extended fast fixed order rls adaptive filters the existing derivations of conventional fast rls adaptive filters are intrinsically dependent on the shift structure in the input regression vectors this structure arises when a tapped delay line fir filter is used as a modeling filter we show unlike what original derivations may suggest that fast fixed order rls adaptive algorithms are not limited to fir filter structures we show that fast recursions in both explicit and array forms exist for more general data structures such as orthonormally based models one of the benefits of working with orthonormal bases is that fewer parameters can be used to model long impulse responses

an immersed boundary method with direct forcing for the simulation of particulate flows we present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid the main idea is to incorporate peskin s regularized delta function approach acta numerica 11 2002 1 into a direct formulation of the fluid solid interaction force in order to allow for a smooth transfer between eulerian and lagrangian representations while at the same time avoiding strong restrictions of the time step this technique was implemented in a finite difference and fractional step context a variety of two and three dimensional simulations are presented ranging from the flow around a single cylinder to the sedimentation of 1000 spherical particles the accuracy and efficiency of the current method are clearly demonstrated

a minimal rotation based frls lattice algorithm we propose an alternate givens rotation based least squares lattice algorithm based on spherical trigonometry principles this algorithm turns out to be a normalized version of the fast qrd based least squares lattice filter introduced independently by ling 1991 and by proudler et al 1990 1991 in contrast with that algorithm the storage requirements of the new algorithm are minimal in the system theory sense from this we show that the new algorithm satisfies the backward consistency property and hence enjoys stable error propagation

immersed boundary and overset grid methods assessed for stokes flow due to an oscillating sphere abstract a systematic comparison of three types of immersed boundary methods and an overset grid method is performed for incompressible stokes flow due to an oscillating sphere for each simulation the error between the numerical solution and the analytical solution is reported in terms of the maximum and l2 norms of the errors in the velocity the pressure and the velocity gradient fields the three types of immersed boundary methods are a a diffuse interface immersed boundary method ibm b a sharp interface ibm with standard treatment of the pressure and c a sharp interface ibm with pressure decoupling at interfaces upon grid refinement the velocity gradient and pressure fields generated by methods a and b do not converge to the analytical solution in the maximum norm while the total force on the sphere does converge an inspection of the norms as function of the distance to the surface shows that the lack of convergence mainly occurs in the first layer of grid cells outside the sphere if the pressure poisson equation is not solved inside the sphere method c the velocity gradient and pressure seem to converge in the maximum norm however high resolution is required to achieve a smaller maximum error in the pressure in method c than in methods a and b overall method c is somewhat more accurate than method b and the latter is somewhat more accurate than method a in this assessment the overset grid method clearly outperforms the ibms and is able to produce errors down to one percent in the maximum norm at 32 grid points per sphere diameter within each of the four classes of methods several variants are tested for the overset grid method and in several sharp interface ibms nonincremental projection is found to produce a more accurate pressure than incremental projection does finally variants of method c and the overset grid method are proposed in which the projection method is replaced by an artificial compressibility method while the staggered grid is maintained this simplifies the methods and it strongly reduces the maximum error in the pressure in case c at the expense of an increased maximum error in the velocity divergence

paper error propagation properties of recursive least squares adaptation algorithms the numerical properties of implementations of the recursive least squares identification algorithm are of great importance for their continuous use in various adaptive schemes here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates it is shown that conventional ls algorithms including bierman s ud factorization algorithm are exponentially stable with respect to such errors i e the effect of the error decays exponentially the base of the decay is equal to the forgetting factor the same is true for fast lattice algorithms the fast least squares algorithm sometimes known as the fast kalman algorithm is however shown to be unstable with respect to such errors

numerical stability properties of a qr based fast least squares algorithm the numerical stability of a recent qr based fast least squares algorithm is established from a backward stability perspective a stability domain approach applicable to any least squares algorithm constructed from the set of reachable states in exact arithmetic is presented the error propagation question is shown to be subordinate to a backward consistency constraint which requires that the set of numerically reachable variables be contained within the stability domain associated to the algorithm this leads to a conceptually lucid approach to the numerical stability question which frees the analysis of stationary assumptions on the filtered sequences and obviates the tedious linearization methods of previous approaches moreover initialization phenomena and considerations related to poorly exciting inputs admit clear interpretations from this perspective the algorithm under study is proved in contrast to many fast algorithms to be minimal

modeling a no slip flow boundary with an external force field abstract a novel technique related to peskin s immersed boundary approach is used to introduce solid surfaces into a simulated flow field the navier stokes equations permit the presence of an externally imposed body force that may vary in space and time forces are chosen to lie along a desired surface and to have a magnitude and direction opposing the local flow such that the flow is brought to rest on an element of the surface for unsteady viscous flow the direct calculation of the needed force is facilitated by a feedback scheme in which the velocity is used to iteratively determine the desired value in particular we determine the surface body force from the relation f x 5 t t 0 u x 5 t dt u x 5 t for surface points x 5 velocity u time t and negative constants and examples are presented which include 2d flow around cylinders 3d turbulent channel flow where one boundary is simulated with a force field and turbulent channel flow over a riblet covered surface while the new method may be applied to complex geometries on a non cartesian mesh we have chosen to use a simple cartesian grid all simulations are done with a spectral code in a single computational domain without any mapping of the mesh

