appraisal of the generalized likelihood uncertainty estimation glue method 1 recent research documents that the widely accepted generalized likelihood uncertainty estimation glue method for describing forecasting precision and the impact of parameter uncertainty in rainfall runoff watershed models fails to achieve the intended purpose when used with an informal likelihood measure in particular glue generally fails to produce intervals that capture the precision of estimated parameters and the difference between predictions and future observations this paper illustrates these problems with glue using a simple linear rainfall runoff model so that model calibration is a linear regression problem for which exact expressions for prediction precision and parameter uncertainty are well known and understood the simple regression example enables us to clearly and simply illustrate glue deficiencies beven and others have suggested that the choice of the likelihood measure used in a glue computation is subjective and may be selected to reflect the goals of the modeler if an arbitrary likelihood is adopted that does not reasonably reflect the sampling distribution of the model errors then glue generates arbitrary results without statistical validity that should not be used in scientific work the traditional subjective likelihood measures that have been used with glue also fail to reflect the nonnormality heteroscedasticity and serial correlation among the residual errors generally found in real problems and hence are poor metrics for even simple sensitivity analyses and model calibration most previous applications of glue only produce uncertainty intervals for the average model prediction which by construction should not be expected to include future observations with the prescribed probability we show how the glue methodology when properly implemented with a statistically valid likelihood function can provide prediction intervals for future observations which will agree with widely accepted and statistically valid analyses

bayesian estimation of uncertainty in runoff prediction and the value of data an application of the glue approach this paper addresses the problem of evaluating the predictive uncertainty of topmodel using the bayesian generalised likelihood uncertainty estimation glue methodology in an application to the small ringelbach research catchment in the vosges france the wide range of parameter sets giving acceptable simulations is demonstrated and uncertainty bands are presented based on different likelihood measures it is shown how the distributions of predicted discharges are non gaussian and vary in shape through time and with discharge updating of the likelihood weights using bayes equation is demonstrated after each year of record and it is shown how the additional data can be evaluated in terms of the way they constrain the uncertainty bands

the small dispersion limit of the korteweg de vries equation iii in parts i and ii we have derived explicit formulas for the distribution limit u of the solution of the kdv equation as the coefficient of uxxx tends to zero this formula contains n parameters 1 n whose values as well as whose number depends on x and t in section 4 we have shown that for t tb n 1 and the value of was determined in section 5 we have shown that the parameters i satisfy a nonlinear system of partial differential equations in part iii section 6 we show that for t large n 3 and we determine the asymptotic behavior of 1 2 3 and of u and u2 for t large the explicit formulas show that u and u2 are o t 1 and o t 2 respectively see formulas 6 2 and 6 24 in section 7 we study initial data whose value tends to zero as x and to 1 as x if one accepts some plausible guesses about the behavior of solutions with such initial data we derive an explicit formula for the solution and determine the large scale asymptotic behavior of the solution the function s is expressible in terms of complete elliptic integrals a similar formula is derived for u2 in section 8 we indicate how to extend the treatment of this series of papers to multihumped but still negative initial data

geometry of the modulational instability iii homoclinic orbits for the periodic sine gordon equation in this paper the homoclinic geometric structure of the integrable sine gordon equation under periodic boundary conditions is developed specifically focus is given to orbits homoclinic to n tori simple examples of such homoclinic orbits are constructed and a physical interpretation of these states is given a labeling is provided which identifies and catalogues all such orbits these orbits are related in a one to one manner to linearized instabilities explicit formulas for all homoclinic orbits are given in terms of backlund transformations

on constraining the predictions of a distributed model the incorporation of fuzzy estimates of saturated areas into the calibration process distributed hydrological models are generally overparameterized resulting in the possibility of multiple parameterizations from many areas of the parameter space providing acceptable fits to observed data in this study topmodel parameterizations are conditioned on discharges and then further conditioned on estimates of saturated areas derived from ers i synthetic aperture radar sar images combined with the in tan topographic index and compared to ground truth saturation measurements made in one small subcatchment the uncertainty associated with the catchment wide predictions of saturated area is explicitly incorporated into the conditioning through the weighting of estimates within a fuzzy set framework the predictive uncertainty associated with the parameterizations is then assessed using the generalized likelihood uncertainty estimation glue methodology it is shown that despite the uncertainty in the predictions of saturated area the methodology can reject many previously acceptable parameterizations with the consequence of a marked reduction in the acceptable range of a catchment average transmissivity parameter and of improved predictions of some discharge events

forced lattice vibrations part ii this is the first part of a two part series on forced lattice vibrations in which a semi infinite lattice of one dimensional particles xn n 1 is driven from one end by a particle x0 this particle undergoes a given periodically perturbed uniform motion x0 t at h yt where a and are constants and h has period 2 for a wide variety of restoring forces f i e f 0 numerical calculations indicate the existence of a sequence of thresholds 1 1 a h f 2 2 a h f k k a h f k 0 as k if k k 1 a k phase wave that is well described by the wave form emerges and travels through the lattice the goal of this series is to describe the emergence and calculate some properties of these wave forms in part i the authors first consider the case where f x ex i e toda forces but h is arbitrary and show how to compute a basic diagnostic see j formula 1 26 for the system in terms of the solution of an associated scalar riemann hilbert problem once a certain finite set of numbers is known in another direction the authors consider the case where f x is restoring but arbitrary and h is small here the authors prove a general result asserting that if there exists a sufficiently ample family of traveling wave solutions of the doubly infinite lattice then it is possible to construct time periodic k phase wave solutions with asymptotics in n of type iii for the driven system i in part ii the authors prove that sufficiently ample families of traveling wave solutions of the system iv exist in the cases 1 and 1 2 for general restoring forces f in the case with toda forces f x ex the authors prove that sufficiently ample families of traveling wave solutions

spectral instability of the semiclassical zakharov shabat eigenvalue problem abstract we present some brief numerical results indicating that in the semiclassical limit the zakharov shabat eigenvalue problem exhibits severe spectral instability and that small changes in the potential can result in large changes in the spectrum

