a forward in time advection scheme and adaptive multilevel flow solver for nearly incompressible atmospheric flow this paper presents a new forward in time advection method for nearly incompressible flow mu and its application to an adaptive multilevel flow solver for atmospheric flows mu is a modification of leonardet al sutopia scheme mu like utopia is based on third order accurate semi lagrangian multidimensional upwinding for constant velocity flows for varying velocity fields mu is a second order conservative method mu has greater stability and accuracy than utopia and naturally decomposes into a monotone low order method and a higher order accurate correction for use with flux limiting its stability and accuracy make it a computationally efficient alternative to current finite difference advection methods we present a fully second order accurate flow solver for the anelastic equations a prototypical low mach number flow the flow solver is based on mu which is used for both momentum and scalar transport equations this flow solver can also be implemented with any forward in time advection scheme the multilevel flow solver conserves discrete global integrals of advected quantities and includes adaptive mesh refinement its second order accuracy is verified using a nonlinear energy conservation integral for the anelastic equations for a typical geophysical problem in which the flow is most rapidly varying in a small part of the domain the multilevel flow solver achieves global accuracy comparable to a uniform resolution simulation for 10 of the computational cost

receiver operating characteristic analysis under tree orderings of disease classes receiver operating characteristic roc curve and its summary statistics e g the area under curve auc are commonly used to evaluate the diagnostic accuracy for disease processes with binary classification the roc curve has been extended to roc surface for scenarios with three ordinal classes or to hyper surface for scenarios with more than three classes for classifier under tree or umbrella ordering in which the marker measurement for one class is lower or higher than those for the other classes the commonly adopted diagnostic measures are the naive auc nauc based on a pooled class of all the unordered classes and the umbrella volume uv based on the concept of volume under surface however both nauc and uv have some limitations for example nauc depends on the sampling weights for all the classes in population and uv has only been introduced for three class settings in this article we initiate the idea of a new roc framework for tree or umbrella ordering denoted as troc and propose the area under troc curve denoted as tauc as an appropriate diagnostic measure the proposed troc and tauc share many nice features with the traditional roc and auc both parametric and nonparametric approaches are explored to construct the confidence interval estimation of tauc the performances of these methods are compared in simulation studies under a variety settings at the end the proposed methods are applied to a published microarray data set

stable schemes for partial differential equations non linear diffusion equations with numerical stability problems are common in many branches of science an example is the k diffusion parametrization for vertical turbulent mixing in atmospheric models that creates a system of non linear diffusion equations with stability problems in this paper a new algorithm to solve the one dimensional diffusion equation is presented this method which is stable by design is quite general and can be used in other partial differential equations results with the new scheme compare well with analytical solutions and a study with a system of two non linear diffusion equations shows that the new method is more stable than more traditional schemes

comparing the areas under two or more correlated receiver operating characteristic curves a nonparametric approach methods of evaluating and comparing the performance of diagnostic tests are of increasing importance as new tests are developed and marketed when a test is based on an observed variable that lies on a continuous or graded scale an assessment of the overall value of the test can be made through the use of a receiver operating characteristic roc curve the curve is constructed by varying the cutpoint used to determine which values of the observed variable will be considered abnormal and then plotting the resulting sensitivities against the corresponding false positive rates when two or more empirical curves are constructed based on tests performed on the same individuals statistical analysis on differences between curves must take into account the correlated nature of the data this paper presents a nonparametric approach to the analysis of areas under correlated roc curves by using the theory on generalized u statistics to generate an estimated covariance matrix

a cartesian grid embedded boundary method for hyperbolic conservation laws we present a second order godunov algorithm to solve time dependent hyperbolic systems of conservation laws on irregular domains our approach is based on a formally consistent discretization of the conservation laws on a finite volume grid obtained from intersecting the domain with a cartesian grid we address the small cell stability problem associated with such methods by hybridizing our conservative discretization with a stable nonconservative discretization at irregular control volumes and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation the resulting method is second order accurate in l 1 for smooth problems and is robust in the presence of large amplitude discontinuities intersecting the irregular boundary

optimal linear combination of biomarkers for multi category diagnosis the receiver operating characteristic roc curve and the area under the roc curve have been popularly employed in evaluating the diagnosis accuracy for diseases with binary outcome categories and have been naturally used as the utility measures for finding the optimal linear combination of multiple biomarkers in the hope to improve the diagnostic accuracy based on each single biomarker for diseases with more than two outcome categories the roc manifold and the hypervolume under the roc manifold hum have been analogously proposed as diagnostic accuracy measures however finding optimal combinations of biomarkers based on the hum criterion is less easily feasible in computation especially when the number of disease categories is more than three and the number of biomarkers is large in this study we propose two new indices for evaluating the diagnostic accuracy for multi category diagnosis which are related to the lower and upper bounds of hum and involve only diagnostic accuracies for comparing adjacent pairs of outcome categories we then propose finding the optimal linear combinations of biomarkers for multi category diagnosis using the new indices as the criterion functions simulations and real data examples show that the optimal linear combinations identified by the new proposal perform quite well in diagnostic accuracy and can be much more efficient in computation than the hum based method

