bayesian long run prediction in time series models this paper considers bayesian long run prediction in time series models we allow time series to exhibit stationary or nonstationary behavior and show how differences between prior structures which have little effect on posterior inferences can have a large effect in a prediction exercise in particular the jeffreys prior given in phillips 1991 is seen to prevent the existence of one period ahead predictive moments in a more general context a bayesian counterpart is provided to sampson 1991 who takes parameter uncertainty into account in a classical framework an empirical example illustrates our results

block truncated newton methods for parallel optimization truncated newton methods are a class of optimization methods suitable for large scale problems at each iteration a search direction is obtained by approximately solving the newton equations using an iterative method in this way matrix costs and second derivative calculations are avoided hence removing the major drawbacks of newton s method in this form the algorithms are well suited for vectorization further improvements in performance are sought by using block iterative methods for computing the search direction in particular conjugate gradient type methods are considered computational experience on a hypercube computer is reported indicating that on some problems the improvements in performance can be better than that attributable to parallelism alone

the phase transition of the directed polymer on disordered hierarchical lattices the directed polymer on disordered hierarchical lattices is studied using an exact renormalization scheme the phase transition is studied and a hyperscaling relation is derived the fixed distributions of the renormalized energies are obtained numerically the specific heat and associated exponents are computed from the fixed distributions

bayesian reconstructions from emission tomography data using a modified em algorithm a novel method of reconstruction from single photon emission computerized tomography data is proposed this method builds on the expectation maximization em approach to maximum likelihood reconstruction from emission tomography data but aims instead at maximum posterior probability estimation which takes account of prior belief about smoothness in the isotope concentration a novel modification to the em algorithm yields a practical method the method is illustrated by an application to data from brain scans

convergence of em image reconstruction algorithms with gibbs smoothing p j green has defined an osl one step late algorithm that retains the e step of the em algorithm for image reconstruction in emission tomography but provides an approximate solution to the m step further modifications of the osl algorithm guarantee convergence to the unique maximum of the log posterior function convergence is proved under a specific set of sufficient conditions several of these conditions concern the potential function of the gibb s prior and a number of candidate potential functions are identified generalization of the osl algorithm to transmission tomography is also considered

polymers with a bimodal disorder distribution and directed percolation the ground state scaling properties of directed paths on a 1 1 dimensional lattice are reanalysed to each bond energy 0 or 1 is randomly assigned with probability p or 1 p respectively at variance with previous claims the result strongly suggests that only one universality class exists for 0 p 1 except for the directed percolation threshold

practical tradeoffs between noise quantitation and number of iterations for maximum likelihood based reconstructions emission computerised tomography images reconstructed using a maximum likelihood expectation maximization ml based method with different reconstruction kernels and 1 200 iterations are compared to images reconstructed using filtered backprojection fbp ml based reconstructions using a single pixel sp kernel with or without a sieve filter show no quantitative advantage over fbp except in the background where a reduction of noise is possible if the number of iterations is kept small

yang lee edge singularity on a class of tree like lattices the density of zeros of the partition function of the ising model on a class of tree like lattices is studied an exact closed form expression for the pertinent critical exponents is derived by using a couple of recursion relations which have a singular behaviour near the yang lee edge

penalized maximum likelihood image reconstruction using space alternating generalized em algorithms most expectation maximization em type algorithms for penalized maximum likelihood image reconstruction converge slowly particularly when one incorporates additive background effects such as scatter random coincidences dark current or cosmic radiation in addition regularizing smoothness penalties or priors introduce parameter coupling rendering intractable the m steps of most em type algorithms this paper presents space alternating generalized em sage algorithms for image reconstruction which update the parameters sequentially using a sequence of small hidden data spaces rather than simultaneously using one large complete data space the sequential update decouples the m step so the maximization can typically be performed analytically we introduce new hidden data spaces that are less informative than the conventional complete data space for poisson data and that yield significant improvements in convergence rate this acceleration is due to statistical considerations not numerical overrelaxation methods so monotonic increases in the objective function are guaranteed we provide a general global convergence proof for sage methods with nonnegativity constraints

