on two functions of a matrix with positive definite hermitian part let a be a square complex matrix with positive definite hermitian part h a a a h 2 and let f a g a be two functions defined by f a h a 1 1 g a a 1 a h this paper derives

development of a formal likelihood function for improved bayesian inference of ephemeral catchments 1 the application of formal bayesian inferential approaches in hydrologic modeling is often criticized for requiring explicit assumptions to be made about the distribution of the errors via the likelihood function these assumptions can be adequate in some situations but often little attention is paid to the selection of an appropriate likelihood function this paper investigates the application of bayesian methods in modeling ephemeral catchments we consider two modeling case studies including a synthetically generated data set and a real data set of an arid australian catchment the case studies investigate some typical forms of the likelihood function which have been applied widely by previous researchers as well as introducing new implementations aimed at better addressing likelihood function assumptions in dry catchments the results of the case studies indicate the importance of explicitly accounting for model residuals that are highly positively skewed due to the presence of many zeros zero inflation arising from the dry spells experienced by the catchment specifically the form of the likelihood function was found to significantly impact the calibrated parameter posterior distributions which in turn have the potential to greatly affect the uncertainty estimates in each application the likelihood function that explicitly accounted for the nonconstant variance of the errors and the zero inflation of the errors resulted in 1 equivalent or better fits to the observed discharge in both timing and volume 2 superior estimation of the uncertainty as measured by the reliability and sharpness metrics and 3 more linear quantile quantile plots indicating the errors were more closely matched to the assumptions of this form of the likelihood function

on the spatial bandwidth of scattered fields it is shown that the scattered fields are almost space bandlimited functions the effective bandwidth w is introduced and evaluated for a very general scattering system as well as the error made using functions bandlimited to w w for representing the scattered field the effective bandwidth is very simply related to the maximum dimension of the scattering system the error drops to negligible values for modest increases of w compared to w in the case of large scatterers important consequences of the above general results are finally stressed

a limited feedback joint precoding for amplify and forward relaying this paper deals with the practical precoding design for a dual hop downlink with multiple input multiple output mimo amplify and forward relaying first assuming that full channel state information csi of the two hop channels is available a suboptimal dual hop joint precoding scheme i e precoding at both the base station and relay station is investigated based on its structure a scheme of limited feedback joint precoding using joint codebooks is then proposed which uses a distributed codeword selection to concurrently choose two joint precoders such that the feedback delay is considerably decreased finally the joint codebook design for the limited feedback joint precoding system is analyzed and results reveal that independent codebook designs at the base station and relay station using the conventional grassmannian subspace packing method is able to guarantee that the overall performance of the dual hop joint precoding scheme improves with the size of each of the two codebooks simulation results show that the proposed dual hop joint precoding system using distributed codeword selection scheme exhibits a rate or ber performance close to the one using the optimal centralized codeword selection scheme while having lower computational complexity and shorter feedback delay

a fast analysis of scattering and radiation of large microstrip antenna arrays an accurate and efficient method that combines the precorrected fast fourier transform fft method and the discrete complex image method dcim is presented to characterize the scattering and radiation properties of arbitrarily shaped microstrip patch antennas in this method the mixed potential integral equation mpie is discretized in the spatial domain by means of the discrete complex image method the resultant system is solved iteratively using the generalized conjugate residual method gcr and the precorrected fft technique is used to speed up the matrix vector multiplication the precorrected fft eliminates the need to generate and store the usual square impedance matrix and thus leads to a significant reduction in memory requirement and computational cost numerical results are presented for arbitrarily shaped microstrip antenna arrays to demonstrate the accuracy and efficiency of this technique

improved impedance matrix localization method em problems moment method calculations have the well known limitations of requiring excessive storage and execution times for even modestly large electromagnetics problems the impedance matrix localization iml method was introduced as a modification to standard moment method calculations to ease these limitations it utilizes a matrix transformation which effectively changes the basis testing functions into ones resembling traveling waves an improved method that uses an orthogonal transformation to generate standing wave like basis functions is presented here remarkable improvements are achieved in the numerical stability of the method and in its compatibility with iterative solvers furthermore the correspondence of the large elements in this matrix to geometrical theory of diffraction gtd terms is strengthened as is the possibility of further increasing the speed of iterative solutions by constructing preconditioners based on the pattern of nonzero matrix elements

