on the global well posedness theory for a class of pde models for criminal activity abstract we study a class of reaction advection diffusion system of partial differential equations which can be taken as basic models for criminal activity this class of models are based on routine activity theory and other theories such as the repeat and near repeat victimization effect and were first introduced in short et al 2008 11 in these models the criminal density is advected by a velocity field that depends on a scalar field which measures the appeal to commit a crime we refer to this scalar field as the attractiveness field we prove local well posedness of solutions for the general class of models furthermore we prove global well posedness of solutions to a fully parabolic system with a velocity field that depends logarithmically on the attractiveness field our final result is the global well posedness of solutions the fully parabolic system with velocity field that depends linearly on the attractiveness field for small initial mass

sharp dimension transition in a shortcut model earlier studies of a parametrized class of models the shortcut models whose fractal dimension transitions between integer values indicated that the transition occurs infinitely sharply at the parameter value p 0 as the system size increases to infinity in this work we explain the cause as being due to the combinatorially large increase in the available number of paths connecting a pair of points as the path length is increased

mean and variance of implicitly defined biased estimators such as penalized maximum likelihood applications to tomography many estimators in signal processing problems are defined implicitly as the maximum of some objective function examples of implicitly defined estimators include maximum likelihood penalized likelihood maximum a posteriori and nonlinear least squares estimation for such estimators exact analytical expressions for the mean and variance are usually unavailable therefore investigators usually resort to numerical simulations to examine the properties of the mean and variance of such estimators this paper describes approximate expressions for the mean and variance of implicitly defined estimators of unconstrained continuous parameters we derive the approximations using the implicit function theorem the taylor expansion and the chain rule the expressions are defined solely in terms of the partial derivatives of whatever objective function one uses for estimation as illustrations we demonstrate that the approximations work well in two tomographic imaging applications with poisson statistics we also describe a plug in approximation that provides a remarkably accurate estimate of variability even from a single noisy poisson sinogram measurement the approximations should be useful in a wide range of estimation problems

characterizing emerging european stock markets through complex networks from local properties to self similar characteristics abstract we investigate the properties of the returns of the main emerging stock markets from europe by means of complex networks we transform the series of daily returns into complex networks and analyze the local properties of these networks with respect to degree distributions clustering or average line length we further use the clustering coefficients as quantities describing the local structure of the network and approach them by using multifractal analysis we find evidence of scale free networks and multifractality of clustering coefficients

iterative tomographic image reconstruction using fourier based forward and back projectors iterative image reconstruction algorithms play an increasingly important role in modern tomographic systems especially in emission tomography with the fast increase of the sizes of the tomographic data reduction of the computation demands of the reconstruction algorithms is of great importance fourier based forward and back projection methods have the potential to considerably reduce the computation time in iterative reconstruction additional substantial speed up of those approaches can be obtained utilizing powerful and cheap off the shelf fast fourier transform fft processing hardware the fourier reconstruction approaches are based on the relationship between the fourier transform of the image and fourier transformation of the parallel ray projections the critical two steps are the estimations of the samples of the projection transform on the central section through the origin of fourier space from the samples of the transform of the image and vice versa for back projection interpolation errors are a limitation of fourier based reconstruction methods we have applied min max optimized kaiser bessel interpolation within the nonuniform fft nufft framework and devised ways of incorporation of resolution models into the fourier based iterative approaches numerical and computer simulation results show that the min max nufft approach provides substantially lower approximation errors in tomographic forward and back projection than conventional interpolation methods our studies have further confirmed that fourier based projectors using the nufft approach provide accurate approximations to their space based counterparts but with about ten times faster computation and that they are viable candidates for fast iterative image reconstruction

nonparametric estimation of a point spread function in multivariate problems the removal of blur from a signal in the presence of noise is readily accomplished if the blur can be described in precise mathematical terms however there is growing interest in problems where the extent of blur is known only approximately for example in terms of a blur function which depends on unknown parameters that must be computed from data more challenging still is the case where no parametric assumptions are made about the blur function there has been a limited amount of work in this setting but it invariably relies on iterative methods sometimes under assumptions that are mathematically convenient but physically unrealistic e g that the operator defined by the blur function has an integrable inverse in this paper we suggest a direct noniterative approach to nonparametric blind restoration of a signal our method is based on a new ridge based method for deconvolution and requires only mild restrictions on the blur function we show that the convergence rate of the method is close to optimal from some viewpoints and demonstrate its practical performance by applying it to real images

