a full bayesian approach to the groundwater inverse problem for steady state flow a full bayesian approach to the estimation of transmissivity from hydraulic head and transmissivity measurements is developed for two dimensional steady state groundwater flow the approach combines both bayesian and maximum entropy viewpoints of probability in the first phase log transmissivity measurements are incorporated into bayes theorem and the prior probability density function is updated yielding posterior estimates of the mean value of the log transmissivity field and covariance the two central moments are generated assuming that the prior mean variance and integral scales are hyperparameters that is they are treated as random variables in themselves which is contrary to classical statistical approaches the probability density functions pdfs of these hyperparameters are in turn determined from maximum entropy considerations in other words pdfs are chosen for each of the hyperparameters that are maximally uncommitted with respect to unknown information this methodology is quite general and provides an alternative to kriging for spatial interpolation the final step consists of updating the conditioned natural logarithm transmissivity ln t field with hydraulic head measurements utilizing a linearized aquifer equation it is assumed that the statistical properties of the noise in the hydraulic head measurements are also uncertain at each step uncertainties in all pertinent hyperparameters are removed by marginalization finally what is produced is a ln t field conditioned on measurements of both hydraulic heads and log transmissivity and covariances of the ln t field in addition we can also produce resolution matrices confidence credibility limits and the like for the ln t field it is shown that the application of the methodology yields good estimates of transmissivities even when hydraulic head measurements are noisy and little or no information is specified on mean values of ln t variance of ln t and integral scales

solution of deterministic stochastic epidemic models by dynamical monte carlo method abstract this work is concerned with dynamical monte carlo mc method and its application to models originally formulated in a continuous deterministic approach specifically a susceptible infected removed susceptible sirs model is used in order to analyze aspects of the dynamical mc algorithm and achieve its applications in epidemic contexts we first examine two known approaches to the dynamical interpretation of the mc method and follow with the application of one of them in the sirs model the working method chosen is based on the poisson process where hierarchy of events properly calculated waiting time between events and independence of the events simulated are the basic requirements to verify the consistence of the method some preliminary mc results are compared against exact steady state solutions and other general numerical results provided by runge kutta method good agreement is found finally a space dependent extension of the sirs model is introduced and treated by mc the results are interpreted under and in accordance with aspects of the herd immunity concept

iterative algorithms for computing the shape of a hard scattering object computing the shape derivative the problem of determining the shape of an acoustically hard scattering object from remote scattering measurements is considered an iterative approach is used to find the object shape that minimizes the mean squared difference between a set of actual and predicted scattering observations a crucial task in this minimization is the computation of the shape derivative or functional gradient of the mean square error with respect to the object s shape or boundary the shape derivative tells us how to update the object s shape to reduce the mean square error at each iteration if for example the object s boundary is parameterized with n variables a brute force approach to computing the shape derivative using finite differences would require a minimum of n 1 forward solutions per iteration we show how the shape derivative can be computed with just two forward solutions one ordinary forward solution and a suitably constructed adjoint solution this approach is independent of n and is not only far more

estimation and statistical bounds for three dimensional polar shapes in diffuse optical tomography voxel based reconstructions in diffuse optical tomography dot using a quadratic regularization functional tend to produce very smooth images due to the attenuation of high spatial frequencies this then causes difficulty in estimating the spatial extent and contrast of anomalous regions such as tumors given an assumption that the target image is piecewise constant we can employ a parametric model to estimate the boundaries and contrast of an inhomogeneity directly in this paper we describe a method to directly reconstruct such a shape boundary from diffuse optical measurements we parameterized the object boundary using a spherical harmonic basis and derived a method to compute sensitivities of measurements with respect to shape parameters we introduced a centroid constraint to ensure uniqueness of the combined shape center parameter estimate and a projected newton method was utilized to optimize the object center position and shape parameters simultaneously using the shape jacobian we also computed the cramer rao lower bound on the theoretical estimator accuracy given a particular measurement configuration object shape and level of measurement noise knowledge of the shape sensitivity matrix and of the measurement noise variance allows us to visualize the shape uncertainty region in three dimensions giving a confidence region for our shape estimate we have implemented our shape reconstruction method using a finite difference based forward model to compute the forward and adjoint fields reconstruction results are shown for a number of simulated target shapes and we investigate the problem of model order selection using realistic levels of measurement noise assuming a signal to noise ratio in the amplitude measurements of 40 db and a standard deviation in the phase measurements of 0 1deg we are able to estimate an object represented with an eighth order spherical harmonic model having an absorption contrast of 0 15 cm 1 and a volume of 4 82 cm3 with errors of less than 10 in object volume and absorption contrast we also investigate the robustness of our shape based reconstruction approach to a violation of the assumption that the medium is purely piecewise constant

a remark on computing distance functions we propose a new method for the reconstruction of the signed distance function in the context of level set methods the new method is a modification of the algorithm which makes use of the pde equation for the distance function introduced by m sussman p smereka and s osher 1994 j comput phys 119 146 it is based mainly on the use of a truly upwind discretization near the interface comparison with the previous algorithm shows a definite improvement when used with a first order upwind scheme the method provides first order accuracy for the signed distance function in the whole computational domain and second order accuracy in the location of the interface a second order version of the method is also presented

adjoint active surfaces for localization and imaging this paper addresses the problem of localizing and segmenting regions embedded within a surrounding medium by characterizing their boundaries as opposed to imaging the entirety of the volume active surfaces are used to directly reconstruct the shape of the region of interest we describe the procedure for finding the optimal surface which is computed iteratively via gradient descent that exploits the sensitivity of an error minimization functional to changes of the active surface in doing so we introduce the adjoint model to compute the sensitivity and in this respect the method shares common ground with several other disciplines such as optimal control finally we illustrate the proposed active surface technique in the framework of wave propagation governed by the scalar helmholtz equation potential applications include electromagnetics acoustics geophysics nondestructive testing and medical imaging

reconstruction of shapes and impedance functions using few far field measurements we consider the reconstruction of complex obstacles from few far field acoustic measurements the complex obstacle is characterized by its shape and an impedance function distributed along its boundary through robin type boundary conditions this is done by minimizing an objective functional which is the l 2 distance between the given far field information g and the far field of the scattered wave u corresponding to the computed shape and impedance function we design an algorithm to update the shape and the impedance function alternatively along the descent direction of the objective functional the derivative with respect to the shape or the impedance function involves solving the original helmholtz problem and the corresponding adjoint problem where boundary integral methods are used further we implement level set methods to update the shape of the obstacle to combine level set methods and boundary integral methods we perform a parametrization step for a newly updated level set function in addition since the computed shape derivative is defined only on the boundary of the obstacle we extend the shape derivative to the whole domain by a linear transport equation finally we demonstrate by numerical experiments that our algorithm reconstruct both shapes and impedance functions quite accurately for non convex shape obstacles and constant or non constant impedance functions the algorithm is also shown to be robust with respect to the initial guess of the shape the initial guess of the impedance function and even large percentage of noise