a spectral domain integral equation method utilizing analytically derived characteristic basis functions for the scattering from large faceted objects a novel technique based on a spectral domain integral equation method with analytically derived characteristic basis functions is introduced in this paper it enables us to treat scattering problems from electrically large faceted bodies in a numerically rigorous and computationally efficient manner in terms of both time and memory the analytically derived characteristic basis functions include certain desirable features of the asymptotic schemes and are defined on subdomains that can be electrically large not being bound to the typical discretization size of the conventional method of moments by properly weighting through a galerkin procedure the resulting electric field integral equation the problem is reduced to a matrix equation having dimensions that do not depend on the size of the scatterer but only on its shape electrically large problems can be handled in a computationally efficient manner by using the proposed method since the associated matrix size is relatively small moreover all the reduced matrix elements are calculated in the spectral domain without evaluating any convolution products

music like doa estimation without estimating the number of sources this paper presents a new direction of arrival doa estimation algorithm where doa estimation is realized in the framework of beamforming by introducing a new optimization problem the new optimization problem aims to minimize the variance of the array output subject to retaining the output power at the look direction and precluding a trivial solution the proposed algorithm is equivalent to the multiple signal classification music algorithm in some special cases it is therefore named as the music like method however different from the classical music algorithm the new method is not based on subspace decomposition and the number of sources is hence not required for direction finding this enables us to avoid performance deterioration caused by incorrect source number estimation the effectiveness and advantage of the proposed algorithm is theoretically investigated and computational complexity is also addressed to verify the theoretical analysis computer simulations are implemented and comparisons with other algorithms are made

a note on stewart s theorem for definite matrix pairs abstract let a and b be n n hermitian matrices the matrix pair a b is called definite pair and the corresponding eigenvalue problem ax bx is definite if c a b inf x 1 h a ib x 0 in this note we develop a uniform upper bound for differences of corresponding eigenvalues of two definite pairs and so improve a result which is obtained by g w stewart 2 moreover we prove that this upper bound is a projective metric in the set of n n definite pairs

comparison of joint versus postprocessor approaches for hydrological uncertainty estimation accounting for error autocorrelation and heteroscedasticity the paper appraises two approaches for the treatment of heteroscedasticity and autocorrelation in residual errors of hydrological models both approaches use weighted least squares wls with heteroscedasticity modeled as a linear function of predicted flows and autocorrelation represented using an ar 1 process in the first approach heteroscedasticity and autocorrelation parameters are inferred jointly with hydrological model parameters the second approach is a two stage postprocessor scheme where stage 1 infers the hydrological parameters ignoring autocorrelation and stage 2 conditionally infers the heteroscedasticity and autocorrelation parameters these approaches are compared to a wls scheme that ignores autocorrelation empirical analysis is carried out using daily data from 12 us catchments from the mopex set using two conceptual rainfall runoff models gr4j and hbv under synthetic conditions the postprocessor and joint approaches provide similar predictive performance though the postprocessor approach tends to underestimate parameter uncertainty however the mopex results indicate that the joint approach can be nonrobust in particular when applied to gr4j it often produces poor predictions due to strong multiway interactions between a hydrological water balance parameter and the error model parameters the postprocessor approach is more robust precisely because it ignores these interactions practical benefits of accounting for error autocorrelation are demonstrated by analyzing streamflow predictions aggregated to a monthly scale where ignoring daily scale error autocorrelation leads to significantly underestimated predictive uncertainty and by analyzing one day ahead predictions where accounting for the error autocorrelation produces clearly higher precision and better tracking of observed data including autocorrelation into the residual error model also significantly affects calibrated parameter values and uncertainty estimates the paper concludes with a summary of outstanding challenges in residual error modeling particularly in ephemeral catchments

stability behavior for unsupervised learning abstract we consider models proposed by oja karhunen cox and adams for a task of unsupervised learning questions of existence of solutions and stability behavior of those solutions are addressed we also discuss the impact of temporary connections in the stability of the learning process