lp theory for the multidimensional aggregation equation we consider well posedness of the aggregation equation tu div uv 0 v k u with initial data in input amssym cal p 2 rm bbb r d rm cap l p bbb r d in dimensions 2 and higher we consider radially symmetric kernels where the singularity at the origin is of order x 2 d and prove local well posedness in input amssym cal p 2 bbb r d rm cap l p bbb r d for sufficiently large p ps in the special case of k x x the exponent ps d d 1 is sharp for local well posedness in that solutions can instantaneously concentrate mass for initial data in input amssym cal p 2 bbb r d rm cap l p bbb r d with p ps we also give an osgood condition on the potential k x that guarantees global existence and uniqueness in input amssym cal p 2 bbb r d rm cap l p bbb r d 2010 wiley periodicals inc

multifractal characterization of protein contact networks abstract the multifractal detrended fluctuation analysis of time series is able to reveal the presence of long range correlations and at the same time to characterize the self similarity of the series the rich information derivable from the characteristic exponents and the multifractal spectrum can be further analyzed to discover important insights into the underlying dynamical process in this paper we employ multifractal analysis techniques in the study of protein contact networks to this end initially a network is mapped to three different time series each of which is generated by a stationary unbiased random walk to capture the peculiarities of the networks at different levels we accordingly consider three observables at each vertex the degree the clustering coefficient and the closeness centrality to compare the results with suitable references we consider also instances of three well known network models and two typical time series with pure monofractal and multifractal properties the first result of notable interest is that time series associated to protein contact networks exhibit long range correlations strong persistence which are consistent with signals in between the typical monofractal and multifractal behavior successively a suitable embedding of the multifractal spectra allows to focus on ensemble properties which in turn gives us the possibility to make further observations regarding the considered networks in particular we highlight the different role that small and large fluctuations of the considered observables play in the characterization of the network topology

globally convergent image reconstruction for emission tomography using relaxed ordered subsets algorithms we present two types of globally convergent relaxed ordered subsets os algorithms for penalized likelihood image reconstruction in emission tomography modified block sequential regularized expectation maximization bsrem and relaxed os separable paraboloidal surrogates os sps the global convergence proof of the existing bsrem de pierro and yamagishi 2001 required a few a posteriori assumptions by modifying the scaling functions of bsrem we are able to prove the convergence of the modified bsrem under realistic assumptions our modification also makes stepsize selection more convenient in addition we introduce relaxation into the os sps algorithm erdogan and fessler 1999 that otherwise would converge to a limit cycle we prove the global convergence of diagonally scaled incremental gradient methods of which the relaxed os sps is a special case main results of the proofs are from nedic and bertsekas 2001 and correa and lemarechal 1993 simulation results showed that both new algorithms achieve global convergence yet retain the fast initial convergence speed of conventional unrelaxed ordered subsets algorithms

resolution and noise properties of map reconstruction for fully 3 d pet derives approximate analytical expressions for the local impulse response and covariance of images reconstructed from fully three dimensional 3 d positron emission tomography pet data using maximum a posteriori map estimation these expressions explicitly account for the spatially variant detector response and sensitivity of a 3 d tomograph the resulting spatially variant impulse response and covariance are computed using 3 d fourier transforms a truncated gaussian distribution is used to account for the effect on the variance of the nonnegativity constraint used in map reconstruction using monte carlo simulations and phantom data from the micropet small animal scanner the authors show that the approximations provide reasonably accurate estimates of contrast recovery and covariance of map reconstruction for priors with quadratic energy functions they also describe how these analytical results can be used to achieve near uniform contrast recovery throughout the reconstructed volume

