morse theory for periodic solutions of hamiltonian systems and the maslov index in this paper we prove morse type inequalities for the contractible 1 periodic solutions of time dependent hamiltonian differential equations on those compact symplectic manifolds m for which the symplectic form and the first chern class of the tangent bundle vanish over q m the proof is based on a version of infinite dimensional morse theory which is due to floer the key point is an index theorem for the fredholm operator which plays a central role in floer homology the index formula involves the maslov index of nondegenerate contractible periodic solutions this maslov index plays the same role as the morse index of a nondegenerate critical point does in finite dimensional morse theory we shall use this connection between floer homology and maslov index to establish the existence of infinitely many periodic solutions having integer periods provided that every i periodic solution has at least one floquet multiplier which is not equal to 1

highly flexible distributions to fit multiple frequency financial returns abstract financial data are usually studied via low flexible distributions independently of the frequency of the data due to their simplicity and analytical tractability in this paper we analyze two highly flexible five parameter distributions into fitting financial returns these are the skewed generalized t sgt and the generalized hyperbolic gh applications carried on two exchange rates euro dollar and dollar yen and two indexes s p 500 and nikkei 225 over four frequencies weekly daily 30 min and 5 min confirm the superiority of the sgt and gh in approximating the distribution of a given data at a remarkable precision moreover as we move from higher to lower frequency the distribution s overall shape does indeed change radically and the estimated parameters refute the tendency to normality which calls into question the aggregational gaussianity s stylized fact

regression models for relative survival four approaches to estimating a regression model for relative survival using the method of maximum likelihood are described and compared the underlying model is an additive hazards model where the total hazard is written as the sum of the known baseline hazard and the excess hazard associated with a diagnosis of cancer the excess hazards are assumed to be constant within pre specified bands of follow up the likelihood can be maximized directly or in the framework of generalized linear models minor differences exist due to for example the way the data are presented individual aggregated or grouped and in some assumptions e g distributional assumptions the four approaches are applied to two real data sets and produce very similar estimates even when the assumption of proportional excess hazards is violated the choice of approach to use in practice can therefore be guided by ease of use and availability of software we recommend using a generalized linear model with a poisson error structure based on collapsed data using exact survival times the model can be estimated in any software package that estimates glms with user defined link functions including sas stata s plus and r and utilizes the theory of generalized linear models for assessing goodness of fit and studying regression diagnostics

a nonparametric test for spatial isotropy using subsampling a common requirement for spatial modeling is the development of an appropriate correlation structure although the assumption of isotropy is often made for this structure it is not always appropriate a conventional practice when checking for isotropy is to informally assess plots of direction specific sample semi variograms although a useful diagnostic these graphical techniques are difficult to assess and open to interpretation formal alternatives to graphical diagnostics are valuable but have been applied to a limited class of models in this article we propose a formal approach to test for isotropy that is both objective and valid for a wide class of models this approach which is based on the asymptotic joint normality of the sample variogram can be used to compare sample variograms in multiple directions an l2 consistent subsampling estimator for the asymptotic covariance matrix of the sample variogram is derived and used to construct a test statistic a subsampling approach and a limiting

a superquadratic indefinite elliptic system and its morse conley floer homology we study critical points of the indefinite functional f h u v int nabla u cdot nabla v h x u v mathrm d x by applying floer s homology construction to the ordinary gradient flow of the functional f on a suitable sobolev space one of our main observations is that even though this flow is well posed in both time directions and lacks any kind of smoothing property one can still obtain compactness of connecting orbit spaces and thus define the floer homology for f h

an infinite dimensional morse theory with applications in this paper we construct an infinite dimensional extraordinary cohomology theory and a morse theory corresponding to it these theories have some special properties which make them useful in the study of critical points of strongly indefinite functionals by strongly indefinite we mean a functional unbounded from below and from above on any subspace of finite codimension several applications are given to hamiltonian systems the onedimensional wave equation of vibrating string type and systems of elliptic partial differential equations 0 introduction let e be a real hilbert space with an inner product and let be a twice continuously differentiable functional denote the frechet derivative and the gradient of at x by x and x respectively where as usual x y x y y e recall that a point x0 e is said to be critical if x0 0 or equivalently if x0 0 the level c r will be called regular if 1 c contains no critical points and critical if x0 0 for some x0 1 c let a b a b be two regular levels of denote m 1 a b and consider the restriction of to m in morse theory one is interested in the local topological structure of the level sets of m near a critical point and in the relation between this local structure and the topological structure of the set m to be more specific suppose that x0 m is an isolated critical point of then one defines a sequence of critical groups of at x0 by setting cq x0 hq c u u x0 q 0 1 2 0 1 where c x0 c x e x c hq is the q th singular homology group with coefficients in some field f and u is a neighbourhood of x0 define the morse index of x0 to be the maximal dimension of a subspace of e on which the quadratic form x0 y y is negative definite one shows that if x0 is a nondegenerate critical point i e if x0 e e is invertible then cq x0 f received by the editors march 20 1995 1991 mathematics subject classification primary 58e05 secondary 34c25 35j65 35l05 55n20 58f05