anomalous roughening in three dimensional polynucleation growth abstract the surface properties of the three dimensional polynucleation growth model were studied at the kinetic roughening transition the dependence of the surface width w on time t and linear size l of the substrate is determined by anomalous roughening w x log l tf t l z where tf is a scaling function for the exponents x 2 8 0 2 and z 1 79 0 05 were found the latter being related to directed percolation

self avoiding walks in quenched random environments the self avoiding walk in a quenched random environment is studied using realspace and field theoretic renormalization and flory arguments these methods indicate that the system is described for d de by a strong disorder fixed point corresponding to a glass state in which the polymer is confined to the lowest energy path this fixed point is characterized by scaling laws for the size of the walk l n with n the number of steps and the fluctuations in the free energy af l the bound 1 co pore and suggests that this inequality holds for d 2 and 3 although pure cannot be excluded particularly for d 2 for d d c there is a transition between strong and weak disorder phases at which pure the strong disorder fixed point for saws on percolation clusters is discussed the analogy with directed walks is emphasized

optimal estimation of deterioration from diagnostic image sequence estimation of mechanical structure damage can greatly benefit from the knowledge that the damage accumulates irreversibly over time this paper formulates a problem of estimation of a pixel wise monotonic increasing or decreasing time series of images from noisy blurred image data our formulation includes temporal monotonicity constraints and a spatial regularization penalty we cast the estimation problem as a large scale quadratic programming qp optimization and describe an efficient interior point method for solving this problem the method exploits the special structure of the qp and scales well to problems with more than a million of decision variables and constraints the proposed estimation approach performs well for simulated data we demonstrate an application of the approach to diagnostic images obtained in structural health monitoring experiments and show that it provides a good estimate of the damage accumulation trend while suppressing spatial and temporal noises

grouped coordinate ascent algorithms for penalized likelihood transmission image reconstruction presents a new class of algorithms for penalized likelihood reconstruction of attenuation maps from low count transmission scans we derive the algorithms by applying to the transmission log likelihood a version of the convexity technique developed by de pierro for emission tomography the new class includes the single coordinate ascent sca algorithm and lange s convex algorithm for transmission tomography as special cases the new grouped coordinate ascent gca algorithms in the class overcome several limitations associated with previous algorithms 1 fewer exponentiations are required than in the transmission maximum likelihood expectation maximization ml em algorithm or in the sca algorithm 2 the algorithms intrinsically accommodate nonnegativity constraints unlike many gradient based methods 3 the algorithms are easily parallelizable unlike the sca algorithm and perhaps line search algorithms we show that the gca algorithms converge faster than the sca algorithm even on conventional workstations an example from a low count positron emission tomography pet transmission scan illustrates the method

an affine scaling interior point cbb method for box constrained optimization we develop an affine scaling algorithm for box constrained optimization which has the property that each iterate is a scaled cyclic barzilai borwein cbb gradient iterate that lies in the interior of the feasible set global convergence is established for a nonmonotone line search while there is local r linear convergence at a nondegenerate local minimizer where the second order sufficient optimality conditions are satisfied numerical experiments show that the convergence speed is insensitive to problem conditioning the algorithm is particularly well suited for image restoration problems which arise in positron emission tomography where the cost function can be infinite on the boundary of the feasible set

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

polymers on disordered hierarchical lattices a nonlinear combination of random variables the problem of directed polymers on disordered hierarchical and hypercubic lattices is considered for the hierarchical lattices the problem can be reduced to the study of the stable laws for combining random variables in a nonlinear way we present the results of numerical simulations of two hierarchical lattices finding evidence of a phase transition in one case for a limiting case we extend the perturbation theory developed by derrida and griffiths to nonzero temperature and to higher order and use this approach to calculate thermal and geometrical properties overlaps of the model in this limit we obtain an interpolation formula allowing one to obtain the noninteger moments of the partition function from the integer moments we obtain bounds for the transition temperature for hierarchical and hypercubic lattices and some similarities between the problem on the two different types of lattice are discussed

about diffusion processes in disordered systems different diffusion processes can be defined on random networks like the infinite incipient clusters at percolation threshold the long time behaviour of two such processes is shown to be the same in particular the mean square displacements and the autocorrelation function scale with the same exponents in the two cases

