on maximally selected chi square statistics two samples can be compared by selecting a cutpoint and then forming a 2 x 2 table of the numbers of observations above and below the cutpoint in each sample miller and siegmund 1982 biometrics 38 1011 1016 investigated asymptotic theory relating to the distribution of the standard chisquare statistic when the cutpoint is selected to maximize its value in a companion article halpern 1982 biometrics 38 1017 1023 studied the finite sample distribution of this maximally selected chi square statistic via simulation exact finite sample distribution theory derived from durbin s 1971 journal of applied probability 8 431 453 1973 distribution theory for tests based on the sample distribution function philadelphia siam combinatorial approach is presented here

testing for measurement invariance with respect to an ordinal variable researchers are often interested in testing for measurement invariance with respect to an ordinal auxiliary variable such as age group income class or school grade in a factor analytic context these tests are traditionally carried out via a likelihood ratio test statistic comparing a model where parameters differ across groups to a model where parameters are equal across groups this test neglects the fact that the auxiliary variable is ordinal and it is also known to be overly sensitive at large sample sizes in this paper we propose test statistics that explicitly account for the ordinality of the auxiliary variable resulting in higher power against monotonic violations of measurement invariance and lower power against non monotonic ones the statistics are derived from a family of tests based on stochastic processes that have recently received attention in the psychometric literature the statistics are illustrated via an application involving real data and their performance is studied via simulation

distance spectra of graphs a survey abstract in 1971 graham and pollack established a relationship between the number of negative eigenvalues of the distance matrix and the addressing problem in data communication systems they also proved that the determinant of the distance matrix of a tree is a function of the number of vertices only since then several mathematicians were interested in studying the spectral properties of the distance matrix of a connected graph computing the distance characteristic polynomial and its coefficients was the first research subject of interest thereafter the eigenvalues attracted much more attention in the present paper we report on the results related to the distance matrix of a graph and its spectral properties

on isometric embeddings of graphs si g est un graphe connexe fini v e une facon standard de definir une distance d g sur g est de definir d g x y comme etant le nombre d aretes dans un chemin le plus court joignant x et y dans v on etudie la theorie des plongements isometriques de graphes dans des produits cartesiens d espaces metriques

an improved bonferroni inequality and applications summary we present an improved bonferroni inequality which gives an upper bound for the probability of the union of an arbitrary sequence of events the bound is constructed in terms of the joint probability of pairs of events which are represented by edges on a graph examples of applications to periodicity location shift detection kolmogorovsmirnov tests and outlier detection are given

accuracy and cut off point selection in three class classification problems using a generalization of the youden index we study properties of the index j 3 defined as the accuracy or the maximum correct classification for a given three class classification problem specifically using j 3 one can assess the discrimination between the three distributions and obtain an optimal pair of cut off points c 1 c 2 in the sense that the sum of the correct classification proportions will be maximized it also serves as the generalization of the youden index in three class problems parametric and non parametric approaches for estimation and testing are considered and methods are applied to data from an mrs study on human immunodeficiency virus hiv patients

approximating the distribution of maximally selected mcnemar s statistics summary it is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold with paired data and with a threshold chosen without reference to the outcomes mcnemar s test of marginal homogeneity may be applied to the resulting dichotomous pairs when testing for equality of the marginal distributions of the underlying continuous outcomes if the threshold is chosen to maximize the test statistic however referring the resulting test statistic to the nominal x2 distribution is incorrect instead the p value must be adjusted for the multiple comparisons here the distribution of a maximally selected mcnemar s statistic is derived and it is shown that an approximation due to durbin 1985 journal of applied probability22 99 122 may be used to estimate approximate p values the methodology is illustrated by an application to measurements of insulin like growth factor i igf i in matched prostate cancer cases and controls from the physicians health study the results of simulation experiments that assess the accuracy of the approximation in moderate sample sizes are reported