multifractal analysis and topological properties of a new family of weighted koch networks abstract weighted complex networks especially scale free networks which characterize real life systems better than non weighted networks have attracted considerable interest in recent years studies on the multifractality of weighted complex networks are still to be undertaken in this paper inspired by the concepts of koch networks and koch island we propose a new family of weighted koch networks and investigate their multifractal behavior and topological properties we find some key topological properties of the new networks their vertex cumulative strength has a power law distribution there is a power law relationship between their topological degree and weight strength the networks have a high weighted clustering coefficient of 0 41004 which is independent of the scaling factor c in the limit of large generation t the second smallest eigenvalue 2 and the maximum eigenvalue n are approximated by quartic polynomials of the scaling factor c for the general laplacian operator while 2 is approximately a quartic polynomial of c and n 1 5 for the normalized laplacian operator then we find that weighted koch networks are both fractal and multifractal their fractal dimension is influenced by the scaling factor c we also apply these analyses to six real world networks and find that the multifractality in three of them are strong

a multilevel domain decomposition algorithm for fast o n sup 2 logn reprojection of tomographic images a novel algorithm for fast computation of tomographic image projections is presented the method comprises a decomposition of an image into subimages followed by an aggregation of projections computed for the subimages the multilevel domain decomposition algorithm is formulated as a recursive procedure the computational cost of the proposed algorithm is comparable to that of fft based techniques while it appears to be more flexible than the latter numerical results demonstrate the effectiveness of the method

blind deblurring of spiral ct images to discriminate fine anatomical features in the inner ear it has been desirable that spiral computed tomography ct may perform beyond their current resolution limits with the aid of digital image processing techniques in this paper we develop a blind deblurring approach to enhance image resolution retrospectively without complete knowledge of the underlying point spread function psf an oblique ct image can be approximated as the convolution of an isotropic gaussian psf and the actual cross section practically the parameter of the psf is often unavailable hence estimation of the parameter for the underlying psf is crucially important for blind image deblurring based on the iterative deblurring theory we formulate an edge to noise ratio enr to characterize the image quality change due to deblurring our blind deblurring algorithm estimates the parameter of the psf by maximizing the enr and deblurs images in the phantom studies the blind deblurring algorithm reduces image blurring by about 24 according to our blurring residual measure also the blind deblurring algorithm works well in patient studies after fully automatic blind deblurring the conspicuity of the submillimeter features of the cochlea is substantially improved

conditional propagation of chaos and a class of quasilinear pde s we consider conditional propagation of chaos and use it to solve a class of quasilinear equations of parabolic type in addition we construct a class of continuous stochastic processes associated with the above nonlinear equations our method imposes fewer smoothness conditions on the coefficients and allows a degenerate nonlinear weight before a divergence form operator we hope this probabilistic approach will introduce a better microscopic picture for understanding some stefan type problems

numerical approximation of a time dependent nonlinear space fractional diffusion equation in this article we analyze a fully discrete numerical approximation to a time dependent fractional order diffusion equation which contains a nonlocal quadratic nonlinearity the analysis is performed for a general fractional order diffusion operator the nonlinear term studied is a product of the unknown function and a convolution operator of order 0 convergence of the approximation and a priori error estimates are given numerical computations are included which confirm the theoretical predictions

statistical self similar properties of complex networks it has been shown that many complex networks shared distinctive features which differ in many ways from the random and the regular networks although these features capture important characteristics of complex networks their applicability depends on the type of networks to unravel ubiquitous characteristics that complex networks may have in common we adopt the clustering coefficient as the probability measure and present a systematic analysis of various types of complex networks from the perspective of statistical self similarity we find that the probability distribution of the clustering coefficient is best characterized by the multifractal moreover the support of the measure had a fractal dimension these two features enable us to describe complex networks in a unified way at the same time offer unforeseen possibilities to comprehend complex networks

numerical study of interacting particles approximation for integro differential equations the paper develops a numerical method based on the interacting particles approximation propagation of chaos for the solution of a large class of evolution problems involving the fractional laplacian operator and a non local quadratic type non linearity coupled stochastic differential equations driven by levy symmetric a stable processes are integrated numerically using euler s method and the solutions of the governing equations are obtained from their statistics the method is tested on several one and two dimensional examples and established analytical properties of the solutions are verified for the numerical approximates when they are available for initial conditions that are either integrable or monotone bounded functions it is shown that these methods represent viable tools for constructing the solution to the cauchy problem