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

polynomial methods for structure from motion the authors analyze the limitations of structure from motion sfm methods presented in the literature and propose the use of a polynomial system of equations with the unit quaternions representing rotation to recover sfm under perspective projection the authors combine the equations by the method of resultants with the maxima symbolic algebra system reducing the system to a single polynomial its real roots are then found with sturm sequences since this system has multiple solutions a hypothesize and verify scheme is used to eliminate incorrect ones the scheme diminishes the sensitivity of using polynomial equations the authors examine the effect of different rotation axes and angles on sfm accuracy and compare the performance of the algorithm to a few earlier approaches generally it is found that a large amount of motion is the most important factor in getting good sfm accuracy

a multiple criteria decision support system for testing integrated environmental models abstract spatial models of ecological and hydrological processes are widely used tools for studying natural systems over large areas however these models lack specific mechanisms for reporting output uncertainty contributed by model structure and so testing their suitability for studying a large range of problems is difficult this paper describes a method of evaluating the uncertainty contributed by underlying assumptions used in constructing integrated environmental models from two or more sub models that were developed for different purposes integrated environmental models are typically constructed from many individual process based models conflicting assumptions between these sub models e g spatial scale differences are easily overlooked during model development and application this semantic error cannot be predicted prior to simulation as it may only emerge through the interaction of sub models applied to a particular set of data used to drive a simulation model agreement is proposed and demonstrated as a way to detect problems of model integration at the state variable level within an integrated ecosystem model this model agreement is then propagated to model response variables using multiple criteria to examine their sensitivity predictability and synchronicity to the measured uncertainty in state variables these three properties are combined under fuzzy logic in order to provide decision support on where for a given time during simulation the sub models agree on a particular response variable this paper describes the details of the approach and its application using an existing integrated environmental model the results show that for a given set of model inputs and application integrated environmental models may have spatially variable levels of agreement at the sub model level the results using rhessysd a spatially integrated ecosystem hydrology model indicate that semantic error in estimates of plant available soil moisture are consistent with observations of the need for resetting events such as flooding to initialize the model to a point where further simulation results can be trusted these results suggest that a dynamic selection of sub models may be warranted given a reasonable method of determining sub model disagreement during simulation fuzzy set theory may be a useful tool in arriving at such a model selection process as it allows for a relatively straightforward synthesis of numerous model evaluation criteria with a large quantity of output from the model

efficient prediction uncertainty approximation in the calibration of environmental simulation models 1 this paper is aimed at improving the efficiency of model uncertainty analyses that are conditioned on measured calibration data specifically the focus is on developing an alternative methodology to the generalized likelihood uncertainty estimation glue technique when pseudolikelihood functions are utilized instead of a traditional statistical likelihood function we demonstrate for multiple calibration case studies that the most common sampling approach utilized in glue applications uniform random sampling is much too inefficient and can generate misleading estimates of prediction uncertainty we present how the new dynamically dimensioned search dds optimization algorithm can be used to independently identify multiple acceptable or behavioral model parameter sets in two ways dds could replace random sampling in typical applications of glue more importantly we present a new practical and efficient uncertainty analysis methodology called dds approximation of uncertainty dds au that quantifies prediction uncertainty using prediction bounds rather than prediction limits results for 13 14 26 and 30 parameter calibration problems show that dds au can be hundreds or thousands of times more efficient at finding behavioral parameter sets than glue with random sampling results for one example show that for the same limited computational effort dds au prediction bounds can simultaneously be smaller and contain more of the measured data in comparison to glue prediction bounds we also argue and then demonstrate that within the glue framework when behavioral parameter sets are not sampled frequently enough latin hypercube sampling does not offer any improvements over simple random sampling

a new bayesian recursive technique for parameter estimation 1 the performance of any model depends on how well its associated parameters are estimated in the current application a localized bayesian recursive estimation lobare approach is devised for parameter estimation the lobare methodology is an extension of the bayesian recursive estimation bare method it is applied in this paper on two different types of models an artificial intelligence ai model in the form of a support vector machine svm application for forecasting soil moisture and a conceptual rainfall runoff crr model represented by the sacramento soil moisture accounting sac sma model support vector machines based on statistical learning theory slt represent the modeling task as a quadratic optimization problem and have already been used in various applications in hydrology they require estimation of three parameters sac sma is a very well known model that estimates runoff it has a 13 dimensional parameter space in the lobare approach presented here bayesian inference is used in an iterative fashion to estimate the parameter space that will most likely enclose a best parameter set this is done by narrowing the sampling space through updating the parent bounds based on their fitness these bounds are actually the parameter sets that were selected by bare runs on subspaces of the initial parameter space the new approach results in faster convergence toward the optimal parameter set using minimum training calibration data and fewer sets of parameter values the efficacy of the localized methodology is also compared with the previously used bare algorithm