the geostatistical characteristics of the borden aquifer a complete reexamination of sudicky s 1986 field experiment for the geostatistical characterization of hydraulic conductivity at the borden aquifer in ontario canada is performed the sampled data reveal that a number of outliers low ln k values are present in the data base these low values cause difficulties in both variogram estimation and determining population statistics the analysis shows that assuming either a normal distribution or exponential distribution for log conductivity is appropriate the classical cressie hawkins and squared median of the absolute deviations smad estimators are used to compute experimental variograms none of these estimators provides completely satisfactory variograms for the borden data with the exception of the classical estimator with outliers removed from the data set theoretical exponential variogram parameters are determined from nonlinear nl estimation differences are obtained between nl fits and those of sudicky 1986 for the classical screened estimated variogram nl fits produce an ln k variance of 0 24 nugget of 0 07 and integral scales of 5 1 m horizontal and 0 21 m vertical along a a for b b these values are 0 37 0 11 8 3 and 0 34 the fitted parameter set for b b data horizontal and vertical is statistically different than the parameter set determined for a a we also evaluate a probabilistic form of dagan s 1982 1987 equations relating geostatistical parameters to a tracer cloud s spreading moments the equations are evaluated using the parameter estimates and covariances determined from line a a as input with a velocity equal to 9 0 cm day the results are compared with actual values determined from the field test but evaluated by both freyberg 1986 and rajaram and gelhar 1988 the geostatistical parameters developed from this study produce an excellent fit to both sets of calculated plume moments when combined with dagan s stochastic theory for predicting the spread of a tracer cloud

stochastic lattice gas model for a predator prey system we propose a stochastic lattice gas model to describe the dynamics of two animal species population one being a predator and the other a prey this model comprehends the mechanisms of the lotka volterra model our analysis was performed by using a dynamical mean field approximation and computer simulations our results show that the system exhibits an oscillatory behavior of the population densities of prey and predators for the sets of parameters used in our computer simulations these oscillations occur at a local level mean field results predict synchronized collective oscillations

estimating nonpoint source pollution an application of a sequential entropy filter 1 this paper develops a sequential entropy filter for disaggregating nonpoint sources from ambient data a numerical simulation based on sediment loading is provided to illustrate the ability of the sequential entropy filter to recover the underlying parameters and optimally disaggregate ambient sediment load among nonpoint sources in the process we show the equivalence of this sequential entropy filter with bayes theorem and given this equivalence argue that the sequential entropy filter is more applicable than traditional bayesian estimators are when the parameter distributions are unknown or when the sample is undersized which is typically the case when dealing with natural resource data

robust numerical algorithm to the european option with illiquid markets abstract in this paper we consider illiquid european call option which is arisen in nonlinear black scholes equation in this respect we apply the newton s method to linearize it based on the obtained linear equation we obtain the approximate solutions recursively in two steps finally based on the conditions of kantorovich theorem we investigate the convergence analysis of the newton s method on the proposed problem finally the positivity of the solution is discussed

inversion of the borden tracer experiment data investigation of stochastic moment models inversion of dagan s two and three dimensional stochastic models using freyberg s 1986 rajaram and gelhar s 1988 1991 and barry and sposito s 1990 moment data from the borden experiment is carried out to examine 1 the validity of the two dimensional dagan 1982 and three dimensional dagan 1988 models and 2 the reduction in uncertainty of the spatial moments over nonconditioned estimates a direct application of bayesian statistical inference in conjunction with monte carlo integration is used to produce posterior probability density functions for the parameters the parameter ranges from all methods show horizontal integral scales between 1 85 and 4 04 m vertical integral scales z between 0 144 and 0 459 m and log hydraulic conductivities in k between 0 120 and 0 197 these results compare well to the earlier estimates of woodbury and sudicky 1991 and robin et al 1991 we show that moment prediction uncertainty is substantially reduced when both tracer moment data and prior estimates of the in k geostatistical parameters are incorporated into theoretical formulae based on stochastic dispersion 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

minimum relative entropy forward probabilistic modeling the pioneering work of jaynes in bayesian maximum entropy methods has been successfully explored in many disciplines the principle of maximum entropy pme is a powerful and versatile tool of inferring a probability distribution from constraints that do not completely characterize that distribution minimum relative entropy mre is a method which has all the important attributes of the maximum entropy approach with the advantage that prior information may be easily included in this paper we use mre to determine the prior probability density function pdf of a set of model parameters based on limited information the resulting pdf is used in monte carlo simulations to provide expected values in field variables such as concentration and confidence limits we compare the probabilistic results from a traditional advection dispersion ade model based on volumetric averaging concepts with that of a model based on the assumption that the hydraulic conductivity is a stationary stochastic process the results suggest that although naff s 1990 model satisfies the observed data to a better degree than ade model the upper and lower confidence bands about the mean value are larger than the ade results this result we attribute to the fact that naff s 1990 model simply contains more parameters each of which is unknown and has to be estimated there is no statistical difference between the expected values of second spatial moments for the two models the examples presented in this paper illustrate problems associated with assigning gaussian pdfs as priors in a probabilistic model first such an assumption for the input parameters actually injects more information into the problem than may actually exist whether consciously or unconsciously this fact is borne out by comparison with minimum relative entropy theory second the output parameters as suggested from the monte carlo analysis cannot be assumed to be gaussian distributed even when the prior pdf is gaussian in form in a practical setting the significance of this result and the approximation of gaussian form would depend on the toxicity and environmental standards that apply to the problem

level set based topology optimization for electromagnetic dipole antenna design this paper presents a level set framework for a typical electromagnetic design problem of dipole antenna in this study the geometrical configuration of an antenna is represented by the zero level contour of a higher dimensional level set function the governing equation for the induced current flow on a metal surface is the electric field integral equation efie which takes into account the electric component of the incident wave the design objective is formulated in terms of the surface current and incident electric field the normal velocity of the level set model which reflects the sensitivity of the objective function is derived from the adjoint variable method and shape derivative by optimizing the objective function the area with the highest current density to which the voltage feeding should be applied can be reshaped the advantages of adopting the level set technique for electromagnetic design lie in its capacity for capturing sophisticated topological changes and facilitation in mathematical representation of the design configuration the demonstrative examples of dipole antenna design show that the level set method results in a fairly smooth optimization process where the vacuum metal interface gradually attains its optimal configuration a series of design cases with self adjoint and non self adjoint sensitivity analyses are studied and compared to the benchmarking problems in dipole antenna

consistent inference of probabilities for reproducible experiments the need for inducing a probability distribution from partial data and the complementary problem of the analysis of an observed distribution in terms of fewer relevant variables occur in many branches of physics for reproducible experiments consistency conditions which must be satisfied by any algorithm for inferring a discrete probability distribution with given averages are formulated the only consistent algorithm is the one leading to the distribution of maximal entropy subject to the given constraints