accelerated image reconstruction using ordered subsets of projection data the authors define ordered subset processing for standard algorithms such as expectation maximization em for image restoration from projections ordered subsets methods group projection data into an ordered sequence of subsets or blocks an iteration of ordered subsets em is defined as a single pass through all the subsets in each subset using the current estimate to initialize application of em with that data subset this approach is similar in concept to block kaczmarz methods introduced by eggermont et al 1981 for iterative reconstruction simultaneous iterative reconstruction sirt and multiplicative algebraic reconstruction mart techniques are well known special cases ordered subsets em os em provides a restoration imposing a natural positivity condition and with close links to the em algorithm os em is applicable in both single photon spect and positron emission tomography pet in simulation studies in spect the os em algorithm provides an order of magnitude acceleration over em with restoration quality maintained

global existence versus blow up in a high dimensional keller segel equation with degenerate diffusion and nonlocal aggregation abstract in this paper we study the degenerate keller segel equation with nonlocal aggregation u t u m u b u in r d r where m 1 d 3 and b u 2 u with 2 d by analyzing the interaction between the degenerate diffusion and the nonlocal aggregation we determine the conditions for initial data under which weak solutions globally exist or blow up in finite time with m 1 d d d furthermore a sharper criterion is given for global existence and finite time blow up of weak solutions with m in the subrange 2 d 2 d d d 1 d d

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

scaling in nonlinear parabolic equations the cauchy problem for parabolic equations with quadratic nonlinearity is studied we investigate the existence of global in time solutions and their large time behavior assuming some scaling property of the equation as well as of the norm of the banach space in which the solutions are constructed some applications of these abstract results are indicated

propagation of chaos and the burgers equation we establish a connection between the burgers equation and the limit of an n body problem when n to infty then we use this connection to linearize the burgers equation

a novel sure based criterion for parametric psf estimation we propose an unbiased estimate of a filtered version of the mean squared error the blur sure stein s unbiased risk estimate as a novel criterion for estimating an unknown point spread function psf from the degraded image only the psf is obtained by minimizing this new objective functional over a family of wiener processings based on this estimated blur kernel we then perform nonblind deconvolution using our recently developed algorithm the sure based framework is exemplified with a number of parametric psf involving a scaling factor that controls the blur size a typical example of such parametrization is the gaussian kernel the experimental results demonstrate that minimizing the blur sure yields highly accurate estimates of the psf parameters which also result in a restoration quality that is very similar to the one obtained with the exact psf when plugged into our recent multi wiener sure let deconvolution algorithm the highly competitive results obtained outline the great potential of developing more powerful blind deconvolution algorithms based on sure like estimates

analysis of a nonlocal model for spontaneous cell polarization in this work we investigate the dynamics of a nonlocal model describing spontaneous cell polarization it consists of a drift diffusion equation set in the half space with the coupling involving the trace value on the boundary we characterize the following behaviors in the one dimensional case solutions are global if the mass is below the critical mass and they blow up in finite time above the critical mass the higher dimensional case is also discussed the results are reminiscent of the classical keller segel system but critical spaces are different l n instead of l n 2 due to the coupling on the boundary in addition in the one dimensional case we prove quantitative convergence results using relative entropy techniques this work is complemented with a more realistic model that takes into account dynamical exchange of molecular content at the boundary in the one dimensional case we prove that blow up is prevented furthermore density converges toward a nontrivial stationary configuration

overcoming ho lder continuity in ill posed continuation problems many ill posed continuation problems in partial differential equations obey a logarithmic convexity inequality and can be stabilized in an appropriate banach space by imposing an a priori bound on

o n sup 2 log sub 2 n filtered backprojection reconstruction algorithm for tomography we present a new fast reconstruction algorithm for parallel beam tomography the new algorithm is an accelerated version of the standard filtered backprojection fbp reconstruction and uses a hierarchical decomposition of the backprojection operation to reduce the computational cost from o n sup 3 to o n sup 2 log sub 2 n we discuss the choice of the various parameters that affect the behavior of the algorithm and present numerical studies that demonstrate the cost versus distortion tradeoff comparisons with fourier reconstruction algorithms and a multilevel inversion algorithm by brandt et al both of which also have o n sup 2 log sub 2 n cost suggest that the proposed hierarchical scheme has a superior cost versus distortion performance it offers rms reconstruction errors comparable to the fbp with considerable speedup for an example with a 512 spl times 512 pixel image and 1024 views the speedup achieved with a particular implementation is over 40 fold with reconstructions visually indistinguishable from the fbp