infinitely many solutions for symmetric and non symmetric elliptic systems we study an elliptic system equivalent to a fourth order elliptic equation by using variational and perturbative methods we prove the existence of infinitely many solutions both in the symmetric and in the non symmetric case

homological approach to problems with jumping non linearity abstract in this paper we use a perturbed version of the rabinowitz floer homology to find solutions to pde s with jumping nonlinearities as applications we find branches for the fucik spectrum for the laplace equation and for systems on manifolds that fiber over s 1

aerodynamic influence coefficient computations using euler navier stokes equations on parallel computers an efficient procedure to compute aerodynamic influence coefficients aic using high fidelity flow equations such as euler navier stokes equations is presented the aic s are computed by perturbing structures using mode shapes the procedure is developed on a multiple instruction multiple data mimd parallel computer in addition to discipline parallelization and coarse grain parallelization of the flow domain embarrassingly parallel implementation of ens aero code demonstrates linear speedup for a large number of processors demonstration of the aic computation for static aeroelasticity analysis is made on an arrow wing body configuration the computations show that some of the aic s do not converge at the lower perturbation range since the perturbation is too small to prevail over the initial aerodynamic loads the effect of initial aerodynamic loads disappears with increasing perturbation amplitude the demonstrated linear scalability for multiple concurrent analyses shows that the threelevel parallelism in the code is well suited for the computation of the aic s

canonical multi symplectic structure on the total exterior algebra bundle exterior algebra bundle on m on the fibre which has dimension 2 n the form q can be locally decomposed into n classical symplectic structures when concatenated these nsymplectic structures define a partial differential operator jv which turns out to be a dirac operator with multi symplectic structure the operator jv generalizes the product operator j d dt in classical symplectic geometry and m is a generalization of the base manifold i e time in classical hamiltonian dynamics the structure generated by q provides a natural setting for analysing a class of covariant nonlinear gradient elliptic operators the operator jv is elliptic and the generalization of hamiltonian systems jvzzvs z for a section z of the total exterior algebra bundle is also an elliptic pde the inverse problem find s z for a given elliptic pde is shown to be related to a variant of the legendre transform on k forms the theory is developed for flat base manifolds but the constructions are coordinate free and generalize to riemannian manifolds with non trivial curvature some applications and implications of the theory are also discussed

solution adaptive grid strategies based on point redistribution solution adaptive grid strategies based on the redistribution of a fixed number of points are described in this paper the redistribution is performed using weight functions that vary based on significant flow features the weight functions are evaluated using an equidistribution principle in this paper emphasis is placed on the development of weight functions applicable to compressible flows exhibiting large scale separated vortical flows vortex vortex and vortex surface interactions separated shear layers and multiple shocks of diaerent intensities algebraic elliptic and parabolic methods of grid generation have been utilized for structured grid redistribution additionally a point movement scheme is presented for generalized structured unstructured hybrid grid adaptation computer aided geometry design cagd techniques are combined with redistribution schemes to maintain the fidelity of solid boundaries in particular solid boundaries are represented using non uniform rational b splines nurbs a grid generation software system parallel multiblock adaptive grid generation pmag using an elliptic redistribution scheme is also described with emphasis placed on the parallel implementation for multiblock structured grids with unstructured blocking topologies and on interpolation issues computational examples demonstrating the influence of diaerent weight functions and grid redistribution strategies are presented 2000 elsevier science s a all rights reserved

morse homology for asymptotically linear dirac equations on compact manifolds abstract we give constructions and calculations of morse co homologies for asymptotically linear dirac equations on compact manifolds which are non resonance at infinity or resonance at infinity and satisfy landesman lazer type conditions for the non resonance case we show that the homology depends only on the homotopy class of the linear part at infinity while for the resonance case the co homology is isomorphic with the morse co homology of the restriction of the perturbation term to the degenerate space at infinity from these co homologies are explicitly calculated applications to the existence of solutions of asymptotically linear dirac equations is also given

powerful goodness of fit tests based on the likelihood ratio summary a new approach of parameterization is proposed to construct a general goodnessof fit test it can not only generate traditional tests including the kolmogorov smirnov cramer von mises and anderson darling tests but also produce new types of omnibus tests which are generally much more powerful than the old ones

entropy based tests of uniformity abstract the power properties of an entropy based test are investigated when used for testing uniformity on 0 1 percentage points and power against seven alternatives are reported compared with other tests of uniformity the entropy based test possesses good power properties for many alternatives some asymptotic null and alternative distributions are derived for sample sizes up to 100 the table of percentage points provides a practical guide for using this test a theory of entropy based tests of distributional hypotheses other than uniformity is outlined

variational identities and applications to differential systems j serrin 1 introduction in the work of ponos p and in recent work of pucci serrin ps variational identities are discussed which are useful for solving various ques tions about elliptic differential equations and particular elliptic systems here we obtain a number of further applications of these identities to systems it was noted in ps that these identities are closely related to noether s theorem for variational problems by working out the divergence term arising in noether s theorem and making some simplifications one obtains a general identity for variational problems if a variational integral has a symmetry group g with the following infinitesimal generator