maximally selected chi square statistics two samples can be compared by selecting a cut point and then forming a 2 x 2 table of the numbers of observations above and below the cut point in each sample when the cut point is selected so as to maximize the standard chi square statistic the chi square percentile points are inappropriate actual significance levels are computed for large samples and correct percentile poillts are tabulated

asymptotic analysis of a slightly rarefied gas with nonlocal boundary conditions in this paper nonlocal boundary conditions for the navier stokes equations are derived starting from the boltzmann equation in the limit for the knudsen number being vanishingly small in the same spirit of lombardo et al in j stat phys 130 69 82 2008 where a nonlocal poisson scattering kernel was introduced a gaussian scattering kernel which models nonlocal interactions between the gas molecules and the wall boundary is proposed it is proved to satisfy the global mass conservation and a generalized reciprocity relation the asymptotic expansion of the boundary value problem for the boltzmann equation provides in the continuum limit the navier stokes equations associated with a class of nonlocal boundary conditions of the type used in turbulence modeling

inverted velocity profile in the cylindrical couette flow of a rarefied gas the cylindrical couette flow of a rarefied gas is investigated under the diffuse specular reflection condition of maxwell s type on the cylinders in the case where the inner cylinder is rotating whereas the outer cylinder is at rest the inverted velocity profile for small accommodation coefficients pointed out by tibbs baras and garcia phys rev e 56 2282 1997 on the basis of a monte carlo simulation is investigated extensively by means of a systematic asymptotic analysis for small knudsen numbers as well as the direct numerical analysis of the boltzmann equation and the parameter range in which the phenomenon appears is clarified

maximally selected x2 statistics for kx 2 tables summary it is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold with such a dichotomized outcome the usual x2 statistics for association or trend can be used to test for equality of proportions across strata of the study population however if the threshold is chosen to maximize the test statistic the nominal x2 reference distributions are incorrect in this paper the asymptotic distributions of maximally selected x2 statistics for association and for trend for the k 2 table are derived the methodology is illustrated with data from an aids clinical trial the results of simulation experiments that assess the accuracy of the asymptotic distributions in moderate sample sizes are also reported

the numerical evaluation of certain multivariate normal integrals abstract we show that a multivariate normal integral with tridiagonal covariance matrix can be computed efficiently using iterated integration

implicit high order method for calculating rarefied gas flow in a planar microchannel an efficient numerical algorithm for calculating rarefied gas flows in planar microchannels on the basis of the boltzmann kinetic equation with the linearized s model collision integral is presented the algorithm consists of a high order spatial discretisation on unstructured meshes conservative procedure to calculate macroscopic quantities and efficient one step implicit time evolution method it therefore works across all flow regimes from the free molecular to nearly continuum ones and provides rapid convergence to steady state solutions the parallel implementation is provided via mpi programming paradigm the performance of the method is illustrated by computing the flow for length to the width ratios for up to 10 3 in the wide range of knudsen numbers numerical estimates of efficiency of implicit time marching and parallel performance as well as convergence studies in both physical and velocity spaces are provided the end effects and other essentially two dimensional features of the flow are analysed and a detailed comparison with the case of an infinitely long channel is carried out the presented numerical data can be used as reference for future studies of nonlinear flows as well as for comparison with other numerical approaches and flow models

