from time series to linear system part i finite dimensional linear time invariant systems abstract in the first part of this paper the definition of a dynamical system as simply consisting of a family of time series will be developed in this context the notions of linearity time invariance and finite dimensionality will be introduced it will be shown that a given family of time series may be represented by a system of ar equations riw t l rl 1w t l 1 r0w t 0 or equivalently by a finite dimensional linear time invariant system x t 1 ax t bu t y t cx t du t w u y if and only if this family is linear shift invariant and complete or as is equivalent closed in the topology of pointwise convergence this yields a very high level and elegant set of axioms which characterize these familiar objects it is emphasized however that no a priori choice is made as to which components of w are inputs and which are outputs such a separation always exists in any specific linear time invariant model starting from these definitions the structural indices of such systems are introduced and it is shown how an ar representation of a system having a given behaviour can be constructed these results will be used in a modelling context in part ii of the paper

a note on the optimal quadrature inhp the existence of optimal nodes with preassigned multiplicities is proved for the hardy spacesh p 1 p this is then used to show that the exact order of convergence for the optimal qudrature formula withn nodes including multiplicity is n 1 2q exp pi sqrt n q where 1 p 1 q 1 and 1 p

a robust double exponential formula for fourier type integrals abstract a double exponential transformation is presented to obtain a quadrature formula for fourier type integrals 0 f x sin x d x or 0 f x cos x d x where f x is a slowly decaying analytic function on 0 it is an improved version of what we previously proposed in 1991 the transformation x t is such that it maps the interval 0 onto and that while the integrand after the transformation decreases double exponentially at large negative t the points of the formula approaches to zeros of sin x or cos x double exponentially at large positive t then the trapezoidal formula with an equal mesh size is applied to the integral over after the transformation which gives an efficient quadrature formula for the fourier type integrals the present transformation is improved in the sense that it can integrate a function f z with singularities in the finite z plane more efficiently than the one previously proposed

a sinc approximation for the indefinite integral a method for computing fo f t dt x 0 1 is outlined where f t may have singularities at t 0 and t 1 the method depends on the approximation properties of whittaker cardinal or sinc function expansions the general technique may be used for semi infinite or infinite intervals in addition to 0 1 tables of numerical results are given

imposing boundary conditions in sinc method using highest derivative approximation sinc approximate methods are often used to solve complex boundary value problems such as problems on unbounded domains or problems with endpoint singularities a recent implementation of the sinc method li c and wu x numerical solution of differential equations using sinc method based on the interpolation of the highest derivatives applied mathematical modeling 31 1 2007 1 9 in which sinc basis functions are used to approximate the highest derivative in the governing equation of the boundary value problem is evaluated for structural mechanics applications in which interlaminar stresses are desired we suggest an alternative approach for specifying the boundary conditions and we compare the numerical results for analysis of a laminated composite timoshenko beam implementing both li and wu s approach and our alternative approach for applying the boundary conditions for the timoshenko beam problem we obtain accurate results using both approaches including transverse shear stress by integration of the 3d equilibrium equations of elasticity the beam results indicate our approach is less dependent on the selection of the sinc mesh size than li and wu s sihd we also apply sihd to analyze a classical laminated composite plate for the plate example we experience difficulty in obtaining a complete system of equations using li and wu s approach for our approach we suggest that additional necessary information may be obtained by applying the derivatives of the boundary conditions on each edge using this technique we obtain accurate results for deflection and stresses including interlaminar stresses by integration of the 3d equilibrium equations of elasticity our results for both the beam and the plate problems indicate that this approach is easily implemented has a high level of accuracy and good convergence properties

why do stabilizing controllers stabilize an alternative notion of a stabilizing controller is presented being defined in terms of the trajectories of plant and controller it is well suited for situations in which the controller s action is an interconnecting one in the second part of the paper a parametrization is given of the kernel representations of all controllers that give rise to an a priori specified closed loop behavior as a special case the parametrization yields all stabilizing controllers unlike the youla parametrization it also includes the so called singular stabilizing controllers