contact in a multi material eulerian finite element formulation in a multi material eulerian formulation for problems in solid mechanics the default interaction between the surfaces of adjacent materials is perfect bonding in contrast for the lagrangian formulation the surfaces don t interact and may pass through each other freely unless a contact algorithm is introduced to enforce the contact inequality constraints sophisticated contact algorithms have been developed for lagrangian calculations and are routinely used in large deformation applications such as automobile crashworthiness in comparison the eulerian finite element method lags far behind the lagrangian finite element method in modeling contact a natural application for the eulerian formulation is machining which includes large deformations material failure and contact of a tool with a workpiece making its simulation a challenging problem the simulation of the isolated chips involving material failure due to shear bands is used as a test problem to investigate the strength and weakness of the different approaches to implementing contact in multi material eulerian calculations

multidimensional upwind methods for hyperbolic conservation laws abstract we present a class of second order conservative finite difference algorithms for solving numerically time dependent problems for hyperbolic conservation laws in several space variables these methods are upwind and multidimensional in that the numerical fluxes are obtained by solving the characteristic form of the full multidimensional equations at the zone edge and that all fluxes are evaluated and differenced at the same time in particular operator splitting is not used correct behavior at discontinuities is obtained by the use of solutions to the riemann problem and by limiting some of the second order terms numerical results are presented which show that the methods described here yield the same high resolution as the corresponding operator split methods

a distribution free procedure for comparing receiver operating characteristic curves from a paired experiment summary a distribution free permutation test procedure is proposed for comparing receiver operating characteristic curves based on continuous data from a paired design the method tests the hypothesis that the two curves are identical for all operating points unlike previously proposed methods which test the equivalence of the areas under the curves the new test is shown by simulation to have very similar operating characteristics to the standard method based on comparisons of the areas when the curves are parallel but markedly superior power when the curves cross that is when the curves are different but have similar areas the prospects of generalising the approach to unpaired experiments and to comparisons of ordinal rating data are discussed

cumulative voting consensus method for partitions with variable number of clusters over the past few years there has been a renewed interest in the consensus clustering problem several new methods have been proposed for finding a consensus partition for a set of n data objects that optimally summarizes an ensemble in this paper we propose new consensus clustering algorithms with linear computational complexity in n we consider clusterings generated with a random number of clusters which we describe by categorical random variables we introduce the idea of cumulative voting as a solution for the problem of cluster label alignment where unlike the common one to one voting scheme a probabilistic mapping is computed we seek a first summary of the ensemble that minimizes the average squared distance between the mapped partitions and the optimal representation of the ensemble where the selection criterion of the reference clustering is defined based on maximizing the information content as measured by the entropy we describe cumulative vote weighting schemes and corresponding algorithms to compute an empirical probability distribution summarizing the ensemble given the arbitrary number of clusters of the input partitions we formulate the problem of extracting the optimal consensus as that of finding a compressed summary of the estimated distribution that preserves the maximum relevant information an efficient solution is obtained using an agglomerative algorithm that minimizes the average generalized jensen shannon divergence within the cluster the empirical study demonstrates significant gains in accuracy and superior performance compared to several recent consensus clustering algorithms

derivative pricing as a transport problem mpdata solutions to black scholes type equations abstract we discuss applications of the multidimensional positive definite advection transport algorithm mpdata to numerically solve partial differential equations arising from stochastic models in quantitative finance in particular we develop a framework for solving black scholes type equations by transforming them into advection diffusion problems the equations are then numerically integrated backward in time using an iterative explicit finite difference approach in which the fickian term is represented as an additional advective term we discuss the correspondence between transport phenomena and financial models uncovering the possibility of expressing the no arbitrage principle as a conservation law we show second order accuracy in time and space of the embraced numerical scheme this is done via a convergence analysis comparing mpdata numerical solutions with classic black scholes analytical formulae for the valuation of european options we demonstrate in addition a way of applying mpdata to solve the free boundary problem leading to a linear complementarity problem for the valuation of american options we finally comment on the potential of mpdata methods with respect to more complex models typically used in quantitative finance

the multidimensional positive definite advection transport algorithm nonoscillatory option abstract this paper presents a nonoscillatory option i e free of dispersive ripples of the advection algorithm described previously in j comput phys 54 1984 325 67 1986 396 the approach adopted merges the flux corrected transport methodology with the iterative formalism of the algorithm further discussion of the algorithm s accuracy is included theoretical considerations are illustrated through numerical tests and examples of applications to atmospheric fluid dynamics problems