the semiclassical limit of the defocusing nls hierarchy we establish the semiclassical limit of the one dimensional defocusing cubic nonlinear schrodinger nls equation complete integrability is exploited to obtain a global characterization of the weak limits of the entire nls hierarchy of conserved densities as the field evolves from reflectionless initial data under all the associated commuting flows consequently this also establishes the zero dispersion limit of the modified korteweg de vries equation that resides in that hierarchy we have adapted and clarified the strategy introduced by lax and levermore to study the zero dispersion limit of the korteweg de vries equation expanding it to treat entire integrable hierarchies and strengthening the limits obtained a crucial role is played by the convexity of the underlying log determinant with respect to the times associated with the commuting flows c 1999 john wiley sons inc

the semiclassical modified nonlinear schrodinger equation i modulation theory and spectral analysis abstract we study an integrable modification of the focusing nonlinear schrodinger equation from the point of view of semiclassical asymptotics in particular i we establish several important consequences of the mixed type limiting quasilinear system including the existence of maps that embed the limiting forms of both the focusing and defocusing nonlinear schrodinger equations into the framework of a single limiting system for the modified equation ii we obtain bounds for the location of the discrete spectrum for the associated spectral problem that are particularly suited to the semiclassical limit and that generalize known results for the spectrum of the nonselfadjoint zakharov shabat spectral problem and iii we present a multiparameter family of initial data for which we solve the associated spectral problem in terms of special functions for all values of the semiclassical scaling parameter we view our results as part of a broader project to analyze the semiclassical limit of the modified nonlinear schrodinger equation via the noncommutative steepest descent procedure of deift and zhou and we also present a selfcontained development of a riemann hilbert problem of inverse scattering that differs from those given in the literature and that is well adapted to semiclassical asymptotics

effective and efficient global optimization for conceptual rainfall runoff models the successful application of a conceptual rainfall runoff crr model depends on how well it is calibrated despite the popularity of crr models reports in the literature indicate that it is typically difficult if not impossible to obtain unique optimal values for their parameters using automatic calibration methods unless the best set of parameters associated with a given calibration data set can be found it is difficult to determine how sensitive the parameter estimates and hence the model forecasts are to factors such as input and output data error model error quantity and quality of data objective function used and so on results are presented that establish clearly the nature of the multiple optima problem for the research crr model sixpar these results suggest that the crr model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets next the performance of three existing global search procedures are evaluated on the model sixpar finally a powerful new global optimization procedure is presented entitled the shuffled complex evolution sce ua method which was able to consistently locate the global optimum of the sixpar model and appears to be capable of efficiently and effectively solving the crr model optimization problem

some remarks on a wkb method for the nonselfadjoint zakharov shabat eigenvalue problem with analytic potentials and fast phase abstract a formal method for approximating eigenvalues of the nonselfadjoint zakharov shabat eigenvalue problem in the semiclassical scaling is described analyticity of the potential is assumed and appears to be crucial the method involves finding appropriate paths between pairs of complex turning points and reproduces the y shaped spectra observed by bronski physica d 97 1996 376 an application to all optical ultrashort pulse generation is briefly described and the kind of tools that are required to make the results rigorous are indicated

stochastic capture zone delineation within the generalized likelihood uncertainty estimation methodology conditioning on head observations a stochastic methodology to evaluate the predictive uncertainty in well capture zones in heterogeneous aquifers with uncertain parameters is presented the approach is based on the generalized likelihood uncertainty estimation methodology the hydraulic conductivity is modeled as a random space function allowing for the uncertainty that stems from the imperfect knowledge of the parameters of the correlation structure parameters are sampled from prior distributions and are used for the generation of a large number of hydraulic conductivity fields which are subsequently used to solve the groundwater flow equation a likelihood is calculated for every simulation based on some goodness of fit measure between simulated heads and available observations using inverse particle tracking a capture zone is determined which is assigned the likelihood calculated for that particular simulation statistical analysis of the ensemble of all simulations enables the predictive uncertainty of the well capture zones to be defined results are presented for a hypothetical test case and different likelihood definitions used in the conditioning process the results show that the delineated capture zones are most sensitive to the mean hydraulic conductivity and the variance whereas the integral scale of the variogram is the parameter with the smallest influence for all likelihood measures the prior uncertainty is reduced considerably by introducing the observation heads but the reduction is most effective for the very selective likelihood definition the method presented can be used in real applications to quantify the uncertainty in the location and extent of well capture zones when little or no information is available about the hydraulic properties through the conditioning on head observations

on the semi classical limit for the focusing nonlinear schrodinger equation sensitivity to analytic properties of the initial data we present the results of a large number of careful numerical experiments carried out to investigate the way that the solution of the integrable focusing nonlinear schroodinger equation with fixed initial data when taken to be close to the semiclassical limit depends on analyticity properties of the data in particular we study a family of initial data that have complex singularities at an adjustable distance from the real axis we also make use of a simple relation that provides the exact solution at the centre of the wave field of the elliptic quasilinear system that appears formally as a leading order model for the semi classical dynamics among other things we conclude that the semi classical limit cannot be expected to be continuous with respect to the initial data even for real analytic data if there are certain complex singularities present we argue that in order to have well posedness of the semiclassical limit the correct setting is a physically relevant space of functions with compactly supported fourier transforms