minimality and observability of group systems abstract group systems are a generalization of willems type linear systems that are useful in error control coding it is shown that the basic ideas of willems s treatment of linear systems are easily generalized to linear systems over arbitrary rings and to group systems the interplay between systems behaviors and trellises evolution laws is discussed with respect to completeness minimality controllability and observability it is pointed out that for trellises of group systems and willems type linear systems minimality is essentially the same as observability the development is universal algebraic in nature and holds unconditionally for linear systems over the real numbers

theoretical analysis of a sinc nystrom method for volterra integro differential equations and its improvement abstract a sinc nystrom method for volterra integro differential equations was developed by zarebnia 2010 the method is quite efficient in the sense that exponential convergence can be obtained even if the given problem has endpoint singularity however its exponential convergence has not been proved theoretically in addition to implement the method the regularity of the solution is required although the solution is an unknown function in practice this paper reinforces the method by presenting two theoretical results 1 the regularity of the solution is analyzed and 2 its convergence rate is rigorously analyzed moreover this paper improves the method so that a much higher convergence rate can be attained and theoretical results similar to those listed above are provided numerical comparisons are also provided

integrated local petrov galerkin sinc method for structural mechanics problems an integrated local petrov galerkin sinc method is introduced and applied to static structural mechanics problems the method approximates the highest derivative in the local weak form of the governing equation on a rectangular grid and the lower derivatives and unknown function are found by numerical indenite integration we suggest that the essential boundary conditions may be applied by the traditional penalty method or by a method in which the stiness matrix is reduced to eliminate dependent degrees of freedom we propose and compare the performance of three basis functions in terms of their accuracy and convergence properties for two problems a one dimensional tapered bar and a two dimensional plane stress elasticity problem our results indicate that the present method can provide greater accuracy than the sinc method based on interpolation of highest derivative an integration based collocation method suggested by li and wu li c and wu x numerical solution of dierential equations using sinc method based on

numerical solution of integral equations by means of the sinc collocation method based on the double exponential transformation numerical solution of linear integral equations by means of the sinc collocation method based on the double exponential transformation abbreviated the de transformation is considered we first apply the method to the volterra integral equation of the second kind and then to the volterra equation of the first kind this method is also applied to the fredholm integral equation of the second kind for the volterra equations we employed a formula for numerical indefinite integration developed by muhammad and mori obtained by applying the de transformation incorporated into the sinc expansion of the integrand while for the fredholm equation we employed the conventional de transformation for definite integrals an error analysis of the method is given and in every case a convergence rate of o exp cn logn for the error is established where n is a parameter representing the number of terms of the sinc expansion also the condition of the matrix of the main system of linear equations is watched through an estimate of the condition number returned by the program numerical examples show the convergence rate mentioned above and confirm the high efficiency of the present method

penalized weighted least squares image reconstruction for positron emission tomography presents an image reconstruction method for positron emission tomography pet based on a penalized weighted least squares pwls objective for pet measurements that are precorrected for accidental coincidences the author argues statistically that a least squares objective function is as appropriate if not more so than the popular poisson likelihood objective the author proposes a simple data based method for determining the weights that accounts for attenuation and detector efficiency a nonnegative successive over relaxation sor algorithm converges rapidly to the global minimum of the pwls objective quantitative simulation results demonstrate that the bias variance tradeoff of the pwls sor method is comparable to the maximum likelihood expectation maximization ml em method but with fewer iterations and is improved relative to the conventional filtered backprojection fbp method qualitative results suggest that the streak artifacts common to the fbp method are nearly eliminated by the pwls sor method and indicate that the proposed method for weighting the measurements is a significant factor in the improvement over fbp

