flat g bundles with canonical metrics on considere la relation entre la theorie invariante des actions de groupes algebriques semi simples sur des varietes algebriques complexes et le comportement de l application de moment et des donnees quantiques fournies par une structure symplectique associee on etudie un exemple de dimension infinie comprenant des fibres plats sur des varietes de riemann compactes

uniformization of mathcal g bundles we show some of the conjectures of pappas and rapoport concerning the moduli stack bung of g torsors on a curve c where g is a semisimple bruhat tits groupschemeon c inparticularweprovetheanalogoftheuniformizationtheoremof drinfeld simpson in this setting furthermore we apply this to compute the connected components of these moduli stacks and to calculate the picard group of bung in case g is simply connected

estimation of aquifer parameters under transient and steady state conditions 2 uniqueness stability and solution algorithms paper 2 of this three part series starts with a discussion of the question under what conditions is the aquifer inverse problem well posed after defining the terms uniqueness identifiability and stability theoretical considerations and synthetic examples are used to demonstrate that ill posedness can be mitigated by including prior information about the parameters in the estimation criterion to be minimized at the same time the inclusion of such information is shown to be insufficient to guarantee uniqueness and stability in all cases several test problems in the recent literature which have resulted in pessimistic conclusions about the solvability of the aquifer inverse problem are shown to be ill posed a question is thus raised about the validity of these conclusions in the general case various conjugate gradient algorithms coupled with the adjoint state finite element method for computing the gradient of the estimation criterion and with newton s method for determining the optimum step size downgradient are compared a marked improvement in the rate at which these algorithms converge is shown to be achieved by switching from one method to another when the former slows down or fails to converge

enhancing random heterogeneity representation by mixing the kriging method with the zonation structure 1 this research develops a zonation kriging zk method and extends the geostatistical theory to investigate the spatially distributed random field and obtain an optimal nonsmooth conditional estimate in the zk method the zonal structure honors the parameter measurements such that each sample location represents a distinct zone while the kriging method also honors the same data set and results in a smooth distribution the zk method integrates the conditional estimates of the zonal structure and the kriged field over a set of weighting coefficients on the sample data the extended geostatistical theory using the zk method is applied to the intrinsic field stationary field and nonstationary field the study shows that the conditional variance using the zk method is bounded between the kriging variance and variogram when estimating hydraulic conductivity by inversion of a groundwater model the optimal values of weighting coefficients are determined via predictive probability of the bayesian decision theory the numerical examples show that the zk method has less dependence on the semivariogram model the zk method outperforms the kriging method in both smooth and nonsmooth fields the zk method shows high efficiency to better the conditional estimate of hydraulic conductivity distribution with low conditional uncertainty and good agreement to the groundwater head observations

convex functions on symmetric spaces side lengths of polygons and the stability inequalities for weighted configurations at infinity in a symmetric space of noncompact type x g k oriented geodesic segments correspond modulo isometries to vectors in the euclidean weyl chamber we can hence assign vector valued lengths to segments our main result is a system of homogeneous linear inequalities which we call the generalized triangle inequalities or stability inequalities describing the restrictions on the vector valued side lengths of oriented polygons it is based on the mod 2 schubert calculus in the real grassmannians g p for maximal parabolic subgroups p the side lengths of polygons in euclidean buildings are studied in the related paper klm2 applications of the geometric results in both papers to algebraic group theory are given in klm3

stable bundles and integrable systems on considere la geometrie symplectique des fibres cotangents aux espaces de modules de fibres vectoriels stables sur une surface de riemann on montre que ce sont des systemes dynamiques hamiltoniens algebriquement completement integrables

level set and total variation regularization for elliptic inverse problems with discontinuous coefficients we propose a level set approach for elliptic inverse problems with piecewise constant coefficients the geometry of the discontinuity of the coefficient is represented implicitly by level set functions the inverse problem is solved using a variational augmented lagrangian formulation with total variation regularization of the coefficient the corresponding euler lagrange equation gives the evolution equation for the level set functions and the constant values of the coefficients we use a multiple level set representation which allows the coefficient to have multiple constant regions knowledge of the exact number of regions is not required only an upper bound is needed numerical experiments show that the method can recover coefficients with rather complicated geometries of discontinuities under moderate amount of noise in the observation data the method is also robust with respect to the initial guess for the geometry of the coefficient discontinuities

the capacity of the quantum multiple access channel we define classical quantum multiway channels for transmission of classical information after the previous work by allahverdyan and saakian see quantum computing and quantum communications lecture notes in computer science berlin germany springer verlag vol 1509 1999 bounds on the capacity region are derived in a uniform way which are analogous to the classically known ones simply replacing shannon 1961 entropy with von neumann 1955 entropy for the single receiver case multiple access channel the elect capacity region is determined these results are applied to the case of noisy channels with arbitrary input signal states a second issue of this work is the presentation of a calculus of quantum information quantities based on the algebraic formulation of quantum theory

three dimensional stochastic analysis of macrodispersion in aquifers the dispersive mixing resulting from complex flow in three dimensionally heterogeneous porous media is analyzed using stochastic continuum theory stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three dimensional statistically anisotropic input covariance describing the hydraulic conductivity with a statistically isotropic input covariance the longitudinal macrodispersivity is convectively controlled but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term with an arbitrarily oriented anisotropic conductivity covariance all components of the macrodispersivity tensor are convectively controlled and the ratio of transverse to longitudinal dispersivity is of the order of 10 1 in this case the off diagonal components of the dispersivity tensor are significant being numerically larger than the diagonal transverse terms and the transverse dispersion process can be highly anisotropic dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and monte carlo simulations the theory which treats the asymptotic condition of large displacement indicates that a classical gradient transport fickian relationship is valid for large scale displacements

a comparison of four inverse approaches to groundwater flow and transport parameter identification four different methods of parameterizing spatially varying log transmissivities in an inverse approach are compared with respect to prediction accuracy of simulated flow and transport transport parameter estimation is included by two stage feedback optimization in stage one the log transmissivities are estimated by fitting both head and concentration data given initial values of the source concentration and the dispersivities in stage two the source concentration and the dispersivities are estimated by fitting the concentration data with the updated transport parameters final estimates of the log transmissivities are obtained by repeating the optimization of stage one the formulated objective functions are minimized using levenberg marquardt s algorithm the models are applied to synthetic two dimensional transport problems in steady state flow regimes the true log transmissivity fields are generated by the turning bands method thereby incorporating spatial variability the test cases differ in the input variances of the generated fields and with respect to the amount and accuracy of observed transmissivity data