probabilistic sensitivity analysis for one dimensional reactive transport in porous media a reliability approach for probabilistic modeling of reactive transport in porous media provides two important quantitative results 1 an estimate of the probability that dimensionless concentration equals or exceeds some specified level and 2 a probabilistic sensitivity measure which quantifies the relative importance of each uncertain variable with respect to the probabilistic outcome the approach is potentially attractive because it can provide both a probability estimate and probabilistic sensitivity measures this is especially important for relatively low probability events where monte carlo simulation may require hundreds of thousands of realizations for reasonable results the reliability method can incorporate marginal probability distribution functions pdf and correlation between uncertain variables and the general method can be used with existing analytical or numerical solutions however a first order reliability approach provides only an approximate probability measure the accuracy is a function of performance criterion and statistical characteristics of the uncertain variables the methodology and results here focus on probabilistic sensitivity measures which indicate the importance of any uncertain variable to the probabilistic outcome in this work one dimensional reactive transport is investigated with the following uncertain variables groundwater flow velocity diffusion coefficient dispersivity distribution coefficient porosity and bulk density we examine how probabilistic outcome and sensitivity are influenced by choice of marginal pdf correlation and magnitude of uncertainty for the variables we also compare the probabilistic sensitivity results to typical deterministic sensitivity measures results indicate that the probabilistic outcome is most sensitive to likely changes in flow velocity and the reaction terms diffusion coefficient can also be an important uncertain variable but only when it has significantly higher uncertainty coefficient of variation than any other variable for some cases shown in this paper dispersivity and diffusion coefficient can be treated as deterministic variables with little impact on the probabilistic outcome

stochastic lattice gas model describing the dynamics of the sirs epidemic process abstract we study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes susceptible s infected i and recovered r the stochastic process is defined by local rules and involves the following cyclic process s i r s sirs the open process s i r sir is studied as a particular case of the sirs process the epidemic process is analyzed at different levels of description by a stochastic lattice gas model and by a birth and death process by means of monte carlo simulations and dynamical mean field approximations we show that the sirs stochastic lattice gas model exhibit a line of critical points separating the two phases an absorbing phase where the lattice is completely full of s individuals and an active phase where s i and r individuals coexist which may or may not present population cycles the critical line that corresponds to the onset of epidemic spreading is shown to belong in the directed percolation universality class by considering the birth and death process we analyze the role of noise in stabilizing the oscillations

frechet derivatives for some bilinear inverse problems in many inverse problems a functional of u is given by measurements where u solves a partial differential equation of the type l p u su q here q is a known source term and l p s are operators with p as an unknown parameter of the inverse problem for the numerical reconstruction of p the heuristically derived frechet derivative r of the mapping r p rightarrow measurementfunctional of u is often used we show for three problems a transport problem in optical tomography an elliptic equation governing near infrared tomography and the wave equation in moving media that r is the derivative in the strict sense our method is applicable to more general problems than are established methods for similar inverse problems

coupled complex adjoint sensitivities for frequency domain fluorescence tomography theory and vectorized implementation we present a computationally efficient and accurate adjoint method for calculating coupled sensitivities of complex frequency domain excitation and emission fluence to any underlying optical parameters in highly scattering media the method is shown to be general and accurate novel vectorized implementations for finite element global matrix assembly and adjoint sensitivity calculations are shown to speed up calculations by orders of magnitude over traditional loop implementations thereby making least squares approaches to fluorescence tomography computationally practical

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

exploring the threshold of epidemic spreading for a stochastic sir model with local and global contacts abstract the spread of an epidemic process is considered in the context of a spatial sir stochastic model that includes a parameter 0 p 1 that assigns weights p and 1 p to global and local infective contacts respectively the model was previously studied by other authors in different contexts in this work we characterized the behavior of the system around the threshold for epidemic spreading we first used a deterministic approximation of the stochastic model and checked the existence of a threshold value of p for exponential epidemic spread an analytical expression which defines a function of the quotient between the transmission and recovery rates is obtained to approximate this threshold we then performed different analyzes based on intensive stochastic simulations and found that this expression is also a good estimate for a similar threshold value of p obtained in the stochastic model the dynamics of the average number of infected individuals and the average size of outbreaks show a behavior across the threshold that is well described by the deterministic approximation the distributions of the outbreak sizes at the threshold present common features for all the cases considered corresponding to different values of 1 these features are otherwise already known to hold for the standard stochastic sir model at its threshold 1 i the probability of having an outbreak of size n goes asymptotically as n 3 2 for an infinite system ii the maximal size of an outbreak scales as n 2 3 for a finite system of size n

noise propagation in linear and nonlinear inverse scattering the propagation of noise from the data to the reconstructed speed of sound image by inverse scattering within the framework of the lippmann schwinger integral equation of scattering is discussed the inversion algorithm that was used consisted in minimizing a tikhonov functional in the unknown speed of sound the gradient of the objective functional was computed by the method of the adjoint fields an analytical expression for the inverse scattering covariance matrix of the image noise was derived it was shown that the covariance matrix in the linear x ray computed tomography is a special case of the inverse scattering matrix derived in this paper the matrix was also analyzed in the limit of the linearized born approximation and the results were found to be in qualitative agreement with those recently reported in the literature for born inversion using filtered backpropagation algorithm finally the applicability of the analysis reported here to the obstacle problem and the physical optics approximation was discussed

inversion of seismic reflection data in the acoustic approximation the nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation the method is based on the generalized least squares criterion and it can handle errors in the data set and a priori information on the model multiply reflected energy is naturally taken into account as well as refracted energy or surface waves the inverse problem can be solved using an iterative algorithm which gives at each iteration updated values of bulk modulus density and time source function each step of the iterative algorithm essentially consists of a forward propagation of the actual sources in the current model and a forward propagation backward in time of the data residuals the correlation at each point of the space of the two fields thus obtained yields the corrections of the bulk modulus and density models this shows in particular that the general solution of the inverse problem can be attained by methods strongly related to the methods of migration of unstacked data and commerc

reconstruction of the shape and surface impedance from acoustic scattering data for an arbitrary cylinder the inverse scattering for an obstacle d subset r 2 with mixed boundary condition can be considered as a prototype for radar detection of complex obstacles with coated and noncoated parts of the boundary we construct some indicator functions for this inverse problem using the far field pattern directly without the necessity of transforming the far field to the near field based on careful singularity analysis these indicator functions enable us to reconstruct the shape of the obstacle and distinguish the coated from the noncoated part of the boundary moreover an explicit representation formula for the surface impedance in the coated part of the boundary is also given our reconstruction scheme reveals that the coated part of the obstacle is less visible than the noncoated one which corresponds to the physical fact that the coated boundary absorbs some part of the scattered wave numerics are presented for the reconstruction formulas which show that both the boundary shape and the surface impedan

a full bayesian approach to parameter inference from tracer travel time moments and investigation of scale effects at the cape cod experimental site a method for inverting the travel time moments of solutes in heterogeneous aquifers is presented and is based on peak concentration arrival times as measured at various samplers in an aquifer the approach combines a lagrangian rubin and dagan 1992 solute transport framework with full bayesian hydrogeological parameter inference in the full bayesian approach the noise values in the observed data are treated as hyperparameters and their effects are removed by marginalization the prior probability density functions pdfs for the model parameters horizontal integral scale velocity and log k variance and noise values are represented by prior pdfs developed from minimum relative entropy considerations analysis of the cape cod massachusetts field experiment is presented inverse results for the hydraulic parameters indicate an expected value for the velocity variance of log hydraulic conductivity and horizontal integral scale of 0 42 m d 0 26 and 3 0 m respectively while these results are consistent with various direct field determinations the importance of the findings is in the reduction of confidence range about the various expected values on selected control planes we compare observed travel time frequency histograms with the theoretical pdf conditioned on the observed travel time moments we observe a positive skew in the travel time pdf which tends to decrease as the travel time distance grows we also test the hypothesis that there is no scale dependence of the integral scale with the scale of the experiment at cape cod we adopt two strategies the first strategy is to use subsets of the full data set and then to see if the resulting parameter fits are different as we use different data from control planes at expanding distances from the source the second approach is from the viewpoint of entropy concentration no increase in integral scale with distance is inferred from either approach over the range of the cape cod tracer experiment