practical identifiability analysis of large environmental simulation models large environmental simulation models are usually overparameterized with respect to given sets of observations this results in poorly identifiable or nonidentifiable model parameters for small models plots of sensitivity functions have proven to be useful for the analysis of parameter identifiability for models with many parameters however near linear dependence of sensitivity functions can no longer be assessed graphically in this paper a systematic approach for tackling the parameter identifiability problem of large models based on local sensitivity analysis is presented the calculation of two identifiability measures that are easy to handle and interpret is suggested the first accounts for the sensitivity of model results to single parameters and the second accounts for the degree of near linear dependence of sensitivity functions of parameter subsets it is shown how these measures provide identifiability diagnosis for parameter subsets how they are able to guide the selection of identifiable parameter subsets for parameter estimation and how they facilitate the interpretation of the correlation matrix of the parameter estimate with respect to parameter identifiability in addition we show how potential bias of the parameter estimates due to a priori fixing of some of the parameters can be analyzed finally two case studies are presented in order to illustrate the suggested approach

the small dispersion limit of the korteweg de vries equation ii in part i the scattering transform method is used to study the weak limit of solutions to the initial value problem for the korteweg devries kdv equation as the dispersion tends to zero in that limit the associated schrodinger operator becomes semiclassical so the exact scattering data is replaced by its corresponding wkb expressions only nonpositive initial data are considered in that case the limiting reflection coefficient vanishes the explicit solution of kay and moses for the reflectionless inverse transform is then analyzed and the weak limit valid for all time is characterized by a quadratic minimum problem with constraints this minimum problem is reduced to a riemann hilbert problem in function theory in parts ii and iii we use function theoretical methods to solve the riemann hilbert problem in terms of solutions to an auxiliary initial value problem the weak limit satisfies the kdv equation with the dispersive term dropped until its derivatives become infinite up to that time the weak limit is a strong l2 limit at later times the weak limit is locally described by whitham s averaged equations or more generally by the equations found by flaschka et al using multiphase averaging for large times behavior of the weak limit is studied directly from the minimum problem

large oscillations arising in a dispersive numerical scheme abstract we study the oscillatory behavior that arises in solutions of a dispersive numerical scheme for the hopf equation whenever the classical solution of the equation develops a singularity modulation equations are derived that describe period two oscillations so long as the solution of those equations takes values for which the equations are hyperbolic however those equations have an elliptic region that may be entered by its solutions in a finite time after which the corresponding period two oscillations are seen to break down this kind of phenomenon has not been observed for integrable schemes the generation and propagation of period two oscillations are asymptotically analyzed and a matching formula is found for the transition between oscillatory and nonoscillatory regions modulation equations are also presented for period three oscillations numerical experiments are carried out that illustrate our analysis

macroscopic lattice dynamics abstract fully nonlinear modulation equations are presented that govern the slow evolution of single phase harmonic wavetrains under a large family of spatially discrete nonintegrable flows among which is the discrete nonlinear schrodinger equation dnls these modulation equations are a pair of partial differential equations in conservation form that are hyperbolic for some data and elliptic for other data in some cases these equations are capable of dynamically changing type from hyperbolic to elliptic a phenomenon that has been associated with the modulational instability of the underlying wavetrain by putting the modulation equations in riemann invariant form one can select initial data that avoid this dynamic change of type numerical experiments demonstrating the theoretical results are presented

ensemble evaluation of hydrological model hypotheses it is demonstrated for the first time how model parameter structural and data uncertainties can be accounted for explicitly and simultaneously within the generalized likelihood uncertainty estimation glue methodology as an example application 72 variants of a single soil moisture accounting store are tested as simplified hypotheses of runoff generation at six experimental grassland field scale lysimeters through model rejection and a novel diagnostic scheme the fields designed as replicates exhibit different hydrological behaviors which yield different model performances for fields with low initial discharge levels at the beginning of events the conceptual stores considered reach their limit of applicability conversely one of the fields yielding more discharge than the others but having larger data gaps allows for greater flexibility in the choice of model structures as a model learning exercise the study points to a leaking of the fields not evident from previous field experiments it is discussed how understanding observational uncertainties and incorporating these into model diagnostics can help appreciate the scale of model structural error

using geometric distance fits for 3 d object modeling and recognition addresses the problems of automatically constructing algebraic surface models from sets of 2d and 3d images and using these models in pose computation motion and deformation estimation and object recognition we propose using a combination of constrained optimization and nonlinear least squares estimation techniques to minimize the mean squared geometric distance between a set of points or rays and a parameterized surface in modeling tasks the unknown parameters are the surface coefficients while in pose and deformation estimation tasks they represent the transformation which maps the observer s coordinate system onto the modeled surface s own coordinate system we have applied this approach to a variety of real range computerized tomography and video images

the behavior of the weyl function in the zero dispersion kdv limit the moment formulas that globally characterize the zero dispersion limit of the korteweg devries kdv equation are known to be expressed in terms of the solution of a maximization problem here we establish a direct relation between this maximizer and the zero dispersion limit of the logarithm of the jost functions associated with the inverse spectral transform all the kdv conserved densities are encoded in the spatial derivative of these functions known as weyl functions we show the weyl functions are densities of measures that converge in the weak sense to a limiting measure this limiting measure encodes all of the weak limits of the kdv conserved densities moreover we establish the weak limit of spectral measures associated with the dirichlet problem

a note on a capillarity model and the nonlinear schrodinger equation a system of two equations governing the irrotational flow of a capillary fluid is shown for a particular class of free energy functions to reduce to a nonlinear schrodinger equation