hybrid optimization methods for geophysical inversion local and global optimization algorithms are used commonly in geophysical data inversion each type of algorithm has unique advantages and disadvantages here we propose several methods of combining the two algorithms such that we can overcome their drawbacks and make use of the salient features of the two methods in particular we combined a local conjugate gradient cg method with a global very fast simulated annealing vfsa approach to solve problems of geophysical interests we conducted a systematic study to find an efficient strategy to combine cg and vfsa optimization schemes and recommend a couple of ways for future implementations seven different hybrid algorithms were first tested on a set of field 1 d schlumberger resistivity sounding data and their performances were compared with stand alone genetic algorithm ga simulated annealing and local search algorithms almost all of the proposed hybrid algorithms were found to be computationally more efficient than the conventional global optim

quasi linear geostatistical theory for inversing a quasi linear theory is presented for the geostatistical solution to the inverse problem the archetypal problem is to estimate the log transmissivity function from observations of head and log transmissivity at selected locations the unknown is parameterized as a realization of a random field and the estimation problem is solved in two phases structural analysis where the random field is characterized followed by estimation of the log transmissivity conditional on all observations the proposed method generalizes the linear approach of kitanidis and vomvoris 1983 the generalized method is superior to the linear method in cases of large contrast in formation properties but informative measurements i e there are enough observations that the variance of estimation error of the log transmissivity is small the methodology deals rigorously with unknown drift coefficients and yields estimates of covariance parameters that are unbiased and grid independent the applicability of the methodology is demonstrated through an example that includes structural analysis determination of best estimates and conditional simulations

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

inverse groundwater modeling with emphasis on model parameterization 1 this study develops an inverse method aiming to circumvent the subjective decision regarding model parameterization and complexity in inverse groundwater modeling the number of parameters is included as a decision variable along with parameter values a parameterization based on b spline surfaces bss is selected to approximate transmissivity and genetic algorithms were selected to perform error minimization a transform based on linear least squares lls is developed so that different parameterizations may be combined by standard genetic algorithm operators first three applications with isotropic anisotropic and zoned aquifer parameters are examined in a single objective optimization problem and the estimated transmissivity is found to be near the true one interestingly in the anisotropic case the algorithm converged to a solution with an anisotropic distribution of control points next a single objective optimization with regularization penalizing complex models is considered and last the problem is expressed in a multiobjective optimization framework moo where the goals are simultaneous minimization of calibration error and model complexity the result of moo is a pareto set of potential solutions where the user can examine the tradeoffs between calibration error and model complexity and select the most suitable model by comparing calibration with prediction errors it appears that the most promising models are the ones near a region where the rate of decrease of calibration error as model complexity increases drops bend of error curve this is a useful result of practical interest in real inverse modeling applications

a proposed stepwise regression method for model structure identification this paper proposes a new methodology for constructing groundwater models the proposed methodology which determines simultaneously both model structure and model parameters is based on the following ideas 1 when solving the inverse problem different model structures always produce different model parameters 2 since the number of possible model structures of an aquifer is infinite the number of possible representative parameters is also infinite 3 to obtain a set of appropriate representative model parameters we must have an appropriate model structure and 4 an appropriate model structure should be determined not only by observation data and prior information but also by the accuracy requirements of model applications in this proposed methodology we start with a homogeneous model structure and step by step gradually increase the complexity of the model structure at each level of complexity we calculate not only the fitting residual of parameter identification but also the error of model structure to determine if a more complex model structure is needed the model structure error of using one model structure to replace another model structure is defined by a maximum minimum max min problem that is based on the distance between the two models and is measured in parameter observation and prediction or decision spaces this proposed methodology is used to solve a hypothetical remediation design problem in which the true hydraulic conductivity is a random field with a certain trend we have found that for the example problem virtually identical pumping policy is obtained when a five zone model with an optimized zonation pattern is used to represent the nonstationary random field we have also found that observation errors have minimum impact on management solution in comparison with structure errors to calculate the model structure error for this example the inverse solution is coupled with a management problem we have also developed an effective iteration method to handle nonlinear water quality constraints

parabolic higgs bundles and representations of the fundamental group of a punctured surface into a real group abstract we study parabolic g higgs bundles over a compact riemann surface with fixed punctures when g is a real reductive lie group and establish a correspondence between these objects and representations of the fundamental group of the punctured surface in g with arbitrary holonomy around the punctures this generalizes simpson s results for gl n c to arbitrary complex and real reductive lie groups three interesting features are the relation between the parabolic degree and the tits geometry of the boundary at infinity of the symmetric space the treatment of the case when the logarithm of the monodromy is on the boundary of a weyl alcove and the correspondence of the orbits encoding the singularity via the kostant sekiguchi correspondence we also describe some special features of the moduli spaces when g is a split real form or a group of hermitian type

stochastic models of subsurface flow log linearized gaussian models are exact for covariances stochastic solutions for steady state infinite domain flow models are studied under the assumptions that log conductivity and head are second order stationary jointly gaussian processes it is shown that the covariance relationships previously derived are exact solutions for the nonlinearized equations no matter how large the input variance is

stochastic analysis of head spatial variability in bounded rectangular heterogeneous aquifers groundwater flow through bounded rectangular aquifers is analyzed in a stochastic framework new analytical expressions of the head covariance and variance and the log transmissivity head cross covariance are derived for the simplified first order problem effects of different boundary conditions the aquifer size and the log transmissivity correlation scale upon head moments are studied the results are compared to analytical half plane solutions demonstrating significant differences in several cases finally the problem is solved numerically using the monte carlo simulation method the realizations of the log transmissivity field are generated in two different ways through comparisons with the analytical results the accuracy of the numerical methods is shown to be excellent

simultaneous estimation of transmissivity values and zonation the extended kalmanfilter ekf has long been recognized as a powerful yet computationally intensive methodology for stochastic parameter estimation three improvements to traditional algorithms are presented and applied to heterogeneous transmissivity estimation first the costly ekf covariance updates are replaced by more efficient approximations second the zonation structure of the distributed parameterfield being estimated is dynamically determined and refined using a partitional clustering algorithm third a new method of mergingfirst and second moments of randomfields that have heterogeneous statistics is introduced we apply this method called random field union as an alternative to conventional randomfield averaging for the systematic shrinking of covariance matrices as the dimensionality of the parameter space is reduced the effects of these three improvements are examined in applications to steady state groundwaterflow test problems we show that thefirst and second improvements reduce the computational time requirements dramatically while the second and third can improve the accuracy and stability of the results the resulting integrated method is successfully applied to a larger more realistic calibration test case under steady and cyclostationary flow conditions similar to regular seasonalfluctuations whenflow is steady the method can be viewed as iterative whenflow is transient the method is fully recursive