the derivative of a waveguide acoustic field with respect to a three dimensional sound speed perturbation semianalytic expressions are derived for the first order derivative of a pressure field in a laterally homogeneous waveguide with respect to an arbitrary three dimensional refractive index perturbation in either the water column or ocean bottom these expressions for the environmental derivative derived using an adjoint method require a three dimensional spatial correlation between two green s functions weighted by an environmental parameter basis function with the green s functions expressed in terms of normal modes when a particular set of orthogonal spatial basis functions is chosen the three dimensional spatial integral can be converted into a set of one dimensional integrations over depth and azimuth the use of the orthogonal basis permits environmental derivatives to be computed for an arbitrary sound speed perturbation to illustrate the formulas a simple sensitivity study is presented that explores under what circumstances three dimensional plane wave and cylindrical perturbations produ

a comparison of exact and approximate adjoint sensitivities in fluorescence tomography many approaches to fluorescence tomography utilize some form of regularized nonlinear least squares algorithm for data inversion thus requiring repeated computation of the jacobian sensitivity matrix relating changes in observable quantities such as emission fluence to changes in underlying optical parameters such as fluorescence absorption an exact adjoint formulation of these sensitivities comprises three terms reflecting the individual contributions of 1 sensitivities of diffusion and decay coefficients at the emission wavelength 2 sensitivities of diffusion and decay coefficients at the excitation wavelength and 3 sensitivity of the emission source term simplifying linearity assumptions are computationally attractive in that they cause the first and second terms to drop out of the formulation the relative importance of the three terms is thus explored in order to determine the extent to which these approximations introduce error computational experiments show that while the third term of the sensitivity matrix has the largest magnitude the second term becomes increasingly significant as target fluorophore concentration or volume increases image reconstructions from experimental data confirm that neglecting the second term results in overestimation of sensitivities and consequently overestimation of the value and volume of the fluorescent target whereas contributions of the first term are so low that they are probably not worth the additional computational costs

minimum relative entropy inversion theory and application to recovering the release history of a groundwater contaminant in this paper we show that given prior information in terms of a lower and upper bound a prior bias and constraints in terms of measured data minimum relative entropy mre yields exact expressions for the posterior probability density function pdf and the expected value of the linear inverse problem in addition we are able to produce any desired confidence intervals in numerical simulations we use the mre approach to recover the release and evolution histories of plume in a one dimensional constant known velocity and dispersivity system for noise free data we find that the reconstructed plume evolution history is indistinguishable from the true history an exact match to the observed data is evident two methods are chosen for dissociating signal from a noisy data set the first uses a modification of mre for uncertain data the second method uses presmoothing by fast fourier transforms and butterworth filters to attempt to remove noise from the signal before the noise free variant of mre inversion is used both methods appear to work very well in recovering the true signal and qualitatively appear superior to that of skaggs and kabala 1994 we also solve for a degenerate case with a very high standard deviation in the noise the recovered model indicates that the mre inverse method did manage to recover the salient features of the source history once the plume source history has been developed future behavior of a plume can then be cast in a probabilistic framework for an example simulation the mre approach not only was able to resolve the source function from noisy data but also was able to correctly predict future behavior

stochastic dynamics for two biological species and ecological niches abstract we consider an ecological system in which two species interact with two niches to this end we introduce a stochastic model with four states our analysis is founded in three approaches monte carlo simulations of the model on a square lattice mean field approximation and birth and death master equation from this last approach we obtain a description in terms of langevin equations which show in an explicit way the role of noise in population biology we focus mainly on the description of time oscillations of the species population and the alternating dominance between them the model treated here may provide insights on these properties

minimum cross entropy spectral analysis the principle of minimum cross entropy minimum directed divergence minimum discrimination information minimum relative entropy is summarized discussed and applied to the classical problem of estimating power spectra given values of the autocorrelation function this new method differs from previous methods in its explicit inclusion of a prior estimate of the power spectrum and it reduces to maximum entropy spectral analysis as a special case the prior estimate can be viewed as a means of shaping the spectral estimator cross entropy minimization yields a family of shaped spectral estimators consistent with known autocorrelations results are derived in two equivalent ways once by minimizing the cross entropy of underlying probability densities and once by arguments concerning the cross entropy between the input and output of linear filters several example minimum cross entropy spectra are included

the inverse source problem based on the radiative transfer equation in optical molecular imaging we present the first tomographic reconstruction algorithm for optical molecular imaging that is based on the equation of radiative transfer the reconstruction code recovers the spatial distribution of fluorescent sources in highly scattering biological tissue an objective function which describes the discrepancy of measured near infrared light with predicted numerical data on the tissue surface is iteratively minimized to find a solution of the inverse source problem at each iteration step the predicted data are calculated by a forward model for light propagation based on the equation of radiative transfer the unknown source distribution is updated along a search direction that is provided by an adjoint differentiation technique

stability estimates for obstacles in inverse scattering abstract in this paper we estimate distances between two soft obstacles in terms of corresponding scattering amplitudes the estimate is of logarithmic type and it is obtained by using estimates for continuation of solutions of elliptic equations and some methods of potential theory scattering amplitudes are given for one frequency comparable with size of scatterer and for all directions of receiver

new approach to dynamical monte carlo methods application to an epidemic model abstract in this work we introduce a new approach to dynamical monte carlo methods to simulate markovian processes we apply this approach to formulate and study an epidemic generalized sirs model the results are in excellent agreement with the forth order runge kutta method in a region of deterministic solution we also show that purely local interactions reproduce a poissonian like process at mesoscopic level the simulations for this case are checked self consistently using a stochastic version of the euler method

multiscale seismic waveform inversion iterative inversion methods have been unsuccessful at inverting seismic data obtained from complicated earth models e g the marmousi model the primary difficulty being the presence of numerous local minima in the objective function the presence of local minima at all scales in the seismic inversion problem prevent iterative methods of inversion from attaining a reasonable degree of convergence to the neighborhood of the global minimum the multigrid method is a technique that improves the performance of iterative inversion by decomposing the problem by scale at long scales there are fewer local minima and those that remain are further apart from each other thus at long scales iterative methods can get closer to the neighborhood of the global minimum we apply the multigrid method to a subsampled low frequency version of the marmousi data set although issues of source estimation source bandwidth and noise are not treated results show that iterative inversion methods perform much better when employed with a decomposition by scale furthermore the method greatly reduces the computational burden of the inversion that will be of importance for 3 d extensions to the method

