth in fact non lipschitz function of the matrix argument x and finding a global minimizer of a x is hard we introduce a novel random gradient bundle method for approximating local minimizers motivated by recent work on nonsmooth analysis of the function x our second approach is to minimize a related function a x where is a robustness parameter in 0 1 one motivation for the definition of the robust spectral abscissa x is that it bounds transient peaks as well as asymptotic decay of trajectories of xz the function x is lipschitz but non convex for 0 1

a spatio temporal regression model for the analysis of functional mri data the standard method for analyzing functional magnetic resonance imaging fmri data applies the general linear model to the time series of each voxel separately such a voxelwise approach however does not consider the spatial autocorrelation between neighboring voxels in its model formulation and parameter estimation we propose a spatio temporal regression analysis for detecting activation in fmri data its main features are that 1 each voxel has a regression model that involves the time series of the neighboring voxels together with its own 2 the regression coefficient assigned to the center voxel is estimated so that the time series of these multiple voxels will best fit the model 3 a generalized least squares gls method was employed instead of the ordinary least squares ols to put intrinsic autocorrelation structures into the model and 4 the underlying spatial and temporal correlation structures are modeled using a separable model which expresses the combined correlation structures as a product of the two we evaluated the statistical power of our model in comparison with voxelwise ols gls models and a multivoxel ols model our model s power to detect clustered activation was higher than that of the two voxelwise models and comparable to that of the multivoxel ols we examined the usefulness and goodness of fit of our model using real experimental data our model successfully detected neural activity in expected brain regions and realized better fit than the other models these results suggest that our spatio temporal regression model can serve as a reliable analysis suited for the nature of fmri data

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

convergence properties of an augmented lagrangian algorithm for optimization with a combination of general equality and linear constraints we consider the global and local convergence properties of a class of augmented lagrangian methods for solving nonlinear programming problems in these methods linear and more general constraints are handled in different ways the general constraints are combined with the objective function in an augmented lagrangian the iteration consists of solving a sequence of subproblems in each subproblem the augmented lagrangian is approximately minimized in the region defined by the linear constraints a subproblem is terminated as soon as a stopping condition is satisfied the stopping rules that we consider here encompass practical tests used in several existing packages for linearly constrained optimization our algorithm also allows different penalty parameters to be associated with disjoint subsets of the general constraints in this paper we analyze the convergence of the sequence of iterates generated by such an algorithm and prove global and fast linear convergence as well as show that potentially troublesome penalty parameters remain bounded away from zero

partially augmented lagrangian method for matrix inequality constraints we discuss a partially augmented lagrangian method for optimization programs with matrix inequality constraints a global convergence result is obtained applications to hard problems in feedback control are presented to validate the method numerically

parametric robust structured control design we present a new approach to parametric robust controller design where we compute controllers of arbitrary order and structure which minimize the worst case h infty norm over a pre specified set of uncertain parameters at the core of our method is a nonsmooth minimization method tailored to functions which are semi infinite minima of smooth functions a rich test bench and a more detailed example illustrate the potential of the technique which can deal with complex problems involving multiple possibly repeated uncertain parameters

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a perturbation method for optimizing matrix stability we present the first practical perturbation method for optimizing matrix stability using spectral abscissa minimization using perturbation theory for a matrix with simple eigenvalues and coupling this with linear programming we successively reduce the spectral abscissa of a matrix until it reaches a local minimum optimality conditions for a local minimizer of the spectral abscissa are provided and proved for both the affine matrix problem and the output feedback control problem experiments show that this novel perturbation method is efficient especially for a matrix with the majority of whose eigenvalues are already located in the left half of the complex plane moreover unlike most available methods the method does not require the introduction of lyapunov variables the method is illustrated for a small size matrix from an affine matrix problem and is then applied to large matrices actually arising from more sophisticated control problems used in the design of the boeing 767 jet and a nuclear powered turbo generator

robust control via sequential semidefinite programming this paper discusses nonlinear optimization techniques in robust control synthesis with special emphasis on design problems which may be cast as minimizing a linear objective function under linear matrix inequality lmi constraints in tandem with nonlinear matrix equality constraints the latter type of constraints renders the design numerically and algorithmically difficult we solve the optimization problem via sequential semidefinite programming ssdp a technique which expands on sequential quadratic programming sqp known in nonlinear optimization global and fast local convergence properties of ssdp are similar to those of sqp and ssdp is conveniently implemented with available semidefinite programming sdp solvers using two test examples we compare ssdp to the augmented lagrangian method another classical scheme in nonlinear optimization and to an approach using concave optimization

second order nonsmooth optimization for h synthesis the standard way to compute h feedback controllers uses algebraic riccati equations and is therefore of limited applicability here we present a new approach to the h output feedback control design problem which is based on nonlinear and nonsmooth mathematical programming techniques our approach avoids the use of lyapunov variables and is therefore flexible in many practical situations