inverse groundwater modeling for hydraulic conductivity estimation using bayesian model averaging and variance window 1 this study proposes a bayesian model averaging bma method to address parameter estimation uncertainty arising from nonuniqueness in parameterization methods bma is able to incorporate multiple parameterization methods for prediction through the law of total probability and to obtain an ensemble average of hydraulic conductivity estimates two major issues in applying bma to hydraulic conductivity estimation are discussed the first problem is using occam s window in usual bma applications to measure approximated posterior model probabilities occam s window only accepts models in a very narrow range tending to single out the best method and discard other good methods we propose a variance window to replace occam s window to cope with this problem the second problem is the kashyap information criterion kic in the approximated posterior model probabilities which tends to prefer highly uncertain parameterization methods by considering the fisher information matrix with sufficient amounts of observation data the bayesian information criterion bic is a good approximation and is able to avoid controversial results from using kic this study adopts multiple generalized parameterization gp methods such as the bma models to estimate spatially correlated hydraulic conductivity numerical examples illustrate the issues of using kic and occam s window and show the advantages of using bic and the variance window in bma application finally we apply bma to the hydraulic conductivity estimation of the 1500 foot sand in east baton rouge parish louisiana

stochastic analysis of three dimensional flow in a bounded domain a commonly accepted first order approximation of the equation for steady state flow in a fully saturated spatially random medium has the form of poisson s equation this form allows for the advantageous use of green s functions to solve for the random output hydraulic heads in terms of a convolution over the random input the logarithm of hydraulic conductivity a solution for steady state three dimensional flow in an aquifer bounded above and below is presented consideration of these boundaries is made possible by use of green s functions to solve poisson s equation within the bounded domain the medium hydraulic conductivity is assumed to be a second order stationary random process as represented by a simple three dimensional covariance function upper and lower boundaries are taken to be no flow boundaries the mean flow vector lies entirely in the horizontal dimensions the resulting hydraulic head covariance function exhibits nonstationary effects resulting from the imposition of boundary conditions comparisons are made with existing infinite domain solutions

a father protocol for quantum broadcast channels a new protocol for quantum broadcast channels based on the fully quantum slepian wolf protocol is presented the protocol yields an achievable rate region for entanglement assisted transmission of quantum information through a quantum broadcast channel that can be considered the quantum analogue of marton s region for classical broadcast channels the protocol can be adapted to yield achievable rate regions for unassisted quantum communication and for entanglement assisted classical communication in the case of unassisted transmission the region we obtain has no independent constraint on the sum rate only on the individual transmission rates regularized versions of all three rate regions are provably optimal

electrical impedance tomography using level set representation and total variational regularization in this paper we propose a numerical scheme for the identification of piecewise constant conductivity coefficient for a problem arising from electrical impedance tomography the key feature of the scheme is the use of level set method for the representation of interface between domains with different values of coefficients numerical tests show that our method can recover sharp interfaces and can tolerate a relatively high level of noise in the observation data results concerning the effects of number of measurements noise level in the data as well as the regularization parameters on the accuracy of the scheme are also given

classical communication over a quantum interference channel calculating the capacity of interference channels is a notorious open problem in classical information theory such channels have two senders and two receivers and each sender would like to communicate with a partner receiver the capacity of such channels is known exactly in the settings of very strong and strong interference while the han kobayashi coding strategy gives the best known achievable rate region in the general case here we introduce and study the quantum interference channel a natural generalization of the interference channel to the setting of quantum information theory we restrict ourselves for the most part to channels with two classical inputs and two quantum outputs in order to simplify the presentation of our results though generalizations of our results to channels with quantum inputs are straightforward we are able to determine the exact classical capacity of this channel in the settings of very strong and strong interference by exploiting winter s successive decoding strategy and a novel two sender quantum simultaneous decoder respectively we provide a proof that a han kobayashi strategy is achievable with holevo information rates up to a conjecture regarding the existence of a three sender quantum simultaneous decoder this conjecture holds for a special class of quantum multiple access channels with average output states that commute and we discuss some other variations of the conjecture that hold finally we detail a connection between the quantum interference channel and prior work on the capacity of bipartite unitary gates

capacity theorems for quantum multiple access channels classical quantum and quantum quantum capacity regions in this paper we consider quantum channels with two senders and one receiver for an arbitrary such channel we give multiletter characterizations of two different two dimensional capacity regions the first region comprises the rates at which it is possible for one sender to send classical information while the other sends quantum information the second region consists of the rates at which each sender can send quantum information for each region we give an example of a channel for which the corresponding region has a single letter description one of our examples relies on a new result proved here perhaps of independent interest stating that the coherent information over any degradable channel is concave in the input density operator we conclude with connections to other work and a discussion on generalizations where each user simultaneously sends classical and quantum information

an application of the geostatistical approach to the inverse problem in two dimensional groundwater modeling the geostatistical approach to the estimation of transmissivity from head and transmissivity measurements is developed for two dimensional steady flow the field of the logarithm of transmissivity log transmissivity is represented as a zero order intrinsic random field its spatial structure is described in this application through a two term covariance function that is linear in the parameters 1 and 2 linearization of the discretized flow equations allows the construction of the joint covariance matrix of the head and log transmissivity measurements as a linear function of 1 and 2 in this particular application the coefficient matrices are calculated numerically in a noniterative fashion maximum likelihood estimation is employed to estimate 1 and 2 as well as additional parameters from measurements linear estimation theory cokriging then yields point or block averaged estimates of transmissivity the approach is first applied to a test case with favorable results it is shown that the application of the methodology gives good estimates of transmissivities it is also shown that when the transmissivities are used in a numerical model they reproduce the head measurements quite well results from the application of the methodology to the jordan aquifer in iowa are also presented

estimation of aquifer parameters under transient and steady state conditions 1 maximum likelihood method incorporating prior information in this series of three papers a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions the parameters include values and directions of principal hydraulic conductivities or transmissivities in anisotropic media specific storage or storativity interior and boundary recharge or leakage rates coefficients of head dependent interior and boundary sources and boundary heads in transient situations the initial head distribution can also be estimated if the system is originally at a steady state paper 1 of the series discusses some of the advantage in treating the inverse problem statistically and in regularizing its solution by means of penalty criteria based on prior estimates of the parameters the inverse problem is posed in the framework of maximum likelihood theory cast in a manner that accounts for prior information about the parameters since not all the factors which contribute to the prior errors can be quantified statistically at the outset the covariance matrices of these errors are expressed in terms of several parameters which if unknown can be estimated jointly with the hydraulic parameters by a stagewise optimization process when transient head data are separated by a fixed time interval the temporal structure of these data is approximated by a lag one autoregressive model with a correlation coefficient that can be treated as another unknown parameter estimation errors are analyzed by examining the lower bound of their covariance matrix in the eigenspace paper 1 concludes by suggesting that certain model identification criteria developed in the time series literature all of which are based on the maximum likelihood concept might be useful for selecting the best groundwater model or the best method of parameterizing a particular model among a number of given alternatives