critical behavior of the susceptible infected recovered model on a square lattice by means of numerical simulations and epidemic analysis the transition point of the stochastic asynchronous susceptible infected recovered model on a square lattice is found to be c0 0 176 500 510 where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor this point corresponds to an infection recovery rate of c 1 c0 c0 4 665 713 and a net transmissibility of 1 c0 1 3 c0 0 538 4102 which falls between the rigorous bounds of the site and bond thresholds the critical behavior of the model is consistent with the two dimensional percolation universality class but local growth probabilities differ from those of dynamic percolation cluster growth as is demonstrated explicitly

born expansion and frechet derivatives in nonlinear diffuse optical tomography the nonlinear diffuse optical tomography dot problem involves the inversion of the associated coefficient to measurement operator which maps the spatially varying optical coefficients of turbid medium to the boundary measurements the inversion of the coefficient to measurement operator is approximated by using the frechet derivative of the operator in this work we first analyze the born expansion show the conditions which ensure the existence and convergence of the born expansion and compute the error in the mth order born approximation then we derive the mth order frechet derivatives of the coefficient to measurement operator using the relationship between the frechet derivatives and the born expansion

comparison of inverse methods for reconstructing the release history of a groundwater contamination source inverse methods can be used to reconstruct the release history of a known source of groundwater contamination from concentration data describing the present day spatial distribution of the contaminant plume using hypothetical release history functions and contaminant plumes we evaluate the relative effectiveness of two proposed inverse methods tikhonov regularization tr and minimum relative entropy mre inversion in reconstructing the release history of a conservative contaminant in a one dimensional domain skaggs and kabala 1994 woodbury and ulrych 1996 we also address issues of reproducibility of the solution and the appropriateness of models for simulating random measurement error the results show that if error free plume concentration data are available both methods perform well in reconstructing a smooth source history function with error free data the mre method is more robust than tr in reconstructing a nonsmooth source history function however the tr method is more robust if the data contain measurement error two error models were evaluated in this study and we found that the particular error model does not affect the reliability of the solutions the results for the tr method have somewhat greater reproducibility because in some cases its input parameters are less subjective than those of the mre method however the mre solution can identify regions where the data give little or no information about the source history function while the tr solution cannot

differentiability of the objective in a class of coefficient inverse problems abstract in this paper we study the frechet differentiability of the objective functional for a quite general class of coefficient inverse problems we present sufficient conditions for the existence of arbitrary order differentials as well as formulae for the calculation of first and second order derivatives the general case theorems are then applied to two real world geophysical inverse problems

a hypothesis driven approach to optimize field campaigns 1 most field campaigns aim at helping in specified scientific or practical tasks such as modeling prediction optimization or management often these tasks involve binary decisions or seek answers to yes no questions under uncertainty e g is a model adequate will contamination exceed a critical level in this context the information needs of hydro geo logical modeling should be satisfied with efficient and rational field campaigns e g because budgets are limited we propose a new framework to optimize field campaigns that defines the quest for defensible decisions as the ultimate goal the key steps are to formulate yes no questions under uncertainty as bayesian hypothesis tests and then use the expected failure probability of hypothesis testing as objective function our formalism is unique in that it optimizes field campaigns for maximum confidence in decisions on model choice binary engineering or management decisions or questions concerning compliance with environmental performance metrics it is goal oriented recognizing that different models questions or metrics deserve different treatment we use a formal bayesian scheme called predia which is free of linearization and can handle arbitrary data types scientific tasks and sources of uncertainty e g conceptual physical geo statistical measurement errors this reduces the bias due to possibly subjective assumptions prior to data collection and improves the chances of successful field campaigns even under conditions of model uncertainty we illustrate our approach on two instructive examples from stochastic hydrogeology with increasing complexity

focalization environmental focusing and source localization conventional matched field processing mfp requires accurate knowledge of the ocean acoustic environment focalization which simultaneously focuses and localizes eliminates this stringent requirement by including the environment in the parameter search space this generalization of mfp involves defining an appropriate high resolution cost function parametrizing the search space of the environment and source constructing solutions of the wave equation and utilizing a nonlinear optimization method to search the parameter landscape for the global minimum of the cost function focalization is implemented using cost functions based on ray theory and wave theory empirical orthogonal functions for the environmental description and simulated annealing for optimization numerical simulations are presented to demonstrate the feasibility of focalization

linearization of the matched field processing approach to acoustic tomography this paper continues the approach presented in tolstoy et al j acoust soc am 89 1119 1127 1991 but offers a much improved inversion technique i e a linearization of the problem which reformats the computations in terms of a simple nonsquare matrix inversion for an overdetermined system this work was motivated by the desire to improve upon the speed and accuracy of the original algorithm that had a tendency to stall unpredictably tolstoy and frazer in computational acoustics edited by d lee a cakmak and r vichnevetsky north holland amsterdam 1991 this work has the additional bonus that sound speed accuracies are now an order of magnitude better than the earlier technique in addition calculations confirm that for simulations with white gaussian uncorrelated noise the linear bartlett processor results are identical to those of the minimum variance capon processor finally optimal source receiver configurations have been determined by exhaustively computing the condition numbe

a bayesian approach for inverse modeling data assimilation and conditional simulation of spatial random fields 1 this paper addresses the inverse problem in spatially variable fields such as hydraulic conductivity in groundwater aquifers or rainfall intensity in hydrology common to all these problems is the existence of a complex pattern of spatial variability of the target variables and observations the multiple sources of data available for characterizing the fields the complex relations between the observed and target variables and the multiple scales and frequencies of the observations the method of anchored distributions mad that we propose here is a general bayesian method of inverse modeling of spatial random fields that addresses this complexity the central elements of mad are a modular classification of all relevant data and a new concept called anchors data types are classified by the way they relate to the target variable as either local or nonlocal and as either direct or indirect anchors are devices for localization of data they are used to convert nonlocal indirect data into local distributions of the target variables the target of the inversion is the derivation of the joint distribution of the anchors and structural parameters conditional to all measurements regardless of scale or frequency of measurement the structural parameters describe large scale trends of the target variable fields whereas the anchors capture local inhomogeneities following inversion the joint distribution of anchors and structural parameters is used for generating random fields of the target variable s that are conditioned on the nonlocal indirect data through their anchor representation we demonstrate mad through a detailed case study that assimilates point measurements of the conductivity with head measurements from natural gradient flow the resulting statistical distributions of the parameters are non gaussian similarly the moments of the estimates of the hydraulic head are non gaussian we provide an extended discussion of mad vis a vis other inversion methods including maximum likelihood and maximum a posteriori with an emphasis on the differences between mad and the pilot points method

the inverse scattering problem and global convergence in solving nonlinear inverse scattering problems an iterative approach is usually required particularly if the nonlinearity is strong a typical approach is to use a descent algorithm to minimize a global error norm such as the mean square error to arrive at a set of parameters that best predicts the data based on an assumed model of the unknown scattering object in minimizing the error norm the possibility of converging to a local minimum can lead to false solutions a different strategy is proposed that is not based on gradient descent which at least in principle should avoid local minima and converge to the true solution the global minimum a simple inverse scattering problem is used as an illustration