limit theorem for continuous time quantum walk on the line concerning a discrete time quantum walk x t d with a symmetric distribution on the line whose evolution is described by the hadamard transformation it was proved by the author that the following weak limit theorem holds x t d t ensuremath rightarrow dx ensuremath pi 1 ensuremath x 2 sqrt 1 ensuremath 2 x 2 as t ensuremath rightarrow ensuremath infty the present paper shows that a similar type of weak limit theorem is satisfied for a continuous time quantum walk x t c on the line as follows x t c t ensuremath rightarrow dx ensuremath pi sqrt 1 ensuremath x 2 as t ensuremath rightarrow ensuremath infty these results for quantum walks form a striking contrast to the central limit theorem for symmetric discrete and continuous time classical random walks y t sqrt t ensuremath rightarrow e ensuremath x 2 2 dx sqrt 2 ensuremath pi as t ensuremath rightarrow ensuremath infty the work deals also with the issue of the relationship between discrete and continuous time quantum walks this topic subject of a long debate in the previous literature is treated within the formalism of matrix representation and the limit distributions are exhaustively compared in the two cases

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

first and second order epi differentiability in eigenvalue optimization abstract the subject of this work is the first and second order sensitivity analysis of some spectral functions which are essential in eigenvalue optimization by the way of epi differentiability we show that the sum of the m largest eigenvalues of a real symmetric matrix is twice epi differentiable and we derive an explicit expression of its second order epi derivative we also prove that the mth largest eigenvalue function is twice epi differentiable if and only if it ranks first in a group of equal eigenvalues finally we derive chain rules and then we obtain optimality conditions for an important class of eigenvalue optimization problems

controllability and observability of grid graphs via reduction and symmetries in this paper we investigate the controllability and observability properties of a family of linear dynamical systems whose structure is induced by the laplacian of a grid graph this analysis is motivated by several applications in network control and estimation quantum computation and discretization of partial differential equations specifically we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph for each eigenvalue based on its multiplicity and on suitable symmetries of the corresponding eigenvectors we provide necessary and sufficient conditions to characterize all and only the nodes from which the induced dynamical system is controllable observable we discuss the proposed criteria and show through suitable examples how such criteria reduce the complexity of the controllability respectively observability analysis of the grid

geometrically induced force interaction for three dimensional deformable models in this paper we propose a novel 3 d deformable model that is based upon a geometrically induced external force field which can be conveniently generalized to arbitrary dimensions this external force field is based upon hypothesized interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient the evolution of the deformable model is solved using the level set method so that topological changes are handled automatically the relative geometrical configurations between the deformable model and the object boundaries contribute to a dynamic vector force field that changes accordingly as the deformable model evolves the geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries and it gives the deformable model a high invariancy in initialization configurations the voxel interactions across the whole image domain provide a global view of the object boundary representation giving the external force a long attraction range the bidirectionality of the external force field allows the new deformable model to deal with arbitrary cross boundary initializations and facilitates the handling of weak edges and broken boundaries in addition we show that by enhancing the geometrical interaction field with a nonlocal edge preserving algorithm the new deformable model can effectively overcome image noise we provide a comparative study on the segmentation of various geometries with different topologies from both synthetic and real images and show that the proposed method achieves significant improvements against existing image gradient techniques

the rate of escape for anisotropic random walks in a tree let g be the group generated by l free involutions whose cayley graph t is the infinite homogeneous tree with l edges at every node a general central limit theorem and law of the iterated logarithm is proven for left invariant random walks z n on g or t which applies to the distance of z n from a fixed point as well as to the distribution of the last r letters in z n for nearest neighbor random walks we also derive a generating function identity that yields formulas for the asymptotic mean and variance of the distance from a fixed point a generalization for z n with a finitely supported step distribution is derived and discussed

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

fast sampling of gaussian markov random fields this paper demonstrates how gaussian markov random fields conditional autoregressions can be sampled quickly by using numerical techniques for sparse matrices the algorithm is general and efficient and expands easily to various forms for conditional simulation and evaluation of normalization constants we demonstrate its use by constructing efficient block updates in markov chain monte carlo algorithms for disease mapping

low dose ct perfusion with k space weighted image average kwia ctp computed tomography perfusion is widely used in clinical practice for the evaluation of cerebrovascular disorders however ctp involves high radiation dose 200mgy as the x ray source remains continuously on during the passage of contrast media the purpose of this study is to present a low dose ctp technique termed k space weighted image average kwia using a novel projection view shared averaging algorithm with reduced tube current kwia takes advantage of k space signal property that the image contrast is primarily determined by the k space center with low spatial frequencies and oversampled projections kwia divides each 2d fourier transform ft or k space ctp data into multiple rings the outer rings are averaged with neighboring time frames to achieve adequate signal to noise ratio snr while the center region of k space remains unchanged to preserve high temporal resolution reduced dose sinogram data were simulated by adding poisson distributed noise with zero mean on digital phantom and clinical ctp scans a physical ctp phantom study was also performed with different x ray tube currents the sinogram data with simulated and real low doses were then reconstructed with kwia and compared with those reconstructed by standard filtered back projection fbp and simultaneous algebraic reconstruction with regularization of total variation sart tv evaluation of image quality and perfusion metrics using parameters including snr cnr contrast to noise ratio auc area under the curve and cbf cerebral blood flow demonstrated that kwia is able to preserve the image quality spatial and temporal resolution as well as the accuracy of perfusion quantification of ctp scans with considerable 50 75 dose savings