a hilbert mumford criterion for polystability in kaehler geometry consider a hamiltonian action of a compact lie group k on a kaehler manifold x with moment map x assume that the action of k extends to a holomorphic action of the complexification g of k we characterize which g orbits in x intersect 1 0 in terms of the maximal weights lim t e its x s where s we do not impose any a priori restriction on the stabilizer of x under some mild restrictions on the action k x we view the maximal weights as defining a collection of maps for each x x x k g where k g is the boundary at infinity of the symmetric space k g we prove that g x 1 0 0 if 1 x is everywhere nonnegative 2 any boundary point y such that x y 0 can be connected with a geodesic in k g to another boundary point y satisfying x y 0 we also prove that the maximal weight functions are g equivariant for any g g and any y k g we have g x y x y g

the capacity of the quantum channel with general signal states it is shown that the capacity of a classical quantum channel with arbitrary possibly mixed states equals the maximum of the entropy bound with respect to all a priori distributions this completes the recent result of hausladen jozsa schumacher westmoreland and wootters 1996 who proved the equality for the pure state channel

characterization and identification of aquifer heterogeneity with generalized parameterization and bayesian estimation 1 this research proposes a generalized parameterization method referred to as gp and bayesian estimation for parameter heterogeneity characterization and identification in groundwater modeling gp unifies zonation and interpolation through a set of weighting coefficients and is capable of creating a zonation structure a continuous distribution or a mixed structure gp shows greater flexibility not only in manipulating the highly complex spatial distribution but also in identifying the parameter structure with gp parameter structure identification seeks to identify the parameter dimension parameter pattern parameter values as well as the values of the weighting coefficients simultaneously through a set of basis points additionally this study develops an embedded genetic algorithm ga for solving the structure identification problem a bayesian estimator that estimates the basis point values as well as the values of the weighing coefficients is embedded in the ga which searches for the best basis point locations we demonstrate the inverse methodology by a numerical example in which the distributed transmissivity in a two dimensional confined aquifer is identified we calculate the jacobian matrix by the adjoint state method with gp we have successfully identified the transmissivity structure with four basis points that results in a good fitting in groundwater heads and captures the nonsmooth characteristic as well as the trend of the true transmissivity field we compare gp with voronoi tessellation zonation and natural neighbor interpolation results show that gp outperforms the other two parameterization methods in that gp identified the transmissivity field with a smaller parameter uncertainty along with a sufficiently small fitting residual and without over parameterization

continuous time stochastic analysis of groundwater flow in heterogeneous aquifers the problem of depth averaged groundwater flow in heterogeneous aquifers is looked at from a stochastic point of view the galerkin finite element version of the linearized stochastic equation governing the flow is solved analytically in time using an eigenvalue eigenvector technique the stochastic solution which is valid for small variance of aquifer log transmissivity relates spatial and temporal variabilities of aquifer head to aquifer heterogeneity stochastic recharge and random initial head the computational effort requires the evaluation of integrals of matrices whose elements are linear functions of the nodal mean heads the solutions are obtained for the exact i e continuous and quasi steady approximation of the mean head aquifer head temporal covariances are evaluated using standard matrix operations once the storage matrix is inverted and the associated generalized eigenvalue problem is solved implication of the level of spatial discretization on the performance of the solution is examined and the influence of aquifer heterogeneity on spatial and temporal variances of hydraulic heads is investigated in the presence of a semipervious boundary

surface group representations with maximal toledo invariant we develop the theory of maximal representations of the fundamental group 1 of a compact connected oriented surface possibly with boundary into lie groups g of hermitian type for any homomorphism p 1 g we define the toledo invariant t p a numerical invariant which has both topological and analytical interpretations we establish important properties of t among which continuity uniform boundedness on the representation variety additivity under connected sum of surfaces and congruence relations mod we thus obtain information about the representation variety as well as striking geometric properties of maximal representations that is representations whose toledo invariant achieves the maximum value moreover we establish properties of boundary maps associated to maximal representations which generalize naturally monotonicity properties of semiconjugations of the circle we define a rotation number function for general locally compact groups and study it in detail for groups of hermitian type properties of the rotation number together with the existence of boundary maps lead to additional invariants for maximal representations and show that the subset of maximal representations is always real semialgebraic

a geostatistical approach to the inverse problem in groundwater modeling steady state and one dimensional simulations the problem of estimating hydrogeologic parameters in particular permeability from input output measurements is reexamined in a geostatistical framework the field of the unknown parameters is represented as a random field and the estimation procedure consists of two main steps first the structure of the parameter field is identified i e mathematical representations of the variogram and the trend are selected and their parameters are established by using all available information including measurements of hydraulic head and permeability second linear estimation theory is applied to provide minimum variance and unbiased point estimates of hydrogeologic parameters kriging structure identification is achieved iteratively in three substeps structure selection maximum likelihood estimation and model validation and diagnostic checking the methodology was extensively tested through simulations on a simple one dimensional case the results are remarkably stable and well behaved the estimated field is smooth while small scale variability is statistically described as the quality of measurements improves the procedure reproduces more features of the original field the results are also shown to be rather insensitive to deviations from assumptions about the geostatistical structure of the field

bayesian inversion for facies detection an extensible level set framework 1 in many cases it has been assumed that the variability in hydrologic parameters can be adequately described through a simple geostatistical model with a given variogram in other cases variability may be best described as a series of jumps in parameter behavior e g those that occur at geologic facies contacts when using indirect measurements such as pump tests to try to map such heterogeneity during inverse modeling the resulting images of the subsurface are always affected by the assumptions invoked in this paper we discuss inversion for parameter fields where prior information has suggested that major variability can be described by boundaries between geologic units or facies in order to identify such parameter fields we propose a bayesian level set inversion protocol framework which allows for flexible zones of any shape size and number we review formulas for defining facies locations using the level set method and for moving the boundaries between zones using a gradient based technique that improves fit through iterative deformation of the boundaries we describe the optimization algorithm employed when multiple level set functions are used to represent a field with more than two facies we extend these formulas to the investigation of the inverse problem in a bayesian context in which prior information is taken into account and through which measures of uncertainty can be derived we also demonstrate that the level set method is well suited for joint inversion problems and present a strategy for integrating different data types such as hydrologic and geophysical without assuming strict petrophysical relations our framework for joint inversion also contrasts with many previous methods in that all data sources e g both hydrologic and geophysical contribute to boundary delineation at once