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

sensitivity and specificity of a monitoring test summary the usefulness of a diagnostic test is generally assessed by calculating the sensitivity and specificity or the predictive value positive and predictive value negative of the test when subjects are monitored periodically for evidence of disease these calculations must incorporate the varying amounts of information per individual if in addition the test results lie on a continuous scale these quantities vary with the cutoff value cutpoint used to define a positive test they are usually calculated for a spectrum of potential cutpoints in order to produce receiver operator characteristic curves in this paper we use a partial likelihood solution to the discrete logistic model in order to obtain estimates of the diagnostic test indices and to provide a significance test when the diagnostic test is administered repeatedly to individuals

eulag a computational model for multiscale flows an mhd extension eulag is an established high performance computational model for simulating fluid flows across a wide range of scales and physical scenarios prusa et al comput fluids 37 2008 1193 historically driven by interests in simulating weather and climate processes the numerics of eulag are unique owing to a synergistic blend of non oscillatory forward in time mpdata methods robust elliptic solver and generalized coordinate formulation enabling grid adaptivity in this paper the numerical apparatus of an ideal magnetohydrodynamic mhd extension of the eulag model is discussed the robust workings of which have been recently revealed in global large eddy simulations of solar magneto convection producing solar like magnetic cycles and dynamo action ghizaru et al apjl 715 2010 l133 racine et al apj 735 2011 46 here a specialized nonoscillatory forward in time scheme for integrating ideal anelastic mhd equations is presented in detail and illustrated with an abstract example of magnetized three dimensional flow in time dependent geometry for a weak moderate and strong magnetic field an analysis of the model performance reveals that multiple solutions of elliptic problems do not have to imply proportionally larger computational expense

an unstructured mesh finite volume mpdata for compressible atmospheric dynamics abstract an advancement of the unstructured mesh finite volume mpdata multidimensional positive definite advection transport algorithm is presented that formulates the error compensative pseudo velocity of the scheme to rely only on face normal advective fluxes to the dual cells in contrast to the full vector employed in previous implementations this is essentially achieved by expressing the temporal truncation error underlying the pseudo velocity in a form consistent with the flux divergence of the governing conservation law the development is especially important for integrating fluid dynamics equations on non rectilinear meshes whenever face normal advective mass fluxes are employed for transport compatible with mass continuity the latter being essential for flux form schemes in particular the proposed formulation enables large time step semi implicit finite volume integration of the compressible euler equations using mpdata on arbitrary hybrid computational meshes furthermore it facilitates multiple error compensative iterations of the finite volume mpdata and improved overall accuracy the advancement combines straightforwardly with earlier developments such as the nonoscillatory option the infinite gauge variant and moving curvilinear meshes a comprehensive description of the scheme is provided for a hybrid horizontally unstructured vertically structured computational mesh for efficient global atmospheric flow modelling the proposed finite volume mpdata is verified using selected 3d global atmospheric benchmark simulations representative of hydrostatic and non hydrostatic flow regimes besides the added capabilities the scheme retains fully the efficacy of established finite volume mpdata formulations

the generalized c index for internal fuzzy cluster validity the c index is an internal cluster validity index that was introduced in 1970 as a way to define and identify a best crisp partition on n objects represented by either unlabeled feature vectors or dissimilarity matrix data this index is often one of the better performers among the plethora of internal indices available for this task this paper develops a soft generalization of the c index that can be used to evaluate sets of candidate partitions found by either fuzzy or probabilistic clustering algorithms we define four generalizations based on relational transformations of the soft partition and then compare their performance to eight other popular internal fuzzy cluster indices using two methods of comparison internal best c and internal external i e best match six synthetic datasets and six real world labeled datasets our main conclusion is that the sum min generalization is the second best performer in the best c tests and the best performer in the i e tests on small data