a relative survival regression model using b spline functions to model non proportional hazards relative survival a method for assessing prognostic factors for disease specific mortality in unselected populations is frequently used in population based studies however most relative survival models assume that the effects of covariates on disease specific mortality conform with the proportional hazards hypothesis which may not hold in some long term studies to accommodate variation over time of a predictor s effect on disease specific mortality we developed a new relative survival regression model using b splines to model the hazard ratio as a flexible function of time without having to specify a particular functional form our method also allows for testing the hypotheses of hazards proportionality and no association on disease specific hazard accuracy of estimation and inference were evaluated in simulations the method is illustrated by an analysis of a population based study of colon cancer

affine processes a test of isotropy based on level sets the class of affine processes is defined as a reasonable alternative to test the null hypothesis that a given process is isotropic estimators for the affinity parameters based only on one level set of the observed process are provided and they are shown to be consistent under partial independence assumptions then asymptotic procedures are proposed to test the isotropy of a stationary process with parameter in bf r 2

dirac operators coupled to instantons on positive definite four manifolds we study the moduli space of instantons on a simply connected positive definite closed four manifold by analyzing the classifying map of the index bundle of a family of dirac operators parameterized by the moduli space as an application we compute the cohomology rings for the charge 1 and 2 moduli spaces in the rank stable limit

morse homology of super quadratic hamiltonian systems on r2n abstract we study periodic solutions of the hamiltonian system x t j h t x where j is the standard symplectic matrix h is 2 periodic in t and super quadratic in x in some sense using the morse homology theory developed in a abbondandolo p majer morse homology on hilbert spaces comm pure appl math 54 2001 689 758 we get some existence results of periodic solutions

braid floer homology abstract area preserving diffeomorphisms of a 2 disc can be regarded as time 1 maps of non autonomous hamiltonian flows on r z d 2 the periodic flow lines define braid conjugacy classes up to full twists we examine the dynamics relative to such braid classes and define a new invariant for such classes the braid floer homology this refinement of floer homology originally used for the arnol d conjecture yields a morse type forcing theory for periodic points of area preserving diffeomorphisms of the 2 disc based on braiding contributions of this paper include 1 a monotonicity lemma for the behavior of the nonlinear cauchy riemann equations with respect to algebraic lengths of braids 2 establishment of the topological invariance of the resulting braid floer homology 3 a shift theorem describing the effect of twisting braids in terms of shifting the braid floer homology 4 computation of examples and 5 a forcing theorem for the dynamics of hamiltonian disc maps based on braid floer homology

the role of the green s function in a non linear elliptic equation involving the critical sobolev exponent this paper is concerned with non linear elliptic problems of the type pe u u n 2 n 2 eu u 0 on u 0 on where is a smooth and bounded domain in rn n 4 and e 0 we show that if the ue are solutions of pe which concentrate around a point as e 0 then this point cannot be on the boundary of and is a critical point of the regular part of the green s function conversely we show that for n 5 and any non degenerate critical point x0 of the regular part of the green s function there exist solutions of pe concentrating around x0 as e 0

wavelet variance analysis for random fields on a regular lattice there has been considerable recent interest in using wavelets to analyze time series and images that can be regarded as realizations of certain 1 d and 2 d stochastic processes on a regular lattice wavelets give rise to the concept of the wavelet variance or wavelet power spectrum which decomposes the variance of a stochastic process on a scale by scale basis the wavelet variance has been applied to a variety of time series and a statistical theory for estimators of this variance has been developed while there have been applications of the wavelet variance in the 2 d context in particular in works by unser in 1995 on wavelet based texture analysis for images and by lark and webster in 2004 on analysis of soil properties a formal statistical theory for such analysis has been lacking in this paper we develop the statistical theory by generalizing and extending some of the approaches developed for time series thus leading to a large sample theory for estimators of 2 d wavelet variances we apply our theory to simulated data from gaussian random fields with exponential covariances and from fractional brownian surfaces we demonstrate that the wavelet variance is potentially useful for texture discrimination we also use our methodology to analyze images of four types of clouds observed over the southeast pacific ocean

estimating net survival the importance of allowing for informative censoring net survival the one that would be observed if cancer were the only cause of death is the most appropriate indicator to compare cancer mortality between areas or countries several parametric and non parametric methods have been developed to estimate net survival particularly when the cause of death is unknown these methods are based either on the relative survival ratio or on the additive excess hazard model the latter using the general population mortality hazard to estimate the excess mortality hazard the hazard related to net survival the present work used simulations to compare estimator abilities to estimate net survival in different settings such as the presence absence of an age effect on the excess mortality hazard or on the potential time of follow up knowing that this covariate has an effect on the general population mortality hazard too it showed that when age affected the excess mortality hazard most estimators including specific survival were biased only two estimators were appropriate to estimate net survival the first is based on a multivariable excess hazard model that includes age as covariate the second is non parametric and is based on the inverse probability weighting these estimators take differently into account the informative censoring induced by the expected mortality process the former offers great flexibility whereas the latter requires neither the assumption of a specific distribution nor a model building strategy because of its simplicity and availability in commonly used software the nonparametric estimator should be considered by cancer registries for population based studies