on the control of finite support behaviors abstract in the paper the main properties of finite support behaviors are introduced and characterized in terms of the polynomial matrices involved in their representation necessary and sufficient conditions for the existence of an input output possibly non anticipating description of a finite support behavior are given the control problem is also addressed and properly restated in the behavior theory context as an interconnection problem conditions for the existence of controllers that make the resulting connected system observable as well as a complete description of the class of characteristic polynomials that the resulting controlled system possibly exhibits are given finally the problem of controlling a dynamical system in input output from by means of a controller with the same structure is investigated and solved

a generalized em algorithm for 3 d bayesian reconstruction from poisson data using gibbs priors a generalized expectation maximization gem algorithm is developed for bayesian reconstruction based on locally correlated markov random field priors in the form of gibbs functions and on the poisson data model for the m step of the algorithm a form of coordinate gradient ascent is derived the algorithm reduces to the em maximum likelihood algorithm as the markov random field prior tends towards a uniform distribution three different gibbs function priors are examined reconstructions of 3 d images obtained from the poisson model of single photon emission computed tomography are presented

an efficient numerical scheme for a nonlinear integro differential equations with an integral boundary condition nonlinear functional integro differential equations with an integral boundary condition is appeared in chemical engineering underground water flow and population dynamics phenomena and other field of physics and mathematical chemistry so this paper presents a powerful numerical approach based on an iterative technique and sinc quadrature to estimate a solution for this equation then convergence of this technique is discussed by preparing a theorem which guarantees the applicability of that finally some numerical examples are given to confirm efficiency and accuracy of the numerical scheme

error estimates with explicit constants for sinc approximation sinc quadrature and sinc indefinite integration error estimates with explicit constants are given for approximations of functions definite integrals and indefinite integrals by means of the sinc approximation although in the literature various error estimates have already been given for these approximations those estimates were basically for examining the rates of convergence and several constants were left unevaluated giving more explicit estimates i e evaluating these constants is of great practical importance since by this means we can reinforce the useful formulas with the concept of verified numerical computations in this paper we reveal the explicit form of all constants in a computable form under the same assumptions of the existing theorems the function to be approximated is analytic in a suitable region we also improve some formulas themselves to decrease their computational costs numerical examples that confirm the theory are also given

paradigms and puzzles in the theory of dynamical systems a self contained exposition is given of an approach to mathematical models in particular to the theory of dynamical systems the basic ingredients form a triptych with the behavior of a system in the center and behavioral equations with latent variables as side panels the author discusses a variety of representation and parametrization problems in particular questions related to input output and state models the proposed concept of a dynamical system leads to a new view of the notions of controllability and observability and of the interconnection of systems in particular to what constitutes a feedback control law the final issue addressed is that of system identification it is argued that exact system identification leads to the question of computing the most powerful unfalsified model

de sinc methods have almost the same convergence property as se sinc methods even for a family of functions fitting the se sinc methods in this paper the theoretical convergence rate of the trapezoidal rule combined with the double exponential de transformation is given for a class of functions for which the single exponential se transformation is suitable it is well known that the de transformation enables the rule to achieve a much higher rate of convergence than the se transformation and the convergence rate has been analyzed and justified theoretically under a proper assumption here it should be emphasized that the assumption is more severe than the one for the se transformation and there actually exist some examples such that the trapezoidal rule with the se transformation achieves its usual rate whereas the rule with de does not such cases have been observed numerically but no theoretical analysis has been given thus far this paper reveals the theoretical rate of convergence in such cases and it turns out that the de s rate is almost the same as but slightly lower than that of the se by using the analysis technique developed here the theoretical convergence rate of the sinc approximation with the de transformation is also given for a class of functions for which the se transformation is suitable the result is quite similar to above the convergence rate in the de case is slightly lower than in the se case numerical examples which support those two theoretical results are also given

quadrature formulas obtained by variable transformation and the de rule abstract this paper gives a survey of the results known to date about quadrature formulas obtained by variable transformation followed by an application of the trapezoidal rule with an equal mesh size it has been shown that a formula obtained by an appropriate transformation is in general efficient and also robust against the end point singularity various kinds of useful transformations together with the asymptotic error behaviors of the resulting quadrature formulas are summarized in particular special emphasis is placed on an asymptotically optimal formula called the double exponential formula abbreviated as the de rule which is characterized by the double exponential decrease of its weights in the neighborhood of the end points of the transformed interval of integration