a markov chain monte carlo scheme for parameter estimation and inference in conceptual rainfall runoff modeling a fully bayesian approach to parameter estimation and inference in conceptual rainfall runoff models crrms is presented computations are performed using a markov chain monte carlo mcmc method based on the metropolis hastings algorithm single site and block updating schemes are used for model parameters subject to nonnegativity restrictions as well as interval equality and order constraints diagnostics for the convergence of the markov chain and crrm assessment are also considered the mcmc approach produces samples from the joint posterior distribution of the model parameters this provides more information than single point estimates and avoids the need to use a normal approximation to the posterior as the basis for inference the methodology is demonstrated using an eight parameter conceptual rainfall runoff model and two case studies from southeastern australia the first case study considers a watershed with high runoff yield over a 12 year period the second case study considers a watershed with low yield over a 17 year period the results indicate that 1 bayesian methods provide an objective framework for model criticism and choice 2 the proposed strategies for handling constraints on model parameters are effective 3 the model parameters are sensitive to likelihood function selection 4 the conventional approach of using a power transformation and an autoregressive process to stabilize error variance and model dependence in the residuals may have limited success and 5 some care is required in the implementation of the mcmc approach and reliable results will be difficult to obtain when crrm complexity exceeds the limitations of the rainfall runoff data at hand a key finding is that the mcmc scheme presented herein provides a powerful means of identifying specific inadequacies in the structure of crrms

the n soliton of the focusing nonlinear schrodinger equation for n large we present a detailed analysis of the solution of the focusing nonlinear schrodinger equation with initial condition x 0 n sech x in the limit n 1 we begin by presenting new and more accurate numerical reconstructions of the n soliton by inverse scattering numerical linear algebra for n 5 10 20 and 40 we then recast the inverse scattering problem as a riemann hilbert problem and provide a rigorous asymptotic analysis of this problem in the large n limit for those x t where results have been obtained by other authors we improve the error estimates from o n 1 3 to o n 1 we also analyze the fourier power spectrum in this regime and relate the results to the optical phenomenon of supercontinuum generation we then study the n soliton for values of x t where analysis has not been carried out before and we uncover new phenomena the main discovery of this paper is the mathematical mechanism for a secondary caustic phase transition which turns out to differ from the mechanism that generates the primary caustic the mechanism for the generation of the secondary caustic depends essentially on the discrete nature of the spectrum for the n soliton and more significantly cannot be recovered from an analysis of an ostensibly similar riemann hilbert problem in the conditions of which a certain formal continuum limit is taken on an ad hoc basis

toward a generalization of the topmodel concepts topographic indices of hydrological similarity preliminary studies of the application of topmodel to the 36 ha ringelbach catchment suggested that the original form of exponential transmissivity function leading to the in a tan topographic index and first order hyperbolic base flow recession curve is not appropriate to this catchment two alternative forms of topographic index and soil topographic index are developed based on parabolic and linear transmissivity functions leading to the more frequently observed second order hyperbolic and exponential recession curves respectively it is shown how these can be used in the same way as the original to relate catchment average water table depths to local water table depths so that patterns of saturation can be evaluated two companion ambroise et al this issue freer et al this issue papers show how the new parabolic index is used in the prediction of ringelbach discharges and how the limitations of the model are reflected in the estimated predictive uncertainties using the generalised likelihood uncertainty estimation glue approach

on recognizing and positioning curved 3 d objects from image contours an approach for explicitly relating the shape of image contours to models of curved three dimensional objects is presented this relationship is used for object recognition and positioning object models consist of collections of parametric surface patches and their intersection curves this includes nearly all representations used in computer aided geometric design and computer vision the image contours considered are the projections of surface discontinuities and occluding contours elimination theory provides a method for constructing the implicit equation of these contours for an object observed under orthographic or perspective projection this equation is parameterized by the object s position and orientation with respect to the observer determining these parameters is reduced to a fitting problem between the theoretical contour and the observed data points the proposed approach readily extends to parameterized models it has been implemented for a simple world composed of various surfaces of revolution and tested on several real images

dispersive approximations in fluid dynamics we have compared the results of a von neumann richtmyer calculation with the weak limit of calculations performed by von neumann s original method although there are discernible differences they are surprisingly small we analyze von newmann s algorithm for solving the initial value problem for the lagrangian equations of compressible flow

semiclassical limit of focusing nls for a family of square barrier initial data the small dispersion limit of the focusing nonlinear schrodinger equation nls exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales the non self adjoint scattering problem and ill posed limiting whitham equations associated to focusing nls make rigorous asymptotic results difficult previous studies have focused on special classes of analytic initial data for which the limiting elliptic whitham equations are wellposed in this paper we consider another exactly solvable family of initial data the family of square barriers 0 x q l l for real amplitudes q using riemann hilbert techniques we obtain rigorous pointwise asymptotics for the semiclassical limit of focusing nls globally in space and up to an o 1 maximal time in particular we show that the discontinuities in our initial data regularize by the immediate generation of genus one oscillations emitted into the support of the initial data to the best of our knowledge this is the first case in which the genus structure of the semiclassical asymptotics for focusing nls have been calculated for nonanalytic initial data 2013 wiley periodicals inc