enumeration of genus two curves with a fixed complex structure in ℙ 2 and ℙ 3 the main concrete result of this paper is enumeration of genus two curves with complex structure fixed in p and p along the way rational curves with certain simple singularities are counted as well while the methods described can be used to count positive genus curves in some other cases the most powerful direct applications of the machinery developed are to enumeration of rational curves with a very large class of singularities in projective spaces

solutions of superlinear elliptic equations and their morse indices we consider here solutions of semilinear second order elliptic equations with superlinear nonlinearities and we present some relationships between their morse indices and some qualitative properties in particular we show that for uo subcritical nonlinearities bounds on solutions are equivalent to bounds on their morse indices

on critical point theory for indefinite functionals in the presence of symmetries we consider functionals which are not bounded from above or from below even modulo compact perturbations and which exhibit certain symmetries with respect to the action of a compact lie group we develop a method which permits us to prove the existence of multiple critical points for such functionals the proofs are carried out directly in an infinite dimensional hilbert space and they are based on minimax arguments the applications given here are to hamiltonian systems of ordinary differential equations where the existence of multiple time periodic solutions is established for several classes of hamiltonians symmetry properties of these hamiltonians such as time translation invariancy or evenness are exploited introduction many variational problems which arise from physics or mathematical physics are indefinite in the sense that the functionals involved are not bounded from below or from above however some of these functionals defined in an appropriate function space are semidefinite in the sense that they are bounded from below or from above if perturbed with a weakly continuous functional this paper deals with functionals which are not semidefinite usually problems involving indefinite functionals are more difficult to handle and only very recently a method has been developed which permits us to treat such problems directly in an infinite dimensional function space 7 in 7 some theorems have been proved which establish the existence of at least one nontrivial critical point for such functionals in many physical situations there are problems which have symmetries with respect to the action of some lie group in this case we expect the existence of many critical points this has been established for semidefinite functionals cf e g 8 and 3 for even functionals 9 for a zp action with p prime numbers 15 16 10 and 6 for an s action in this paper we develop a method which allows us to estimate the number of critical points of indefinite functionals in the presence of symmetries more precisely received by the editors july 16 1980 and in revised form june 26 1981 1980 mathematics subject classification primary 58e05 70h05 secondary 34c25

calculation of interlaminar stresses in laminated plates using walsh transforms the walsh differential operator approach has much to recommend it from the point of view of computational efficiency over the standard methods for determining the interlaminar tractions from finite element displacement data as may be seen from the simplicity of the fortran routine and the ease with which the nonlinear traction tems may be modeled

goodness of fit of relative survival models additive regression models are preferred over multiplicative models in the analysis of relative survival data such preferences are mainly grounded in practical experience with mostly cancer registries data where the basic assumption of the additivity of hazards is more likely to be met also the interpretation of coefficients is more meaningful in additive than in multiplicative models nonetheless the question of goodness of fit of the assumed model must still be addressed and while there is an abundance of methods to check the goodness of fit of multiplicative models the respective arsenal for additive models is almost empty we propose here a variety of procedures for testing the null hypothesis of a good fit these are based on partial residuals defined similarly to schoenfeld residuals familiar for cox model diagnostics the tests have appropriate sizes under the null hypothesis and good power under different alternatives we investigate their performance through simulations and apply the methods to data from a study into survival of colon cancer patients

a bahri lions theorem revisited abstract in 1988 a bahri and p l lions a bahri p l lions morse index of some min max critical points i application to multiplicity results comm pure appl math 41 1988 1027 1037 studied the following elliptic problem u u p 2 u f x u u h 0 1 where is a bounded smooth domain of r n 2 p 2 n 2 n 2 and f x u is not assumed to be odd in u they proved the existence of infinitely many solutions under an appropriate growth restriction on f in the present paper we improve this result by showing that under the same growth assumption on f the problem admits in fact infinitely many sign changing solutions in addition we derive an estimate on the number of their nodal domains we also deal with the corresponding fourth order equation 2 u u p 2 u f x u with both dirichlet and navier boundary conditions as well as with strongly coupled elliptic systems

flexible modeling of the effects of continuous prognostic factors in relative survival relative survival methods permit separating the effects of prognostic factors on disease related excess mortality from their effects on other causes natural mortality even when individual causes of death are unknown as in conventional crude survival accurate assessment of prognostic factors requires testing and possibly modeling of non proportional effects and for continuous covariates of non linear relationships with the hazard we propose a flexible extension of the additive hazards relative survival model in which the observed all causes mortality hazard is represented by a sum of disease related excess and natural mortality hazards in our flexible model the three functions representing i the baseline hazard for excess mortality ii the time dependent effects and iii for continuous covariates non linear effects on the logarithm of this hazard are all modeled by low dimension cubic regression splines non parametric likelihood ratio tests are proposed to test the time dependent and non linear effects the accuracy of the estimated functions is evaluated in multivariable simulations to illustrate the new insights offered by the proposed model we apply it to re assess the effects of patient age and of secular trends on disease related mortality in colon cancer

numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh a finite difference method using a nonuniform triangle mesh is described for the numerical solution of the nonlinear two dimensional poisson equation s 0 where is a function of or its derivatives sis a function of position and or its normal derivative is specified on the boundary the finite difference equations are solved by successive overrelaxation the triangle mesh which is constructed numerically by solving laplace s equation is easily adapted to nonrectangular boundaries and interfaces examples of numerical results are given for the magnetostatic problem with iron and other possible applications are mentioned

proportional excess hazards assume that the excess risk of an individual over a known background rate can be well approximated by the proportional hazards model such might be the case for a cohort at risk of dying from causes that are independent of those that affect the general population we propose estimators for both the regression parameters and the nonparametric baseline hazard function the estimators are shown to be consistent asymptotically normal and efficient analogues of the wald score and likelihood ratio test are provided the relevance of the asymptotic results to samples of sizes 500 and 100 is illustrated by simulation the model is used to estimate the prognostic significance of stage and histology in adults with non hodgkin s lymphoma

an obstruction bundle relating gromov witten invariants of curves and kahler surfaces in a previous paper the authors defined symplectic local gromov witten invariants associated to spin curves and showed that the gw invariants of a k ahler surface x with p g 0 are a sum of such local gw invariants this paper describes how the local gw invariants arise from an obstruction bundle in the sense of taubes over the space of stable maps into curves together with the results of our earlier paper this reduces the calculation of the gw invariants of elliptic and general type complex surfaces to computations in the gw theory of curves with additional classes the euler classes of the real obstruction bundles

a morse complex for infinite dimensional manifolds part i abstract in this paper and in the forthcoming part ii we introduce a morse complex for a class of functions f defined on an infinite dimensional hilbert manifold m possibly having critical points of infinite morse index and co index the idea is to consider an infinite dimensional subbundle or more generally an essential subbundle of the tangent bundle of m suitably related with the gradient flow of f this part i deals with the following questions about the intersection w of the unstable manifold of a critical point x and the stable manifold of another critical point y finite dimensionality of w possibility that different components of w have different dimension orientability of w and coherence in the choice of an orientation compactness of the closure of w classification up to topological conjugacy of the gradient flow on the closure of w in the case dim w 2

on superquadratic elliptic systems in this article we study the existence of solutions for the elliptic system updelta u frac partial h partial v left u v x right text in upomega updelta v frac partial h partial v left u v x right text in upomega u 0 v 0 text on partial upomega where upomega is a bounded open subset of mathbb r n with smooth boundary partial upomega and the function h mathbb r 2 times overline upomega to mathbb r is of class c 1

intrinsic autoregressions and related models on the two dimensional lattice summary stationary autoregressions on a two dimensional lattice are generalized to intrinsic models where only increments are assumed to be stationary prediction formulae and the asymptotic behaviour of the semivariogram are derived for parameter estimation we propose an approximate maximum likelihood estimator a generalization of whittle s estimator it is derived also for general intrinsic models

additive and multiplicative models for relative survival rates the relative survival rate is the ratio of the overall survival rate to that expected for demographically similar individuals in a reference population it is commonly used to estimate the effect of a particular disease on mortality when the cause of death is not reliably known the effect of the disease on the underlying hazards may be multiplicative or additive the former case has been considered elsewhere but seems biologically less plausible than the latter both models are examined in this paper the effect of the disease is assumed to be constant throughout the follow up period or to be piecewise constant within k follow up intervals maximum likelihood estimates and related statistics are presented as are simpler statistics based on moment estimators of the disease effect the moment based statistic for testing the homogeneity of r groups may be expressed as a sum of individual scores which are shown to be closely related to the logrank scores when follow up intervals are made arbitrarily small

an entropy satisfying boundary layer surface mesh generation a method is presented to generate surface boundary layers the novelty of the method consists in a uniform treatment of the concave and convex regions based on offsetting the initial front in particular concave situations are enforced to respect the entropy satisfying solution local solutions of the offset of edges in the planes and triangles in the three dimensional space are also given showing the relationship between normal computation distance extrusion and the generalized voronoi diagram the boundary layer mesh generation is cast as a weak solution of the eikonal equation computed locally layer by layer to mimic the hyperbolic character of the eikonal equation augmented by a possibly nonbijective mapping between layers this provides a theoretical framework to rely on for practical answers such as configurations where the adjacent topologies to a boundary layer may be curved or at least not aligned with the offset direction or if the boundary layer mesh must be generated as a mapping betw

cryptocurrencies dust in the wind abstract analogous to the way wind blows single grains of sand and the subsequent settling back atop sand dunes we find statistical evidence to claim that the prices of cryptocurrencies exhibit similar unpredicted patterns characterized by positive or negative jumps motivated by extant evidence of asset returns non normality we capture distributional properties of the log returns of the bitcoin and the following three cryptocurrencies in terms of market capitalization ethereum ripple and bitcoin cash the total error induced by the fitted distribution is remarkably decreased when the generalized hyperbolic distribution is used a finding further validated by a series of goodness of fit type statistical tests a complementary analysis for the foreign exchange market is conducted with inherent similarities to that of cryptocurrencies we reveal that the generalized hyperbolic distribution can also be used to model very widely traded currency pairs significantly more accurately than the log normal

