outlier detection with the kernelized spatial depth function statistical depth functions provide from the deepest point a center outward ordering of multidimensional data in this sense depth functions can measure the extremeness or outlyingness of a data point with respect to a given data set hence they can detect outliers observations that appear extreme relative to the rest of the observations of the various statistical depths the spatial depth is especially appealing because of its computational efficiency and mathematical tractability in this article we propose a novel statistical depth the kernelized spatial depth ksd which generalizes the spatial depth via positive definite kernels by choosing a proper kernel the ksd can capture the local structure of a data set while the spatial depth fails we demonstrate this by the half moon data and the ring shaped data based on the ksd we propose a novel outlier detection algorithm by which an observation with a depth value less than a threshold is declared as an outlier the proposed algorithm is simple in structure the threshold is the only one parameter for a given kernel it applies to a one class learning setting in which normal observations are given as the training data as well as to a missing label scenario where the training set consists of a mixture of normal observations and outliers with unknown labels we give upper bounds on the false alarm probability of a depth based detector these upper bounds can be used to determine the threshold we perform extensive experiments on synthetic data and data sets from real applications the proposed outlier detector is compared with existing methods the ksd outlier detector demonstrates a competitive performance

the calderon problem with partial data in this paper we improve an earlier result by bukhgeim and uhlmann 1 by showing that in dimension n 3 the knowledge of the cauchy data for the schr nodinger equation measured on possibly very small subsets of the boundary determines uniquely the potential we follow the general strategy of 1 but use a richer set of solutions to the dirichlet problem this implies a similar result for the problem of electrical impedance tomography which consists in determining the conductivity of a body by making voltage and current measurements at the boundary

evaluation of the external force term in the discrete boltzmann equation a representation of the forcing term in the boltzmann equation based on a hermite expansion of the boltzmann distribution function in velocity phase space is derived based on this description of the forcing term a systematic comparison of previous lattice boltzmann models describing a nonideal gas behavior is given

an inverse boundary value problem for schrodinger operators with vector potentials we consider the schrodinger operator for a magnetic potential a and an electric potential q which are supported in a bounded domain in r n with n 3 we prove that knowledge of the dirichlet to neumann map associated to the schrodinger operator determines the magnetic field rot a and the electric potential 4 simultaneously provided rot a is small in the l topology

lattice boltzmann model for the incompressible navier stokes equation in this paper a lattice boltzmann lb model to simulate incompressible flow is developed the main idea is to explicitly eliminate the terms of o m2 where m is the mach number due to the density fluctuation in the existing lb models in the proposed incompressible lb model the pressure p instead of the mass density is the independent dynamic variable the incompressible navier stokes equations are derived from the incompressible lb model via chapman enskog procedure numerical results of simulations of the plane poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2d womersley flow are presented the numerical results are found to be in excellent agreement with theory

three dimensional microscale flow simulation and colloid transport modeling in saturated soil porous media transport of sub micron colloid particles in soil porous media has been mostly studied numerically with unit cell based grain scale geometries in this study we develop a more general approach by combining a multiple grain pore scale flow simulation with lagrangian tracking of individual colloids first two numerical methods are applied simultaneously to solve viscous flows in a channel partially or fully packed with spherical grain particles this allows cross validation of the numerical methods for considered model geometries it is demonstrated that the mesoscopic lattice boltzmann approach can more accurately simulate three dimensional pore scale flows with multiple grain grain and grain wall contact points colloid transport is simulated under the combined influence of hydrodynamic forces brownian force and physicochemical forces preliminary results demonstrate the capture of colloids by the secondary energy minimum sem well the local hydrodynamic retardation is shown to reduce the ability for colloids to move into the sem well but does not prevent this trajectories before and after the capture are also discussed