two formulas for numerical indefinite integration we derive two formulas for approximating the indefinite integral over a finite interval the approximation error is 0 c cv uniformly where m is the number of integrand evaluations the integrand is required to be analytic in the interior of the integration interval but may be singular at the endpoints some sample calculations indicate that the actual convergence rate accords with the error bound derived

parameter tuning and repeated application of the imt type transformation in numerical quadrature the imt rule which is especially suited for the integration of functions with end point singularities is generalized by introducing parameters and also by repeatedly applying the parametrized imt transformation the quadrature formulas thus obtained are improved considerably both in efficiency and in robustness against end point singularities asymptotic error estimates and numerical results are also given

sinc galerkin method based on the de transformation for the boundary value problem of fourth order ode in this paper a sinc galerkin method incorporated with the double exponential transformation abbreviated as the de transformation for the two point boundary value problem of fourth order ordinary differential equation is considered in this method the error bound o exp c n logn c 0 is attained as in the sinc collocation method based on the de transformation where n is a parameter representing the number of terms in the sinc approximation high efficiency of the sinc galerkin method with the de transformation is confirmed by some numerical examples and the numerical results were compared with ones obtained by sinc collocation method based on the de transformation

double exponential transformation in the sinc collocation method for a boundary value problem with fourth order ordinary differential equation in this paper we consider a sinc collocation method for the two point boundary value problem of fourth order ordinary differential equation incorporated with the double exponential transformation abbreviated as the de transformation by this method a convergence rate o exp cn log n where n is a parameter representing the number of terms in the sinc approximation is attained we compared the result with ones based on the single exponential transformation which made us confirm the high efficiency of the present method

multivariate integration over r s with exponential rate of convergence in this paper we analyze the approximation of multivariate integrals over the euclidean space for functions which are analytic we show explicit upper bounds which attain the exponential rate of convergence we use an infinite grid with different mesh sizes in each direction to sample the function and then truncate it in our analysis the mesh sizes and the truncated domain are chosen by optimally balancing the truncation error and the discretization error this paper derives results in comparable function space settings extended to r s as which were recently obtained in the unit cube by dick larcher pillichshammer and wo niakowski see dick et al 2011 they showed that both lattice rules and regular grids with different mesh sizes in each direction attain exponential rates hence motivating us to analyze only cubature formula based on regular meshes we further also amend the analysis of older publications e g sloan and osborn 1987 and sugihara 1987 using lattice rules on r s by taking the truncation error into account and extending them to take the anisotropy of the function space into account

map based kinetic analysis for voxel by voxel compartment model estimation detailed imaging of the cerebral glucose metabolism using fdg we propose a novel algorithm for voxel by voxel compartment model analysis based on a maximum a posteriori map algorithm voxel by voxel compartment model analysis can derive functional images of living tissues but it suffers from high noise statistics in voxel based pet data and extended calculation times we initially set up a feature space of the target radiopharmaceutical composed of a measured plasma time activity curve and a set of compartment model parameters and measured the noise distribution of the pet data the dynamic pet data were projected onto the feature space and then clustered using the mahalanobis distance our method was validated using simulation studies and compared with roi based ordinary kinetic analysis for fdg the parametric images exhibited an acceptable linear relation with the simulations and the roi based results and the calculation time took about 10 min we therefore concluded that our proposed map based algorithm is practical

numerical indefinite integration by double exponential sinc method we present a numerical method for approximating an indefinite integral by the double exponential sinc method the approximation error of the proposed method with n integrand function evaluations is o exp c 1 n log c 2 n for a reasonably wide class of integrands including those with endpoint singularities the proposed method compares favorably with the existing formulas based on the ordinary sinc method computational results show the accordance of the actual convergence rates with the theoretical estimate