multiplicative models and cohort analysis abstract three methods of cohort analysis are presented for a statistical model wherein the explanatory or exposure variables act multiplicatively on age calendar year specific death rates the first method which assumes that the baseline rates are known from national vital statistics is a multiple regression analysis of the standardized mortality ratio the second method is a variant of cox s proportional hazards analysis in which the baseline rates are treated as unknown nuisance parameters the third method consists of case control sampling from the risk sets formed in the course of applying cox s model it requires substantially less computation than do the other two in illustrative analysis of respiratory cancer deaths among a cohort of smelter workers all three approaches yield roughly equivalent estimates of the relative risk associated with arsenic exposure the discussion centers on the tradeoff between efficiency and bias in the selection of a particular method of analysis and on practica

3 d mesh sequence compression using wavelet based multi resolution analysis in this paper we present two compression methods for irregular three dimensional 3 d mesh sequences with constant connectivity the proposed methods mainly use an exact integer spatial wavelet analysis swa technique to efficiently decorrelate the spatial coherence of each mesh frame and also to adaptively transmit mesh frames with various spatial resolutions to reduce the temporal redundancy the first proposed method applies multi order differential coding mdc to the temporal sequences obtained from swa mdc determines the optimal order of the differential coder by analyzing the variance of prediction errors comparing with the first order differential coding fdc scheme the method can improve the compression performance the second proposed method applies temporal wavelet analysis twa to the temporal sequences in particular this method offers spatio temporal multi resolution coding through simulations we prove that our methods enable efficient lossy to lossless compression for 3 d mesh sequences in a single frame work

ordinary differential operators in hilbert spaces and fredholm pairs let a t be a path of bounded operators on a real hilbert space hyperbolic at pm infty we study the fredholm theory of the operator f a d dt a t we relate the fredholm property of f a to the stable and unstable linear spaces of the associated system x prime a t x several examples are included to point out the differences with respect to the finite dimensional case in particular concerning the role of the spectral flow we define a general class of paths a for which many properties typical of the finite dimensional framework still hold our motivation is to develop the linear theory which is necessary for the set up of morse homology on hilbert manifolds

three dimensional hyperbolic grid generation with inherent dissipation and laplacian smoothing based on upwind differencing of the governing equations inherent dissipation terms are derived for three dimensional hyperbolic grid generation these terms taking only a negligible amount of mathematic operations can effectively eliminate grid oscillation that is often encountered in hyperbolic grid generation in addition to these dissipation terms a laplacian type smoothing is incorporated to increase smoothness both implicit and explicit schemes for three dimensional hyperbolic grid generation are investigated and a comparison of these two schemes is made several different geometries are used to demonstrate the robustness of the new methods finally a wing body configuration with severe concave and convex corners is used to evaluate the versatility of the present methods

dynamic regression hazards models for relative survival a natural way of modelling relative survival through regression analysis is to assume an additive form between the expected population hazard and the excess hazard due to the presence of an additional cause of mortality within this context the existing approaches in the parametric semiparametric and non parametric setting are compared and discussed we study the additive excess hazards models where the excess hazard is on additive form this makes it possible to assess the importance of time varying effects for regression models in the relative survival framework we show how recent developments can be used to make inferential statements about the non parametric version of the model this makes it possible to test the key hypothesis that an excess risk effect is time varying in contrast to being constant over time in case some covariate effects are constant we show how the semiparametric additive risk model can be considered in the excess risk setting providing a better and more useful summary of the data estimators have explicit form and inference based on a resampling scheme is presented for both the non parametric and semiparametric models we also describe a new suggestion for goodness of fit of relative survival models which consists on statistical and graphical tests based on cumulative martingale residuals this is illustrated on the semiparametric model with proportional excess hazards we analyze data from the trace study using different approaches and show the need for more flexible models in relative survival

towards data driven selection of a penalty function for data driven neyman tests the data driven neyman statistic consists of two elements a score statistic in a finite dimensional submodel and a selection rule to determine the best fitted submodel for instance schwarz bic and akaike aic rules are often applied in such constructions for moderate sample sizes aic is sensitive in detecting complex models while bic works well for relatively simple structures when the sample size is moderate the choice of selection rule for determining a best fitted model from a number of models has a substantial influence on the power of the related data driven neyman test this paper proposes a new solution in which the type of penalty aic or bic is chosen on the basis of the data the resulting refined data driven test combines the advantages of these two selection rules