the wentzel kramers brillouin approximation of semiclassical eigenvalues of the zakharov shabat problem the wkb approximation of semiclassical eigenvalues of the non self adjoint zakharov shabat problem is a standard element in the theory of the integrable focusing nonlinear schrodinger equation this approximation is based on a reformulation of the eigenvalue problem as the eigenvalue problem for a self adjoint schrodinger operator with a correction term that depends on the spectral parameter the approximation results from neglecting the correction term we perform a numerical experiment which gives new evidence to support the validity of this procedure in the context of the semiclassical limit problem for the focusing nonlinear schrodinger equation in particular our results suggest that the rate of convergence of the approximate eigenvalues to the true ones is of the order of the square of the small parameter this information is relevant to the task of rigorously incorporating this approximation into the asymptotic analysis of the singular limit for the focusing nonlinear schrodinger equation

bayesian analysis for uncertainty estimation of a canopy transpiration model 1 a bayesian approach was used to fit a conceptual transpiration model to half hourly transpiration rates for a sugar maple acer saccharum stand collected over a 5 month period and probabilistically estimate its parameter and prediction uncertainties the model used the penman monteith equation with the jarvis model for canopy conductance this deterministic model was extended by adding a normally distributed error term this extension enabled using markov chain monte carlo simulations to sample the posterior parameter distributions the residuals revealed approximate conformance to the assumption of normally distributed errors however minor systematic structures in the residuals at fine timescales suggested model changes that would potentially improve the modeling of transpiration results also indicated considerable uncertainties in the parameter and transpiration estimates this simple methodology of uncertainty analysis would facilitate the deductive step during the development cycle of deterministic conceptual models by accounting for these uncertainties while drawing inferences from data

invariant descriptors for 3d object recognition and pose invariant descriptors are shape descriptors that are unaffected by object pose by perspective projection or by the intrinsic parameters of the camera these descriptors can be constructed using the methods of invariant theory which are briefly surveyed a range of applications of invariant descriptors in 3d model based vision is demonstrated first a model based vision system that recognizes curved plane objects irrespective of their pose is demonstrated curves are not reduced to polyhedral approximations but are handled as objects in their own right models are generated directly from image data once objects have been recognized their pose can be computed invariant descriptors for 3d objects with plane faces are described all these ideas are demonstrated using images of real scenes the stability of a range of invariant descriptors to measurement error is treated in detail

time varying sensitivity analysis clarifies the effects of watershed model formulation on model behavior 1 lumped rainfall runoff models are widely used for flow prediction but a long recognized need exists for diagnostic tools to determine whether the process level behavior of a model aligns with the expectations inherent in its formulation to this end we develop a comprehensive exploration of dominant parameters in the hymod hbv and sacramento soil moisture accounting sac sma model structures model controls are isolated using time varying sobol sensitivity analysis for twelve mopex watersheds in the eastern united states over a 10 year period sensitivity indices are visualized along gradients of observed precipitation and streamflow to identify key behavioral differences between the three models and to connect these back to the models underlying assumptions results indicate that the models dominant parameters strongly depend on time varying hydroclimatic conditions parameters associated with surface processes such as evapotranspiration and runoff generally dominate under dry conditions when high evaporative fluxes are required for accurate simulation parameters associated with routing processes typically dominate under high flow conditions when performance depends on the timing of flow events the results highlight significant inter model differences in performance controls even in cases where the models share similar process formulations the dominant parameters identified can be counterintuitive even these simple models represent complex nonlinear systems and the links between formulation and behavior are difficult to discern a priori as complexity increases scrutinizing the links between model formulation and behavior becomes an important diagnostic approach particularly in applications such as predictions under change where dominant model controls will shift under hydrologic extremes

a generalized grid connectivity based parameterization for subsurface flow model calibration 1 we develop a novel method of parameterization for spatial hydraulic property characterization to mitigate the challenges associated with the nonlinear inverse problem of subsurface flow model calibration the parameterization is performed by the projection of the estimable hydraulic property field onto an orthonormal basis derived from the grid connectivity structure the basis functions represent the modal shapes or harmonics of the grid are defined by a modal frequency and converge to special cases of the discrete fourier series under certain grid geometries and boundary assumptions therefore hydraulic property updates are performed in the spectral domain and merge with fourier analysis in ideal cases dependence on the grid alone implies that the basis may characterize any grid geometry including corner point and unstructured is model independent and is constructed off line and only once prior to flow data assimilation we apply the parameterization in an adaptive multiscale model calibration workflow for three subsurface flow models several different grid geometries are considered in each case the prior hydraulic property model is updated using a parameterized multiplier field that is superimposed onto the grid and assigned an initial value of unity at each cell the special case corresponding to a constant multiplier is always applied through the constant basis function higher modes are adaptively employed during minimization of data misfit to resolve multiscale heterogeneity in the geomodel the parameterization demonstrates selective updating of heterogeneity at locations and spatial scales sensitive to the available data otherwise leaving the prior model unchanged as desired

semiclassical eigenvalue distribution of the zakharov shabat eigenvalue problem abstract in this paper we consider the semi classical limit of the non self adjoint zakharov shabat eigenvalue problem we conduct a series of careful numerical experiments which provide strong evidence that the number of eigenvalues scales like 1 just as in the self adjoint case and that the eigenvalues appear to approach a limiting curve one general choice of potential functions produces a y shaped spectrum we give an asymptotic argument which predicts a critical value for the phase for which the straight line spectra bifurcates to produce the y shaped spectra this asymptotic prediction agrees quite well with numerical experiments the asymptotic argument also predicts a symmetry breaking in the eigenfunctions which we are able to observe numerically we also show that the number of eigenvalues living away from the real axis for a restricted class of potentials is bounded by c 1 where c is an explicit constant a complete theory of the shape of the eigenvalue curve and a general bound on the number of eigenvalues is still lacking