fast dual mgs block factorization algorithm for dense mom matrices a robust method is introduced for efficiently compressing dense method of moments mom matrices using a dual modified gram schmidt block qr factorization algorithm based on low rank singular value decomposition the compression is achieved without generating the full matrix or even full subblocks of the matrix the compressed matrix may then be used in the iterative solution of the mom problem the method is very robust because it uses a reduced set of the original matrix entries to perform the compression furthermore it does not depend on the analytic form of the green s function so it may be applied to arbitrarily complex media

on the use of wavelet expansions in the method of moments em scattering an approach which incorporates the theory of wavelet transforms in method of moments solutions for electromagnetic wave interaction problems is presented the unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function which is often referred to as the mother wavelet the wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer the approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths using a galerkin method and subsequently applying a threshold procedure the moment method matrix is rendered sparsely populated the structure of the matrix reveals the localized scale fitting distribution long before the matrix equation is solved the performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double slot aperture

efficient solution of efie via low rank compression of multilevel predetermined interactions this paper describes the predetermined interaction list oct tree pilot algorithm and its application in expediting the solution of full wave electric field integral equation efie based scattering problems for three dimensional arbitrarily shaped conductors pilot combines features of the fast multipole method fmm and qr decomposition based matrix compression techniques to optimize setup times solve times and memory requirements the method is kernel independent and stable for electrically small structures unlike traditional fmm the novel features of the algorithm namely the mixed potential compression scheme and the hierarchical multilevel predetermined matrix structure are explained in detail a complexity estimate is presented to demonstrate the scaling in time and memory requirements examples exhibiting the accuracy and the time and memory performances are also presented finally a quantitative study is included to address the expected but gradual degradation of qr based compression techniques for electrically large structures

improving probabilistic prediction of daily streamflow by identifying pareto optimal approaches for modeling heteroscedastic residual errors reliable and precise probabilistic prediction of daily catchment scale streamflow requires statistical characterization of residual errors of hydrological models this study focuses on approaches for representing error heteroscedasticity with respect to simulated streamflow i e the pattern of larger errors in higher streamflow predictions we evaluate 8 common residual error schemes including standard and weighted least squares the box cox transformation with fixed and calibrated power parameter and the log sinh transformation case studies include 17 perennial and 6 ephemeral catchments in australia and usa and two lumped hydrological models performance is quantified using predictive reliability precision and volumetric bias metrics we find the choice of heteroscedastic error modelling approach significantly impacts on predictive performance though no single scheme simultaneously optimizes all performance metrics the set of pareto optimal schemes reflecting performance trade offs comprises box cox schemes with of 0 2 and 0 5 and the log scheme 0 perennial catchments only these schemes significantly outperform even the average performing remaining schemes e g across ephemeral catchments median precision tightens from 105 to 40 of observed streamflow and median biases decrease from 25 to 4 theoretical interpretations of empirical results highlight the importance of capturing the skew kurtosis of raw residuals and reproducing zero flows paradoxically calibration of is often counterproductive in perennial catchments it tends to overfit low flows at the expense of abysmal precision in high flows the log sinh transformation is dominated by the simpler pareto optimal schemes listed above recommendations for researchers and practitioners seeking robust residual error schemes for practical work are provided this article is protected by copyright all rights reserved

electromagnetic degrees of freedom in 2 d scattering environments the electromagnetic em degrees of freedom dof of a noise limited system in two dimensions with random multiple scattering is evaluated numerically following a rigorous dof theory first developed by miller and piestun for optical systems the received em fields are efficiently calculated by fast multipole method fmm and the ensemble average of the dof number is obtained through monte carlo simulation technique the results show that the average em dof number is strongly dependent on the sizes of the transmit volume the receive volume and the scattering region in particular the average number of dof generally increases with both the transmit and receive volumes however this increase is a non linear process and will not continue indefinitely as the transmit volume or the receive volume expands an upper bound of the average dof number is expected due to noise effects due to the lack of criteria for choosing a critical parameter involved in miller and piestun s original dof definition a modified definition is also considered even though the modified definition is snr dependent it provides a clearer physical meaning of the dof in addition the simulations also suggest that it might not be appropriate to ignore the influence of the snr on the dof number when the system concerned is of general form and relative small where no critical point of the channel quality can be identified a logarithmic dependence of the dof number on the total source power is demonstrated for such systems