error estimates with explicit constants for the sinc approximation over infinite intervals abstract the sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis even for other functions the sinc approximation works accurately when combined with a proper variable transformation the convergence rate has been analyzed for typical cases including finite semi infinite and infinite intervals recently for verified numerical computations a more explicit computable error bound has been given in the case of a finite interval in this paper such explicit error bounds are derived for other cases

function classes for double exponential integration formulas the double exponential de formulas for numerical integration are known to be highly efficient more efficient than the single exponential se formulas in many cases function classes suited to the se formulas have already been investigated in the literature through rigorous mathematical analysis whereas this is not the case with the de formulas this paper identifies function classes suited to the de formulas in a way compatible with the existing theoretical results for the se formulas the de formulas are good for more restricted classes of functions but more efficient for such functions two concrete examples demonstrate the subtlety in the behavior of the de formulas that is revealed by our theoretical analysis

optimal quadrature algorithms inhp spaces the problem of finding optimal error quadrature formulas for evaluating int limits 1 1 f x dx wherehp and wherep 1 has been investigated in some recent papers e g 1 3 4 10 in this paper we study a class of almost optimal quadrature formulas which were introduced by stenger 8 11 for computing the integral int limits w 1 1 1 f z dz f in h p d hered is a simply connected domain in the complex plane andw is a conformal map ofd onto the unit discu the cost of our quadratures to obtain an approximation to the above integral is at most twice as much as the cost using the optimal formulas

near optimality of the sinc approximation near optimality of the sinc approximation is established in a variety of spaces of functions analytic in a strip region about the real axis each space being characterized by the decay rate of their elements functions in the neighborhood of the infinity

summary of sinc numerical methods sinc approximation methods excel for problems whose solutions may have singularities or infinite domains or boundary layers this article summarizes results obtained to date on sinc numerical methods of computation sinc methods provide procedures for function approximation over bounded or unbounded regions encompassing interpolation approximation of derivatives approximate definite and indefinite integration solving initial value ordinary differential equation problems approximation and inversion of fourier and laplace transforms approximation of hilbert transforms and approximation of indefinite convolutions the approximate solution of partial differential equations and the approximate solution of integral equations methods for constructing conformal maps and methods for analytic continuation indeed sinc are ubiquitous for approximating every operation of calculus

the dynamics of group codes state spaces trellis diagrams and canonical encoders a group code c over a group g is a set of sequences of group elements that itself forms a group under a component wise group operation a group code has a well defined state space sigma sub k at each time k each code sequence passes through a well defined state sequence the set of all state sequences is also a group code the state code of c the state code defines an essentially unique minimal realization of c the trellis diagram of c is defined by the state code of c and by labels associated with each state transition the set of all label sequences forms a group code the label code of c which is isomorphic to the state code of c if c is complete and strongly controllable then a minimal encoder in controller canonical feedbackfree form may be constructed from certain sets of shortest possible code sequences called granules the size of the state space sigma sub k is equal to the size of the state space of this canonical encoder which is given by a decomposition of the input groups of c at each time k if c is time invariant and nu controllable then mod sigma sub k mod pi sub 1

double exponential formulas for numerical indefinite integration in this paper we derive a formula for indefinite integration of analytic functions over 1 s where 1 s 1 by means of the double exponential transformation and the sinc method the integrand must be analytic on 1 x 1 but may have a singularity at the end points x 1 the error of the formula behaves approximately as exp c1n logc2n where n is the number of function evaluations of the integrand this error term shows a much faster convergence to zero when n becomes large than that of the known formula by haber also we derive efficient double exponential formulas for numerical evaluation of indefinite integrals over 0 s 0 s and over s s several numerical examples indicate high efficiency of the formulas

on behaviors and convolutional codes it is well known that a convolutional code is essentially a linear system defined over a finite field in this paper we elaborate on this connection we define a convolutional code as the dual of a complete linear behavior in the sense of willems 1979 using ideas from systems theory we describe a set of generalized first order descriptions for convolutional codes as an application of these ideas we present a new algebraic construction for convolutional codes