least squares adaptive lattice and transversal filters a unified geometric theory a unified theory is presented to characterize least squares adaptive filters in either lattice or transversal filter form for nonstationary processes the derivations are based upon a geometric formulation of least squares estimation and on the concept of displacement rank a few basic geometric relations are shown to underlie the various algorithms insights into the fundamental concepts that unify lattice and transversal filter approaches to least squares adaptive filters are also given the general results are illustrated by applications to the so called pre windowed and growing memory covariance formulations of the deterministic least squares problem

lossless inverse scattering digital filters and estimation theory methods to construct rational solutions of the lossless inverse scattering lis problem for one port passive digital systems are described the first method is recursive and can be viewed as a generalization of the celebrated schur algorithm the second method is global and leads to a parametrization of what we call fundamental solutions from which all lis solutions may be constructed quite a few classical problems in estimation theory and network theory may be viewed as special cases of the lis problem with each fundamental solution there is a solution of a corresponding estimation problem leading to a prediction and a modeling filter for a given stochastic process

rotation based rls algorithms unified derivations numerical properties and parallel implementations this work presents a unified derivation of four rotation based recursive least squares rls algorithms they solve the adaptive least squares problems of the linear combiner the linear combiner without a desired signal the single channel and the multichannel linear prediction and transversal filtering compared to other approaches the authors derivation is simpler and unified and may be useful to readers for better understanding the algorithms and their relationships moreover it enables improvements of some algorithms in the literature in both the computational and the numerical issues all algorithms derived in this work are based on givens rotations they offer superior numerical properties as shown by computer simulations they are computationally efficient and highly concurrent aspects of parallel implementation and parameter identification are discussed

sliding window adaptive fast qr and qr lattice algorithms sliding window formulations of the fast qr and fast qr lattice algorithms are presented the derivations are based on the partial triangularization of raw data matrices three methods for window downdating are discussed the method of plane hyperbolic rotations the chambers method and the linpack algorithm a numerically ill conditioned stationary signal and a speech signal are used in finite wordlength simulations of the full qr nonfast fast qr and qr lattice algorithms all algorithms are observed to be numerically stable over billions of iterations for double precision mantissas 53 bits but as the number of bits is decreased in the mantissa the algorithms exhibit divergent behavior hence practically the algorithms can de regarded as numerically stable for long wordlengths

a sharp interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations a method for reducing the spurious pressure oscillations observed when simulating moving boundary flow problems with sharp interface immersed boundary methods ibms is proposed by first identifying the primary cause of these oscillations to be the violation of the geometric conservation law near the immersed boundary we adopt a cut cell based approach to strictly enforce geometric conservation in order to limit the complexity associated with the cut cell method the cut cell based discretization is limited only to the pressure poisson and velocity correction equations in the fractional step method and the small cell problem tackled by introducing a virtual cell merging technique the method is shown to retain all the desirable properties of the original finite difference based ibm while at the same time reducing pressure oscillations for moving boundaries by roughly an order of magnitude

an immersed boundary method with formal second order accuracy and reduced numerical viscosity a formally second order accurate immersed boundary method is presented and tested in this paper we apply this new scheme to simulate the flow past a circular cylinder and study the effect of numerical viscosity on the accuracy of the computation by comparing the numerical results with those of a first order method the numerical evidence shows that the new scheme has less numerical viscosity and is therefore a better choice for the simulation of high reynolds number flows with immersed boundaries

the limiting distribution of the maximum rank correlation estimator han s maximum rank correlation mrc estimator is shown to be 4 consistent and asymptotically normal the proof rests on a general method for determining the asymptotic distribution of a maximization estimator a simple u statistic decomposition and a uniform bound for degenerate u processes a consistent estimator of the asymptotic covariance matrix is provided along with a result giving the explicit form of this matrix for any model within the scope of the mrc estimator the latter result is applied to the binary choice model and it is found that the mrc estimator does not achieve the semiparametric efficiency bound

adjusting for covariate effects on classification accuracy using the covariate adjusted receiver operating characteristic curve recent scientific and technological innovations have produced an abundance of potential markers that are being investigated for their use in disease screening and diagnosis in evaluating these markers it is often necessary to account for covariates associated with the marker of interest covariates may include subject characteristics expertise of the test operator test procedures or aspects of specimen handling in this paper we propose the covariate adjusted receiver operating characteristic curve a measure of covariate adjusted classification accuracy nonparametric and semiparametric estimators are proposed asymptotic distribution theory is provided and finite sample performance is investigated for illustration we characterize the age adjusted discriminatory accuracy of prostate specific antigen as a biomarker for prostate cancer