the strength of evidence for unit autoregressive roots and structural breaks a bayesian perspective economic time series may be generated by a process with a unit autoregressive root and the generating process may exhibit an abrupt break in trend it is well known that the outcomes of classical tests for either one of these phenomena can be seriously influenced when the presence of the other is ignored therefore care is required in disentangling evidence in the data supporting the two phenomena and there is some question as to the extent to which such disentanglement is feasible we approach this question from a bayesian perspective assessing the impact on the strength of evidence for each of the phenomena in the presence of the other

testing for unit roots in a bayesian framework abstract classical tests for unit roots have been criticized for their unusual asymptotic theory leading to disconnected confidence intervals and their lack of power in small samples such critiques were initiated by sims 1988 who promoted a bayesian approach to the question various papers then appeared which took up this idea the bayesian approach is however not exempt from criticism as shown by phillips 1991 who emphasizes the role of the prior as a bias toward stationarity in this paper i emphasize the role of the model and of the initial conditions i show that with a structural model and an adequate treatment of the first observation a bayesian unit root test based on the computation of pr p 1 y can produce results which are more or less in accordance with classical results the extended nelson plosser data set serves as an illustration

a general purpose parallel algorithm for unconstrained optimization this paper describes a general purpose algorithm for unconstrained optimization that is suitable for a parallel computer it is designed to be as easy to use as traditional algorithms for this problem requiring only that a scalar subroutine be provided to evaluate the objective function and its gradient vector of first derivatives the algorithm used is a block truncated newton method truncated newton methods are a class of methods that compromise on newton s method so that large problems can be solved enhancements to the basic method suitable for a parallel computer are described these include a revised data storage scheme new preconditioning and initialization strategies to accelerate the method a parallel line search revised stopping rules for the inner algorithm and a new nonlinearity test to determine the adequacy of the quadratic model numerical results are presented to illustrate the performance of the method and comparisons are made with other scalar and parallel algorithms

preconditioning methods for improved convergence rates in iterative reconstructions because of the characteristics of the tomographic inversion problem iterative reconstruction techniques often suffer from poor convergence rates especially at high spatial frequencies by using preconditioning methods the convergence properties of most iterative methods can be greatly enhanced without changing their ultimate solution to increase reconstruction speed spatially invariant preconditioning filters that can be designed using the tomographic system response and implemented using 2 d frequency domain filtering techniques have been applied in a sample application reconstructions from noiseless simulated projection data were performed using preconditioned and conventional steepest descent algorithms the preconditioned methods demonstrated residuals that were up to a factor of 30 lower than the assisted algorithms at the same iteration applications of these methods to regularized reconstructions from projection data containing poisson noise showed similar although not as dramatic behavior

diffusion of directed polymers in a random environment we consider a system of random walks or directed polymers interacting weakly with an environment which is random in space and time in spatial dimensionsd 2 we establish that the behavior is diffusive with probability one the diffusion constant is not renormalized by the interaction

on use of the em algorithm for penalized likelihood estimation summary the em algorithm is a popular approach to maximum likelihood estimation but has not been much used for penalized likelihood or maximum a posteriori estimation this paper discusses properties of the em algorithm in such contexts concentrating on rates of conver gence and presents an alternative that is usually more practical and converges at least as quickly the em algorithm is a general approach to maximum likelihood estimation rather than a specific algorithm dempster et al 1977 discussed the method and derived basic properties demonstrating that a variety of procedures previously developed rather informally could be unified the common strand to problems where the approach is applicable is a notion of incomplete data this includes the conventional sense of missing data but is much broader than that the em algorithm demon strates its strength in situations where some hypothetical experiment yields data from which estimation is particularly convenient and economical the incomplete data actually at hand are regarded as observable functions of these complete data the resulting algorithms while usually slow to converge are often extremely simple and remain practical in large problems where no other approaches may be feasible dempster et al 1977 briefly refer to the use of the same approach to the problem of finding the posterior mode maximum a posteriori estimate in a bayesian estima