extending the applicability of the generalized likelihood function for zero inflated data series proper uncertainty estimation for data series with a high proportion of zero and near zero observations has been a challenge in hydrologic studies this technical note proposes a modification to the generalized likelihood function that accounts for zero inflation of the error distribution zi gl we compare the performance of the proposed zi gl with the original generalized likelihood function using the entire data series gl and by simply suppressing zero observations gly 0 these approaches were applied to two interception modeling examples characterized by data series with a significant number of zeros the zi gl produced better uncertainty ranges than the gl as measured by the precision reliability and volumetric bias metrics the comparison between zi gl and gly 0 highlights the need for further improvement in the treatment of residuals from near zero simulations when a linear heteroscedastic error model is considered aside from the interception modeling examples illustrated herein the proposed zi gl may be useful for other hydrologic studies such as for the modeling of the runoff generation in hillslopes and ephemeral catchments

a single level low rank ie qr algorithm for pec scattering problems using efie formulation this paper presents a single level matrix compression algorithm termed ie qr based on a low rank approximation to speed up the electric field integral equation efie formulation it is shown with the number of groups chosen to be proportional to n sup 1 2 where n is the number of unknowns the memory and cpu time for the resulting algorithm are both o n sup 1 5 the unique features of the algorithm are a the ie qr algorithm is based on the near rank deficiency property for well separated groups this near rank deficiency assumption holds true for many integral equation methods such as laplacian radiation and scattering problems in electromagnetics em the same algorithm can be adapted to other applications outside em with few or no modifications and b the rank estimation is achieved by a dual rank process which ranks the transmitting and receiving groups respectively thus the ie qr algorithm can achieve matrix compression without assembling the entire system matrix also a geometric neighboring preconditioner is presented in this paper this geometric neighboring preconditioner when used in conjunction with gmres is proven to be both efficient and effective for solving the compressed matrix equations

a multilevel implementation of the qr compression for method of moments we present a multilevel version of a previously reported compression technique for the method of moments poirier j r et al ibid vol 46 p 1175 6 1998 this method is based on qr compression of the impedance matrix off diagonal blocks the block structure of the matrix is built up to optimize the compression rate it results from the study that the compression threshold is the unique adjustment parameter which makes this method very easy to handle some results are presented which stress the improvement in memory storage and computation time obtained through this approach with respect to the mono level algorithm

a multilevel matrix decomposition algorithm for analyzing scattering from large structures a multilevel algorithm is presented for analyzing scattering from electrically large surfaces the algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics the algorithm permits a fast matrix vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks with each describing the interaction between distant scatterers the multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast fourier transform fft and that only relies on well known algebraic techniques the computational complexity and the memory requirements of the proposed algorithm are o n log sup 2 n

estimation of the eigenvalues of ab for a 0 b 0 abstract for positive definite hermitian matrices a and b we obtain an upper and a lower bound for the eigenvalues of ab in terms of those of a and b

a high performance upgrade of the perfectly matched layer multilevel fast multipole algorithm for large planar microwave structures an improvement of the perfectly matched layer multilevel fast multipole algorithm pml mlfma for simulating large planar microwave structures is presented by exploiting the low rank property of the pml mlfma multimodal aggregation and disaggregation matrices considerable reductions in memory usage and computation time are obtained the method has been extensively validated demonstrating complete error controllability when simulating large planar microwave structures reductions in memory requirements and cpu time of more than 60 and 40 have been achieved

bayesian inference of uncertainties in precipitation streamflow modeling in a snow affected catchment 1 bayesian inference is used to study the effect of precipitation and model structural uncertainty on estimates of model parameters and confidence limits of predictive variables in a conceptual rainfall runoff model in the snow fed rudback catchment 142 ha in southern finland the ihacres model is coupled with a simple degree day model to account for snow accumulation and melt the posterior probability distribution of the model parameters is sampled by using the differential evolution adaptive metropolis dream zs algorithm and the generalized likelihood function precipitation uncertainty is taken into account by introducing additional latent variables that were used as multipliers for individual storm events results suggest that occasional snow water equivalent swe observations together with daily streamflow observations do not contain enough information to simultaneously identify model parameters precipitation uncertainty and model structural uncertainty in the rudback catchment the addition of an autoregressive component to account for model structure error and latent variables having uniform priors to account for input uncertainty lead to dubious posterior distributions of model parameters thus our hypothesis that informative priors for latent variables could be replaced by additional swe data could not be confirmed the model was found to work adequately in 1 day ahead simulation mode but the results were poor in the simulation batch mode this was caused by the interaction of parameters that were used to describe different sources of uncertainty the findings may have lessons for other cases where parameterizations are similarly high in relation to available prior information