an immersed boundary finite volume method for simulations of flow in complex geometries abstract a new immersed boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source sink as well as a momentum forcing the present method is based on a finite volume approach on a staggered mesh together with a fractional step method both momentum forcing and mass source are applied on the body surface or inside the body to satisfy the no slip boundary condition on the immersed boundary and also to satisfy the continuity for the cell containing the immersed boundary in the immersed boundary method the choice of an accurate interpolation scheme satisfying the no slip condition on the immersed boundary is important because the grid lines generally do not coincide with the immersed boundary therefore a stable second order interpolation scheme for evaluating the momentum forcing on the body surface or inside the body is proposed three different flow problems decaying vortices and flows over a cylinder and a sphere are simulated using the immersed boundary method proposed in this study and the results agree very well with previous numerical and experimental results verifying the accuracy of the present method

non parametric analysis of a generalized regression model the maximum rank correlation estimator the paper considers estimation of a model yi d f x i 0 ui where the composite transformation d f is only specified that d r r is non degenerate monotonic and f r2 r is strictly monotonic in each of its variables the paper thus generalizes standard data analysis which assumes that the functional form of d f is known and additive the estimator which it proposes is the maximum rank correlation estimator which is non parametric in the functional form of d f and non parametric in the distribution of the error terms ui the estimator is shown to be strongly consistent for the parameters 0 up to a scale coefficient

sources of spurious force oscillations from an immersed boundary method for moving body problems when a discrete forcing immersed boundary method is applied to moving body problems it produces spurious force oscillations on a solid body in the present study we identify two sources of these force oscillations one source is from the spatial discontinuity in the pressure across the immersed boundary when a grid point located inside a solid body becomes that of fluid with a body motion the addition of mass source sink together with momentum forcing proposed by kim et al j kim d kim h choi an immersed boundary finite volume method for simulations of flow in complex geometries journal of computational physics 171 2001 132 150 reduces the spurious force oscillations by alleviating this pressure discontinuity the other source is from the temporal discontinuity in the velocity at the grid points where fluid becomes solid with a body motion the magnitude of velocity discontinuity decreases with decreasing the grid spacing near the immersed boundary four moving body problems are simulated by varying the grid spacing at a fixed computational time step and at a constant cfl number respectively it is found that the spurious force oscillations decrease with decreasing the grid spacing and increasing the computational time step size but they depend more on the grid spacing than on the computational time step size

round off error propagation in four generally applicable recursive least squares estimation schemes abstract the numerical robustness of four generally applicable recursive least squares estimation schemes is analysed by means of a theoretical round off propagation study this study highlights a number of practical interesting insights into the widely used recursive least squares schemes these insights have been confirmed in an experimental verification study

combining biomarkers for classification with covariate adjustment combining multiple markers can improve classification accuracy compared with using a single marker in practice covariates associated with markers or disease outcome can affect the performance of a biomarker or biomarker combination in the population the covariate adjusted receiver operating characteristic roc curve has been proposed as a tool to tease out the covariate effect in the evaluation of a single marker this curve characterizes the classification accuracy solely because of the marker of interest however research on the effect of covariates on the performance of marker combinations and on how to adjust for the covariate effect when combining markers is still lacking in this article we examine the effect of covariates on classification performance of linear marker combinations and propose to adjust for covariates in combining markers by maximizing the nonparametric estimate of the area under the covariate adjusted roc curve the proposed method provides a way to estimate the best linear biomarker combination that is robust to risk model assumptions underlying alternative regression model based methods the proposed estimator is shown to be consistent and asymptotically normally distributed we conduct simulations to evaluate the performance of our estimator in cohort and case control designs and compare several different weighting strategies during estimation with respect to efficiency our estimator is also compared with alternative regression model based estimators or estimators that maximize the empirical area under the roc curve with respect to bias and efficiency we apply the proposed method to a biomarker study from an human immunodeficiency virus vaccine trial copyright 2017 john wiley sons ltd

on the duality between fast qr methods and lattice methods in least squares adaptive filtering the authors show that fast qr methods and lattice methods in least squares adaptive filtering are duals and follow from identical geometric principles whereas the lattice methods compute the residuals of a projection operation via the forward and backward prediction errors the qr methods compute instead the weights used in the projections within this framework the parameter identification problem is solved using fast qr methods by showing that the reflection coefficients and tap parameters of a least squares lattice filter operating in the joint process mode are immediately available as internal variables in the fast qr algorithms this parameter set can be readily exploited in system identification signal analysis and linear predictive coding for example the relations derived also lead to a fast least squares algorithm of minimal complexity that is a hybrid between a qr and a lattice algorithm the algorithm combines the order recursive properties of the lattice approach with the robust numerical behavior of the qr approach

accurate immersed boundary reconstructions for viscous flow simulations cells crossed by the immersed boundary is treated a novel interpolation method based on momentum balance and massconservationbasedon finitevolumemethodareintroducedtocorrectlypredictthevelocityandpressure fieldin the vicinity of the boundaries the assessment of the solution quality is based on calculations of taylor decaying vortices examples of laminar and turbulent flow calculations are also reported