bayesian inversion of mualem van genuchten parameters in a multilayer soil profile a data driven assumption free likelihood function this paper introduces a hierarchical simulation and modeling framework that allows for inference and validation of the likelihood function in bayesian inversion of vadose zone hydraulic properties the likelihood function or its analogs objective functions and likelihood measures are commonly assumed to be multivariate gaussian in form however this assumption is not possible to verify without a hierarchical simulation and modeling framework in this paper we present the necessary statistical mechanisms for utilizing the hierarchical framework we apply the hierarchical framework to the inversion of the vadose zone hydraulic properties within a multilayer soil profile conditioned on moisture content observations collected in the uppermost four layers the key result of our work is that the goodness of fit validated likelihood function form provides empirical justification for the assumption of multivariate gaussian likelihood functions in past and future inversions at similar sites as an alternative the likelihood function need not be assumed to follow a parametric statistical distribution and can be computed directly using nonparametric methods the nonparametric methods are considerably more computationally demanding and to demonstrate this approach we present a smaller dimension synthetic case study of evaporation from a soil column the main drawback of our work is the increased computational expense of the inversion

pair approximation of the stochastic susceptible infected recovered susceptible epidemic model on the hypercubic lattice we investigate the time evolution and steady states of the stochastic susceptible infected recovered susceptible sirs epidemic model on one and two dimensional lattices we compare the behavior of this system obtained from computer simulations with those obtained from the mean field approximation mfa and pair approximation pa the former latter approximates higher order moments in terms of first second order ones we find that the pa gives consistently better results than the mfa in one dimension the improvement is even qualitative

inversion of seismoacoustic data using genetic algorithms and a posteriori probability distributions the goal of many underwater acoustic modeling problems is to find the physical parameters of the environment with the increase in computer power and the development of advanced numerical models it is now feasible to carry out multiparameter inversion the inversion is posed as an optimization problem which is solved by a directed monte carlo search using genetic algorithms the genetic algorithm presented in this paper is formulated by steady state reproduction without duplicates for the selection of parents the object function is scaled according to a boltzmann distribution with a temperature equal to the fitness of one of the members in the population the inversion would be incomplete if not followed by an analysis of the uncertainties of the result when using genetic algorithms the response from many environmental parameter sets has to be computed in order to estimate the solution the many samples of the models are used to estimate the a posteriori probabilities of the model parameters t

the threshold of coexistence and critical behaviour of a predator prey cellular automaton we study a probabilistic cellular automaton to describe two population biology problems the threshold of species coexistence in a predator prey system and the spreading of an epidemic in a population by carrying out mean field approximations and numerical simulations we obtain the phase boundaries thresholds related to the transition between an active state where prey and predators present a stable coexistence and a prey absorbing state the numerical estimates for the critical exponents show that the transition belongs to the directed percolation universality class in the limit where the cellular automaton maps into a model for the spreading of an epidemic with immunization we observe a crossover from directed percolation class to the dynamic percolation class patterns of growing clusters related to species coexistence and spreading of epidemic are shown and discussed

adjoint modeling for acoustic inversion the use of adjoint modeling for acoustic inversion is investigated an adjoint model is derived from a linearized forward propagation model to propagate data model misfit at the observation points back through the medium to the medium perturbations not being accounted for in the model this adjoint model can be used to aid in inverting for these unaccounted medium perturbations adjoint methods are being applied to a variety of inversion problems but have not drawn much attention from the underwater acoustic community this paper presents an application of adjoint methods to acoustic inversion inversions are demonstrated in simulation for both range independent and range dependent sound speed profiles using the adjoint of a parabolic equation model sensitivity and error analyses are discussed showing how the adjoint model enables calculations to be performed in the space of observations rather than the often much larger space of model parameters using an adjoint model enables directions of steepest descent in the model parameters what we invert for to be calculated using far fewer modeling runs than if a forward model only were used

domain derivatives in dielectric rough surface scattering the inverse scattering solution of shape and or material parameter reconstruction is often posed as a problem in nonlinear minimization of an objective function with respect to n usually large number of unknown model parameters characterizing the scatterer the minimization procedures are usually iterative and require the gradient of the objective function in the unknown model parameter vector in each stage of iteration for large n finite differencing becomes numerically intensive and an efficient alternative is domain differentiation in which the full gradient is obtained by solving a single scattering problem of an auxiliary field using the same scattering operator as that of the forward solution a well known technique in this direction is the so called adjoint field method which obtains the gradient by variationally minimizing an augmented objective function that includes the reduced wave equation via a lagrange multiplier results are reported mostly for compact objects this paper presents the domain derivative calculation of the gradient for an one dimensional locally perturbed and infinitely long dielectric interface the method is nonvariational and algebraic in nature in that it evaluates the gradient by directly domain differentiating the scattering equations the computations are straightforward and easy to follow the mathematical transformation of the scattering problem into the corresponding problem for the differentiated fields can be visualized explicitly the formulation of and the motivation behind introducing the auxiliary field are explicitly demonstrated closed form analytic expressions are obtained for the gradients for electromagnetic te tm scattering from dielectric rough surfaces and for scalar wave scattering from neumann and dirichlet rough surfaces results are compared with those of compact scatterers finally the relationship between our results and lorentz reciprocity is pointed out and clarified

geological entropy and solute transport in heterogeneous porous media we propose a novel approach to link solute transport behavior to the physical heterogeneity of the aquifer which we fully characterize with two measurable parameters the variance of the log k values math formula and a new indicator hr that integrates multiple properties of the k field into a global measure of spatial disorder or geological entropy from the results of a detailed numerical experiment considering solute transport in k fields representing realistic distributions of hydrofacies in alluvial aquifers we identify empirical relationship between the two parameters and the first three central moments of the distributions of arrival times of solute particles at a selected control plane the analysis of experimental data indicates that the mean and the variance of the solutes arrival times tend to increase with spatial disorder i e hr increasing while highly skewed distributions are observed in more orderly structures i e hr decreasing or at higher math formula we found that simple closed form empirical expressions of the bivariate dependency of skewness on hr and math formula can be used to predict the emergence of non fickian transport in k fields considering a range of structures and heterogeneity levels some of which based on documented real aquifers the accuracy of these predictions and in general the results from this study indicate that a description of the global variability and structure of the k field in terms of variance and geological entropy offers a valid and broadly applicable approach for the interpretation and prediction of transport in heterogeneous porous media

finite size scaling analysis of the critical behavior of a general epidemic process in 2d abstract we investigate the critical behavior of a stochastic lattice model describing a general epidemic process by means of a monte carlo procedure we simulate the model on a regular square lattice and follow the spreading of an epidemic process with immunization a finite size scaling analysis is employed to determine the critical point as well as some critical exponents we show that the usual scaling analysis of the order parameter moment ratio does not provide an accurate estimate of the critical point precise estimates of the critical quantities are obtained from data of the order parameter variation rate and its fluctuations our numerical results corroborate that this model belongs to the dynamic isotropic percolation universality class we also check the validity of the hyperscaling relation and present data collapse curves which reinforce the accuracy of the estimated critical parameters