directed random walks on directed percolation clusters 0 63 this probability distribution is independent of the cluster s length t up to d values comparable to the cluster s width t n the results are shown to be consistent with a tree description of the directed percolation clusters pacs number s 61 66 dk 64 60 cn 71 20 be the subject of random walks on percolation clusters known as the ant in the labyrinth problem 1 has drawn quite intensive attention in the physical literature 2 however in spite of the numerous efforts no simple connection was found between the static and dynamical exponents of percolation though the alexander orbach conjecture 3 comes close to this goal in this article it is shown that such a simple connection does exist in the special case of directed random walks on directed percolation clusters in the directed percolation model 4 there is a predefined direction in which the percolation clusters can grow in the directed random walk considered in the present study walks are also performed only in the same predefined direction balents and kardar 5 have already studied random walks on directed percolation clusters but while their main concern was the variability of distances between different clusters the main concern of the present article is the variability of distances within each cluster in order to study this issue numerical results were obtained for directed random walks performed along twodimensional directed percolation clusters grown at the critical probability pc these numerical results indicated that the distance d of the directed random walkers from their most probable end point is determined by a probability distribution p d d 2 11w n where w 0 50 and n 0 63 this probability distribution is independent of the cluster s length t up to d values comparable to the cluster s width t n the known values of these two exponents are shown to be consistent with a tree description of the directed percolation clusters the article starts with a description of the model and the way the numerical data were gathered the second part presents the numerical results which have similar characteristics to previous results 6 obtained for the directed polymer model 7 8 this similarity is investigated further in the final part of the article the connection between the directed percolation model and the directed polymer model was studied in a number of articles 9 13 and the present study points to some similarity between entropy in the directed percolation model and energy in the directed polymer model on an arbitrary lattice structure a directed percolation cluster can be defined as the set of lattice points sites which are connected to some origin while the connecting paths are oriented in a predefined direction thus all of them are of

on the connection between directed percolation and directed polymers we consider the scaling behaviour of the directed paths of minimum energy on a lattice to each bond of which energy 0 or 1 is randomly assigned in 1 1 dimensions it is shown by numerical transfer matrix calculations that in all the regions below the directed percolation threshold these paths still scale with the directed percolation exponent at the same time degeneracy of these paths at and below the threshold is found to be very different the problem of stability of the directed percolation ground state and the case when the energy on each bond can take randomly q 2 different values are also considered

priors for unit root models abstract a method of assessing an economist s subjective prior for a unit root model is given and applied the methods extend previous work by allowing a family of piecewise conjugate prior distribution that permit different opinions when 1 this larger family is still closed under sampling so it retains the simplicity that is the principal advantage of conjugate analysis

a theoretical study of some maximum likelihood algorithms for emission and transmission tomography this paper has the dual purpose of introducing some new algorithms for emission and transmission tomography and proving mathematically that these algorithms and related antecedent algorithms converge like the em algorithms for positron single photon and transmission tomography the algorithms provide maximum likelihood estimates of pixel concentration or linear attenuation parameters one particular innovation we discuss is a computationally practical scheme for modifying the em algorithms to include a bayesian prior the bayesian versions of the em algorithms are shown to have superior convergence properties in a vicinity of the maximum we anticipate that some of the other algorithms will also converge faster than the em algorithms

on the convergence of an em type algorithm for penalized likelihood estimation in emission tomography recently we proposed an extension of the expectation maximization em algorithm that was able to handle regularization terms in a natural way although very general convergence proofs were not valid for many possibly useful regularizations we present here a simple convergence result that is valid assuming only continuous differentiability of the penalty term and can be also extended to other methods for penalized likelihood estimation in tomography

a new maximum likelihood algorithm for piecewise regression abstract this paper presents a piecewise regression method for continuous models containing max or min operators or both this method does not require knowledge of the zone in which a shift in regimes occurs moreover it allows the application of analytical derivatives to maximize the likelihood function which greatly simplifies the estimation of the model the method proposed exhibits fast convergence and can be used for an arbitrary number of regimes and variables