numerically robust least squares lattice ladder algorithms with direct updating of the reflection coefficients new time recursive equations are derived for the reflection coefficients and the ladder gains in the a priori and a posteriori forms of the exact least squares ls lattice ladder filtering algorithms the numerical accuracy of the ls lattice ladder algorithms obtained by use of these new direct time update equations is analyzed and compared to the accuracy resulting from the conventional ls lattice ladder algorithms the analysis and a number of simulation results which are presented lead us to conclude that the new a priori and a posteriori forms of the ls lattice ladder algorithms yield superior performance

an embedded boundary formulation for large eddy simulation of turbulent flows interacting with moving boundaries a non boundary conforming formulation for simulating complex turbulent flows with dynamically moving boundaries on fixed cartesian grids is proposed the underlying finite difference solver for the filtered incompressible navier stokes equations is based on a second order fractional step method on a staggered grid to satisfy the boundary conditions on an arbitrary immersed interface the velocity field at the grid points near the interface is reconstructed using momentum forcing without smearing the sharp interface the concept of field extension is also introduced to treat the points emerging from a moving solid body to the fluid laminar flow cases and large eddy simulations les are presented to demonstrate the formal accuracy and range of applicability of the method in particular simulations of laminar flow induced by the harmonic in line oscillation of a circular cylinder in quiescent fluid and from a transversely oscillating cylinder in a free stream are presented and compared to reference simulations and experiments les of turbulent flow over a traveling wavy wall and transitional flow through a bileaflet prosthetic heart valve are also shown all results are in very good agreement with reference results in the literature

a unified approach to structured covariances fast generalized sliding window rls recursions for arbitrary basis this paper extends the existing fast rls recursions originally intended to exponentially windowed problems for general models to a generalized sliding window formulation gswrls from a matrix algebra perspective we show explicitly how the displacement rank of the underlying inverse covariance matrix associated to any operator is defined as a function of the number of window breakpoints and how the fast gswrls calculates these rank factors in a fast manner the recursions hold regardless of the first order data structure induced and show that fast fixed order and order recursive rls algorithms can still be obtained for unwindowed data matrices exhibiting a fixed arbitrary relation between successive regressors our approach highlights the existence of a certain degree of freedom inherent to structured data matrices induced by general models showing that efficient representations of their inverse covariances are not limited to factor circulants but rather constructed from any arbitrary operator these bezoutians usually expressed via reproducing kernel relations can be represented exactly in matrix form along with a precise correspondence to variables of a gswrls as a fallout we obtain a vector relation stating the so called minimality property for extended models and windows as opposed to analogous generating function arguments normally seen in original approaches these results pave the way to a more general framework of polynomial vandermonde covariance decompositions which arise naturally via a proper choice of recurrence related polynomials this has further impact on several signal processing applications including superfast realization of equalizers in communications scenarios

a ghost cell immersed boundary method for flow in complex geometry an efficient ghost cell immersed boundary method gcibm for simulating turbulent flows in complex geometries is presented a boundary condition is enforced through a ghost cell method the reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second order accuracy of the base solver both dirichlet and neumann boundary conditions can be treated the current ghost cell treatment is both suitable for staggered and non staggered cartesian grids the accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface numerical results are compared with experimental data and boundary fitted grid results the method is further extended to an existing ocean model mitgcm to simulate geophysical flow over a three dimensional bump the method is easily implemented as evidenced by our use of several existing codes

lattice filter parameterization and modeling of nonstationary processes a general theory of constant parameter modular lattice models for discrete time nonstationary second order processes is presented a complete parametrization of such processes in terms of schur and congruence coefficients is derived by developing a natural connection between the displacement structure of a covariance matrix and schur s test for positive definiteness of matrices schur coeffieients provide a simple solution to problems of covariance extension and rational spectral approximation for nonstationary covariances and they coincide with the well known reflection or parcor coefficients when the covariance is stationary the congruence coefficients provide the time varying gains of a tapped delay line realization of the whitening filter for the process a constant parameter realization of the same filter is derived by combining a lattice filter structure with a tapped delay line both with time invariant gains this configuration also provides a recursive relation for the congruence coefficients namely a generalized levinson szego recursion the tapped delay line part of the realization can be eliminated by introducing the concept of admissibility admissibility also reduces the parametrization of a nonstationary process to schur coefficients alone in analogy to stationary processes which are completely characterized by their parcor coefficients

error accumulation effects for the a posteriori rlsl prediction filter this paper presents a numerical analysis of the a posteriori recursive least squares lattice filter with indirect updating the important problem of finite precision effects in adaptive rls lattice filters is addressed for this particular filter algorithm but the technique is applicable to many other versions new recursions for the filter residuals and the filter powers forward and backward are derived which describe the effects of arithmetic errors that originate at one stage m and are passed to the next stage m 1 these recursions permit an arithmetic error analysis at the zeroth filter stage to have meaning at all future filter stages effects from machine precision spl eta are linked to the forgetting factor spl lambda and time n to derive bounds for arithmetic error growth at the zeroth filter stage these results provide an explicit upper bound on the forgetting factor that ensures acceptable error propagation additionally we offer a computationally inexpensive way to monitor arithmetic error effects during the normal execution of the filter algorithm through a running error analysis