parabolic higgs bundles and teichmuller spaces for punctured surfaces in this paper we study the relation between parabolic higgs vector bundles and irreducible representations of the fundamental group of punctured riemann surfaces established by simpson we generalize a result of hitchin identifying those parabolic higgs bundles that correspond to fuchsian representations we also study the higgs bundles that give representations whose image is contained after conjugation in sl k r we compute the real dimension of one of the components of this space of representations which in the absence of punctures is the generalized teichmuller space introduced by hitchin and which in the case of k 2 is the usual teichmuller space of the punctured surface

aquifer parameter identification with kriging and optimum parameterization a new parameter identification method is developed for a two dimensional unsteady state groundwater flow model the method is a direct approach as it requires no iterative searching of parameters the unknown functional coefficients parameters are optimally determined by a generalized matrix inversion scheme kriging an unbiased minimum variance estimator is used as a presampling filter to reconstruct the head distribution for the entire flow domain the ill posedness of the inverse problem as characterized by instability and nonuniqueness is controlled by reparameterization utilizing the technique of finite elements a set of statistics are developed to quantify explicitly the tradeoff between the system modeling error and the error associated with the parameter uncertainty these two types of errors are shown to be a function of the parameter dimension residual mean square and trace of the covariance matrix of the estimated parameters serve as good indicators for the determination of the optimum parameter dimension a set of numerical experiments are conducted to illustrate the methodology

stochastic analysis of spatial variability in two dimensional steady groundwater flow assuming stationary and nonstationary heads two dimensional steady groundwater flow in a confined aquifer with spatially variable transmissivity t is analyzed stochastically using spectral analysis and the theory of intrinsic random functions conditions that ensure a stationary statistically homogeneous head process are derived and using two convenient forms for the covariance function of the ln t process the head covariance function is studied in addition the head variogram is obtained for a particular nonstationary case and the asymptotic head variogram is derived under very general conditions results are compared to those obtained by gelhar 1976 for one and two dimensional phreatic flow and bakr et al 1978 for one and three dimensional confined flow multidimensional flow analysis results in a significantly reduced head variance the head correlation remains high over much greater distances than the ln t correlation the variogram obtained when stationary heads are assumed is identical to that obtained for nonstationary heads for dimensionless lag distances up to 2 times the correlation scale of the log transmissivity the variogram for nonstationary heads continues to grow logarithmically as lag distance increases independent of the form of the input covariance in the nonstationary case the conditions for stationarity are contrasted with the corresponding results obtained for the one and three dimensional cases of gutjahr and gelhar 1981 the head variance calculated from the stationary theory is found to agree with that of previous monte carlo simulations

an iterative geostatistical inverse method for steady flow in the vadose zone an iterative geostatistical inverse approach is developed to estimate conditional effective unsaturated hydraulic conductivity parameters soil water pressure head and degree of saturation in heterogeneous vadose zones this approach is similar to the classical cokriging technique and it uses a linear estimator that depends on covariances and cross covariances of unsaturated hydraulic parameters soil water pressure head and degree of saturation the linear estimator is however improved successively by solving the governing flow equation and by updating the residual covariance and cross covariance functions in an iterative manner as a result the nonlinear relationship between unsaturated hydraulic conductivity parameters and head is incorporated in the estimation and the estimated fields are approximate conditional means the ability of the iterative approach is demonstrated through some numerical examples

a multipopulation genetic algorithm to solve the inverse problem in hydrogeology the inverse problem of groundwater flow is treated with an automatic method that can produce several alternative solutions at once during their joint optimization these solutions can exchange information in order to maintain some diversity and thus avoid a systematic premature convergence toward a single local minimum although genetic algorithms are capable of doing this they have not often been used in groundwater inverse optimization first a specific multipopulation genetic algorithm is developed it is then tested on two synthetic cases of steady state flow with transmissivity values extending over 4 orders of magnitude the first test is nonparametric and optimizes as many parameters as those used to define the reference case the second test uses a sort of pilot point parametrization the optimization is carried out on a limited number of perturbations that are interpolated and superimposed on an initial transmissivity field in view of the good quality of the results these initial attempts provide incentives to further develop genetic algorithms in groundwater inverse problems

velocity log upscaling based on reversible jump markov chain monte carlo simulated annealing abstractupscaling log measurements acquired at high frequencies and correlating them with corresponding low frequency values from surface seismic and vertical seismic profile data is a challenging task we have applied a sampling technique called the reversible jump markov chain monte carlo rjmcmc method to this problem a key property of our approach is that it treats the number of unknowns itself as a parameter to be determined specifically we have considered upscaling as an inverse problem in which we considered the number of coarse layers layer boundary depths and material properties as the unknowns the method applies bayesian inversion with rjmcmc sampling and uses simulated annealing to guide the optimization at each iteration the algorithm will randomly move a boundary in the current model add a new boundary or delete an existing boundary in each case a random perturbation is applied to backus average values we have developed examples showing that the mismatch between seismograms com

identification of three dimensional electric conductivity changes from time lapse electromagnetic observations we present a novel solution algorithm for 3d parameter identification based on low frequency electromagnetic data with focus on large scale applications such as monitoring of subsea oil production co 2 sequestration and geothermal systems the proposed solution algorithm is designed to meet challenges related to low parameter sensitivity nonuniqueness of the inverse solutions nonlinearity in the mapping from the data to the parameter space and costly numerical simulations motivated by earlier investigations on the relation between sensitivity nonlinearity and scale the proposed solution approach is based on a reduced composite parameter representation though a reduced representation restricts the solution space flexibility with respect to which parameter functions that can be represented is obtained by facilitating the estimation of the structure and smoothness of the representation itself moreover the resolution of the parameter function is detached from the computational grid and determined as part of the estimation the performance of the proposed solution algorithm is illustrated through numerical examples for identification of underground electric conductivity changes from time lapse electromagnetic observations

simultaneous joint inversion of amplitude versus offset and controlled source electromagnetic data by implicit representation of common parameter structure abstracti evaluated a simultaneous joint inversion of seismic amplitude versus offset avo and controlled source electromagnetic csem data for fluid flow monitoring a new approach for structure coupled joint inversion was presented in which the coupling of the two data types was obtained by allowing for the direct identification of parameter structure that is shared by the different geophysical model parameters the main idea was to use a composite parameter representation which enables inversion with respect to the parameter magnitude and parameter structure in the current application parameter structure refers to transitions between dominating property values and is represented by the position and shape of the flooding front hence with this approach the position and shape of the flooding front are inverted for directly and the coupling between the different data sets is obtained without the inclusion of an additional penalizing term in the objective function regularization of the inverse pr