a lattice boltzmann scheme of the navier stokes equation on a three dimensional cuboid lattice abstract the standard lattice boltzmann method lbm for fluid flow simulation is based on a square in 2d or a cubic in 3d lattice grids recently two new lattice boltzmann schemes have been developed on a 2d rectangular grid using the mrt multiple relaxation time collision model either by adding a free parameter in the definition of moments or by extending the equilibrium moments these models satisfy all isotropy conditions and are fully consistent to the navier stokes equations here we developed a lattice boltzmann model on a 3d cuboid lattice namely a lattice grid with different grid lengths in different spatial directions we designed the moment equations derived from our mrt lbm model through the chapman enskog analysis to be fully consistent with the navier stokes equations a second order term is added to the equilibrium moments in order to not only satisfy all isotropy conditions but also to better accommodate different values of shear and bulk viscosities the form of the second order term and the coefficients of the extended equilibrium moments are determined through an inverse design process an additional benefit of the model is that the shear viscosity can be adjusted independent of the stress moment relaxation parameter thus potentially improving the numerical stability of the model the resulting cuboid mrt lbm model is then validated through benchmark simulations using the laminar channel flow the turbulent channel flow and the 3d time dependent energy cascading taylor green vortex flow the second order accuracy of the proposed model is also demonstrated the aspect ratios for numerical stability appear to be constrained at high flow reynolds numbers especially for turbulent flow simulations an aspect requiring further investigation

an inverse design analysis of mesoscopic implementation of non uniform forcing in mrt lattice boltzmann models abstract in this paper the mesoscopic representation of non uniform forcing is investigated by an inverse design approach for several mrt multiple relaxation time lattice boltzmann models first the mesoscopic forcing representation of a standard lbm mrt model on a square lattice is re visited by the multiscale chapman enskog expansion we derive the most general form of the representation by taking advantage of the mrt formulation in particular we show that there are three free components in the mesoscopic representation of forcing second by the same methodology the forcing scheme of two new rectangular mrt lattice boltzmann models are derived based on the requirements of the navier stokes equations these theoretical results are then validated by numerical simulations of a forced taylor green vortex flow with several different forms of non uniform forcing to alter the kinetic energy evolution of the system the numerical results are in excellent agreement with the corresponding time dependent analytical solution of flow

on the range of the attenuated radon transform in strictly convex sets we present new necessary and sufficient conditions for a function on s 1 to be in the range of the attenuated radon transform of a sufficiently smooth function support in the convex set r 2 the approach is based on an explicit hilbert transform associated with traces of the boundary of a analytic functions in the sense of bukhgeim in this paper we are concerned with the range characterization of the attenuated radon transform of function of compact support in the plane necessary and sufficient constraints on range of the non att enuated clas sical radon transform in the euclidean space have been known since the works in 6 7 and 10 these constraints known as the cavalieri or the moment conditions are in terms of the angular variable for function in the schwartz class they are essentially unique due to a paley wiener type the orem moreover the helgason support theorem extends the conditions to smooth functions of compact support 8 however in the case of functions of compact support it is possible to obtain essentially dif ferent range con ditions since more than one operator can annihilate functions of compact support in the range of the radon transform the results here constitute one such example inversion methods of the attenuated radon transform in the plane ap peared first in 1 and 14 and various developments can be found in 13 3 5 2 the interest in range conditions stems out fro m their appli cations to data enhancement in medical imaging methods such as single photon or positron emission computed tomography 12 for the eu clidean attenuated radon transform some range characterization based on the inversion procedure in 14 can be found in 15 these constraints are also in terms of the angular variable different from the existing results above our new characterization is in terms of a hilbert transform associated with the a analytic maps a la

lens rigidity for manifolds with hyperbolic trapped set for a riemannian manifold m g with strictly convex boundary m the lens data consists in the set of lengths of geodesics with endpoints on m together with their endpoints x x m m and tangent exit vectors v v t x m t x m we show deformation lens rigidity for manifolds with hyperbolic trapped set and no conjugate points a class which contains all manifolds with negative curvature and strictly convex boundary including those with non trivial topology and trapped geodesics for the same class of manifolds in dimension 2 we prove that the set of endpoints and exit vectors of geodesics ie the scattering data determines the riemann surface up to conformal diffeomorphism

symplectic phase flow approximation for the numerical integration of canonical systems new methods are presented for the numerical integration of ordinary differential equations of the important family of hamiltonian dynamical systems these methods preserve the poincare invariants and therefore mimic relevant qualitative properties of the exact solutions the methods are based on a runge kutta type ansatz for the generating function to realize the integration steps by canonical transformations a fourth order method is given and its implementation is discussed numerical results are presented for the henon heiles system which describes the motion of a star in an axisymmetric galaxy