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

recursive least squares ladder estimation algorithms recursive least squares ladder estimation algorithms have attracted much attention recently because of their excellent convergence behavior and fast parameter tracking capability compared to gradient based algorithms we present some recently developed square root normalized exact least squares ladder form algorithms that have fewer storage requirements and lower computational requirements than the unnormalized ones a hilbert space approach to the derivations of magnitude normalized signal and gain recursions is presented the normalized forms are expected to have even better numerical properties than the unnormalized versions other normalized forms such as joint process estimators e g adaptive line enhancer and arma pole zero models will also be presented applications of these algorithms to fast or zero startup equalizers adaptive noise and echo cancellers non gaussian event detectors and inverse models for control problems are also mentioned

avoiding divergence in the shalvi weinstein algorithm the most popular algorithms for blind equalization are the constant modulus algorithm cma and the shalvi weinstein algorithm swa it is well known that swa presents a higher convergence rate than cma at the expense of higher computational complexity if the forgetting factor is not sufficiently close to one if the initialization is distant from the optimal solution or if the signal to noise ratio is low swa can converge to undesirable local minima or even diverge in this paper we show that divergence can be caused by an inconsistency in the nonlinear estimate of the transmitted signal or when the algorithm is implemented in finite precision by the loss of positiveness of the estimate of the autocorrelation matrix or by a combination of both in order to avoid the first cause of divergence we propose a dual mode swa in the first mode of operation the new algorithm works as swa in the second mode it rejects inconsistent estimates of the transmitted signal assuming the persistence of excitation condition we present a deterministic stability analysis of the new algorithm to avoid the second cause of divergence we propose a dual mode lattice swa which is stable even in finite precision arithmetic and has a computational complexity that increases linearly with the number of adjustable equalizer coefficients the good performance of the proposed algorithms is confirmed through numerical simulations

immersed boundary method for flow around an arbitrarily moving body for the simulation of flow around an arbitrarily moving body an immersed boundary method is developed in a non inertial reference frame that is fixed to the body the navier stokes equation is formulated in a conservative form such that the force terms due to the rotation and the translational and rotational accelerations are included in the nonlinear term in order to satisfy the no slip condition on the body surface momentum forcing and mass source sink are applied on the body surface or inside the body the numerical method is based on a finite volume approach on a staggered mesh together with a fractional step method the present numerical method is applied to both the forced motion and fluid structure interaction problems in the latter we solve fully coupled navier stokes and dynamic equations for the moving body without introducing any iteration four different flow problems are tested and the results are in excellent agreements with previous numerical and experimental ones

combining predictors for classification using the area under the receiver operating characteristic curve no single biomarker for cancer is considered adequately sensitive and specific for cancer screening it is expected that the results of multiple markers will need to be combined in order to yield adequately accurate classification typically the objective function that is optimized for combining markers is the likelihood function in this article we consider an alternative objective function the area under the empirical receiver operating characteristic curve auc we note that it yields consistent estimates of parameters in a generalized linear model for the risk score but does not require specifying the link function like logistic regression it yields consistent estimation with case control or cohort data simulation studies suggest that auc based classification scores have performance comparable with logistic likelihood based scores when the logistic regression model holds analysis of data from a proteomics biomarker study shows that performance can be far superior to logistic regression derived scores when the logistic regression model does not hold model fitting by maximizing the auc rather than the likelihood should be considered when the goal is to derive a marker combination score for classification or prediction

u processes rates of convergence on introduit un nouveau processus stochastique une collection de statistiques u indicees par une famille de noyaux symetriques on obtient des conditions pour la convergence presque sure uniforme d une suite de tels processus

combining several screening tests optimality of the risk score the development of biomarkers for cancer screening is an active area of research while several biomarkers exist none is sufficiently sensitive and specific on its own for population screening it is likely that successful screening programs will require combinations of multiple markers we consider how to combine multiple disease markers for optimal performance of a screening program we show that the risk score defined as the probability of disease given data on multiple markers is the optimal function in the sense that the receiver operating characteristic roc curve is maximized at every point arguments draw on the neyman pearson lemma this contrasts with the corresponding optimality result of classic decision theory which is set in a bayesian framework and is based on minimizing an expected loss function associated with decision errors ours is an optimality result defined from a strictly frequentist point of view and does not rely on the notion of associating costs with misclassifications the implication for data analysis is that binary regression methods can be used to yield appropriate relative weightings of different biomarkers at least in large samples we propose some modifications to standard binary regression methods for application to the disease screening problem a flexible biologically motivated simulation model for cancer biomarkers is presented and we evaluate our methods by application to it an application to real data concerning two ovarian cancer biomarkers is also presented our results are equally relevant to the more general medical diagnostic testing problem where results of multiple tests or predictors are combined to yield a composite diagnostic test moreover our methods justify the development of clinical prediction scores based on binary regression