a hybrid global optimization method for inverse estimation of hydraulic parameters annealing simplex method inverse estimation of unsaturated hydraulic parameters is often a highly nonlinear optimization problem with multiple parameters the objective functions involved are often topographically complex and may contain many local minima because of these reasons the inverse solutions are commonly very sensitive to the initial guess of the parameters when conventional optimizers are used this paper presents an annealing simplex method that incorporates simulated annealing strategies into a classical downhill simplex method an upward infiltration experiment was used as an example of inverse estimation to test the method numerical experiments of both minimizing an algebraic function and inversion of upward infiltration data showed that the new method successfully converged to the global minimum in all cases irrespective of the initial hydraulic parameter estimates while the classical downhill method often converged to unfavorable local minima the cpu times needed for the annealing simplex method to estimate 5 and 7 hydraulic parameters simultaneously are about a half hour and 1 hour on a pc respectively additionally no special requirements are imposed on the objective function and the method is independent of the details of the simulation submodel therefore the proposed method should be applicable to other optimization problems in water resources when it is important to have a robust global search capability

aquifer parameter identification with optimum dimension in parameterization this paper presents a systematic procedure whereby the functional coefficients imbedded in a two dimensional partial differential equation which governs unsteady groundwater flow are optimally identified the coefficients to be identified are transmissivities which vary spatially finite elements are used to represent the unknown transmissivity function parametrically in terms of nodal values over a suitable discretization of a flow region a modified gauss newton algorithm is used for parameter optimization covariance analysis is used to estimate the reliability of the estimated parameters as the dimension of the unknown parameter increases the modeling error represented by a least squares criterion will generally decrease but errors in data would be propagated to a greater degree into the estimated parameters thus reducing the reliability of estimation the reliability of the estimated parameters is characterized by a norm of the covariance matrix this information is used for the determination of the optimum dimension in parameterization

global local optimization for parameter structure identification in three dimensional groundwater modeling 1 this paper develops two global local optimization methods for three dimensional parameter structure identification in groundwater modeling parameter structure identification is formulated in terms of solving a generalized inverse problem which allows for a determination of an appropriate level of parameter structure complexity and the identification of its pattern and the associated parameter values the structure complexity is determined by calculating the parameter structure error measured in the prediction space or management space while the structure pattern and the associated parameter values are identified simultaneously by minimizing the fitting residual measured in the observation space the former requires solving a continuous maximum minimum max min optimization problem and the latter requires solving a combinatorial optimization problem in this paper voronoi zonation is used to parameterize the unknown distributed parameter for each given level of structure complexity a sequential global local optimization method which consists of a genetic algorithm a quasi newton method and local search is developed to solve the combinatorial problem in addition the continuous max min problem is transformed to a hierarchical optimization problem and solved by a hybrid global local method sensitivities of state variables to the unknown parameters are calculated by the sensitivity equations the validity and applicability of the proposed methodology are demonstrated by numerical experiments we have shown that the choice of an objective function in model application impacts the determination of the parameter structure complexity

the self duality equations on a riemann surface in this paper we shall study a special class of solutions of the self dual yang mills equations the original self duality equations which arose in mathematical physics were defined on euclidean 4 space the physically relevant solutions were the ones with finite action the so called instantons the same equations may be dimensionally reduced to euclidean 3 space by imposing invariance under translation in one direction these equations also have physical relevance the solutions which have finite action in three dimensions are the magnetic monopoles if we take the reduction process one step further and consider solutions which are invariant under two translations we obtain a set of equations in the plane here however there is no clear physical meaning and indeed attempts to find finite action solutions have failed nevertheless these are the equations we shall consider despite the lack of interesting solutions in r2 the equations have the important property conformal invariance which allows them to be defined on manifolds modelled on r2 by conformal maps namely riemann surfaces we shall consider here solutions of the self duality equations defined on a compact riemann surface there are in fact solutions as we shall show and the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure which will be the focus of our study it brings together in a harmonious way the subjects of riemannian geometry topology algebraic geometry and symplectic geometry illuminating all these facets of the same object accounts for the length of this paper the self duality equations are equations from gauge theory geometrically they are defined in terms of connections on principal bundles while the group of the principal bundle may be chosen arbitrarily for the equations to make sense we restrict attention here to the simplest case of su 2 or so 3 there are two reasons for this the first and most obvious is that it simplifies calculations and avoids the use of inductive processes which are inherent in the consideration of a general lie group of higher rank the second reason is that solutions for su 2 have an intimate relationship with the internal structure of the riemann surface as a consequence of results we shall prove about solutions to the self duality equations we learn something about the moduli space of complex structures on the surface itself namely teichmuller space

analysis of the spatial structure of properties of selected aquifers data from 31 regional aquifers are analyzed to identify the horizontal spatial correlation structure of transmissivity hydraulic conductivity and storage coefficient three parameters are estimated the variance of small scale variability or nugget and the variance and integral scale range of an exponential covariance function the assumption of normality of the aforementioned geohydrologic parameters and their logarithmic transformations is also examined results are obtained which indicate that the logarithms of these properties generally pass normality tests

a multiresolution method for distributed parameter estimation a multiresolution method for distributed parameter estimation or inverse problems is studied numerically the identification of the coefficient of an elliptic equation in one dimension is considered as our model problem first multiscale bases are used to analyze the degree of ill posedness of the inverse problem second based on some numerical results it is shown that the method of scale by scale multiresolution yields robust and fast convergence finally it is shown how the method gives a natural regularization approach which is complementary to tikhonov s regularization

review of parameter identification procedures in groundwater hydrology the inverse problem the purpose of this survey is to review parameter identification procedures in groundwater hydrology and to examine computational techniques which have been developed to solve the inverse problem parameter identification methods are classified under the error criterion used in the formulation of the inverse problem the problem of ill posedness in connection with the inverse problem is addressed typical inverse solution techniques are highlighted the review also includes the evaluation of methods used for computing the sensitivity matrix statistics which can be used to estimate the parameter uncertainty are outlined attempts have been made to compare and contrast representative inverse procedures and direction for future research is suggested

coding theorem and strong converse for quantum channels we present a new proof of holevo s 1973 1977 coding theorem for transmitting classical information through quantum channels and its strong converse the technique is largely inspired by wolfwitz s 1964 combinatorial approach using types of sequences as a byproduct of our approach which is independent of previous ones both in the coding theorem and the converse we can give a new proof of holevo s information bound

a note on higher order corrections of the head covariances in steady aquifer flow average uniform flow takes place in a heterogeneous aquifer of infinite extent the input to the problem is the hydraulic conductivity which is regarded as a random space function that is lognormal stationary and statistically isotropic the output is the water head field which is a random function satisfying the equation of steady flow the first order approximation of the head in an asymptotic expansion for small log conductivity variance is a normal function characterized completely by the head log conductivity cross covariance and the head covariance or variogram these covariances are proportional to the log conductivity variance by using spectral methods second order corrections of the head covariances proportional to the log conductivity variance squared are derived explicitly detailed calculations are carried out for an exponential log conductivity covariance the main finding of the note is that the first order approximation is very robust and even for a log conductivity variance equal to unity the second order correction of the head variances is smaller than 10 of the first order approximation