roc graphs for assessing the ability of a diagnostic marker to detect three disease classes with an umbrella ordering receiver operating characteristic roc curves and the area under these curves are commonly used to assess the ability of a continuous diagnostic marker e g dna methylation markers to correctly classify subjects as having a particular disease or not e g cancer these approaches however are not applicable to settings where the gold standard yields more than two disease states or classes roc surfaces and the volume under the surfaces have been proposed for settings with more than two disease classes these approaches however do not allow one to assess the ability of a marker to differentiate two disease classes from a third disease class without requiring a monotone order for the three disease classes under study that is existing approaches do not accommodate an umbrella ordering of disease classes this article proposes the construction of an roc graph that is applicable for an umbrella ordering furthermore this article proposes that a summary measure for this umbrella roc graph can be used to summarize the classification accuracy and corresponding variance estimates can be obtained using u statistics theory or bootstrap methods the proposed methods are illustrated using data from a study assessing the ability of a dna methylation marker to correctly classify lung specimens into three histologic classes squamous cell carcinoma large cell carcinoma and nontumor lung

a family of nonparametric statistics for comparing diagnostic markers with paired or unpaired data summary in this paper we study a broad class of nonparametric statistics for comparing two diagnostic markers one can compare the sensitivities of these diagnostic markers over restricted ranges of specificity by selecting an appropriate statistic from this class as special cases one can compare the entire area under the receiver operator curve hanley mcneil 1982 or one can compare the sensitivities at a fixed common specificity usually we would recommend a comparison based on an average of sensitivities over a restricted high level of specificities test procedures and confidence intervals are based on asymptotic normality these procedures are applicable for paired data in which both diagnostic markers are performed on each subject and for unpaired data the procedures may be used to compare two real functions of multiple diagnostic markers as well as to compare individual markers

reliability based fuzzy clustering ensemble abstract in the clustering ensemble the quality of base clusterings influences the consensus clustering although some researches have been devoted to weighting the base clustering fuzzy cluster level weighting has been ignored more specifically they did not pay attention to the role of cluster reliability in the fuzzy clustering ensemble in this paper we propose a new fuzzy clustering ensemble framework without access to the features of data objects based on fuzzy cluster level weighting the reliability of each fuzzy cluster is computed based on estimation of its unreliability and is considered as its weight in the ensemble the unreliability of fuzzy clusters is estimated by applying the similarity between fuzzy clusters in the ensemble based on an entropic criterion in our framework the final clustering is produced by two types of consensus functions 1 a reliability based weighted fuzzy co association matrix is constructed from the base clusterings and then a single traditional clustering such as hierarchical agglomerative clustering or k means is applied over the matrix to produce the final clustering 2 a new graph based fuzzy consensuses function the graph based consensus function has linear time complexity in the number of data objects experimental results on various standard datasets demonstrated the effectiveness of the proposed approach compared to the state of the art methods in terms of evaluation criteria and clustering robustness

a mass conservative adaptive fas multigrid solver for cell centered finite difference methods on block structured locally cartesian grids abstract we present a mass conservative full approximation storage fas multigrid solver for cell centered finite difference methods on block structured locally cartesian grids the algorithm is essentially a standard adaptive fas afas scheme but with a simple modification that comes in the form of a mass conservative correction to the coarse level force this correction is facilitated by the creation of a zombie variable analogous to a ghost variable but defined on the coarse grid and lying under the fine grid refinement patch we show that a number of different types of fine level ghost cell interpolation strategies could be used in our framework including low order linear interpolation in our approach the smoother prolongation and restriction operations need never be aware of the mass conservation conditions at the coarse fine interface to maintain global mass conservation we need only modify the usual fas algorithm by correcting the coarse level force function at points adjacent to the coarse fine interface we demonstrate through simulations that the solver converges geometrically at a rate that is h independent and we show the generality of the solver applying it to several nonlinear time dependent and multi dimensional problems in several tests we show that second order asymptotic h 0 convergence is observed for the discretizations provided that 1 at least linear interpolation of the ghost variables is employed and 2 the mass conservation corrections are applied to the coarse level force term

iterated upwind schemes for gas dynamics a class of high resolution schemes established in integration of anelastic equations is extended to fully compressible flows and documented for unsteady and steady problems through a span of mach numbers from zero to supersonic the schemes stem from iterated upwind technology of the multidimensional positive definite advection transport algorithm mpdata the derived algorithms employ standard and modified forms of the equations of gas dynamics for conservation of mass momentum and either total or internal energy as well as potential temperature numerical examples from elementary wave propagation through computational aerodynamics benchmarks to atmospheric small and large amplitude acoustics with intricate wave flow interactions verify the approach for both structured and unstructured meshes and demonstrate its flexibility and robustness