semiparametric estimation of the covariate specific roc curve in presence of ignorable verification bias covariate specific roc curves are often used to evaluate the classification accuracy of a medical diagnostic test or a biomarker when the accuracy of the test is associated with certain covariates in many large scale screening tests the gold standard is subject to missingness due to high cost or harmfulness to the patient in this paper we propose a semiparametric estimation of the covariate specific roc curves with a partial missing gold standard a location scale model is constructed for the test result to model the covariates effect but the residual distributions are left unspecified thus the baseline and link functions of the roc curve both have flexible shapes with the gold standard missing at random mar assumption we consider weighted estimating equations for the location scale parameters and weighted kernel estimating equations for the residual distributions three roc curve estimators are proposed and compared namely imputation based inverse probability weighted and doubly robust estimators we derive the asymptotic normality of the estimated roc curve as well as the analytical form the standard error estimator the proposed method is motivated and applied to the data in an alzheimer s disease research

a hybrid least squares qr lattice algorithm using a priori errors this paper presents a new minimal and backward stable qr lsl algorithm obtained through the proper interpretation of the system matrix that describes the adaptation and filtering operations of qr rls algorithms the new algorithm is based on a priori prediction errors normalized by the a posteriori prediction error energy as suggested by the interpretation of the system matrix and uses the fact that the latter quantities can be computed via a lattice structure backward consistency and backward stability become guaranteed under simple numerical conventions in contrast with the known a posteriori qr lsl algorithm the new algorithm present fewer numerical complexity and backward consistency is guaranteed without the constraint of passive rotations in the recursive lattice section furthermore reordering of some operations results in a version with identical numerical behavior and inherent parallelism that can be exploited for fast implementations both a priori and a posteriori qr lsl algorithms are compared by means of simulations for small mantissa wordlengths and forgetting factors spl lambda not too close to 1 the proposed algorithm performs better due to dispensing with passive rotations for forgetting factors very close to one and small wordlengths both algorithms are sensitive to the accuracy of some well identified computations

fast recursive least squares transversal filters for adaptive filtering fast transversal filter ftf implementations of recursive least squares rls adaptive filtering algorithms are presented in this paper substantial improvements in transient behavior in comparison to stochastic gradient or lms adaptive algorithms are efficiently achieved by the presented algorithms the true not approximate solution of the rls problem is always obtained by the ftf algorithms even during the critical initialization period first n iterations of the adaptive filter this true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic gradient algorithms factor of 1 6 to 3 5 depending upon application additionally the fast transversal filter algorithms are shown to offer substantial reductions in computational requirements relative to existing fast rls algorithms such as the fast kalman algorithms of morf ljung and falconer 1976 and the fast ladder lattice algorithms of morf and lee 1977 1981 they are further shown to attain steady state unnormalized or improve upon first n initialization steps the very low computational requirements of the efficient rls solutions of carayannis manolakis and kalouptsidis 1983 finally several efficient procedures are presented by which to ensure the numerical stability of the transversal filter algorithms including the incorporation of soft constraints into the performance criteria internal bounding and rescuing procedures and dynamic range increasing square root normalized variations of the transversal filters

past input reconstruction in fast least squares algorithms this paper solves the following problem given the computed variables in a fast least squares prediction algorithm determine all past input sequences that would have given rise to the variables in question this problem is motivated by the backward consistency approach to numerical stability in this algorithm class the set of reachable variables in exact arithmetic is known to furnish a stability domain our problem is equivalent to a first and second order interpolation problem introduced by mullis and roberts 1976 and studied by others our solution differs in two respects first relations to classical interpolation theory are brought out which allows us to parametrize all solutions by products of our formulation are correct necessary and sufficient conditions for the problem to be solvable in contrast to previous works whose claimed sufficient conditions are shown to fall short second our solution obtains any valid past input as the impulse response of an appropriately constrained orthogonal filter whose rotation parameters derive in a direct manner from the computed variables in a fast least squares prediction algorithm formulas showing explicitly the form of all valid past inputs should facilitate the study of what past input perturbation is necessary to account for accumulated arithmetic errors in this algorithm class this in turn is expected to have an impact in studying accuracy aspects in fast least squares algorithms

the immersed interface method for the navier stokes equations with singular forces abstract peskin s immersed boundary method has been widely used for simulating many fluid mechanics and biology problems one of the essential components of the method is the usage of certain discrete delta functions to deal with singular forces along one or several interfaces in the fluid domain however the immersed boundary method is known to be first order accurate and usually smears out the solutions in this paper we propose an immersed interface method for the incompressible navier stokes equations with singular forces along one or several interfaces in the solution domain the new method is based on a second order projection method with modifications only at grid points near or on the interface from the derivation of the new method we expect fully second order accuracy for the velocity and nearly second order accuracy for the pressure in the maximum norm including those grid points near or on the interface this has been confirmed in our numerical experiments furthermore the computed solutions are sharp across the interface nontrivial numerical results are provided and compared with the immersed boundary method meanwhile a new version of the immersed boundary method using the level set representation of the interface is also proposed in this paper