fixed point method for solving nonlinear quadratic volterra integral equations we consider a paper of banas and sadarangani 2008 11 which deals with monotonicity properties of the superposition operator and their applications an application of the monotonicity properties is to study the solvability of a quadratic volterra integral equation in this paper we prepare an efficient numerical technique based on the fixed point method and quadrature rules to approximate a solution for quadratic volterra integral equation then convergence of numerical scheme is proved by some theorems and some numerical examples are given to show applicability and accuracy of the numerical method and guarantee the theoretical results

interlaminar stresses by sinc method based on interpolation of the highest derivative computation of interlaminar stresses from one dimensional equivalent single layer beam theories using the sinc method based on interpolation of the highest derivative is performed the method is proposed to be an efficient tool for determining through the thickness variations of interlaminar stresses by the equilibrium equations of three dimensional elasticity because the required higher order derivatives of displacements are accurately obtained without postprocessing an improvement over presently used finite element methods in functionally graded material the sinc method offers additional benefits because the method employs numerical indefinite integration by double exponential transformation through the thickness integration can be performed numerically without computing additional integration weights we obtain interlaminar stresses in symmetric cross ply laminates and functionally graded sandwich composites using the sinc method based on interpolation of the highest derivative to approximately solve the static governing equations of the timoshenko beam theory and the bickford beam theory displacements and stresses from the present approach are compared with three dimensional finite element method results obtained with abaqus standard our results indicate that the interlaminar stresses throughout the majority of the length of the beam are accurately approximated with the sinc method the present results are significantly erroneous near the boundary because of three dimensional edge effects not captured by the one dimensional analysis

a local update strategy for iterative reconstruction from projections a method for bayesian reconstruction which relies on updates of single pixel values rather than the entire image at each iteration is presented the technique is similar to gauss seidel gs iteration for the solution of differential equations on finite grids the computational cost per iteration of the gs approach is found to be approximately equal to that of gradient methods for continuously valued images gs is found to have significantly better convergence at modes representing high spatial frequencies in addition gs is well suited to segmentation when the image is constrained to be discretely valued it is shown that bayesian segmentation using gs iteration produces useful estimates at much lower signal to noise ratios than required for continuously valued reconstruction the convergence properties of gradient ascent and gs for reconstruction from integral projections are analyzed and simulations of both maximum likelihood and maximum a posteriori cases are included

analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems a method for approximate solution of spectral problems for sturm liouville equations based on the construction of the delsarte transmutation operators is presented in fact the problem of numerical approximation of solutions and eigenvalues is reduced to approximation of a primitive of the potential by a finite linear combination of generalized wave polynomials introduced in khmelnytskaya et al 2013 and kravchenko and torba 2014 the method allows one to compute both lower and higher eigendata with an extreme accuracy

recent developments of the sinc numerical methods abstract this paper gives a survey of recent developments of the sinc numerical methods a variety of sinc numerical methods have been developed by stenger and his school for a certain class of problems the sinc numerical methods have the convergence rates of o exp n with some 0 where n is the number of nodes or bases used in the methods recently it has turned out that the sinc numerical methods can achieve convergence rates of o exp n log n with some 0 for a smaller but still practically meaningful class of problems and that these convergence rates are best possible the present paper demonstrates these facts for two sinc numerical methods the sinc approximation and the sinc collocation method for two point boundary value problems

the double exponential transformation in numerical analysis the double exponential transformation was first proposed by takahasi and mori in 1974 for the efficient evaluation of integrals of an analytic function with end point singularity afterwards this transformation was improved for the evaluation of oscillatory functions like fourier integrals recently it turned out that the double exponential transformation is useful not only for numerical integration but also for various kinds of sinc numerical methods the purpose of the present paper is to review the double exponential transformation in numerical integration and in a variety of sinc numerical methods