deforming composite grids for solving fluid structure problems we describe a mixed eulerian lagrangian approach for solving fluid structure interaction fsi problems the technique which uses deforming composite grids dcg is applied to fsi problems that couple high speed compressible flow with elastic solids the fluid and solid domains are discretized with composite overlapping grids curvilinear grids are aligned with each interface and these grids deform as the interface evolves the majority of grid points in the fluid domain generally belong to background cartesian grids which do not move during a simulation the fsi dcg approach allows large displacements of the interfaces while retaining high quality grids efficiency is obtained through the use of structured grids and cartesian grids the governing equations in the fluid and solid domains are evolved in a partitioned approach we solve the compressible euler equations in the fluid domains using a high order godunov finite volume scheme we solve the linear elastodynamic equations in the solid domains using a second order upwind scheme we develop interface approximations based on the solution of a fluid solid riemann problem that results in a stable scheme even for the difficult case of light solids coupled to heavy fluids the fsi dcg approach is verified for three problems with known solutions an elastic piston problem the superseismic shock problem and a deforming diffuser in addition a self convergence study is performed for an elastic shock hitting a fluid filled cavity the overall fsi dcg scheme is shown to be second order accurate in the max norm for smooth solutions and robust and stable for problems with discontinuous solutions for a wide range of constitutive parameters

enhancements of a three dimensional hyperbolic grid generation scheme a hyperbolic grid generation scheme formulated from grid orthogonality and cell volume specification has been significantly enhanced so that high quality three dimensional grids can be obtained for a wide variety of geometries while the speed of the scheme remains one to two orders of magnitude faster than typical elliptic grid generation methods the robustness of the scheme has been greatly improved over previous applications of the three dimensional hyperbolic grid generation procedure enhancements included the use of spatially variable smoothing coefficient metric correction procedures local treatment of severe convex corners and new extrapolation treatments of floating and axis boundaries the versatility of the new hyperbolic grid generation scheme is demonstrated by three dimensional grids generated for external components of the integrated space shuttle vehicle and the sofia telescope

hyperbolic equation method of grid generation for enclosed regions in a recent study the authors combined the grid front marching method and the parabolic equation method in this study a similar idea is applied to extend the cordeva and barth hyperbolic equation method to enclosed regions

fractal analysis of surface roughness by using spatial data summary we develop fractal methodology for data taking the form of surfaces an advantage of fractal analysis is that it partitions roughness characteristics of a surface into a scale free component fractal dimension and properties that depend purely on scale particular emphasis is given to anisotropy where we show that for many surfaces the fractal dimension of line transects across a surface must either be constant in every direction or be constant in each direction except one this virtual direction invariance of fractal dimension provides another canonical feature of fractal analysis complementing its scale invariance properties and enhancing its attractiveness as a method for summarizing properties of roughness the dependence of roughness on direction may be explained in terms of scale rather than dimension and can vary with orientation scale may be described by a smooth periodic function and may be estimated nonparametrically our results and techniques are applied to analyse data on the surfaces of soil and plastic food wrapping for the soil data interest centres on the effect of surface roughness on retention of rain water and data are recorded as a series of digital images over time our analysis captures the way in which both the fractal dimension and the scale change with rainfall or equivalently with time the food wrapping data are on a much finer scale than the soil data and are particularly anisotropic the analysis allows us to determine the manufacturing process which produces the smoothest wrapping with least tendency for micro organisms to adhere

marching grid generation using parabolic partial differential equations abstract the unique aspect of grid generation in computational fluid dynamics is that the grid generation equations have no physical meanings so any equation may be used for this purpose if the grids generated are useful this aspect provides a vast freedom in developing new methods of grid generation this paper explores feasibility of using parabolic partial differential equations for grid generation the advantages of using parabolic partial differential equations are as follows 1 parabolic equations are initial value problems so grids are generated by a marching algorithm like the hyperbolic grid generation method 2 the parabolic partial differential equations have most properties of the elliptic equations particularly the diffusion effect which smooths out any singularity of the inner boundary condition if any and 3 the prescribed outer boundary conditions may be satisfied the importance of the marching algorithm stated above is twofold first computational time required is only a very small fraction of that for the elliptic grid generation equations second the fast memory space required during grid generation can be substantially reduced from that required by the elliptic grid generation method the authors consider the grid generation for a two dimensional airfoil flow calculations for simplicity of discussions although the method described in this paper is not restricted to two dimensions or airfoil problems

symplectic fixed points and holomorphic spheres letp be a symplectic manifold whose symplectic form integrated over the spheres inp is proportional to its first chern class on the loop space ofp we consider the variational theory of the symplectic action function perturbed by a hamiltonian term in particular we associate to each isolated invariant set of its gradient flow an abelian group with a cyclic grading it is shown to have properties similar to the homology of the conley index in locally compact spaces as an application we show that if the fixed point set of an exact diffeomorphism onp is nondegenerate then it satisfies the morse inequalities onp we also discuss fixed point estimates for general exact diffeomorphisms

khmaladze type graphical evaluation of the proportional hazards assumption khmaladze type goodness of fit tests are based on transforming an appropriate empirical process to one with a known large sample distribution using donsker s theorem together with a theorem for proportional hazards generalising a theorem of xu o quigley 1999 we indicate how to construct a khmaladze type graphical test for evaluating the proportional hazards assumption an illustration is given in which a partially proportional hazards model can be seen to provide a noticeably improved fit over a fully proportional hazards model