consistent lattice boltzmann modeling of low speed isothermal flows at finite knudsen numbers in slip flow regime ii application to curved boundaries gaseous flows inside microfluidic devices often fall in the slip flow regime according to this theoretical description the navier stokes model remains applicable in bulk while at solid walls a slip velocity boundary model shall be considered physically it is well established that to properly account for the wall curvature the wall slip velocity must be determined by the shear stress rather than the normal component of the velocity derivative alone as commonly applied to planar surfaces it follows that the numerical transcription of this type of boundary condition is generally a challenging task for standard computational fluid dynamics cfd techniques this paper aims to show that the realization of the slip velocity condition on arbitrarily shaped boundaries can be accomplished in a natural way with the lattice boltzmann method lbm to substantiate this conclusion this work undertakes the following three studies first we examine the conditions under which the generic reflection type boundary rules used by lbm become consistent models for the slip velocity boundary condition this effort makes use of the second order chapman enskog expansion method where we address both planar and curved boundaries the analysis also clarifies the capabilities and limitations behind the considered reflection type slip schemes second we revisit the family of parabolic accurate lbm slip boundary schemes originally formulated in phys rev e 96 013311 2017 2470 004510 1103 physreve 96 013311 on the basis of the multireflection framework and discuss their characteristics when operating on curved boundaries as well as the limitations of other less accurate lbm slip boundary formulations such as the linearly accurate slip schemes and the widely popular kinetic based boundary schemes in addition we also discuss the numerical stability of the parabolic slip schemes previously developed providing an heuristic strategy to improve their stable range of operation third we evaluate the performance of the several slip boundary schemes debated in this paper the numerical tests correspond to two classical 2d benchmark flow problems of slip over non planar solid surfaces namely i the velocity profile of the cylindrical couette flow and ii the permeability of a slow rarefied gas over a periodic array of circular cylindrical obstacles the obtained numerical results confirm the competitiveness of the lbm when equipped with slip boundary schemes of parabolic accuracy as cfd tool to simulate slippage phenomena over arbitrarily non planar surfaces indeed although operating on a simple uniform mesh discretization the lbm yields a similar or even superior level of accuracy compared to state of the art fem simulations conducted on hardworking body fitted meshes this conclusion establishes the lbm as a very appealing cfd technique for simulating microfluidic flows in the slip flow regime a result that deserves further exploration in future studies

discrimination surfaces with application to region specific brain asymmetry analysis discrimination surfaces are here introduced as a diagnostic tool for localizing brain regions where discrimination between diseased and nondiseased participants is higher to estimate discrimination surfaces we introduce a mann whitney type of statistic for random fields and present large sample results characterizing its asymptotic behavior simulation results demonstrate that our estimator accurately recovers the true surface and corresponding interval of maximal discrimination the empirical analysis suggests that in the anterior region of the brain schizophrenic patients tend to present lower local asymmetry scores in comparison with participants in the control group

applications of cut polyhedra ii abstract in this paper and in its continuation part ii this issue we group within a unified framework many applications of the following polyhedra cut boolean quadric hypermetric and metric polyhedra we treat in particular the following applications l1 and l1 metrics in functional analysis the max cut problem the boole problem and multicommodity flow problems in combinatorial optimization lattice holes in geometry of numbers density matrices of many fermions systems in quantum mechanics we present some other applications in probability theory statistical data analysis and design theory in this first part after introducing the main definitions and operations for cut polyhedra we describe the connections with l1 metrics and with other metric properties and we consider in particular the applications to some classes of metrics arising from graphs normed spaces and lattices

distance geometry for kissing spheres abstract a kissing sphere is a sphere that is tangent to a fixed reference ball we develop in this paper a distance geometry for kissing spheres which turns out to be a generalization of the classical euclidean distance geometry

on the multidimensional gas kinetic bgk scheme this paper concerns the performance difference among the multidimensional md gas kinetic bgk scheme the corresponding quasi one dimensional q1d extension and the directional splitting ds scheme with kinetic boundary conditions the md scheme includes tangential slopes in the flux calculation which are absent in a q1d or ds method in spite of taking more computational time the md scheme is found to be able to capture the characteristics of rarefied flow having a boundary with curvature or a nonuniform temperature such as the inverted velocity distribution in rarefied cylindrical couette flow and the weak flow field induced by the temperature gradient of a body where the q1d fails the md scheme can also yield clearly better results in high speed microchannel flow and power law fluid flow between concentric rotating cylinders when compared with direct simulation monte carlo studies and analytic solutions in the low reynolds number flow around a naca0012 airfoil case the md scheme and the q1d method predict wall heat flux distribution with obvious difference the ds method predicts results nearly identical to those from q1d in these steady flow cases except that it can hardly give reasonable solutions in power law fluid case with viscous exponential factor away from unity correct prediction of the stress and the wall temperature gradient is considered responsible for this better performance in simulations of the scalar convection diffusion equation it is found that the inclusion of tangential slopes in the flux computation can clearly improve the temporal accuracy of the scheme in this case the ds scheme also shows good performance the present study suggests caution in adopting of the q1d extension or ds method in multidimensional flow when it is sensitive to the accuracy of stress or wall variable gradient calculations it is better to use the md scheme for high performance simulation