stability estimates for the calderon problem with partial data this is a follow up of a previous article where we proved local stability estimates for a potential in a schr odinger equation on an open bounded set in dimension n 3 from the dirichlet to neumann map with partial data the region under control was the penumbra delimited by a source of light outside of the convex hull of the open set these local estimates provided stability of log log type corresponding to the uniqueness results in calder on s inverse problem with partial data proved by kenig sj ostrand and uhlmann in this article we prove the corresponding global estimates in all dimensions higher than three the estimates are based on the construction of solutions of the schr odinger equation by complex geometrical optics developed in the anisotropic setting by dos santos ferreira kenig salo and uhlmann to solve the calder on problem in certain admissible geometries

supervised factorial learning factorial learning finding a statistically independent representation of a sensory image a factorial code is applied here to solve multilayer supervised learning problems that have traditionally required backpropagation this lends support to barlow s argument for factorial sensory processing by demonstrating how it can solve actual pattern recognition problems two techniques for supervised factorial learning are explored one of which gives a novel distributed solution requiring only positive examples also a new nonlinear technique for factorial learning is introduced that uses neural networks based on almost reversible cellular automata due to the special functional connectivity of these networks which resemble some biological microcircuits learning requires only simple local algorithms also supervised factorial learning is shown to be a viable alternative to backpropagation one significant advantage is the existence of a measure for the performance of intermediate learning stages

optimal stability estimate in the inverse boundary value problem for periodic potentials with partial data abstract we consider the inverse boundary value problem for operators of the form q in an infinite domain r r 1 n n 3 with a periodic potential q for dirichlet to neumann data localized on a portion of the boundary of the form 1 r 1 with 1 being the complement either of a flat or spherical portion of we prove that a log type stability estimate holds

discrete lattice effects on the forcing term in the lattice boltzmann method we show that discrete lattice effects must be considered in the introduction of a force into the lattice boltzmann equation a representation of the forcing term is then proposed with the representation the navier stokes equation is derived from the lattice boltzmann equation through the chapman enskog expansion several other existing force treatments are also examined

designing correct fluid hydrodynamics on a rectangular grid using mrt lattice boltzmann approach while the lattice boltzmann method lbm has become a powerful numerical approach for solving complex flows the standard lattice boltzmann method typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions for inhomogeneous and anisotropic flows it is desirable to have a lbm model that utilizes a rectangular grid there were two previous attempts to extend the multiple relaxation time mrt lbm to a rectangular lattice grid in 2d however the resulting hydrodynamic momentum equation was not fully consistent with the navier stokes equation due to anisotropy of the transport coefficients in the present work a new mrt model with an additional degree of freedom is developed in order to match precisely the navier stokes equation when a rectangular lattice grid is used we first revisit the previous attempts to understand the origin and nature of anisotropic transport coefficients by conducting an inverse design analysis within the chapman enskog procedure then an additional adjustable parameter that governs the relative orientation in the energy normal stress subspace is introduced it is shown that this adjustable parameter can be used to fully eliminate the anisotropy of transport coefficients thus the exact navier stokes equation can be derived on a rectangular grid our theoretical findings are confirmed by numerical solutions using three two dimension benchmark problems i e the channel flow the cavity flow and the decaying taylor green vortex flow the numerical results demonstrate that the proposed model shows remarkably good performance with appropriate choice of model parameters

neural tree density estimation for novelty detection in this paper a neural competitive learning tree is introduced as a computationally attractive scheme for adaptive density estimation and novelty detection the learning rule yields equiprobable quantization of the input space and provides an adaptive focusing mechanism capable of tracking time varying distributions it is shown by simulation that the neural tree performs reasonably well while being much faster than any of the other competitive learning algorithms

learning time series evolution by unsupervised extraction of correlations as a consequence we are able to model chaotic and nonchaotic time series furthermore one critical point in modeling time series is the determination of the dimension of the embedding vector used i e the number of components of the past that are needed to predict the future with this method we can detect the embedding dimension by extracting the influence of the past on the future i e the correlation of remote past and future optimal embedding dimensions are obtained for the henon map and the mackey glass series when noisy data corrupted by colored noise are used a model is still possible the noise will then be decorrelated by the network in the case of modeling a chemical reaction the most natural architecture that conserves the volume is a symplectic network which describes a system that conserves the entropy and therefore the transmitted information