deconvolution when classifying noisy data involving transformations in the present study we consider the problem of classifying spatial data distorted by a linear transformation or convolution and contaminated by additive random noise in this setting we show that classifier performance can be improved if we carefully invert the data before the classifier is applied however the inverse transformation is not constructed so as to recover the original signal and in fact we show that taking the latter approach is generally inadvisable we introduce a fully data driven procedure based on cross validation and use several classifiers to illustrate numerical properties of our approach theoretical arguments are given in support of our claims our procedure is applied to data generated by light detection and ranging lidar technology where we improve on earlier approaches to classifying aerosols this article has supplementary materials online

parametric blur estimation for blind restoration of natural images linear motion and out of focus this paper presents a new method to estimate the parameters of two types of blurs linear uniform motion approximated by a line characterized by angle and length and out of focus modeled as a uniform disk characterized by its radius for blind restoration of natural images the method is based on the spectrum of the blurred images and is supported on a weak assumption which is valid for the most natural images the power spectrum is approximately isotropic and has a power law decay with the spatial frequency we introduce two modifications to the radon transform which allow the identification of the blur spectrum pattern of the two types of blurs above mentioned the blur parameters are identified by fitting an appropriate function that accounts separately for the natural image spectrum and the blur frequency response the accuracy of the proposed method is validated by simulations and the effectiveness of the proposed method is assessed by testing the algorithm on real natural blurred images and comparing it with state of the art blind deconvolution methods

direct blind deconvolution blind deconvolution seeks to deblur an image without knowing the cause of the blur iterative methods are commonly applied to that problem but the iterative process is slow uncertain and often ill behaved this paper considers a significant but limited class of blurs that can be expressed as convolutions of two dimensional symmetric levy stable probability density functions this class includes and generalizes gaussian and lorentzian distributions for such blurs methods are developed that can detect the point spread function from one dimensional fourier analysis of the blurred image a separate image deblurring technique uses this detected point spread function to deblur the image each of these two steps uses direct noniterative methods and requires interactive tuning of parameters as a result blind deblurring of 512 512 images can be accomplished in minutes of cpu time on current desktop workstations numerous blind experiments on synthetic data show that for a given blurred image several di

polynomial computations for blind image deconvolution this paper considers the problem of blind image deconvolution bid when the blur arises from a spatially invariant point spread function psf h which implies that a blurred image g is formed by the convolution of h and the exact form f of g since the multiplication of two bivariate polynomials is performed by convolving their coefficient matrices the equivalence of the formation of a blurred image and the product of two bivariate polynomials implies that bid can be performed by considering f g and h to be bivariate polynomials on which polynomial operations are performed these operations allow the psf to be computed which is then deconvolved from the blurred image g thereby obtaining a deblurred image that is a good approximation of the exact image f computational results show that the deblurred image obtained using polynomial computations is better than the deblurred image obtained using other methods for blind image deconvolution

o n sup 3 log n backprojection algorithm for the 3 d radon transform we present a novel backprojection algorithm for three dimensional 3 d radon transform data that requires o n sup 3 log sub 2 n operations for reconstruction of an n spl times n spl times n volume from o n sup 2 plane integral projections our algorithm uses a hierarchical decomposition of the 3 d radon transform to recursively decompose the backprojection operation simulations are presented demonstrating reconstruction quality comparable to the standard filtered backprojection which requires o n sup 5 computations under the same circumstances

hausdorff dimension of regular points in stochastic burgers flows with levy α stable initial data this paper studies statistical properties of shocks for the inviscid burgers equation with an stable levy motion initial data in the absence of analytic results numerical and computer simulation tools are utilized qualitative and quantitative information on the scaling properties of lagrangian regular points of solutions is obtained and in particular their hausdorff dimension is estimated to be 1 this suggestsa possible extension of ya sinai s result for brownian initial data

large global in time solutions to a nonlocal model of chemotaxis abstract we consider the parabolic elliptic model for the chemotaxis with fractional anomalous diffusion global in time solutions are constructed under nearly optimal assumptions on the size of radial initial data moreover criteria for blowup of radial solutions in terms of suitable morrey spaces norms are derived