entanglement assisted capacity of quantum multiple access channels we find a regularized formula for the entanglement assisted ea capacity region for quantum multiple access channels qmac we illustrate the capacity region calculation with the example of the collective phase flip channel which admits a single letter characterization on the way we provide a first principles proof of the ea coding theorem based on a packing argument we observe that the holevo schumacher westmoreland theorem may be obtained from a modification of our ea protocol we remark on the existence of a family hierarchy of protocols for multiparty scenarios with a single receiver in analogy to the two party case in this way we relate several previous results regarding qmacs

a reassessment of the groundwater inverse problem this paper presents a functional formulation of the groundwaterflow inverse problem that is sufficiently general to accommodate most commonly used inverse algorithms unknown hydrogeological properties are assumed to be spatial functions that can be represented in terms of a possibly infinite basis function expansion with random coefficients the unknown parameter function is related to the measurements used for estimation by a forward operator which describes the measurement process in the particular case considered here the parameter of interest is the large scale log hydraulic conductivity the measurements are point values of log conductivity and piezometric head and the forward operator is derived from an upscaled groundwaterflow equation the inverse algorithm seeks the most probable or maximum a posteriori estimate of the unknown parameter function when the measurement errors and parameter function are gaussian and independent the maximum a posteriori estimate may be obtained by minimizing a least squares performance index which can be partitioned into goodness of fit and prior terms when the parameter is a stationary random function the prior portion of the performance index is equivalent to a regularization term which imposes a smoothness constraint on the estimate this constraint tends to make the problem well posed by limiting the range of admissible solutions the gaussian maximum a posteriori problem may be solved with variational methods using functional generalizations of gauss newton or gradient based search techniques several popular groundwater inverse algorithms are either special cases of or variants on the functional maximum a posteriori algorithm these algorithms differ primarily with respect to the way they describe spatial variability and the type of search technique they use linear versus nonlinear the accuracy of estimates produced by both linear and nonlinear inverse algorithms may be measured in terms of a bayesian extension of the cramer rao lower bound on the estimation error covariance this bound suggests how parameter identifiability can be improved by modifying the problem structure and adding new measurements

natural neighbour galerkin methods summary natural neighbour co ordinates sibson co ordinates is a well known interpolation scheme for multivariate data tting and smoothing the numerical implementation of natural neighbour co ordinates in a galerkin method is known as the natural element method nem in the natural element method natural neighbour co ordinates are used to construct the trial and test functions recent studies on nem have shown that natural neighbour co ordinates which are based on the voronoi tessellation of a set of nodes are an appealing choice to construct meshless interpolants for the solution of partial dierential equations in belikov et al computational mathematics and mathematical physics 1997 37 1 9 15 a new interpolation scheme non sibsonian interpolation based on natural neighbours was proposed in the present paper the nonsibsonian interpolation scheme is reviewed and its performance in a galerkin method for the solution of elliptic partial dierential equations that arise in linear elasticity is studied a methodology to couple nite elements to nem is also described two signicant advantages of the non sibson interpolant over the sibson interpolant are revealed and numerically veried the computational eciency of the non sibson algorithm in 2 dimensions which is expected to carry over to 3 dimensions and the ability to exactly impose essential boundary conditions on the boundaries of convex and non convex domains copyright 2001 john wiley sons ltd

surface group representations and u p q higgs bundles using the l2 norm of the higgs field as a morse function we study the moduli spaces of u p q higgs bundles over a riemann surface we require that the genus of the surface be at least two but place no constraints on p q a key step is the identification of the function s local minima as moduli spaces of holomorphic triples in a companion paper 7 we prove that these moduli spaces of triples are nonempty and irreducible because of the relation between flat bundles and fundamental group representations we can interpret our conclusions as results about the number of connected components in the moduli space of semisimple pu p q representations the topological invariants of the flat bundles are used to label subspaces these invariants are bounded by a milnor wood type inequality for each allowed value of the invariants satisfying a certain coprimality condition we prove that the corresponding subspace is nonempty and connected if the coprimality condition does not hold our results apply to the closure of the moduli space of irreducible representations 1 members of vbac vector bundles on algebraic curves which is partially supported by eager ec fp5 contract no hprn ct 2000 00099 and by edge ec fp5 contract no hprn ct 2000 00101 2 partially supported by the national science foundation under grant dms0072073 3 partially supported by the ministerio de ciencia y tecnolo ia spain under grant bfm2000 0024 4 partially supported by the fundacao para a ciencia e a tecnologia portugal through the centro de matematica da universidade do porto and through grant no sfrh bpd 1606 2000 5 partially supported by the portugal spain bilateral programme acciones integradas grant nos hp2000 0015 and ai 01 24 6 partially supported by a british epsrc grant october december 2001 received 11 27 2002

a monte carlo assessment of eulerian flow and transport perturbation models monte carlo studies of flow and transport in two dimensional synthetic conductivity fields are employed to evaluate first order flow and eulerian transport theories hydraulic conductivity is assumed to obey fractional brownian motion fbm statistics with infinite integral scale or to have an exponential covariance structure with finite integral scale the flow problem is solved via a block centered finite difference scheme and a random walk approach is employed to solve the transport equation for a conservative tracer the model is tested for mass conservation and convergence of computed statistics and found to yield accurate results it is then used to address several issues in the context of flow and transport the validity of the first order relation between the fluctuating velocity covariance and the fluctuating log conductivity is examined the simulations show that for exponential covariance this approximation is justified in the mean flow direction for log conductivity variance f2 of the order of unity however as f2 increases the relation for the transverse velocity component deviates from the fully nonlinear monte carlo results eulerian transport models neglect triplet correlation functions that appear in the nonlocal macroscopic flux the relative importance of the triplet correlation term for conservative chemicals is examined this term appears to be small relative to the convolution flux term in mildly heterogeneous media as f2 increases or the integral scale grows the triplet correlation becomes significant in purely convective transport the triplet correlation term is significant if the heterogeneity is evolving the exact nonlocal macroscale flux for the purely convective case significantly differs from that of the convective dispersive transport this is in agreement with recent theoretical analysis and numerical studies and it suggests that neglecting local scale dispersion may lead to large errors localization errors in the flux term are evaluated using monte carlo simulations the nonlocal in time model significantly differs from the fully nonlocal model for small variance and integral scale there is a slight difference between the fully localized flux and the fully nonlocal convolution flux this is also in agreement with recent theories that suggest that moments through the second for the two models are nearly identical for conservative tracers the fully localized model does not perform well in the purely convective cases