on the use of the singular value decomposition in the fast multipole method the authors present a new matrix compression algorithm to improve the efficiency of the fast multipole method fmm the method is based on the application of the singular value decomposition svd to the plane wave fmm aggregation matrices these matrices are low ranked which is exploited to provide alternative sets of orthonormal singular basis functions obtained as linear combinations of the original basis by choosing only the most relevant singular functions a much more compact representation is obtained to accurately handle the interactions between the fmm groups the new formulation provides a reduction close to one order of magnitude both in computational cost and memory requirements with a moderate impact on the accuracy of the solution

a formal likelihood function for parameter and predictive inference of hydrologic models with correlated heteroscedastic and non gaussian errors estimation of parameter and predictive uncertainty of hydrologic models has traditionally relied on several simplifying assumptions residual errors are often assumed to be independent and to be adequately described by a gaussian probability distribution with a mean of zero and a constant variance here we investigate to what extent estimates of parameter and predictive uncertainty are affected when these assumptions are relaxed a formal generalized likelihood function is presented which extends the applicability of previously used likelihood functions to situations where residual errors are correlated heteroscedastic and non gaussian with varying degrees of kurtosis and skewness the approach focuses on a correct statistical description of the data and the total model residuals without separating out various error sources application to bayesian uncertainty analysis of a conceptual rainfall runoff model simultaneously identifies the hydrologic model parameters and the appropriate statistical distribution of the residual errors when applied to daily rainfall runoff data from a humid basin we find that 1 residual errors are much better described by a heteroscedastic first order auto correlated error model with a laplacian distribution function characterized by heavier tails than a gaussian distribution and 2 compared to a standard least squares approach proper representation of the statistical distribution of residual errors yields tighter predictive uncertainty bands and different parameter uncertainty estimates that are less sensitive to the particular time period used for inference application to daily rainfall runoff data from a semiarid basin with more significant residual errors and systematic underprediction of peak flows shows that 1 multiplicative bias factors can be used to compensate for some of the largest errors and 2 a skewed error distribution yields improved estimates of predictive uncertainty in this semiarid basin with near zero flows we conclude that the presented methodology provides improved estimates of parameter and total prediction uncertainty and should be useful for handling complex residual errors in other hydrologic regression models as well

complex multipole beam approach to electromagnetic scattering problems a novel approach to reducing the matrix size associated with the method of moments mom solution of the problem of electromagnetic scattering from arbitrary shaped closed bodies is presented the key step in this approach is to represent the scattered field in terms of a series of beams produced by multipole sources located in a complex space on the scatterer boundary the fields generated by these multipole sources resemble the gabor basis functions by utilizing the properties of the gabor series guidelines for selecting the orders as well as locations of the multipole sources are developed it is shown that the present approach not only reduces the number of unknowns but also generates a generalized impedance matrix with a banded structure and a low condition number the accuracy of the proposed method is verified by comparing the numerical results with those derived by using the method of moments

on fast multipole methods for volterra integral equations with highly oscillatory kernels abstract this paper explores the fast multipole methods fmms to accelerate the approximation for weakly singular volterra integral equations with highly oscillatory trigonometric kernels by constructing the fast translation path the fmm is utilized to speed up the iterative method which reduces the complexity from o n 2 to o n especially we use the collocation method to discretize the volterra integral equation with constants and linear elements respectively then apply the gmres to solve the dense and non symmetric linear system in addition the highly oscillatory integrals derived from the algorithm are calculated effectively by the steepest descent method the proposed method shows that the numerical solutions become more accurate as the frequency increases both of the optimal convergence rates of truncation and the error bounds analysis are represented in the end