linear and nonlinear image deblurring a documented study nonlinear image deblurring procedures based on probabilistic considerations are widely believed to outperform conventional linear methods this paper is exclusively concerned with nonsmooth images such as those that occur in biomedical imaging where reconstruction of high frequency detail is of prime interest and where avoidance of a priori smoothness constraints is a major concern the theoretical basis behind each of the following nonlinear procedures is examined the lucy richardson method the maximum likelihood e m algorithm the poisson maximum a posteriori method and the nunez llacer version of the maximum entropy method a linear iterative method vancittert s iteration is also studied it is shown that each of the first three methods as well as vancittert s method lack a necessary ingredient for successful solution of the ill posed deblurring problem while in the maximum entropy method the enforced smoothness may have adverse consequences in medical imaging a direct linear method the slow evolution from the continuation boundary secb method designed specifically for nonsmooth images is also considered that method is stabilized by constraining the blurring operator as well as the solution and does not require smoothness constraints it is shown that useful error estimates can be obtained in the secb method while this is impossible in tikhonov s method without a priori bounds on derivatives of the unknown solution reconstruction experiments on low noise synthetic mri data show that thousands of iterations are necessary to achieve sufficient resolution in the iterative procedures however the secb method provides higher resolution at considerable savings in computer time at high noise levels the iterative algorithms are shown to diverge at these same noise levels the secb method produces reconstructions comparable in quality to those that would be obtained in the iterative methods were one able to terminate the divergent algorithm at that iteration which best approximates the true solution in the l1 norm

a new approach for a nonlocal nonlinear conservation law we describe an approach to nonlocal nonlinear advection in one dimension that extends the usual pointwise concepts to account for nonlocal contributions to the flux the spatially nonlocal operators we consider do not involve derivatives instead the spatial operator involves an integral that in a distributional sense reduces to a conventional nonlinear advective operator in particular we examine a nonlocal inviscid burgers equation which gives a basic form with which to characterize properties associated with well posedness and to examine numerical results for specific cases we describe the connection to a nonlocal viscous regularization which mimics the viscous burgers equation in an appropriate limit we present numerical results that compare the behavior of the nonlocal burgers formulation to the standard local case the developments presented in this paper form the preliminary building blocks upon which to build a theory of nonlocal advection phenomena consistent within the peridynamic theo

fractal burgers equations abstract the paper studies local and global in time solutions to a class of multidimensional generalized burgers type equations with a fractional power of the laplacian in the principal part and with general algebraic nonlinearity such equations naturally appear in continuum mechanics our results include existence uniqueness regularity and asymptotic behavior of solutions to the cauchy problem as well as a construction of self similar solutions the role of critical exponents is also explained

semi blind image restoration via mumford shah regularization image restoration and segmentation are both classical problems that are known to be difficult and have attracted major research efforts this paper shows that the two problems are tightly coupled and can be successfully solved together mutual support of image restoration and segmentation processes within a joint variational framework is theoretically motivated and validated by successful experimental results the proposed variational method integrates semi blind image deconvolution parametric blur kernel and mumford shah segmentation the functional is formulated using the spl gamma convergence approximation and is iteratively optimized via the alternate minimization method while the major novelty of this work is in the unified treatment of the semi blind restoration and segmentation problems the important special case of known blur is also considered and promising results are obtained

global well posedness for nonlocal fractional keller segel systems in critical besov spaces abstract in this paper we study keller segel systems with fractional diffusion and a nonlocal term we establish the global existence uniqueness and stability of solutions for systems with small initial data in critical besov spaces our main tools are the l p l q estimates for e t 2 in besov spaces and the perturbation of linearization

global existence and asymptotic behavior of the fractional chemotaxis system with signal dependent sensitivity abstract in this paper we study a fractional chemotaxis model with signal dependent sensitivity and the source term which involves two parabolic equations with fractional diffusions we develop a suitable mathematical framework for a unified treatment of the existence and decay estimates based on an appropriate functional space we show the existence uniqueness and temporal decay of the global classical solutions to the problem simultaneously under the smallness initial assumptions