boundary singularity for thermal transpiration problem of the linearized boltzmann equation we study the boundary singularity of the fluid velocity for the thermal transpiration problem in the kinetic theory logarithmic singularity has been demonstrated through the asymptotic and computational analysis the goal of this paper is to confirm this logarithmic singularity through exact analysis we use an iterated scheme with the gain part of the collision operator as a source the iterated scheme is appropriate for large knudsen numbers considered here and yields an explicit leading term

unbiased split variable selection for random survival forests using maximally selected rank statistics the most popular approach for analyzing survival data is the cox regression model the cox model may however be misspecified and its proportionality assumption may not always be fulfilled an alternative approach for survival prediction is random forests for survival outcomes the standard split criterion for random survival forests is the log rank test statistic which favors splitting variables with many possible split points conditional inference forests avoid this split variable selection bias however linear rank statistics are utilized by default in conditional inference forests to select the optimal splitting variable which cannot detect non linear effects in the independent variables an alternative is to use maximally selected rank statistics for the split point selection as in conditional inference forests splitting variables are compared on the p value scale however instead of the conditional monte carlo approach used in conditional inference forests p value approximations are employed we describe several p value approximations and the implementation of the proposed random forest approach a simulation study demonstrates that unbiased split variable selection is possible however there is a trade off between unbiased split variable selection and runtime in benchmark studies of prediction performance on simulated and real datasets the new method performs better than random survival forests if informative dichotomous variables are combined with uninformative variables with more categories and better than conditional inference forests if non linear covariate effects are included in a runtime comparison the method proves to be computationally faster than both alternatives if a simple p value approximation is used copyright 2017 john wiley sons ltd

metric transforms and euclidean embeddings it is proved that if 0 c 0 72 then for any point met ric space x d the metric space x dc is isometrically embeddable into a euclidean space for 6 point metric space c j log2 is the largest exponent that guarantees the existence of isometric embeddings into a euclidean space such largest exponent is also determined for all point graphs with truncated distance

non local scattering kernel and the hydrodynamic limit in this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory we consider the possibility that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall this results in a scattering kernel which is a non local generalization of the classical maxwell scattering kernel the proposed scattering kernel satisfies a global mass conservation law and a generalized reciprocity relation we study the hydrodynamic limit performing a knudsen layer analysis and derive a new class of weakly nonlocal boundary conditions to be imposed to the navier stokes equations

the semigroup of metric measure spaces and its infinitely divisible probability measures a metric measure space is a complete separable metric space equipped with a probability measure that has full support two such spaces are equivalent if they are isometric as metric spaces via an isometry that maps the probability measure on the first space to the probability measure on the second the resulting set of equivalence classes can be metrized with the gromov prohorov metric of greven pfaffelhuber and winter we consider the natural binary operation on this space that takes two metric measure spaces and forms their cartesian product equipped with the sum of the two metrics and the product of the two probability measures we show that the metric measure spaces equipped with this operation form a cancellative commutative polish semigroup with a translation invariant metric there is an explicit family of continuous semicharacters that is extremely useful for inter alia establishing that there are no infinitely divisible elements and that each element has a unique factorization into prime elements we investigate the interaction between the semigroup structure and the natural action of the positive real numbers on this space that arises from scaling the metric for example we show that for any given positive real numbers a b c the trivial space is the only space that satisfies a b c we establish that there is no analogue of the law of large numbers if x1 x2 is an identically distributed independent sequence of random spaces then no subsequence of formula see text converges in distribution unless each xk is almost surely equal to the trivial space we characterize the infinitely divisible probability measures and the levy processes on this semigroup characterize the stable probability measures and establish a counterpart of the lepage representation for the latter class