numerical methods based on whittaker cardinal or sinc functions this paper summarizes the results known to date for using sine functions composed with other functions as bases for approximations in numerical analysis described in this paper are methods of interpolation and approximation of functions and their derivatives quadrature the approximate evaluation of transforms hilbert fourier laplace hankel and mellin and the approximate solution of differential and integral equations the methods have many advantages over classical methods which use polynomials as bases in addition all of the methods converge at an optimal rate if singularities on the boundary of approximation are ignored

function classes for successful de sinc approximations the de sinc formulas resulting from a combination of the sinc approximation formula with the double exponential de transformation provide a highly efficient method for function approximation in many cases they are more efficient than the se sinc formulas which are the sinc approximation formulas combined with the single exponential se transformations function classes suited to the se sinc formulas have already been investigated in the literature through rigorous mathematical analysis whereas this is not the case with the de sinc formulas this paper identifies function classes suited to the de sinc formulas in a way compatible with the existing theoretical results for the se sinc formulas furthermore we identify alternative function classes for the de sinc formulas as well as for the se sinc formulas which are more useful in applications in the sense that the conditions imposed on the functions are easier to verify

global two stage filtering of clinical pet parametric maps application to 11 c r pk11195 abstract introduction in positron emission tomography pet quantification of physiological parameters at the voxel level may result in unreliable estimates due to the high noise of voxel time activity curves global two stage gts an estimation technique belonging to the group of population approaches can be used to tackle this problem gts was previously tested on simulated pet data and yielded substantial improvements when compared to standard estimation approaches such as weighted nonlinear least squares wnlls and basis function method bfm in this work gts performance is assessed in a clinical context using the neuroinflammation marker 11 c r pk11195 applied to a cohort of huntington s disease hd patients with and without symptoms materials and methods parametric maps of binding potential bp nd of 12 normal controls nc 9 symptomatic and 9 presymptomatic hd patients were generated by applying a modified reference tissue model that accounts for tracer vascular activity in both reference and target tissues srtmv gts was then applied to srtmv maps and its performance compared with that of srtmv three smoothed versions of srtmv obtained by filtering the original srtmv maps with gaussian filters of 3 mm 5 mm and 7 mm full width half maximum fwhm were also included in the comparison since striatal degeneration is the hallmark of hd sensitivity was assessed for all methods by computing the mean of z scores in caudate putamen and globus pallidus in the voxel by voxel statistical comparison of bp nd between hd and nc results application of gts to parametric maps brought a substantial qualitative improvement to srtmv maps to the extent that anatomical structures often became visible in addition most parameter estimates that were outside the physiological range with srtmv were corrected by gts gts yielded a 2 3 fold increase in sensitivity with respect to srtmv for the symptomatic cohort mean of striatal z scores of 0 76 for srtmv and 1 79 for gts and an even more substantial increase for the presymptomatic cohort mean of striatal z scores of 0 34 for srtmv and 0 96 for gts the sensitivity of gts was similar to the one obtained with a filter of 7 mm fwhm applied to the initial srtmv maps but gts images were not characterized by the notable loss of resolution typical of smoothed maps gts additionally does not require to change define settings according to the tracer and level of noise whereas the choice of the fwhm value of the gaussian filter normally employed in the smoothing procedure is typically arbitrary conclusions gts is a powerful and robust tool for improving the quality of parametric maps in pet the method is particularly appealing in that it can be applied to any tracer and estimation method provided that initial estimates of the parameter vector and of its covariance are available although the benefits of gts are far from being exhaustively assessed the significant improvements obtained both on real and simulated data suggest that it could become an important tool for dynamic pet in the future

sinc approximation for numerical solution of integral equation arising in conductor like screening model for real solvent in this study we present the existence of solutions for some nonlinear integral equations known as hammerstein type which forms the basis for the conductor like screening model for real solvents cosmo rs by using the techniques of noncompactness measures we employ the basic fixed point theorems such as darbo s theorem to obtain the mentioned aim in banach algebra then this paper presents a powerful numerical approach based on the sinc approximation to solve the equation which forms the basis for the conductor like screening model for real solvents cosmo rs the approach is based on the recognition of the hammerstein integral equation for the determination of the chemical potential of a surface segment as a function of screening charge density then convergence of this technique is discussed by preparing a theorem which shows an exponential type convergence rate and guarantees the applicability of that