statistical analysis of initialization methods for rls adaptive filters theoretical analysis is used to evaluate the mean and second moment properties of recursive least squares algorithms incorporating the fast exact initialization and soft constrained initialization methods during the initialization period it is shown that the weight vector mean and covariance produced by fast exact initialization are undefined for this period theoretical results are derived for soft constrained initialization that show that the weight vector mean and covariance are finite and expressions are given for these quantities simulations for various cases are presented to support the accuracy of these theoretical results

on the existence and construction of solutions to the partial lossless inverse scattering problem with applications to estimation theory the partial lossless inverse scattering plis problem which plays a fundamental role in the solution of a alpha stationary estimation problems is considered some open problems connected with this theory are treated necessary and sufficient conditions for a hermitian matrix to be positive say a covariance matrix are derived in terms of its alpha stationary wave representation a generalization of the recursive construction of plis solutions is proposed it is shown that each invariant subspace of the backward shift operator has a corresponding solution of the plis problem provided the operator that generalized the classical pick matrix is positive definite it is also shown that under fairly general conditions all solutions of the h sup infinity type are essentially obtained in this way and a characterization of the residual wave quantities generated by the scatterer is given stochastic models and forward and backward order recursive innovation filters are derived

givens rotation based least squares lattice and related algorithms the author presents a general and systematic approach for deriving new ls least squares estimation algorithms that are based solely on givens rotations in particular this approach is used to derive efficient givens rotation based ls lattice algorithms the givens lattice algorithms by exploiting the relationship between the givens algorithms and the recursive modified gram schmidt algorithm it is shown that the time and order update of any order recursive ls estimation algorithm can be realized by employing only givens rotations applying this general conclusion to ls estimation of time series signals results in the givens lattice algorithms two givens lattice algorithms one with square roots and the other without are presented it is shown that the givens lattice algorithms are computationally more efficient than the fast qr algorithm of cioffi 1987 the derivation of other givens rotation based ls estimation algorithms and their systolic array implementations are discussed

combining multiple markers for classification using roc summary in biomedical studies it is of great interest to develop methodologies for combining multiple markers for the purpose of disease classification the receiving operating characteristic roc technique has been widely used where classification performance can be measured with the area under the roc curve auc in this article we study a roc based method for effectively combining multiple markers for disease classification we propose a sigmoid auc sauc estimator that maximizes the sigmoid approximation of the empirical auc the sauc estimator is computationally affordable n1 2 consistent and achieves the same asymptotic efficiency as the auc estimator inference based on the weighted bootstrap is investigated we also propose monte carlo methods to assess the overall prediction performance and the relative importance of individual markers finite sample performance is evaluated using simulation studies and two public data sets

the fast adaptive rotor s rls algorithm a fast algorithm for implementation of the qr factorization based recursive least squares rls adaptive filter is discussed this fast adaptive rotors far algorithm can be implemented with a pipelined array of processors called rotors and cisors the rotors compute 2 2 orthogonal givens rotations and the cisors compute the cosines and sines of the angles used in the rotors the algorithm requires 4n rotors and 2n cisors at each iteration to compute the solution to the rls problem the algorithm is numerically stable the far algorithm is derived using a single generic updating formula for orthogonal matrices which is introduced and derived whereas the generic updating formula is reminiscent of previous fast transversal filters and fast lattice algorithms the set of internally propogated adaptive filter quantities is entirely different and constitutes yet another complete characterization of the rls covariance and the forward backward and pinning estimation problems

krylov proportionate adaptive filtering techniques not limited to sparse systems this paper proposes a novel adaptive filtering scheme named the krylov proportionate normalized least mean square kpnlms algorithm kpnlms exploits the benefits i e fast convergence for sparse unknown systems of the proportionate nlms algorithm but its applications are not limited to sparse unknown systems a set of orthonormal basis vectors is generated from a certain krylov sequence it is proven that the unknown system is sparse with respect to the basis vectors in case of fairly uncorrelated input data different adaptation gain is allocated to a coefficient of each basis vector and the gain is roughly proportional to the absolute value of the corresponding coefficient of the current estimate kpnlms enjoys i fast convergence ii linear complexity per iteration and iii no use of any a priori information numerical examples demonstrate significant advantages of the proposed scheme over the reduced rank method based on the multistage wiener filter mwf and the transform domain adaptive filter tdaf both in noisy and silent situations

the immersed boundary method a projection approach a new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion like previous methods a boundary force is applied at the immersed surface to satisfy the no slip constraint this extra constraint can be added to the incompressible navier stokes equations by introducing regularization and interpolation operators the current method gives prominence to the role of the boundary force acting as a lagrange multiplier to satisfy the no slip condition this role is analogous to the effect of pressure on the momentum equation to satisfy the divergence free constraint the current immersed boundary method removes slip and non divergence free components of the velocity field through a projection the boundary force is determined implicitly without any constitutive relations allowing the present formulation to use larger cfl numbers compared to some past methods symmetry and positive definiteness of the system are preserved such that the conjugate gradient method can be used to solve for the flow field examples show that the current formulation achieves second order temporal accuracy and better than first order spatial accuracy in l 2 norms for one and two dimensional test problems results from two dimensional simulations of flows over stationary and moving cylinders are in good agreement with those from previous experimental and numerical studies