ideal chain on a two dimensional critical percolation cluster the authors study the statistics of the ideal chain or equally weighted trajectories for the first time on a two dimensional critical percolation cluster they discuss the asymptotic behaviour of the mean end to end distance and the number of chains for the long chain limit by exact enumeration the results strongly suggest that this problem does not belong to the same universality class as the random walk or kinetically weighted trajectories on the same fractal cluster

diffusion on regular random fractals we study random walks on structures intermediate to statistical and deterministic fractals called regular random fractals constructed introducing randomness in the distribution of lacunas of sierpinski carpets random walks are simulated on finite stages of these fractals and the scaling properties of the mean square displacement of n step walks are analysed the anomalous diffusion exponents obtained are very near the estimates for the carpets with the same dimension this result motivates a discussion on the influence of some types of lattice irregularity random structure dead ends lacunas on based on results on several fractals we also propose to use these and other regular random fractals as models for real self similar structures and to generalize results for statistical systems on fractals

branching interfaces with infinitely strong couplings a hierarchical froth model of the interface of a random q state potts ferromagnet in 2d is studied by recursive methods a fraction p of the nearest neighbour bonds is made inaccessible to domain walls by infinitely strong ferromagnetic couplings energetic and geometric scaling properties of the interface are controlled by zero temperature fixed distributions for the directed percolation threshold the interface behaves as for p 0 and scaling supports random ising q 2 critical behaviour for all q s at three regimes are obtained for different rates of ferro versus antiferromagnetic couplings with rates above a threshold value the interface is linear fractal dimension and its energy fluctuations scale with length as with when the threshold is reached the interface branches at all scales and is fractal with thus at dilution modifies both low temperature interfacial properties and critical scaling below threshold the interface becomes a probe of the backbone geometry backbone fractal dimension which even controls energy fluctuations numerical determinations of directed percolation exponents on diamond hierarchical lattice are also presented

maximum likelihood least squares and penalized least squares for pet the em algorithm is the basic approach used to maximize the log likelihood objective function for the reconstruction problem in positron emission tomography pet the em algorithm is a scaled steepest ascent algorithm that elegantly handles the nonnegativity constraints of the problem it is shown that the same scaled steepest descent algorithm can be applied to the least squares merit function and that it can be accelerated using the conjugate gradient approach the experiments suggest that one can cut the computation by about a factor of 3 by using this technique the results are applied to various penalized least squares functions which might be used to produce a smoother image

analysis of diffusion and trapping efficiency for random walks on non fractal scale free trees abstract in this paper the discrete random walks on the recursive non fractal scale free trees nfsft are studied and a kind of method to calculate the analytic solutions of the mean first passage time mfpt for any pair of nodes the mean trapping time mtt for any target node and mean diffusing time mdt for any starting node are proposed furthermore we compare the trapping efficiency and diffusion efficiency between any two nodes of nfsft by using the mtt and the mdt as the measures of trapping efficiency and diffusion efficiency respectively and find the best or worst trapping sites and the best or worst diffusion sites the results show that the two hubs of nfsft are not only the best trapping site but also the worst diffusion site and that the nodes which are the farthest nodes from the two hubs are not only the worst trapping sites but also the best diffusion sites furthermore we find that the ratio between the maximum and minimum of mtt grows logarithmically with network order but the ratio between the maximum and minimum of mdt is almost equal to 1 the results imply that the trap s position has great effect on the trapping efficiency but the position of starting node has little effect on diffusion efficiency finally the simulation for random walks on nfsft is done and it is consistent with the derived results

adsorption of ideal polymers on an infinitely ramified fractal we study ideal polymer chains interacting attractively with the borders of the lacunas of an infinitely ramified fractal the sierpinski carpet ideal chains are simulated on finite stages of construction of this fractal at various temperatures the mean square displacement and the mean number of adsorbed monomers of n step chains are estimated in these lattices and extrapolations to the fractal limit infinite lattice consider the exact forms of finite size corrections as previously predicted by the series expansion method in the noninteracting case a finite fraction of the monomers is adsorbed and this fraction increases as the temperature decreases however there is evidence that the critical exponent v which governs the growth of the chains varies with the temperature in a nonmonotonic way at high temperatures v increases with decreasing temperature and thus the chains are more stretched than in the noninteracting case at an intermediate temperature v starts to decrease and is still positive at very low temperatures when the chains grow along the borders of several lacunas occasionally crossing the bulk between them