refined blowup criteria and nonsymmetric blowup of an aggregation equation abstract we consider an aggregation equation in r d d 2 with fractional dissipation u t u k u u where 0 0 1 and k x e x we prove a refined blowup criteria by which the global existence of solutions is controlled by its l x q norm for any d d 1 q we prove the finite time blowup of solutions for a general class of nonsymmetric initial data the argument presented works for both the inviscid case 0 and the supercritical case 0 and 0 1 additionally we present new proofs of blowup which does not use free energy arguments

a regularization approach to joint blur identification and image restoration the primary difficulty with blind image restoration or joint blur identification and image restoration is insufficient information this calls for proper incorporation of a priori knowledge about the image and the point spread function psf a well known space adaptive regularization method for image restoration is extended to address this problem this new method effectively utilizes among others the piecewise smoothness of both the image and the psf it attempts to minimize a cost function consisting of a restoration error measure and two regularization terms one for the image and the other for the blur subject to other hard constraints a scale problem inherent to the cost function is identified which if not properly treated may hinder the minimization blind restoration process alternating minimization is proposed to solve this problem so that algorithmic efficiency as well as simplicity is significantly increased two implementations of alternating minimization based on steepest descent and conjugate gradient methods are presented good performance is observed with numerically and photographically blurred images even though no stringent assumptions about the structure of the underlying blur operator is made

a general framework for a class of non linear approximations with applications to image restoration abstract in this paper we establish sufficient conditions for the existence of optimal non linear approximations to a linear subspace generated by a given weakly closed non convex cone of a hilbert space most non linear problems have difficulties to implement good projection based algorithms due to the fact that the subsets where we would like to project the functions do not have the necessary geometric properties to use the classical existence results such as convexity for instance the theoretical results given here overcome some of these difficulties to see this we apply them to a fractional model for image deconvolution in particular we reformulate and prove the convergence of a computational algorithm proposed in a previous paper by some of the authors finally some examples are given

spatial resolution properties of penalized likelihood image reconstruction space invariant tomographs this paper examines the spatial resolution properties of penalized likelihood image reconstruction methods by analyzing the local impulse response the analysis shows that standard regularization penalties induce space variant local impulse response functions even for space invariant tomographic systems paradoxically for emission image reconstruction the local resolution is generally poorest in high count regions we show that the linearized local impulse response induced by quadratic roughness penalties depends on the object only through its projections this analysis leads naturally to a modified regularization penalty that yields reconstructed images with nearly uniform resolution the modified penalty also provides a very practical method for choosing the regularization parameter to obtain a specified resolution in images reconstructed by penalized likelihood methods

stochastic nonlocal conservation laws on whole space abstract after introducing an entropy formulation for stochastic nonlocal conservation laws via an integral formula we develop a uniqueness theory by using a doubling variables technique and an existence theory by using a vanishing viscosity method we further consider the continuous dependence of the entropy solution on initial data

numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion in this paper we study the time space fractional order fractional for simplicity nonlinear subdiffusion and superdiffusion equations which can relate the matter flux vector to concentration gradient in the general sense describing for example the phenomena of anomalous diffusion fractional brownian motion and so on the semi discrete and fully discrete numerical approximations are both analyzed where the galerkin finite element method for the space riemann liouville fractional derivative with order 1 b 1 2 and the finite difference scheme for the time caputo derivative with order a 0 1 for subdiffusion and 1 2 for superdiffusion are analyzed respectively results on the existence and uniqueness of the weak solutions the numerical stability and the error estimates are presented numerical examples are included to confirm the theoretical analysis during our simulations an interesting diffusion phenomenon of particles is observed that is on average the diffusion velocity for 0 a 1 is slower than that for a 1 but the diffusion velocity for 1 a 2 is faster than that for a 1 for the spatial diffusion we have a similar observation

global and exploding solutions for nonlocal quadratic evolution problems nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered the inertial type nonlinearity is quadratic and nonlocal while the diffusive term also nonlocal is anomalous and fractal i e represented by a fractional power of the laplacian conditions for global in time existence versus finite time blow up are studied self similar solutions are constructed for certain homogeneous initial data