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

a theory for learning by weight flow on stiefel grassman manifold recently we introduced the concept of neural network learning on stiefel grassman manifold for multilayer perceptron like networks contributions of other authors have also appeared in the scientific literature about this topic this article presents a general theory for it and illustrates how existing theories may be explained within the general framework proposed here

on the x ray transform of planar symmetric 2 tensors abstract in this paper we study the attenuated x ray transform of 2 tensors supported in convex bounded subsets with sufficiently smooth boundary in the euclidean plane we characterize its range and reconstruct all possible 2 tensors yielding identical x ray data the characterization is in terms of a hilbert transform associated with a analytic maps in the sense of bukhgeim

analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice boltzmann bgk model in this paper we analytically solve the velocity of the lattice boltzmann bgk equation lbgk for several simple flows the analysis provides a framework to theoretically analyze various boundary conditions in particular the analysis is used to derive the slip velocities generated by various schemes for the nonslip boundary condition we find that the slip velocity is zero as long as f e 0 at boundaries no matter what combination of distributions is chosen the schemes proposed by nobleet al and by inamuroet al yield the correct zeroslip velocity while some other schemes such as the bounce back scheme and the equilibrium distribution scheme would inevitably generate a nonzero slip velocity the bounce back scheme with the wall located halfway between a flow node and a bounce back node is also studied for the simple flows considered and is shown to produce results of second order accuracy the momentum exchange at boundaries seems to be highly related to the slip velocity at boundaries to be specific the slip velocity is zero only when the momentum dissipated by boundaries is equal to the stress provided by fluids

effect of the forcing term in the multiple relaxation time lattice boltzmann equation on the shear stress or the strain rate tensor in this work the effect of the forcing term or external force in the multiple relaxation time lattice boltzmann equation mrtlbe on the shear stress or the strain rate tensor is studied theoretically and numerically through a chapman enskog analysis and numerical simulations we show that the shear stress or the strain rate tensor derived from the mrtlbe is second order accurate in space we then examine the influence of the forcing term on the shear stress or the strain rate tensor and demonstrate that the forcing term effect must be included when the shear stress or the strain rate tensor is computed with the nonequilibrium part of the distribution function

the boundary rigidity problem in the presence of a magnetic field abstract for a compact riemannian manifold with boundary endowed with a magnetic potential we consider the problem of restoring the metric g and the magnetic potential from the values of the mane action potential between boundary points and the associated linearized problem we study simple magnetic systems in this case knowledge of the mane action potential is equivalent to knowledge of the scattering relation on the boundary which maps a starting point and a direction of a magnetic geodesic into its end point and direction this problem can only be solved up to an isometry and a gauge transformation of for the linearized problem we show injectivity up to the natural obstruction under explicit bounds on the curvature and on we also show injectivity and stability for g and in a generic class g including real analytic ones for the nonlinear problem we show rigidity for real analytic simple g rigidity for metrics in a given conformal class and locally near any g g we also show that simple magnetic systems on two dimensional manifolds are always rigid

asymptotic analysis of the lattice boltzmann equation in this article we analyze the lattice boltzmann equation lbe by using the asymptotic expansion technique we first relate the lbe to the finite discrete velocity model fdvm of the boltzmann equation with the diffusive scaling the analysis of this model directly leads to the incompressible navier stokes equations as opposed to the compressible navier stokes equations obtained by the chapman enskog analysis with convective scaling we also apply the asymptotic analysis directly to the fully discrete lbe as opposed to the usual practice of analyzing a continuous equation obtained through the taylor expansion of the lbe this leads to a consistency analysis which provides order by order information about the numerical solution of the lbe the asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities such as vorticity it also justifies the use of richardson s extrapolation method as an example a two dimensional taylor vortex flow is used to validate our analysis the numerical results agree very well with our analytic predictions