robust algorithms for object localization model based localization the task of estimating an object s pose from sensed and corresponding model features is a fundamental task in machine vision exact constant time localization algorithms have been developed for the case where the sensed features and the model features are the same type still it is not uncommon for the sensed features and the model features to be of different types i e sensed data points may correspond to model faces or edges previous localization approaches have handled different model and sensed features of different types via sampling and synthesizing virtual features to reduce the problem of matching features of dissimilar types to the problem of matching features of similar types unfortunately these approaches may be suboptimal because they introduce artificial errors other localization approaches have reformulated object localization as a nonlinear least squares problem where the error is between the sensed data and model features in image coordinates the euclidean image error metric unfortunately all of the previous approaches which minimized the euclidean image error metric relied on gradient descent methods to find the global minima and gradient descent methods may suffer from problems of local minima in this paper we describe an exact efficient solution to the nonlinear least squares minimization problem based upon resultants linear algebra and numerical techniques on a sparc 20 our localization algorithm runs in a few microseconds for rectilinear polygonal models a few milliseconds for generic polygonal models and one second for generalized polygonal models models composed of linear edges and circular arcs

recognizing solid objects by alignment with an image in this paper we consider the problem of recognizing solid objects from a single two dimensional image of a three dimensional scene we develop a new method for computing a transformation from a three dimensional model coordinate frame to the two dimensional image coordinate frame using three pairs of model and image points we show that this transformation always exists for three noncollinear points and is unique up to a reflective ambiguity the solution method is closed form and only involves second order equations we have implemented a recognition system that uses this transformation method to determine possible alignments of a model with an image each of these hypothesized matches is verified by comparing the entire edge contours of the aligned object with the image edges using the entire edge contours for verification rather than a few local feature points reduces the chance of finding false matches the system has been tested on partly occluded objects in highly cluttered scenes

least squares matching problems abstract a large class of matching problems can be thought of in the following way one is given a group g which acts on a riemannian manifold and one is given two points x 1 and x 2 in the manifold the problem is to find g g such that d g x 1 x 2 is as small as possible if the group has finite cardinality this is a combinatorial optimization problem whereas if g is a lie group one can use the calculus to obtain necessary conditions our main results establish circumstances under which one can relax the combinatorial problem to an appropriate lie group problem and then solve it by the method of steepest descent an interesting class of applications involves embedding the permutation group on n letters in the orthogonal group o n with the latter acting on r n n 1 2 via a symmetricized tensor product the convergence properties of the descent equation which arises in this way are analyzed in some detail

estimating the uncertain mathematical structure of a water balance model via bayesian data assimilation 1 when constructing a hydrological model at the macroscale e g watershed scale the structure of this model will inherently be uncertain because of many factors including the lack of a robust hydrological theory at that scale in this work we assume that a suitable conceptual model structure for the hydrologic system has already been determined that is the system boundaries have been specified the important state variables and input and output fluxes to be included have been selected the major hydrological processes and geometries of their interconnections have been identified and the continuity equation mass balance has been assumed to hold the remaining structural identification problem that remains then is to select the mathematical form of the dependence of the output on the inputs and state variables so that a computational model can be constructed for making simulations and or predictions of the system input state output behavior the conventional approach to this problem is to preassume some fixed and possibly erroneous mathematical forms for the model output equations we show instead how bayesian data assimilation can be used to directly estimate construct the form of these mathematical relationships such that they are statistically consistent with macroscale measurements of the system inputs outputs and if available state variables the resulting model has a stochastic rather than deterministic form and thereby properly represents both what we know our certainty and what we do not know our uncertainty about the underlying structure and behavior of the system further the bayesian approach enables us to merge prior beliefs in the form of preassumed model equations with information derived from the data to construct a posterior model as a consequence in regions of the model space for which observational data are available the errors in preassumed mathematical form of the model can be corrected improving model performance for regions where no such data are available the prior theoretical assumptions about the model structure and behavior will dominate the approach entitled bayesian estimation of structure is used to estimate water balance models for the leaf river basin mississippi at annual monthly and weekly time scales conditioned on the assumption of a simple single state variable conceptual model structure inputs to the system are uncertain observed precipitation and potential evapotranspiration and outputs are estimated probability distributions of actual evapotranspiration and streamflow discharge results show that the models estimated for the annual and monthly time scales perform quite well however model performance deteriorates for the weekly time scale suggesting limitations in the assumed form of the conceptual model

spectral instability for some schrodinger operators we show that the condition numbers of isolated eigenvalues of typical non self adjoint differential operators such as the harmonic oscillator may be extremely large we describe a stable procedure for computing the condition numbers for schrodinger operators in one dimension and apply it to the complex resonances of a typical operator with a dilation analytic potential