stochastic modeling of groundwater flow by unconditional and conditional probabilities 1 conditional simulation and the direct problem mathematical modeling of groundwater flow in heterogeneous porous formations of large extent is investigated the formation properties hydraulic conductivity transmissivity as well as flow variables head specific discharge solute concentration are regarded as random variables subjected to uncertainty the main aim of the study is to analyze the influence of conditional probability of input variables upon the statistical structure of the dependent variables the unconditional probability density functions are supposed to be stationary multivariate normal while conditioning accounts for the measured values at a few points of the formation two problems of groundwater flow are discussed in part 1 conditional simulation and the direct problem for steady flow analytical results are obtained by using perturbation approximations average uniform head gradient flows as well as recharge and flow to wells are discussed in unconditional modeling the input variable the conductivity or transmissivity log is regarded as stationary and is represented by its constant mean and variogram the ensemble of formations on which statistical calculations are carried out represents all aquifers with same probability density distributions in conditional modeling the measured values at a few points are kept fixed and uncertainty prevails only at other points consequently statistical computations are performed for the subensemble of aquifers which preserve the measured values and as a result both input and output variables are nonstationary the main effect of conditioning is to reduce the variance i e the uncertainty of these variables this effect is particularly important in the case of flow toward wells application of the modeling method to field problems is outlined

identifying arbitrary parameter zonation using multiple level set functions abstract in this paper we extended the analytical level set method 1 2 for identifying a piece wisely heterogeneous zonation binary system to the case with an arbitrary number of materials with unknown material properties in the developed level set approach starting from an initial guess the material interfaces are propagated through iterations such that the residuals between the simulated and observed state variables hydraulic head is minimized we derived an expression for the propagation velocity of the interface between any two materials which is related to the permeability contrast between the materials on two sides of the interface the sensitivity of the head to permeability and the head residual we also formulated an expression for updating the permeability of all materials which is consistent with the steepest descent of the objective function the developed approach has been demonstrated through many examples ranging from totally synthetic cases to a case where the flow conditions are representative of a groundwater contaminant site at the los alamos national laboratory these examples indicate that the level set method can successfully identify zonation structures even if the number of materials in the model domain is not exactly known in advance although the evolution of the material zonation depends on the initial guess field inverse modeling runs starting with different initial guesses fields may converge to the similar final zonation structure these examples also suggest that identifying interfaces of spatially distributed heterogeneities is more important than estimating their permeability values

quantum broadcast channels we consider quantum channels with one sender and two receivers used in several different ways for the simultaneous transmission of independent messages we begin by extending the technique of superposition coding to quantum channels with a classical input to give a general achievable region we also give outer bounds to the capacity regions for various special cases from the classical literature and prove that superposition coding is optimal for a class of channels we then consider extensions of superposition coding for channels with a quantum input where some of the messages transmitted are quantum instead of classical in the sense that the parties establish bipartite or tripartite ghz entanglement we conclude by using state merging to give achievable rates for establishing bipartite entanglement between different pair of parties with the assistance of free classical communication

stochastic models of subsurface flow infinite versus finite domains and stationarity stochastic solutions of the differential equation describing one dimensional flow through a porous medium with spatially variable hydraulic conductivity which is represented by a stationary statistically homogeneous random process are developed using several techniques the analytical approximations using first order analysis propagation of error covariance differential equations and variogram analysis all yield consistent results which demonstrate the important effects of boundary conditions and conditioning using the theory of intrinsic random functions stochastic solutions are developed for the case when the logarithm of the hydraulic conductivity is a three dimensional stationary random field in contrast to the one dimensional case it is found that the resulting three dimensional head perturbation will be locally stationary under very general conditions results from the one dimensional analytical solutions are found to be in agreement with previous monte carlo simulations for a flow system of finite length the solution based on linearization in the logarithm of hydraulic conductivity proved to be very robust showing reasonable agreement with monte carlo results even for the largest input standard deviation of lnk 4 6

polar codes for arbitrary classical quantum channels and arbitrary cq macs we prove polarization theorems for arbitrary classical quantum cq channels the input alphabet is endowed with an arbitrary abelian group operation and an arikan style transformation is applied using this operation it is shown that as the number of polarization steps becomes large the synthetic cq channels polarize to deterministic homomorphism channels that project their input to a quotient group of the input alphabet this result is used to construct polar codes for arbitrary cq channels and arbitrary cq multiple access channels the encoder can be implemented in o n log n operations where n is the blocklength of the code a quantum successive cancellation decoder for the constructed codes is proposed it is shown that the probability of error of this decoder decays faster than 2 n beta for any beta

identification of parameter structure in groundwater inverse problem this paper develops an optimization method that can be used to identify parameter structure as well as its values in connection with the inverse problem in groundwater modeling the complexity of the parameter structure is determined by the quantity and quality of observation data output least square error is used as the criterion of identification sensitivity coefficients at finite element nodes are evaluated by the variational method the problem of identifying the parameter structure is formulated as a problem of combinatorial optimization a new parameterization technique is presented for describing the parameter structure it can represent various distributions of parameters from piecewise constant to continuous variability based on this representation the combinatorial optimization problem for determining the parameter structure is then solved by a simple one at a time searching procedure numerical experimentations are used to demonstrate the efficiency and practicality of the proposed method

development of objective oriented groundwater models 1 robust parameter identification 1 when the structure of an aquifer is complex and unknown determining the complexity of model structure and identifying its spatially distributed parameters become very difficult this two paper series describes an approach for objective oriented model construction that can identify a model with simplified structure and assure its reliability for predetermined model applications the theoretical basis of the methodology includes the definition of structure error the conditions of structure reducibility the calculation of the worst case parameter wcp and the solution of a generalized inverse problem in the first paper of the series we extend the basic theory established in our previous works from zonation parameterization to any kind of parameterization the extension makes the methodology more general and complete we present an effective direct search algorithm that can form a nonnested structure series with an optimized pattern for solving the generalized inverse problem we use numerical examples to show how the wcp depends on the structure complexity prior information boundary conditions and the objectives of model application generally speaking with more prior information simpler boundary conditions fewer objectives and lower accuracy requirement the wcp will have a simpler shape as a result a reliable model can be identified with less observation data in part 2 of this series we will give the conditions of structure reducibility and the method for robust experimental design a robust experimental design is independent of the true parameter and can provide sufficient information for identifying an objective oriented model

twisted harmonic maps and the self duality equations si m est une surface de riemann compacte on utilise des resultats de la theorie des applications harmoniques pour trouver une solution aux equations d auto dualite associees a une representation irreductible p 1 m psl 2 c