stability estimates for the radon transform with restricted data and applications in this article we prove a stability estimate going from the radon transform of a function with limited angle distance data to the l p norm of the function itself under some conditions on the support of the function we apply this theorem to obtain stability estimates for an inverse boundary value problem with partial data

limiting carleman weights and anisotropic inverse problems in this article we consider the anisotropic calderon problem and related inverse problems the approach is based on limiting carleman weights introduced in kenig et al ann math 165 567 591 2007 in the euclidean case we characterize those riemannian manifolds which admit limiting carleman weights and give a complex geometrical optics construction for a class of such manifolds this is used to prove uniqueness results for anisotropic inverse problems via the attenuated geodesic ray transform earlier results in dimension n 3 were restricted to real analytic metrics

generalized lattice boltzmann equation with forcing term for computation of wall bounded turbulent flows in this paper we present a framework based on the generalized lattice boltzmann equation glbe using multiple relaxation times with forcing term for eddy capturing simulation of wall bounded turbulent flows due to its flexibility in using disparate relaxation times the glbe is well suited to maintaining numerical stability on coarser grids and in obtaining improved solution fidelity of near wall turbulent fluctuations the subgrid scale sgs turbulence effects are represented by the standard smagorinsky eddy viscosity model which is modified by using the van driest wall damping function to account for reduction of turbulent length scales near walls in order to be able to simulate a wider class of problems we introduce forcing terms which can represent the effects of general nonuniform forms of forces in the natural moment space of the glbe expressions for the strain rate tensor used in the sgs model are derived in terms of the nonequilibrium moments of the glbe to include such forcing terms which comprise a generalization of those presented in a recent work yu et al comput fluids 35 957 2006 variable resolutions are introduced into this extended glbe framework through a conservative multiblock approach the approach whose optimized implementation is also discussed is assessed for two canonical flow problems bounded by walls viz fully developed turbulent channel flow at a shear or friction reynolds number re of 183 6 based on the channel half width and three dimensional 3d shear driven flows in a cubical cavity at a re of 12 000 based on the side length of the cavity comparisons of detailed computed near wall turbulent flow structure given in terms of various turbulence statistics with available data including those from direct numerical simulations dns and experiments showed good agreement the glbe approach also exhibited markedly better stability characteristics and avoided spurious near wall turbulent fluctuations on coarser grids when compared with the single relaxation time srt based approach moreover its implementation showed excellent parallel scalability on a large parallel cluster with over a thousand processors

the attenuated ray transform on simple surfaces we show that the attenuated geodesic ray transform on two dimensional simple surfaces is injective moreover we give a stability estimate and develop a reconstruction procedure

statistical independence and novelty detection with information preserving nonlinear maps according to barlow 1989 feature extraction can be understood as finding a statistically independent representation of the probability distribution underlying the measured signals the search for a statistically independent representation can be formulated by the criterion of minimal mutual information which reduces to decorrelation in the case of gaussian distributions if nongaussian distributions are to be considered minimal mutual information is the appropriate generalization of decorrelation as used in linear principal component analyses pca we also generalize to nonlinear transformations by only demanding perfect transmission of information this leads to a general class of nonlinear transformations namely symplectic maps conservation of information allows us to consider only the statistics of single coordinates the resulting factorial representation of the joint probability distribution gives a density estimation we apply this concept to the real world problem of electrical motor fault detection treated as a novelty detection task

on emission tomography of inhomogeneous media the problem of finding the source distribution for particles or radiation in a bounded domain d from the emitting flow through the boundary of d is considered the particles are supposed to move with unit velocity along geodesics of a riemannian metric and can be absorbed by the medium the metric and the absorption are known uniqueness of the solution to this problem and a stability estimate are obtained under a certain assumption on the absorption and curvature of the metric