finite size scaling for random walks on fractals random walks are simulated on finite stages of construction of regular fractal lattices it is proved that the mean square displacement rn2 obeys a finite size scaling hypothesis and the critical exponent nu w is estimated the efficiency of the method is proved when applied to finitely ramified fractals in which the problem is exactly solvable nu w is obtained with good accuracy approximately 1 for a class of infinitely ramified fractals the sierpinski carpets the results correct previous estimates based on simulations which did not use finite size scaling it is shown that nu w decreases when dc decreases with very small corrections due to other geometrical properties such as lacunarity the comparison with estimates of the ideal chain exponent nu c shows that the two problems are not equivalent on these fractals and that in general nu w nu c estimates of nu w with the same accuracy are obtained on two sierpinski pastry shells 2 df 3 where anomalous diffusion is also observed

cell renormalisation of growth processes true self avoiding walks and growing animals the authors present a generating function formalism for growth processes in general and introduce a new cell renormalisation scheme as examples they treat the true self avoiding walk and the eden process or growing animals in two and three dimensions using small cells the results in both cases indicate a substantial increase in the fractal dimension d compared with their equilibrium counterparts the case of the eden process may however suggest a peculiar convergence behaviour as the cell size b tends to infinity

a unified approach to statistical tomography using coordinate descent optimization over the past years there has been considerable interest in statistically optimal reconstruction of cross sectional images from tomographic data in particular a variety of such algorithms have been proposed for maximum a posteriori map reconstruction from emission tomographic data while map estimation requires the solution of an optimization problem most existing reconstruction algorithms take an indirect approach based on the expectation maximization em algorithm we propose a new approach to statistically optimal image reconstruction based on direct optimization of the map criterion the key to this direct optimization approach is greedy pixel wise computations known as iterative coordinate decent icd we propose a novel method for computing the icd updates which we call icd newton raphson we show that icd newton raphson requires approximately the same amount of computation per iteration as em based approaches but the new method converges much more rapidly in our experiments typically five to ten iterations other advantages of the icd newton raphson method are that it is easily applied to map estimation of transmission tomograms and typical convex constraints such as positivity are easily incorporated

statistical mechanics of random paths on disordered lattices the dependence of the universality class on the statistical weight of unrestricted random paths is explicitly shown both for deterministic and statistical fractals such as the incipient infinite percolation cluster equally weighted paths ideal chain and kinetically generated paths random walks belong in general to different universality classes for deterministic fractals exact renormalization group techniques are used asymptotic behaviors for the end to end distance ranging from power to logarithmic localization laws are observed for the ideal chain in all these cases random walks in the presence of nonperfect traps are shown to be in the same universality class of the ideal chain logarithmic behavior is reflected insingular renormalization group recursions for the disordered case numerical transfer matrix techniques are exploited on percolation clusters in two and three dimensions the two point correlation function scales with critical exponents not obeying standard scaling relations the distribution of the number of chains and the number of chains returning to the starting point are found to be well approximated by a log normal distribution the logmoment of the number of chains is found to have an essential type of singularity consistent with the log normal distribution a non self averaging behavior is argued to occur on the basis of the results

a maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography the expectation maximization method for maximum likelihood image reconstruction in emission tomography based on the poisson distribution of the statistically independent components of the image and measurement vectors is extended to a maximum aposteriori image reconstruction using a multivariate gaussian a priori probability distribution of the image vector the approach is equivalent to a penalized maximum likelihood estimation with a special choice of the penalty function the expectation maximization method is applied to find the a posteriori probability maximizer a simple iterative formula is derived for a penalty function that is a weighted sum of the squared deviations of image vector components from their a priori mean values the method is demonstrated to be superior to pure likelihood maximization in that the penalty function prevents the occurrence of irregular high amplitude patterns in the image with a large number of iterations the so called checkerboard effect or noise artifact