a pre conditioned implicit direct forcing based immersed boundary method for incompressible viscous flows a novel immersed boundary ib method based on an implicit direct forcing idf scheme is developed for incompressible viscous flows the key idea for the present idf method is to use a block lu decomposition technique in momentum equations with taylor series expansion to construct the implicit ib forcing in a recurrence form which imposes more accurate no slip boundary conditions on the ib surface to accelerate the ib forcing convergence during the iterative procedure a pre conditioner matrix is introduced in the recurrence formulation of the ib forcing a jacobi type parameter is determined in the pre conditioner matrix by minimizing the frobenius norm of the matrix function representing the difference between the ib forcing solution matrix and the pre conditioner matrix in addition the pre conditioning parameter is restricted due to the numerical stability in the recurrence formulation consequently the present pre conditioned idf pidf enables accurate calculation of the ib forcing within a few iterations we perform numerical simulations of two dimensional flows around a circular cylinder and three dimensional flows around a sphere for low and moderate reynolds numbers the result shows that pidf yields a better imposition of no slip boundary conditions on the ib surfaces for low reynolds number with a fairly larger time step than ib methods with different direct forcing schemes due to the implicit treatment of the diffusion term for determining the ib forcing finally we demonstrate the robustness of the present pidf scheme by numerical simulations of flow around a circular array of cylinders flows around a falling sphere and two sedimenting spheres in gravity

a discrete forcing immersed boundary method for the fluid structure interaction of an elastic slender body we present an immersed boundary ib method for the simulation of flow around an elastic slender body the present method is based on the discrete forcing ib method for a stationary rigid body proposed by kim kim and choi 2001 25 the discrete forcing approach is used to relieve the limitation on the computational time step size the incompressible navier stokes equations are implicitly coupled with the dynamic equation for an elastic slender body motion the first is solved in the eulerian coordinate and the latter is described in the lagrangian coordinate the elastic slender body is modeled as a thin and flexible solid and is segmented by finite number of thin blocks each block is moved by external and internal forces such as the hydrodynamic elastic and buoyancy forces where the hydrodynamic force is obtained directly from the discrete forcing used in the ib method all the spatial derivative terms are discretized with the second order central difference scheme the present method is applied to three different fluid structure interaction problems flows around a flexible filament a flapping flag in a free stream and a flexible flapping wing in normal hovering respectively computations are performed at maximum cfl numbers of 0 75 1 the results obtained agree very well with those from previous studies

combined immersed boundary finite difference methods for three dimensional complex flow simulations a second order accurate highly efficient method is developed for simulating unsteady three dimensional incompressible flows in complex geometries this is achieved by using boundary body forces that allow the imposition of the boundary conditions on a given surface not coinciding with the computational grid the governing equations therefore can be discretized and solved on a regular mesh thus retaining the advantages and the efficiency of the standard solution procedures two different forcings are tested showing that while the quality of the results is essentially the same in both cases the efficiency of the calculation strongly depends on the particular expression a major issue is the interpolation of the forcing over the grid that determines the accuracy of the scheme this ranges from zeroth order for the most commonly used interpolations up to second order for an ad hoc velocity interpolation the present scheme has been used to simulate several flows whose results have been validated by experiments and other results available in the literature finally in the last example we show the flow inside an ic piston cylinder assembly at high reynolds number to our knowledge this is the first example in which the immersed boundary technique is applied to a full three dimensional complex flow with moving boundaries and with a reynolds number high enough to require a subgrid scale turbulence model

a consistent and conservative immersed boundary method for mhd flows and moving boundary problems abstract a consistent and conservative immersed boundary method has been developed to accurately and efficiently solve two topics magnetohydrodynamics flows with a complex boundary and moving boundary problems based on a least square interpolation reconstruction method a unified form of boundary condition is described to handle a single domain situation while a mixed boundary condition is used for coupled conditions of multi domain in order to achieve the consistency with a desired wall boundary condition a so called approximation correction procedure is done and an imposing neumann boundary condition is discussed with two kinds of different schemes besides a consistent and conservative scheme is implemented to satisfy both the charge and mass conservation laws on cells around the immersed surface then a conservative interpolation is reconstructed for velocity in moving boundary problems at last the applied numerical method is validated by stationary and moving boundary cases and an excellent agreement is obtained with good accuracy efficiency and conservation especially the consistent and conservative immersed boundary method can obtain almost the same accurate results as those from the cut cell technique seo and mittal 2011 14 for a moving boundary problem by reducing the spurious pressure

stabilizing the fast kalman algorithms the fast kalman algorithms are stabilized by introducing a quantity that measures the accumulation of the roundoff errors this quantity is used to correct the variables of the algorithm at every time step the correction is defined as the solution of a specific minimization problem the resulting algorithm still has the nice complexity properties of the original algorithm linear in the number of parameters to be estimated but it has a much more stable behavior