an inverse polynomial method for the identification of the leading coefficient in the sturm liouville operator from boundary measurements an inverse polynomial method of determining the unknown leading coefficient k k x of the linear sturm liouville operator au k x u x q x u x x 0 1 is presented as an additional condition only two measured data at the boundary x 0 x 1 are used in absence of a singular point u x 0 u x 0 x 0 1 the inverse problem is classified as a well conditioned if there exists at least one singular point then the inverse problem is classified as moderately ill conditioned u x 0 0 x 0 0 1 u x 0 x x 0 u x 0 x 0 1 and severely ill conditioned u x 0 u x 0 0 x 0 0 1 u x 0 u x 0 x x 0 for each of the cases direct problem solution is approximated by corresponding polynomials and the inverse problem is reformulated as a cauchy problem for to the first order differential equation with respect the unknown function k k x an approximate analytical solution of the each cauchy problems are derived in explicit form numerical simulations all the above cases are given for noise free and noisy data an accuracy of the presented approach is demonstrated on numerical test solutions

lattice boltzmann equation on a two dimensional rectangular grid abstract we construct a multirelaxation lattice boltzmann model 1 on a two dimensional rectangular grid the model is partly inspired by a previous work of koelman 2 to construct a lattice bgk model on a two dimensional rectangular grid the linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and galilean invariance for various wave propagations in the model the linear stability of the model is also studied the model is numerically tested for three cases a a vortex moving with a constant velocity on a mesh with periodic boundary conditions b poiseuille flow with an arbitrary inclined angle with respect to the lattice orientation and c a cylinder asymmetrically placed in a channel the numerical results of these tests are compared with either analytic solutions or the results obtained by other methods satisfactory results are obtained for the numerical simulations

blind source separation by sparse decomposition in a signal dictionary the blind source separation problem is to extract the underlying source signals from a set of linear mixtures where the mixing matrix is unknown this situation is common in acoustics radio medical signal and image processing hyperspectral imaging and other areas we suggest a two stage separation process a priori selection of a possibly overcomplete signal dictionary for instance a wavelet frame or a learned dictionary in which the sources are assumed to be sparsely representable followed by unmixing the sources by exploiting the their sparse representability we consider the general case of more sources than mixtures but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques

tensor tomography on surfaces we show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective this solves a long standing inverse problem in the two dimensional case

determining a magnetic schrodinger operator from partial cauchy data in this paper we show in dimension n 3 that knowledge of the cauchy data for the schrodinger equation in the presence of a magnetic potential measured on possibly very small subsets of the boundary determines uniquely the magnetic field and the electric potential we follow the general strategy of 7 using a richer set of solutions to the dirichlet problem that has been used in previous works on this problem

active selection of clustering constraints this paper examines active selection of clustering constraints which has become a topic of significant interest in constrained clustering active selection of clustering constraints which is known as minimizing the cost of acquiring constraints also includes quantifying utility of a given constraint set a sequential method is proposed in this paper to select the most beneficial set of constraints actively the proposed method uses information of boundary points and transition regions extracted by data description methods to introduce a utility measure for constraints since previously selected constraints affect the utility of remaining candidate constraints a method is proposed to update the utility of remaining constraints after selection of each constraint experiments carried out on synthetic and real datasets show that the proposed method improves the accuracy of clustering while reducing human interaction highlightsactive constraint selection as an open issue in constrained clustering is examined the method relies on the information of boundaries and transition regions of data a utility measure based on the description of data is proposed for constraints this utility measure considers the constraint utility dependencies constraints are selected in a sequential approach utilizing the utility measure

a hydrodynamically consistent mrt lattice boltzmann model on a 2d rectangular grid a multiple relaxation time mrt lattice boltzmann lb model on a d2q9 rectangular grid is designed theoretically and validated numerically in the present work by introducing stress components into the equilibrium moments this mrt lb model restores the isotropy of diffusive momentum transport at the macroscopic level or in the continuum limit leading to moment equations that are fully consistent with the navierstokes equations the model is derived by an inverse design process which is described in detail except one moment associated with the energy square all other eight equilibrium moments can be theoretically and uniquely determined the model is then carefully validated using both the two dimensional decaying taylorgreen vortex flow and lid driven cavity flow with different grid aspect ratios the corresponding results from an earlier model bouzidi et al 2001 28 are also presented for comparison the results of bouzidi et al s model show problems associated with anisotropy of viscosity coefficients while the present model exhibits full isotropy and is accurate and stable