interior point methodology for 3 d pet reconstruction interior point methods have been successfully applied to a wide variety of linear and nonlinear programming applications this paper presents a class of algorithms based on path following interior point methodology for performing regularized maximum likelihood ml reconstructions on three dimensional 3 d emission tomography data the algorithms solve a sequence of subproblems that converge to the regularized maximum likelihood solution from the interior of the feasible region the nonnegative orthant the authors propose two methods a primal method which updates only the primal image variables and a primal dual method which simultaneously updates the primal variables and the lagrange multipliers a parallel implementation permits the interior point methods to scale to very large reconstruction problems termination is based on well defined convergence measures namely the karush kuhn tucker first order necessary conditions for optimality the authors demonstrate the rapid convergence of the path following interior point methods using both data from a small animal scanner and monte carlo simulated data the proposed methods can readily be applied to solve the regularized weighted least squares reconstruction problem

directed paths on percolation clusters we consider a variant of the problem of directed polymers on a disordered lattice in which the disorder is geometrical in nature in particular we allow a finite probability for each bond to be absent from the lattice we show through the use of numerical and scaling arguments on both euclidean and hierarchical lattices that the model has two distinct scaling behaviors depending upon whether the concentration of bonds on the lattice is at or above the directed percolation threshold we are particularly interested in the exponents and defined by f t and x t describing the free energy and transverse fluctuations respectively above the percolation threshold the scaling behavior is governed by the standard random energy exponents 1 3 and 2 3 in 1 1 dimensions at the percolation threshold we predict and verify numerically in 1 1 dimensions the exponents 1 2 and v v where v and v are the directed percolation exponents in addition we predict the absence of a free phase in any dimension at the percolation threshold

statistics of equally weighted random paths on a class of self similar structures we study the statistics of equally weighted random walk paths on a family of sierpinski gasket lattices whose members are labelled by an integer b 2 b 2 mean path end to end distance grows more slowly than any power of its length n we provide arguments for the emergence of usual power law critical behaviour in the limit b when fractal lattices become almost compact

exact closed form of the return probability on the bethe lattice an exact closed form solution for the return probability of a random walk on the bethe lattice is given the long time asymptotic form confirms a previously known expression it is however shown that this exact result reduces to the proper expression when the bethe lattice degenerates on a line unlike the asymptotic result which is singular this is shown to be an artefact of the asymptotic expansion the density of states is also calculated

performance evaluation of an iterative image reconstruction algorithm for positron emission tomography an image reconstruction method motivated by positron emission tomography pet is discussed the measurements tend to be noisy and so the reconstruction method should incorporate the statistical nature of the noise the authors set up a discrete model to represent the physical situation and arrive at a nonlinear maximum a posteriori probability map formulation of the problem an iterative approach which requires the solution of simple quadratic equations is proposed the authors also present a methodology which allows them to experimentally optimize an image reconstruction method for a specific medical task and to evaluate the relative efficacy of two reconstruction methods for a particular task in a manner which meets the high standards set by the methodology of statistical hypothesis testing the new map algorithm is compared to a method which maximizes likelihood and with two variants of the filtered backprojection method

priors about observables in vector autoregressions we formulate a prior about observables in a vector autoregression var and then solve the deconvolution problem for the implied prior about var parameters formulating a prior about observables is more intuitive than formulating a prior about var parameters directly because var parameters are hard to interpret our numerical algorithm for approximating the implied prior about parameters works well even in high dimensional problems and can be applied also for models other than vars in the empirical application we formulate a prior about growth rates of the observables in a var model of the united states economy we nd that this prior makes a big dierence for the estimated persistence of output responses to monetary policy shocks compared with the results of standard priors for vars

fast gradient based methods for bayesian reconstruction of transmission and emission pet images the authors describe conjugate gradient algorithms for reconstruction of transmission and emission pet images the reconstructions are based on a bayesian formulation where the data are modeled as a collection of independent poisson random variables and the image is modeled using a markov random field a conjugate gradient algorithm is used to compute a maximum a posteriori map estimate of the image by maximizing over the posterior density to ensure nonnegativity of the solution a penalty function is used to convert the problem to one of unconstrained optimization preconditioners are used to enhance convergence rates these methods generally achieve effective convergence in 15 25 iterations reconstructions are presented of an sup 18 fdg whole body scan from data collected using a siemens cti ecat931 whole body system these results indicate significant improvements in emission image quality using the bayesian approach in comparison to filtered backprojection particularly when reprojections of the map transmission image are used in place of the standard attenuation correction factors