a non staggered grid fractional step method for time dependent incompressible navier stokes equations in curvilinear coordinates a numerical method for solving three dimensional time dependent incompressible navier stokes equations in curvilinear coordinates is presented the non staggered grid method originally developed by c m rhie and w l chow aiaaj 21 1525 1983 for steady state problems is extended to compute unsteady flows in the computational space the cartesian velocity components and the pressure are defined at the center of a control volume while the volume fluxes are defined at the mid point on their corresponding cell faces the momentum equations are integrated semi implicitly by the approximate factorization technique the intermediate velocities are interpolated onto the faces of the control volume to form the source terms of the pressure poisson equation which is solved iteratively with a multigrid method the compatibility condition of the pressure poisson equation is satisfied in the same manner as in a staggered grid method mass conservation can be satisfied to machine accuracy the pressure boundary condition is derived from the momentum equations solutions of both steady and unsteady problems including the large eddy simulation of a rotating and stratified upwelling flow in an irregular container established the favorable accuracy and efficiency of the present method

adaptive solution techniques for simulating underwater explosions and implosions adaptive solution techniques are presented for simulating underwater explosions and implosions the liquid is assumed to be an adiabatic fluid and the solution in the gas is assumed to be uniform in space the solution in water is integrated in time using a semi implicit time discretization of the adiabatic euler equations results are presented either using a non conservative semi implicit algorithm or a conservative semi implicit algorithm a semi implicit algorithm allows one to compute with relatively large time steps compared to an explicit method the interface solver is based on the coupled level set and volume of fluid method clsvof m sussman a second order coupled level set and volume of fluid method for computing growth and collapse of vapor bubbles j comput phys 187 2003 110 136 m sussman e g puckett a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows j comput phys 162 2000 301 337 several underwater explosion and implosion test cases are presented to show the performances of our proposed techniques

ensemble fuzzy clustering using cumulative aggregation on random projections random projection is a popular method for dimensionality reduction due to its simplicity and efficiency in the past few years random projection and fuzzy c means based cluster ensemble approaches have been developed for high dimensional data clustering however they require large amounts of space for storing a big affinity matrix and incur large computation time while clustering in this affinity matrix in this paper we propose a new random projection fuzzy c means based cluster ensemble framework for high dimensional data our framework uses cumulative agreement to aggregate fuzzy partitions fuzzy partitions of random projections are ranked using external and internal cluster validity indices the best partition in the ranked queue is the core or base partition remaining partitions then provide cumulative inputs to the core thus arriving at a consensus best overall partition built from the ensemble experimental results with gaussian mixture datasets and a variety of real datasets demonstrate that our approach outperforms three state of the art methods in terms of accuracy and space time complexity our algorithm runs one to two orders of magnitude faster than other state of the arts algorithms

sample size determination for diagnostic accuracy studies involving binormal roc curve indices receiver operating characteristic roc curves and their associated indices are valuable tools for the assessment of the accuracy of diagnostic tests the area under the roc curve is a popular summary measure of the accuracy of a test the full area under the roc curve however has been criticized because it gives equal weight to all false positive error rates alternative indices include the area under the roc curve in a particular range of false positive rates partial area and the sensitivity of the test for a single fixed false positive rate fpr we present a unified approach for computing sample size for binormal roc curves and their indices our method uses taylor series expansions to derive approximate large sample estimates of the variance and covariance of binormal roc curve parameters several examples from diagnostic radiology illustrate the proposed method

an extensive comparative study of cluster validity indices the validation of the results obtained by clustering algorithms is a fundamental part of the clustering process the most used approaches for cluster validation are based on internal cluster validity indices although many indices have been proposed there is no recent extensive comparative study of their performance in this paper we show the results of an experimental work that compares 30 cluster validity indices in many different environments with different characteristics these results can serve as a guideline for selecting the most suitable index for each possible application and provide a deep insight into the performance differences between the currently available indices

mpdata an edge based unstructured grid formulation we present an advancement in the evolution of mpdata multidimensional positive definite advection transport algorithm over the last two decades mpdata has proven successful in applications using single block structured cuboidal meshes viz cartesian meshes while employing homeomorphic mappings to accommodate time dependent curvilinear domains motivated by the strengths of the cartesian mesh mpdata we develop a new formulation in an arbitrary finite volume framework with a fully unstructured polyhedral hybrid mesh in mpdata as in any taylor series based integration method for pde the choice of data structure has a pronounced impact on the technical details of the algorithm aiming at a broad range of applications with a large number of control volume cells we select a general compact and computationally efficient edge based data structure this facilitates the use of mpdata for problems involving complex geometries and or inhomogeneous anisotropic flows where mesh adaptivity is advantageous in this paper we describe the theory and implementation of the basic finite volume mpdata and document extensions important for applications a fully monotone scheme diffusion scheme and generalization to complete flow solvers theoretical discussions are illustrated with benchmark results in two and three spatial dimensions