euclidean graph distance matrices of generalizations of the star graph abstract in this paper a relation between graph distance matrices of the star graph and its generalizations and euclidean distance matrices is considered it is proven that distance matrices of certain families of graphs are circum euclidean their spectrum and generating points are given in a closed form

second order knudsen layer analysis for the generalized slip flow theory ii curvature effects numerical analyses of the second order knudsen layer are carried out on the basis of the linearized boltzmann equation for hard sphere molecules under the diffuse reflection boundary condition the effects of the boundary curvature have been clarified in details thereby completing the numerical data required up to the second order of the knudsen number for the asymptotic theory of the boltzmann equation the generalized slip flow theory a local singularity appears as a result of the expansion at the level of the velocity distribution function when the curvature exists

slip boundary conditions for the compressible navier stokes equations the slip boundary conditions for the compressible navier stokes equations are derived systematically from the boltzmann equation on the basis of the chapman enskog solution of the boltzmann equation and the analysis of the knudsen layer adjacent to the boundary the resulting formulas of the slip boundary conditions are summarized with explicit values of the slip coefficients for hard sphere molecules as well as the bhatnagar gross krook model these formulas which can be applied to specific problems immediately help to prevent the use of often used slip boundary conditions that are either incorrect or without theoretical basis

maximally selected rank statistics a common statistical problem is the assessment of the predictive power of a quantitative variable for some dependent variable a maximally selected rank statistic regarding the quantitative variable provides a test and implicitly an estimate of a cutpoint as a simple classification rule restricting the selection to an arbitrary given inner part of the support of the quantitative variable we show that the asymptotic null distribution of the maximally selected rank statistic is the distribution of the supremum of the absolute value of a standardized gaussian process on an interval the asymptotic argument holds also in the case of tied or censored observations we compare monte carlo results with an approximation of the asymptotic distribution under the null hypothesis in addition we investigate the behaviour of the test procedure and of the familiar spearman rank test for independence under some alternatives moreover we discuss some aspects of the problem of estimating an underlying cutpoint

analytical solution of axi symmetrical lattice boltzmann model for cylindrical couette flows abstract analytical solution for the axi symmetrical lattice boltzmann model is obtained for the low mach number cylindrical couette flows in the hydrodynamic limit the present solution is in excellent agreement with the result of the navier stokes equation since the kinetic boundary condition is used the present analytical solution using nine discrete velocities can describe flows with the knudsen number up to 0 1 meanwhile the comparison with the simulation data obtained by the direct simulation monte carlo method shows that higher order lattice boltzmann models with more discrete velocities are needed for highly rarefied flows

generalized maximally selected statistics maximally selected statistics for the estimation of simple cutpoint models are embedded into a generalized conceptual framework based on conditional inference procedures this powerful framework contains most of the published procedures in this area as special cases such as maximally selected chi squared and rank statistics but also allows for direct construction of new test procedures for less standard test problems as an application a novel maximally selected rank statistic is derived from this framework for a censored response partitioned with respect to two ordered categorical covariates and potential interactions this new test is employed to search for a high risk group of rectal cancer patients treated with a neo adjuvant chemoradiotherapy moreover a new efficient algorithm for the evaluation of the asymptotic distribution for a large class of maximally selected statistics is given enabling the fast evaluation of a large number of cutpoints

finite metric spaces of strictly negative type abstract we prove that if a finite metric space is of strictly negative type then its transfinite diameter is uniquely realized by the infinite extender load vector finite metric spaces that have this property include all spaces on two three or four points all trees and all finite subspaces of euclidean spaces we prove that if the distance matrix is both hypermetric and regular then it is of strictly negative type we show that the strictly negative type finite subspaces of spheres are precisely those which do not contain two pairs of antipodal points in connection with an open problem raised by kelly we conjecture that all finite subspaces of hyperbolic spaces are hypermetric and regular and hence of strictly negative type