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

bayesian hemodynamic parameter estimation by bolus tracking perfusion weighted imaging a delay insensitive probabilistic method for estimating hemodynamic parameters delays theoretical residue functions and concentration time curves by computed tomography ct and magnetic resonance mr perfusion weighted imaging is presented only a mild stationarity hypothesis is made beyond the standard perfusion model new microvascular parameters with simple hemodynamic interpretation are naturally introduced simulations on standard digital phantoms show that the method outperforms the oscillating singular value decomposition osvd method in terms of goodness of fit linearity statistical and systematic errors on all parameters especially at low signal to noise ratios snrs delay is always estimated sharply with user supplied resolution and is purely arterial by contrast to osvd time to maximum tmax that is very noisy and biased by mean transit time mtt blood volume and snr residue functions and signals estimates do not suffer overfitting anymore one ct acute stroke case confirms simulation results and highlights the ability of the method to reliably estimate mtt when snr is low delays look promising for delineating the arterial occlusion territory and collateral circulation

weak limits for quantum random walks we formulate and prove a general weak limit theorem for quantum random walks in one and more dimensions with x n denoting position at time n we show that x n n converges weakly as stackrel ensuremath rightarrow n ensuremath infty to a certain distribution which is absolutely continuous and of bounded support the proof is rigorous and makes use of fourier transform methods this approach simplifies and extends certain preceding derivations valid in one dimension that make use of combinatorial and path integral methods

an augmented lagrangian method for a class of lmi constrained problems in robust control theory we present a new approach to a class of non convex lmi constrained problems in robust control theory the problems we consider may be recast as the minimization of a linear objective subject to linear matrix inequality lmi constraints in tandem with non convex constraints related to rank deficiency conditions we solve these problems using an extension of the augmented lagrangian technique the lagrangian function combines a multiplier term and a penalty term governing the non convex constraints the lmi constraints due to their special structure are retained explicitly and not included in the lagrangian global and fast local convergence of our approach is then obtained either by an lmi constrained newton type method including line search or by a trust region strategy the method is conveniently implemented with available semi definite programming sdp interior point solvers we compare its performance to the wellknown d k iteration scheme in robust control two test problems are investigated and

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results abstract an extensive literature in econometrics and in numerical analysis has considered the problem of evaluating the multiple integral p b a b n v dv e v 1 v b where v is a m dimensional normal vector with mean covariance matrix and density n v and 1 v b is an indicator for the event b v a a leading case of such an integral is the negative orthant probability where b v v the problem is computationally difficult except in very special cases the multinomial probit mnp model used in econometrics and biometrics has cell probabilities that are negative orthant probabilities with and depending on unknown parameters and in general on covariates estimation of this model requires for each trial parameter vector and each observation in a sample evaluation of p b and of its derivatives with respect to and this paper surveys monte carlo techniques that have been developed for approximations of p b and its linear and logarithmic derivatives that limit computation while possessing properties that facilitate their use in iterative calculations for statistical inference the crude frequency simulator cfs normal importance sampling nis a kernel smoothed frequency simulator kfs stern s decomposition simulator sds the geweke hajivassiliou keane simulator ghk a parabolic cylinder function simulator pcf deak s chi squared simulator dcs an acceptance rejection simulator ars the gibbs sampler simulator gss a sequentially unbiased simulator sus and an approximately unbiased simulator aus we also discuss gauss and fortran implementations of these algorithms and present our computational experience with them we find that ghk is overall the most reliable method

nonsmooth h_infty synthesis we develop nonsmooth optimization techniques to solve h infty synthesis problems under additional structural constraints on the controller our approach avoids the use of lyapunov variables and therefore leads to moderate size optimization programs even for very large systems the proposed framework is versatile and can accommodate a number of challenging design problems including static fixed order fixed structure decentralized control design of pid controllers and simultaneous design and stabilization problems our algorithmic strategy uses generalized gradients and bundling techniques suited for the h infty norm and other nonsmooth performance criteria we compute descent directions by solving quadratic programs and generate steps via line search convergence to a critical point from an arbitrary starting point is proved and numerical tests are included to validate our methods the proposed approach proves to be efficient even for systems with several hundreds of states