an unsplit 3d upwind method for hyperbolic conservation laws abstract an unsplit upwind method for solving hyperbolic conservation laws in three dimensions is developed this paper derives the algorithm by generalizing a two dimensional advection algorithm of van leer and colella to three dimensions and then making appropriate modifications the method is implemented using the equations of gas dynamics several test problems are computed to both verify and display the behavior of the method these test problems include a 1d blast wave a 2d shock reflection off a 30 ramp and a 3d astrophysical jet

the roc manifold for classification systems we define the roc manifold and cc manifold as duals in a given sense their analysis is required to describe the classification system we propose a mathematical definition based on vector space methods to describe both the roc manifolds for n class classification systems fully describe each system in terms of its misclassifications and by conjunction its correct classifications optimal points which minimize misclassifications can be identified even when costs and prior probabilities differ these manifolds can be used to determine the usefulness of a classification system based on a given performance criterion many performance functionals such as summary statistics preferred for cc manifolds can also be evaluated using the roc manifold under certain constraints examples using the roc manifold and performance functionals to compete classification systems are demonstrated with simulated and applied disease detection data

multi domain simulations of the time dependent navier stokes equations benchmark error analysis of some nesting procedures this paper presents a benchmark error analysis of various approaches for treating multiple domain calculations within an anelastic finite difference model one way and two way interactive nesting errors with and without temporal refinement are evaluated the two way interactive nesting approach is one where solutions between fine and coarse grid domains are matched through the simple post insertion of data on the other hand the equations can be matched by using the pressure defect correction approach it is shown that for the present model the two way interactive nesting method gives identical results to multi domain solutions using the pressure defect correction approach the present results indicate that in this type of analastic framework a priori matching of the equations is equivalent to the a posteriori matching of the solutions this result is attributed to the inflexible nature of the neumann boundary conditions on the fine mesh pressure which need to be specified from the coarse mesh since a large number of meterological models employ the hydrostatic assumption it is of interest to know of nesting errors attributable to this approximation the results presented indicate essentially equivalent error levels for both the hydrostatic and nonhydrostatic systems of equations for the present case of airflow over an isolated mountain it is shown how nesting technology can be used in a virtual sense to reduce the central memory requirements for large array sized numerical simulations nesting can be used in this sense to decompose the maximum memory working space required without affecting the results

numerical solution of the reaction advection diffusion equation on the sphere a finite volume algorithm for the solution of the reaction advection diffusion equation on the sphere is derived and evaluated using analytical solutions the proposed approach is based on the principle of semidiscretization the convective and diffusive fluxes are approximated first and then the resulting set of the ordinary differential equations odes is solved using the appropriate time stepping algorithm in the first part of the paper solutions to both the linear advection and the advection diffusion problems for a single conservative scalar are discussed the monotonicity of the scheme is achieved with the explicit adaptive dissipation the development as well as the selected applications of the method are illustrated using a finite volume mesh constructed on the basis of geodesic icosahedral grid which in the past 40 years has been frequently applied in different models of geophysical fluid dynamics the performance of the solver is assessed using a suite of standard tests based on solid body rotation for different initial conditions after analysis of the advection diffusion problem the extension of the method for the equations with reactive terms is presented the performance of the solver is assessed by comparing the results to the analytical solution of the linearized reaction diffusion system in the final part of the paper the application of the solver for studies of nonlinear reactions on the sphere is illustrated the main intended application of the proposed method includes the simulation of transport of chemical constituents in the earth s atmosphere as well as the forecasting of moisture and cloud water fields in numerical weather prediction and climate models

three class roc analysis the equal error utility assumption and the optimality of three class roc surface using the ideal observer previously we have developed a decision model for three class receiver operating characteristic roc analysis based on decision theory the proposed decision model maximizes the expected decision utility under the assumption that incorrect decisions have equal utilities under the same hypothesis equal error utility assumption this assumption reduced the dimensionality of the general three class roc analysis and provided a practical figure of merit to evaluate the three class task performance however it also limits the generality of the resulting model because the equal error utility assumption will not apply for all clinical three class decision tasks the goal of this study was to investigate the optimality of the proposed three class decision model with respect to several other decision criteria in particular besides the maximum expected utility meu criterion used in the previous study we investigated the maximum correctness mc or minimum error maximum likelihood ml and nyman pearson n p criteria we found that by making assumptions for both meu and n p criteria all decision criteria lead to the previously proposed three class decision model as a result this model maximizes the expected utility under the equal error utility assumption maximizes the probability of making correct decisions satisfies the n p criterion in the sense that it maximizes the sensitivity of one class given the sensitivities of the other two classes and the resulting roc surface contains the maximum likelihood decision operating point while the proposed three class roc analysis model is not optimal in the general sense due to the use of the equal error utility assumption the range of criteria for which it is optimal increases its applicability for evaluating and comparing a range of diagnostic systems