significance of higher moments for complete characterization of the travel time probability density function in heterogeneous porous media using the maximum entropy principle 1 the travel time formulation of advective transport in heterogeneous porous media is of interest both conceptually e g for incorporating retention processes and in applications where typically the travel time peak early and late arrivals of contaminants are of major concern in a regulatory or remediation context furthermore the travel time moments are of interest for quantifying uncertainty in advective transport of tracers released from point sources in heterogeneous aquifers in view of this interest the travel time distribution has been studied in the literature however the link to the hydraulic conductivity statistics has been typically restricted to the first two moments here we investigate the influence of higher travel time moments on the travel time probability density function pdf in heterogeneous porous media combining monte carlo simulations with the maximum entropy principle the monte carlo experimental pdf is obtained by the adaptive fup monte carlo method afmcm for advective transport characterized by a multi gaussian structure with exponential covariance considering two injection modes in flux and resident and lnk variance up to 8 a maximum entropy maxent algorithm based on fup basis functions is used for the complete characterization of the travel time pdf all travel time moments become linear with distance initial nonlinearity is found mainly for the resident injection mode which exhibits a strong nonlinearity within first 5iy for high heterogeneity for the resident injection mode the form of variance and all higher moments changes from the familiar concave form predicted by the first order theory to a convex form for the in flux mode linearity is preserved even for high heterogeneity the number of moments sufficient for a complete characterization of the travel time pdf mainly depends on the heterogeneity level mean and variance completely describe travel time pdf for low and mild heterogeneity skewness is dominant for lnk variance around 4 while kurtosis and fifth moment are required for lnk variance higher than 4 including skewness seems sufficient for describing the peak and late arrivals linearity of travel time moments enables the prediction of asymptotic behavior of the travel time pdf which in the limit converges to a symmetric distribution and fickian transport however higher order travel time moments may be important for most practical purposes and in particular for advective transport in highly heterogeneous porous media for a long distance from the source

variational principles surface evolution pdes level set methods and the stereo problem we present a novel geometric approach for solving the stereo problem for an arbitrary number of images spl ges 2 it is based upon the definition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images the euler lagrange equations that are deduced from the variational principle provide a set of partial differential equations pdes that are used to deform an initial set of surfaces which then move toward the objects to be detected the level set implementation of these pdes potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformations i e to deal with multiple objects results of an implementation of our theory also dealing with occlusion and visibility are presented on synthetic and real images

structural optimization using sensitivity analysis and a level set method in the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level set method for front propagation we implement this method in two and three space dimensions for a model of linear or nonlinear elasticity we consider various objective functions with weight and perimeter constraints the shape derivative is computed by an adjoint method the cost of our numerical algorithm is moderate since the shape is captured on a fixed eulerian mesh although this method is not specifically designed for topology optimization it can easily handle topology changes however the resulting optimal shape is strongly dependent on the initial guess

reservoir parameter identification using minimum relative entropy based bayesian inversion of seismic ava and marine csem data a stochastic joint inversion approach for estimating reservoir fluid saturations and porosity is proposed the approach couples seismic amplitude variation with angle ava and marine controlled source electromagnetic csem forward models into a bayesian framework which allows for integration of complementary information to obtain minimally subjective prior probabilities required for the bayesian approach the principle of minimum relative entropy mre is employed instead of single value estimates provided by deterministic methods the approach gives a probability distribution for any unknown parameter of interest such as reservoir fluid saturations or porosity at various locations the distribution means modes and confidence intervals can be calculated providing a more complete understanding of the uncertainty in the parameter estimates the approach is demonstrated using synthetic and field data sets results show that joint inversion using seismic and em data gives better estimates of reservoir parameters than estimates from either geophysical data set used in isolation moreover a more informative prior leads to much narrower predictive intervals of the target parameters with mean values of the posterior distributions closer to logged values

bayesian assessment of the expected data impact on prediction confidence in optimal sampling design 1 incorporating hydro geo logical data such as head and tracer data into stochastic models of subsurface flow and transport helps to reduce prediction uncertainty because of financial limitations for investigation campaigns information needs toward modeling or prediction goals should be satisfied efficiently and rationally optimal design techniques find the best one among a set of investigation strategies they optimize the expected impact of data on prediction confidence or related objectives prior to data collection we introduce a new optimal design method called predia gnosis preposterior data impact assessor predia derives the relevant probability distributions and measures of data utility within a fully bayesian generalized flexible and accurate framework it extends the bootstrap filter bf and related frameworks to optimal design by marginalizing utility measures over the yet unknown data values predia is a strictly formal information processing scheme free of linearizations it works with arbitrary simulation tools provides full flexibility concerning measurement types linear nonlinear direct indirect allows for any desired task driven formulations and can account for various sources of uncertainty e g heterogeneity geostatistical assumptions boundary conditions measurement values model structure uncertainty a large class of model errors via bayesian geostatistics and model averaging existing methods fail to simultaneously provide these crucial advantages which our method buys at relatively higher computational costs we demonstrate the applicability and advantages of predia over conventional linearized methods in a synthetic example of subsurface transport in the example we show that informative data is often invisible for linearized methods that confuse zero correlation with statistical independence hence predia will often lead to substantially better sampling designs finally we extend our example to specifically highlight the consideration of conceptual model uncertainty

adjoint modeling with a split step fourier parabolic equation model previous work on adjoint modeling of underwater acoustic propagation for the purposes of environmental inversions developed the necessary numerical algorithms based on a finite difference implementation of the parabolic equation in this letter the corresponding formulation for the split step fourier implementation is presented although no calculations have yet been made with this approach the method is completely consistent with previous work and the final form of the tangent linear model is exactly the same however the formulation of the operators in the split step fourier approach provides a simple means of estimating both local and global effects on uncertainty this letter is then provided for anyone who may wish to attempt adjoint modeling with a split step fourier model

optimal nonlocal boundary control of the wide angle parabolic equation for inversion of a waveguide acoustic field this paper applies the concept of optimal boundary control for solving inverse problems in shallow water acoustics to treat the controllability problem a continuous analytic adjoint model is derived for the claerbout wide angle parabolic equation pe using a generalized nonlocal impedance boundary condition at the water bottom interface while the potential of adjoint methodology has been recently demonstrated for ocean acoustic tomography this approach combines the advantages of exact transparent boundary conditions for the wide angle pe with the concept of adjoint based optimal control in contrast to meta heuristic approaches the inversion procedure itself is directly controlled by the waveguide physics and in a numerical implementation based on conjugate gradient optimization many fewer iterations are required for assessment of an environment that is supported by the underlying subbottom model furthermore since regularization schemes are particularly important to enhance the performance of full field acoustic inversion special attention is devoted to the application of penalization methods to the adjoint optimization formalism regularization incorporates additional information about the desired solution in order to stabilize ill posed inverse problems and identify useful solutions a feature that is of particular importance for inversion of field data sampled on a vertical receiver array in the presence of measurement noise and modeling uncertainty results with test data show that the acoustic field and the bottom properties embedded in the control parameters can be efficiently retrieved

susceptible infected recovered and susceptible exposed infected models two stochastic epidemic lattice models the susceptible infected recovered and the susceptible exposed infected models are studied on a cayley tree of coordination number k the spreading of the disease in the former is found to occur when the infection probability b is larger than bc k 2 k 1 in the latter which is equivalent to a dynamic site percolation model the spreading occurs when the infection probability p is greater than pc 1 k 1 we set up and solve the time evolution equations for both models and determine the final and time dependent properties including the epidemic curve we show that the two models are closely related by revealing that their relevant properties are exactly mapped into each other when p b k k 1 b these include the cluster size distribution and the density of individuals of each type quantities that have been determined in closed forms