numerical indefinite integration of functions with singularities we derive an indefinite quadrature formula based on a theorem of ganelius for h p functions for p 1 over the interval 1 1 the main factor in the error of our indefinite quadrature formula is o e n q with 2n nodes and 1 p 1 1 the convergence rate of our formula is better than that of the stenger type formulas by a factor of 2 in the constant of the exponential we conjecture that our formula has the best possible value for that constant the results of numerical examples show that our indefinite quadrature formula is better than haber s indefinite quadrature formula for h p functions

optimality of the double exponential formula functional analysis approach in the light of the functional analysis theory we establish the optimality of the double exponential formula the argument consists of the following three ingredients 1 introduction of a number of spaces of functions analytic in a strip region about the real axis each space being characterized by the decay rate of their elements functions in the neighborhood of the infinity 2 proof of the near optimality of the trapezoidal formula in each space introduced in 1 by showing the near equality between an upper estimate for the error norm of the trapezoidal formula and a lower estimate for the minimum error norm of quadratures 3 nonexistence theorem for the spaces the characterizing decay rate of which is more rapid than the double exponential

subspaces of gf q ω and convolutional codes the present paper is a self contained treatment of subspaces of the space gf q of all semi infinite strings over gf q some necessary and sufficient conditions which characterize those subspaces of gf q are derived which are convolutional codes and the classes of subspaces defined by one or more of them are investigated moreover structural parameters of convolutional codes such as block length rate delay and constraint length are considered as parameters of subspaces rather than parameters of an encoding device as a conclusion it is obtained that for error control purposes none of the investigated superclasses of the class of convolutional codes is better suited than the class of convolutional codes itself

multidimensional systems with finite support behaviors signal structure generation and detection the main features of finite multidimensional behaviors are introduced as properties of the trajectories supports and connected with the polynomial matrices adopted for their description observability and local detectability are shown to be equivalent to the kernel representation of a behavior via some parity check matrix ht the main properties of locally undetectable behaviors as well as their connections with the notion of constrained variables are investigated and a general representation result for finite support behaviors is derived the input output representation via generator matrices is finally discussed and some connections between matrix primeness and the constraints every trajectory imposes on the support of the corresponding input are analyzed

on a certain quadrature formula traduction anglaise d un article en japonais publie en aout 1970 dans la serie kokyuroku vol 91 pp 82 118

de sinc methods have almost the same convergence property as se sinc methods even for a family of functions fitting the se sinc methods part ii indefinite integration in this paper the theoretical convergence rate of the sinc indefinite integration combined with the double exponential de transformation is given for a class of functions for which the single exponential se transformation is suitable although the de transformation is considered as an enhanced version of the se transformation for sinc related methods the function space for which the de transformation is suitable is smaller than that for se and therefore there exist some examples such that the de transformation is not better than the se transformation even in such cases however some numerical observations in the literature suggest that there is almost no difference in the convergence rates of se and de in fact recently the observations have been theoretically explained for two explicit approximation formulas the sinc quadrature and the sinc approximation the conclusion is that in such cases the de s rate is slightly lower but almost the same as that of the se the contribution of this study is the derivation of the same conclusion for the sinc indefinite integration numerical examples that support the theoretical result are also provided

double exponential transformation in the sinc collocation method for two point boundary value problems in 1974 takahasi and mori proposed the double exponential transformation for efficient evaluation of integrals of an analytic function with end point singularity recently it has turned out that the double exponential transformation is also useful for various kinds of sinc methods in the present paper we consider the sinc collocation method for two point boundary value problems to show that the method can be considerably enhanced when incorporated with the double exponential transformation technique