linear combinations of biomarkers to improve diagnostic accuracy with three ordinal diagnostic categories many researchers have addressed the problem of finding the optimal linear combination of biomarkers to maximize the area under receiver operating characteristic roc curves for scenarios with binary disease status in practice many disease processes such as alzheimer can be naturally classified into three diagnostic categories such as normal mild cognitive impairment and alzheimer s disease ad and for such diseases the volume under the roc surface vus is the most commonly used index of diagnostic accuracy in this article we propose a few parametric and nonparametric approaches to address the problem of finding the optimal linear combination to maximize the vus we carried out simulation studies to investigate the performance of the proposed methods we apply all of the investigated approaches to a real data set from a cohort study in early stage ad copyright 2012 john wiley sons ltd

a fully multidimensional positive definite advection transport algorithm with small implicit diffusion in numerical modeling of physical phenomena it is often necessary to solve the advective transport equation for positive definite scalar functions numerical schemes of second or higher order accuracy can produce negative values in the solution due to the dispersive ripples lower order schemes such as the donor cell or lax friedrichs or higher order schemes with zeroth order diffusion added produce no ripples but suffer from excessive implicit diffusion in the last ten years a possible resolution of this dilemma has been developed in the form of hybrid schemes in which the advective fluxes are given as a weighted average of a first order positive definite scheme s fluxes and a higher order scheme s fluxes the difference in determination of the weights in the calculation of the average advective fluxes has led to different hybrid schemes two main hybrid type schemes have been developed one the so called flux corrected transport fct method was originated by boris and book i 31 and generalized by zalesak 141 the other was developed by harten and zwas 6 9 in the form of the self adjusting hybrid schemes sahs method both methods were constructed to deal effectively with shocks and contact discontinuities solutions of the advection transport equation obtained by using fct or sahs maintain positive definiteness of the initial condition and as can be seen from presented tests zalesak 141 harten 6 be very accurate unfortunately application of these methods to the modeling of complex multidimensional hydrodynamical systems like atmospheric phenomena is rather limited due to the excessive computer time required furthermore in many hydrodynamical systems

measuring and estimating diagnostic accuracy when there are three ordinal diagnostic groups this article studies the problem of measuring and estimating the diagnostic accuracy when there are three ordinal diagnostic groups we use a receiver operating characteristic roc surface to describe the probabilities of correct classifications into three diagnostic groups based on various sets of diagnostic thresholds of a test and propose to use the entire and the partial volume under the surface to measure the diagnostic accuracy mathematical properties and probabilistic interpretations of the proposed measure of diagnostic accuracy are discussed under the assumption of normal distributions of the diagnostic test from three diagnostic groups we present the maximum likelihood estimate to the volume under the roc surface and give the asymptotic variance to the estimate we further propose several asymptotic confidence interval estimates to the volume under the roc surface the performance of these confidence interval estimates is evaluated in terms of attaining the nominal coverage probability based on a simulation study in addition we develop a method of sample size determination to achieve an adequate accuracy of the confidence interval estimate finally we demonstrate the proposed methodology by applying it to the clinical diagnosis of early stage alzheimer s disease based on the neuropsychological database of the washington university alzheimer s disease research center

clustering ensembles models of consensus and weak partitions clustering ensembles have emerged as a powerful method for improving both the robustness as well as the stability of unsupervised classification solutions however finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph based combinatorial or statistical perspectives this study extends previous research on clustering ensembles in several respects first we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem second we propose a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clusterings a combined partition is found as a solution to the corresponding maximum likelihood problem using the em algorithm third we define a new consensus function that is related to the classical intraclass variance criterion using the generalized mutual information definition finally we demonstrate the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits a simple explanatory model is offered for the behavior of combinations of such weak clustering components combination accuracy is analyzed as a function of several parameters that control the power and resolution of component partitions as well as the number of partitions we also analyze clustering ensembles with incomplete information and the effect of missing cluster labels on the quality of overall consensus experimental results demonstrate the effectiveness of the proposed methods on several real world data sets

an unsplit godunov method for ideal mhd via constrained transport in three dimensions we present a single step second order accurate godunov scheme for ideal mhd which is an extension of the method described in t a gardiner j m stone an unsplit godunov method for ideal mhd via constrained transport j comput phys 205 2005 509 to three dimensions this algorithm combines the corner transport upwind ctu method of colella for multidimensional integration and the constrained transport ct algorithm for preserving the divergence free constraint on the magnetic field we describe the calculation of the ppm interface states for 3d ideal mhd which must include multidimensional mhd source terms and naturally respect the balance implicit in these terms by the b 0 condition we compare two different forms for the ctu integration algorithm which require either 6 or 12 solutions of the riemann problem per cell per time step and present a detailed description of the 6 solve algorithm finally we present solutions for test problems to demonstrate the accuracy and robustness of the algorithm