minimal path on the hierarchical diamond lattice we consider the minimal paths on a hierarchical diamond lattice where bonds are assigned a random weight depending on the initial distribution of weights we find all possible asymptotic scaling properties the different cases found are the small disorder case the analog of levy s distributions with a power law decay at and finally a limit of large disorder which can be identified as a percolation problem the asymptotic shape of the stable distributions of weights of the minimal path are obtained as well as their scaling properties as a side result we obtain the asymptotic form of the distribution of effective percolation thresholds for finite size hierarchical lattices

directed polymers with killing the problem of directed polymers in a random medium is generalized to include a killing probability the model is then studied using results of the theory of extreme statistics these reveal that in a region of parameters the thermodynamics of polymers with killing in finite dimensions is similar to that of the mean field solution of directed polymers on a cayley tree the implication of these results for the behaviour of directed polymers in high dimensions is also discussed

fast em like methods for maximum a posteriori estimates in emission tomography the maximum likelihood ml approach in emission tomography provides images with superior noise characteristics compared to conventional filtered backprojection fbp algorithms the expectation maximization em algorithm is an iterative algorithm for maximizing the poisson likelihood in emission computed tomography that became very popular for solving the ml problem because of its attractive theoretical and practical properties recently browne and depierro 1996 and hudson and larkin 1991 block sequential versions of the em algorithm that take advantage of the scanner s geometry have been proposed in order to accelerate its convergence in hudson and larkin 1991 the ordered subsets em os em method was applied to the hit problem and a modification os gp to the maximum a posteriori map regularized approach without showing convergence in browne and depierro 1996 we presented a relaxed version of os em ramla that converges to an ml solution in this paper we present an extension of ramla for map reconstruction we show that if the sequence generated by this method converges then it must converge to the true map solution experimental evidence of this convergence is also shown to illustrate this behavior we apply the algorithm to positron emission tomography simulated data comparing its performance to os gp

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

a modified expectation maximization algorithm for penalized likelihood estimation in emission tomography the maximum likelihood ml expectation maximization em approach in emission tomography has been very popular in medical imaging for several years in spite of this no satisfactory convergent modifications have been proposed for the regularized approach here a modification of the em algorithm is presented the new method is a natural extension of the em for maximizing likelihood with concave priors convergence proofs are given

nonuniversality and analytical continuation in moments of directed polymers on hierarchical lattices we prove the moments of the directed polymer partition function gz using an exact position space renormalization group scheme on a hierarchical lattice after sufficient iteration the characteristic functionf n ln gzn of the probability z converges to a stable limitf n for smalln the limiting behavior is independent of the initial distribution while for largen f n is completely determined by it and is thus nonuniversal there is a smooth crossover between the two regimes for small effective dimensions and the nonlinear behavior of the small moments can be used to extract information on the universal scaling properties of the distribution for large effective dimensions there is a sharp transition between the two regimes and analytical continuation from integer moments ton 0 is not possible replica arguments can account for most features of the observed results

a general class of preconditioners for statistical iterative reconstruction of emission computed tomography a major drawback of statistical iterative image reconstruction for emission computed tomography is its high computational cost the ill posed nature of tomography leads to slow convergence for standard gradient based iterative approaches such as the steepest descent or the conjugate gradient algorithm here new theory and methods for a class of preconditioners are developed for accelerating the convergence rate of iterative reconstruction to demonstrate the potential of this class of preconditioners a preconditioned conjugate gradient pcg iterative algorithm for weighted least squares reconstruction wls was formulated for emission tomography using simulated positron emission tomography pet data of the hoffman brain phantom it was shown that the convergence rate of the pcg can reduce the number of iterations of the standard conjugate gradient algorithm by a factor of 2 8 times depending on the convergence criterion