numerics of the lattice boltzmann method effects of collision models on the lattice boltzmann simulations we conduct a comparative study to evaluate several lattice boltzmann lb models for solving the near incompressible navier stokes equations including the lattice boltzmann equation with the multiple relaxation time mrt the two relaxation time trt the single relaxation time srt collision models and the entropic lattice boltzmann equation elbe the lid driven square cavity flow in two dimensions is used as a benchmark test our results demonstrate that the elbe does not improve the numerical stability of the srt or the lattice bhatnagar gross krook lbgk model our results also show that the mrt and trt lb models are superior to the elbe and lbgk models in terms of accuracy stability and computational efficiency and that the elbe scheme is the most inferior among the lb models tested in this study thus is unfit for carrying out numerical simulations in practice our study suggests that to optimize the accuracy stability and efficiency in the mrt model it requires at least three independently adjustable relaxation rates one for the shear viscosity ensuremath nu or the reynolds number text re one for the bulk viscosity ensuremath zeta and one to satisfy the criterion imposed by the dirichlet boundary conditions which are realized by the bounce back type boundary conditions

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

gravity in a lattice boltzmann model in this paper we consider the introduction of a body force in the incompressible limit into the lattice boltzmann model a number of methods are considered and their suitability to our objectives determined when there is no density variation across the fluid gravity can be introduced in the form of an altered pressure gradient this method correctly satisfies the navier stokes equation however if there is a non negligible density variation present produced by the body force or otherwise this method becomes less accurate as the density variation increases and the constant density approximation becomes less valid three other methods are also considered for application when there is a non negligible density variation the equations of motion satisfied by these models are found up to second order in the knudsen number and it is seen that only one of these methods satisfies the true navier stokes equation numerical simulations are performed to compare the different models and to assess the range of application of each

on the continuum limit of a discrete inverse spectral problem on optimal finite difference grids we consider finite difference approximations of solutions of inverse stur m liouville problems in bounded intervals using three point finite difference sc hemes we discretize the equations on so called optimal grids constructed as follow s for a staggered grid with 2k points we ask that the finite difference operator a k k jacobi matrix and the sturm liouville differential operator share the k lowest eigenvalues and the values of the orthonormal eigenfunctions at one end of the interval this requirement determines uniquely the entries in the jacobi matrix which are grid cell averages of the coefficients in the continuum problem if these coefficients are known we can find the grid which we call optimal becau se it gives by design a finite difference operator with a prescribed spectr al measure we focus attention on the inverse problem where neither the coefficients n or the grid are known a key question in inversion is how to parametrize the coefficients i e how to choose the grid it is clear that to be successful this grid must be close to the optimal one which is unknown fortunately as we show here the grid dependence on the unknown coefficients is weak so the inversion can be done on a pr ecomputed grid for an a priori guess of the unknown coefficients this obse rvation leads to a simple yet efficient inversion algorithm which gives coefficien ts that converge pointwise to the true solution as the number k of data points tends to infinity the cornerstone of our convergence proof is showing that op timal grids provide an implicit natural regularization of the inverse problem by givin g reconstructions with uniformly bounded total variation the analysis is based on a novel explicit perturbation analysis of lanczos recursions and on a discrete

invariant distributions beurling transforms and tensor tomography in higher dimensions in the recent articles paternain et al j differ geom 98 147 181 2014 invent math 193 229 247 2013 a number of tensor tomography results were proved on two dimensional manifolds the purpose of this paper is to extend some of these methods to manifolds of any dimension a central concept is the surjectivity of the adjoint of the geodesic ray transform or equivalently the existence of certain distributions that are invariant under the geodesic flow we prove that on any anosov manifold one can find invariant distributions with controlled first fourier coefficients the proof is based on subelliptic type estimates and a pestov identity we present an alternative construction valid on manifolds with nonpositive curvature based on the fact that a natural beurling transform on such manifolds turns out to be essentially a contraction finally we obtain uniqueness results in tensor tomography both on simple and anosov manifolds that improve earlier results by assuming a condition on the terminator value for a modified jacobi equation