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer

a new cluster validity for fuzzy clustering abstract fuzzy cluster validity criterion tends to evaluate the quality of fuzzy c partitions produced by fuzzy clustering algorithms many functions have been proposed some methods use only the properties of fuzzy membership degrees to evaluate partitions others techniques combine the properties of membership degrees and the structure of data in this paper a new heuristic method is based on the combination of two functions the search of good clustering is measured by a fuzzy compactness separation ratio the first function calculates this ratio by considering geometrical properties and membership degrees of data the second function evaluates it by using only the properties of membership degrees four numerical examples are used to illustrate its use as a validity functional its effectiveness is compared to some existing cluster validity criterion

the multidimensional positive definite advection transport algorithm further development and applications abstract this paper presents further generalizations of the advection algorithm described in j comput phys 54 1984 325 time dependent velocity fields and a generalized form of the continuity equation are considered applicability of the algorithm to the diffusion equation and to the transport of nonpositive scalars is also discussed theoretical considerations are illustrated through numerical tests and applications to some particular geophysical fluid dynamics problems

cluster ensembles a knowledge reuse framework for combining multiple partitions this paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings we first identify several application scenarios for the resultant knowledge reuse framework that we call cluster ensembles the cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information in addition to a direct maximization approach we propose three effective and efficient techniques for obtaining high quality combiners consensus functions the first combiner induces a similarity measure from the partitionings and then reclusters the objects the second combiner is based on hypergraph partitioning the third one collapses groups of clusters into meta clusters which then compete for each object to determine the combined clustering due to the low computational costs of our techniques it is quite feasible to use a supra consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation we evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios i where the original clusters were formed based on non identical sets of features ii where the original clustering algorithms worked on non identical sets of objects and iii where a common data set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution promising results are obtained in all three situations for synthetic as well as real data sets

comparing fuzzy probabilistic and possibilistic partitions when clustering produces more than one candidate to partition a finite set of objects o there are two approaches to validation i e selection of a best partition and implicitly a best value for c which is the number of clusters in o first we may use an internal index which evaluates each partition separately second we may compare pairs of candidates with each other or with a reference partition that purports to represent the true cluster structure in the objects this paper generalizes many of the classical indices that have been used with outputs of crisp clustering algorithms so that they are applicable for candidate partitions of any type i e crisp or soft with soft comprising the fuzzy probabilistic and possibilistic cases space prevents inclusion of all of the possible generalizations that can be realized this way here we concentrate on the rand index and its modifications we compare our fuzzy rand index with those of campello hullermeier and rifqi and brouwer and show that our extension of the rand index is o n while the other three are all o n2 numerical examples are given to illustrate various facets of the new indices in particular we show that our indices can be used even when the partitions are probabilistic or possibilistic and that our method of generalization is valid for any index that depends only on the entries of the classical i e four pair types contingency table for this problem

three class roc analysis toward a general decision theoretic solution multiclass receiver operating characteristic roc analysis has remained an open theoretical problem since the introduction of binary roc analysis in the 1950s previously we have developed a paradigm for three class roc analysis that extends and unifies decision theoretic linear discriminant analysis and probabilistic foundations of binary roc analysis in a three class paradigm one critical element in this paradigm is the equal error utility eeu assumption this assumption allows us to reduce the intrinsic space of the three class roc analysis 5 d hypersurface in 6 d hyperspace to a 2 d surface in the 3 d space of true positive fractions sensitivity space in this work we show that this 2 d roc surface fully and uniquely provides a complete descriptor for the optimal performance of a system for a three class classification task i e the triplet of likelihood ratio distributions assuming such a triplet exists to be specific we consider two classifiers that utilize likelihood ratios and we assumed each classifier has a continuous and differentiable 2 d sensitivity space roc surface under these conditions we proved that the classifiers have the same triplet of likelihood ratio distributions if and only if they have the same 2 d sensitivity space roc surfaces as a result the 2 d sensitivity surface contains complete information on the optimal three class task performance for the corresponding likelihood ratio classifier