iterative image reconstruction using inverse fourier rebinning for fully 3 d pet we describe a fast forward and back projector pair based on inverse fourier rebinning for use in iterative image reconstruction for fully 3 d positron emission tomography pet the projector pair is used as part of a factored system matrix that takes into account detector pair response by using shift variant sinogram blur kernels thereby combining the computational advantages of fourier rebinning with iterative reconstruction using accurate system models the forward projector consists of a 2 d projector which maps 3 d images into 2 d direct sinograms followed by exact inverse rebinning which maps the 2 d into fully 3 d sinograms the back projector is implemented as the transpose of the forward projector and differs from the true exact rebinning operator in the sense that it does not require reprojection to compute missing lines of response lors we compensate for two types of inaccuracies that arise in a cylindrical pet scanner when using inverse fourier rebinning 1 nonuniform radial sampling and 2 nonconstant oblique angles in the radial direction in a single oblique sinogram we examine the effects of these corrections on sinogram accuracy and reconstructed image quality we evaluate performance of the new projector pair for maximum a posteriori map reconstruction of simulated and in vivo data the new projector results in only a small loss in resolution towards the edge of the field of view when compared to the fully 3 d geometric projector and requires an order of magnitude less computation

on a stochastic nonlinear equation arising from 1d integro differential scalar conservation laws abstract in this paper we study the initial problem for a stochastic nonlinear equation arising from 1d integro differential scalar conservation laws the equation is driven by levy space time white noise in the following form t a u x q u f u g u f t x for u t x 0 r u t x r where a is an integro differential operator associated with a symmetric nonlocal regular dirichlet form and f t x stands for a levy space time white noise the problem is interpreted as a stochastic integral equation of jump type involving certain convolution kernels existence of a unique local in time l 2 r valued solution is obtained

singularity patterns in a chemotaxis model the authors study a chemotactic model under certain assumptions and obtain the existence of a class of solutions which blow up at the center of an open disc in finite time such a finite time blow up of solutions implies chemotactic collapse namely concentration of species to form sporae the model studied is the limiting case of a basic chemotactic model when diffusion of the chemical approaches infinity which has the form ut u u v 0 v u 1 on r2 where is an open disc with no flux homogeneous neumann boundary conditions the initial conditions are continuous functions u x 0 u0 x 0 v x 0 v0 x 0 for x under these conditions the authors prove there exists a radially symmetric solution u r t which blows up at r 0 t t a specific description of such a solution is presented the authors also discuss the strong similarity between the chemotactic model they study and the classical stefan problem

continuum models of cohesive stochastic swarms the effect of motility on aggregation patterns abstract mathematical models of swarms of moving agents with non local interactions have many applications and have been the subject of considerable recent interest for modest numbers of agents cellular automata or related algorithms can be used to study such systems but in the present work instead of considering discrete agents we discuss a class of one dimensional continuum models in which the agents possess a density x t at location x at time t the agents are subject to a stochastic motility mechanism and to a global cohesive inter agent force the motility mechanisms covered include classical diffusion nonlinear diffusion which may be used to model in a phenomenological way volume exclusion or other short range local interactions and a family of linear redistribution operators related to fractional diffusion equations a variety of exact analytic results are discussed including equilibrium solutions and criteria for unimodality of equilibrium distributions full time dependent solutions and transitions between asymptotic collapse and asymptotic escape we address the behaviour of the system for diffusive motility in the low diffusivity limit for both smooth and singular interaction potentials and show how this elucidates puzzling behaviour in fully deterministic non local particle interaction models we conclude with speculative remarks about extensions and applications of the models

jump surface estimation edge detection and image restoration surface estimation is important in many applications when conventional smoothing procedures e g running averages local polynomial kernel smoothing procedures smoothing spline procedures are used for estimating jump surfaces from noisy data jumps are blurred at the same time when noise is removed in recent years new smoothing methodologies have been proposed in the statistical literature for detecting jumps in surfaces and for estimating jump surfaces with jumps preserved we provide a review of these methodologies because a monochrome image can be considered a jump surface of the image intensity function with jumps at the outlines of objects edge detection and image restoration problems in image processing are closely related to the jump surface estimation problem in statistics we also review major methodologies on edge detection and image restoration and discuss connections and differences among these methods and related methods in the statistical literature