comments on and correction to axiomatic derivation of the principle of maximum entropy and the principle of minimum cross entropy jan 80 26 37 corresp an error in the subject paper is pointed out when the axioms given there are restricted to the discrete case they do not imply the discrete case of the principle of minimum cross entropy the principle is shown to follow however from the adoption of an additional axiom if new information is consistent with a prior estimate of a probability distribution then the posterior estimate equals the prior minor other improvements and corrections to the arguments in the paper are made

using discharge data to reduce structural deficits in a hydrological model with a bayesian inference approach and the implications for the prediction of critical source areas 1 a distributed hydrological model was used to simulate the distribution of fast runoff formation as a proxy for critical source areas for herbicide pollution in a small agricultural catchment in switzerland we tested to what degree predictions based on prior knowledge without local measurements could be improved upon relying on observed discharge this learning process consisted of five steps for the prior prediction step 1 knowledge of the model parameters was coarse and predictions were fairly uncertain in the second step discharge data were used to update the prior parameter distribution effects of uncertainty in input data and model structure were accounted for by an autoregressive error model this step decreased the width of the marginal distributions of parameters describing the lower boundary percolation rates but hardly affected soil hydraulic parameters residual analysis step 3 revealed model structure deficits we modified the model and in the subsequent bayesian updating step 4 the widths of the posterior marginal distributions were reduced for most parameters compared to those of the prior this incremental procedure led to a strong reduction in the uncertainty of the spatial prediction thus despite only using spatially integrated data discharge the spatially distributed effect of the improved model structure can be expected to improve the spatially distributed predictions also the fifth step consisted of a test with independent spatial data on herbicide losses and revealed ambiguous results the comparison depended critically on the ratio of event to preevent water that was discharged this ratio cannot be estimated from hydrological data only the results demonstrate that the value of local data is strongly dependent on a correct model structure an iterative procedure of bayesian updating model testing and model modification is suggested

susceptible infected recovered model with recurrent infection abstract we analyze a stochastic lattice model describing the spreading of a disease among a community composed by susceptible infected and removed individuals a susceptible individual becomes infected catalytically an infected individual may spontaneously either become recovered that is acquire a permanent immunization or become again susceptible the critical properties including the phase diagram is obtained by means of mean field theories as well as numerical simulations the model is found to belong to the universality class of dynamic percolation except when the recovering rate vanishes in which case the model belongs to the directed percolation universality class

iterative inverse scattering algorithms methods of computing frechet derivatives iterative approaches to the nonlinear inverse scattering problem generally attempt to find the scattering distribution that best predicts the data by minimizing a global error norm e g the mean square error which quantifies the misfit between a set of measured data and data predicted on the basis of a forward calculation a crucial quantity in this minimization is the frechet derivative of the error norm which tells us how to update the current estimate of the scattering distribution to reduce the global error at each iteration this paper demonstrates how to compute the frechet derivative using three different but fundamentally equivalent methods the conventional adjoint method the lagrange multiplier method and the integral equation method the first two begin with the wave equation while the latter method is based on a lippmann schwinger integral equation these techniques are not only far more efficient but also numerically less error prone than brute force methods for computing derivatives based for example on finite differences for simplicity a variational approach is employed in which the fields and scattering distribution are represented by continuous functions but the finite dimensional discretized problem is shown to follow directly from the continuous space results

adjoint based acoustic inversion for the physical characterization of a shallow water environment recently the concept of adjoint modeling has been introduced in shallow water acoustics for solving inverse problems analytical adjoints have been derived for normal modes and for both the standard parabolic equation and claerbout s wide angle approximation wape this paper proposes the application of a semiautomatic adjoint approach that has been successfully applied in the past for multidimensional variational data assimilation in meteorological and climate modeling starting from a modular graph representation of the underlying forward model a programming tool facilitates the generation and coding of both the tangent linear and the adjoint models the potential of this numerical adjoint approach for the physical characterization of a shallow water environment is illustrated with two applications for geoacoustic inversion and ocean acoustic tomography using claerbout s wape in combination with nonlocal boundary conditions furthermore the adjoint optimization is extended to multiple frequencies and

multiple order derivatives of a waveguide acoustic field with respect to sound speed density and frequency an adjoint perturbative method is used to derive expressions for the first through third order derivatives of a pressure field with respect to sound speed density and frequency for the restricted case of a laterally homogenous waveguide in which environmental parameters are only a function of depth by using a normal mode green s function the three dimensional spatial correlation required by the standard acoustic adjoint equation can be reduced to a set of one dimensional depth integrals the resulting expressions for the first order derivative are similar to those obtained by previous perturbative approaches based on the depth separated wave equation but the approach followed here permits straightforward extension to higher order derivatives explicit evaluations of the expressions for a representative shallow water waveguide model are in excellent agreement with numerical finite difference computations an analysis of the expressions as a function of source receiver range finds the contributions t

stochastic subsurface hydrology from theory to applications research on stochastic analysis of subsurface flow has developed rapidly in the last decade but applications of this approach have been very limited the purpose of this paper is to illustrate how currently available techniques and results can be used to answer important questions about the large scale behavior of naturally heterogeneous aquifers perturbation based spectral theory which presumes local statistical homogeneity provides generic theoretical results for the head variance effective conductivity tensor and macrodispersivity tensor in a field these results emphasize the key role of the variance and spatial correlation scales of the log hydraulic conductivity field field information of variances and correlation scales of natural materials is summarized the validity of some of the generic stochastic results is evaluated through comparisons with monte carlo simulations and field observations a specific field application example is developed to illustrate how the stochastic results are used to estimate large scale parameters and determine the reliability of three dimensional numerical simulations using typical log conductivity covariance parameters the effective hydraulic conductivity tensor and the macrodispersivity tensor are estimated the calculated head variance based on the simulated mean hydraulic gradient is used as a measure of the adequacy of the calculation of the steady state flow model discussion emphasizes limitations and extensions of this approach and ongoing field evaluations of the results

quasicycles in a spatial predator prey model we use spatial models of simple predator prey interactions to predict that predator and prey numbers oscillate in time and space these oscillations are not seen in the deterministic versions of the models but are due to stochastic fluctuations about the time independent solutions of the deterministic equations which are amplified due to the existence of a resonance we calculate the power spectra of the fluctuations analytically and show that they agree well with results obtained from stochastic simulations this work extends the analysis of these quasicycles from that previously developed for well mixed systems to spatial systems and shows that the ideas and methods used for nonspatial models naturally generalize to the spatial case

mean field approximation to a spatial host pathogen model we study the mean field approximation to a simple spatial host pathogen model that has been shown to display interesting evolutionary properties we show that previous derivations of the mean field equations for this model are actually only low density approximations to the true mean field limit we derive the correct equations and the corresponding equations including pair correlations the process of invasion by a mutant type of pathogen is also discussed doi 10 1103 physreve 67 047102