morse and melnikov functions for nls pde s the theory of the focusing nls equation under periodic boundary conditions together with the floquet spectral theory of its associated zakharov shabat linear operator hat l is developed in sufficient detail for later use in studies of perturbations of the nls equation counting lemmas for the non selfadjoint operator hat l are established which control its spectrum and show that all of its eccentricities are finite in number and must reside within a finite discd in the complex eigenvalue plane the radius of the discd is controlled by theh 1 norm of the potential overrightarrow q for this integrable nls hamiltonian system unstable tori are identified and backlund transformations are then used to construct global representations of their stable and unstable manifolds whiskered tori for the nls pde the floquet discriminant delta lambda overrightarrow q is used to introduce a natural sequence of nls constants of motion f j overrightarrow q equiv delta lambda lambda j c overrightarrow q overrightarrow q where denotes thej th critical point of the floquet discriminant a taylor series expansion of the constants f j overrightarrow q with explicit representations of the first and second variations is then used to study neighborhoods of the whiskered tori in particular critical tori with hyperbolic structure are identified through the first and second variations of f j overrightarrow q which themselves are expressed in terms of quadratic products of eigenfunctions of hat l the second variation permits identification within the disc d of important bifurcations in the spectral configurations of the operator hat l the constant f j overrightarrow q as the height of the floquet discriminant over the critical point admits a natural interpretation as a morse function for nls isospectral level sets this morse interpretation is studied in some detail it is valid globally for the infinite tail f j overrightarrow q j n which is associated with critical points outside the discd within this disc the interpretation is only valid locally with the same obstruction to its global validity as to a global ordering of the spectrum nevertheless this local morse theory together with the backlund representations of the whiskered tori produces extremely clear pictures of the stratification of nls invariant sets near these whiskered tori pictures which are useful in the study of perturbations of nls finally a natural connection is noted between the constants f j overrightarrow q of the integrable theory and melnikov functions for the theory of perturbations of the nls equation this connection generates a simple but general representations of the melnikov functions

estimating epistemic and aleatory uncertainties during hydrologic modeling an information theoretic approach 1 with growing interest in understanding the magnitudes and sources of uncertainty in hydrological modeling the difficult problem of characterizing model structure adequacy is now attracting considerable attention here we examine this problem via a model structureindependent approach based in information theory in particular we a discuss how to assess and compute the information content in multivariate hydrological data b present practical methods for quantifying the uncertainty and shared information in data while accounting for heteroscedasticity c show how these tools can be used to estimate the best achievable predictive performance of a model for a system given the available data and d show how model adequacy can be characterized in terms of the magnitude and nature of its aleatory uncertainty that cannot be diminished and is resolvable only up to specification of its density and its epistemic uncertainty that can in principle be suitably resolved by improving the model an illustrative modeling example is provided using catchment scale data from three river basins the leaf and chunky river basins in the united states and the chuzhou basin in china our analysis shows that the aleatory uncertainty associated with making catchment simulations using this data set is significant 50 further estimated epistemic uncertainties of the hymod sac sma and xinanjiang model hypotheses indicate that considerable room for model structural improvements remain

on dispersive difference schemes i etude du comportement oscillatoire et de la convergence faible des solutions des approximations aux differences dispersives de u t 1 2 u 2 x 0

effect of different uncertainty sources on the skill of 10 day ensemble low flow forecasts for two hydrological models the aim of this paper is to investigate the effect of uncertainty originating from model inputs parameters and initial conditions on 10 day ensemble low flow forecasts two hydrological models namely gr4j and hbv are applied to the moselle river and performance in the calibration validation and forecast periods and the effect of different uncertainty sources on the quality of low flow forecasts are compared the forecasts are generated by using ecmwf meteorological ensemble forecasts as input to the gr4j and hbv models the ensembles each consisting of 51 members provided the uncertainty range for the model inputs the generalised likelihood uncertainty estimation glue approach is used to estimate parameter uncertainty part of the glue behavioural parameter set containing parameters directly linked to storage estimates and the observed discharge on the forecast issue day are used to update the model storages and reflect the uncertainty from the initial conditions the quality of the probabilistic low flow forecasts has been assessed by the relative confidence interval reliability and hit false alarm rates the daily observed low flows are captured by the 90 confidence interval for both models most of the time however the gr4j model usually overestimates low flows whereas hbv is prone to underestimate low flows this is particularly the case if the parameter uncertainty is included in the forecasts the total uncertainty in the gr4j model outputs is higher than in the hbv model outputs the forecasts issued by the hbv model incorporating input uncertainty resulted in the most reliable forecast distribution the number of hits is about equal for both models if only the input uncertainty is considered the parameter uncertainty was the main reason reducing the number of hits the number of false alarms in gr4j model is twice the number of false alarms in hbv when considering all uncertainty sources the results of this study in general showed the parameter uncertainty has the largest effect whereas the input uncertainty had the smallest effect on the medium range low flow forecasts

the korteweg de vries equation with small dispersion higher order lax levermore theory we utilize the inverse scattering transformation to study the rapid oscillations which arise in the solution of the initial value problem begin gathered u t 6u u x in 2 u xxx 0 hfill u left x 0 right v left x right hfill end gathered when 0 we refine the lax levermore theory which gives the weak limit of the solution as 0 by introducing a quantum condition this allows us to calculate the waveform of the local oscillations up to phase shifts when is small

motion from point matches multiple of solutions in this paper we study the multiplicity of solutions of the motion problem given n point matches between two frames how many solutions are there to the motion problem we show that the maximum number of solutions is 10 when 5 point matches are available this settles a question that has been around in the computer vision community for a while we follow two tracks we show that the two approaches are compatible and yield the same result we then describe a computer implementation of the second approach that uses maple a language for symbolic computation the program allows us to compute exactly the solutions for any configuration of 5 points some experiments are described