the exact and asymptotic distributions of cramer von mises statistics it is shown that an asymptotically precise one term correction to the asymptotic distribution function of the classical cram r von mises statistic approximates the exact distribution function remarkably closely for sample sizes as small as 7 or even smaller this correction can be quickly evaluated and hence it is suitable for the computation of practically exact p values when testing simple goodness of fit abstract2 it is shown that an asymptotically precise one term correction to the asymptotic distribution function of the classical cramer von mises statistic approximates the exact distribution function remarkably closely for sample sizes as small as 7 or even smaller this correction can be quickly evaluated and hence it is suitable for the computation of practically exact p values when testing simple goodness of fit similar findings hold for watson s rotationally invariant modification where a sample size of 4 appears to suffice

the so 3 monopole cobordism and superconformal simple type abstract we show that the so 3 monopole cobordism formula from 15 implies that all closed oriented smooth four manifolds with b 1 0 and b 3 and odd with seiberg witten simple type satisfy the superconformal simple type condition defined by marino moore and peradze 28 27 this implies the lower bound conjectured by fintushel and stern 18 on the number of seiberg witten basic classes in terms of topological data

simple parametric and nonparametric models for excess and relative mortality this paper studies two classes of hazard rate based models for the mortality in a group of individuals taking normal life expectancy into account in a multiplicative hazard model the estimate for the relative mortality generalises the standardised mortality ratio and the adequacy of a model with constant relative mortality can be tested using a type of total time on test statistic in an additive hazard model continuous time generalisations of a corrected survival curve and a normal survival curve are obtained and the adequacy of a model with constant excess mortality can again be tested using a type of total time on test statistic a model including both the multiplicative hazard model and the additive hazard model is briefly considered the use of the models is illustrated on a set of data concerning survival after operation for malignant melanoma

efficient computation of volume in flow predictions an efficient method for calculating cell volumes for time dependent three dimensional flow predictions by finite volume calculations is presented eight arbitrary corner points are considered and the shape face is divided into two planar triangles the volume is then dependent on the orientation of the partitioning in the case of a hexahedron it is noted that any open surface with a boundary that is a closed curve possesses a surface vector independent of the surface shape expressions are defined for the surface vector which is independent of the partitioning surface diagonal used to quantify the volume using a decomposition of the cell volume involving two corners with each the vertex of three diagonals and six corners which are vertices of one diagonal gives portions which are tetrahedra the resultant mesh is can be used for time dependent finite volume calculations one requires less computer time than previous methods

transformations of the empirical measure and kolmogorov smirnov tests the power of kolmogorov smirnov tests can be increased by transforming the empirical process into a new process that converges to a wiener process under the null hypothesis and by choosing the transformation in such a way that some families of local alternatives become as noticeable as possible

an asymptotically linear non cooperative elliptic system with lack of compactness in this paper we consider an asymptotically linear non cooperative elliptic system at resonance the functional associated to the system is strongly indefinite and so the morse index of each critical point is infinite to overcome this difficulty we will use morse theory for strongly indefinite functionals developed by abbondandolo we shall prove that if the system has a non resonant solution the morse index of which is different from the morse index at infinity then there exists another solution

principal bundles on projective varieties and the donaldson uhlenbeck compactification let h be a semisimple algebraic group we prove the semistable reduction theorem for semistable principal h bundles over a smooth projective variety x defined over the field c when x is a smooth projective surface and h is simple we construct the algebro geometric donaldson uhlenbeck compactification of the moduli space of semistable principal h bundles with fixed characteristic classes and describe its points for large characteristic classes we show that the moduli space of stable principal h bundles is non empty

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

on a generalised fourier transform of instantons over flat tori recently p braam pointed out that nahm s adaption of the adhm procedure to the case of monopoles equally well applies to instantons over flat tori relating them to instantons over the first brillouin zone we show that this construction has an inverse hence the nahm transform actually is a duality transform

powerful two sample tests based on the likelihood ratio a new approach to constructing nonparametric tests for the general two sample problem is proposed this approach not only generates traditional tests including the two sample kolmogorov smirnov cramer von mises and anderson darling tests but also produces new powerful tests based on the likelihood ratio although conventional two sample tests are sensitive to the difference in location most of them lack power to detect changes in scale and shape the new tests are location scale and shape sensitive so they are robust against variation in distribution

differential systems with strongly indefinite variational structure abstract the euler lagrange equations of lagrangians with a strongly indefinite quadratic part are studied by means of the direct min max method of benci and rabinowitz the simplest case is a system of two coupled semilinear poisson equations using an analytic framework of a suitable family of products of fractional sobolev spaces existence results are obtained for all nonlinearities with subcritical growth rates

the rabinowitz floer homology for a class of semilinear problems and applications abstract in this paper we construct a rabinowitz floer type homology for a class of non linear problems having a starshaped potential we consider some equivariant cases as well we give an explicit computation of the homology and we apply it to obtain results of existence and multiplicity of solutions for several model equations

a multiscale wavelet based test for isotropy of random fields on a regular lattice a test for isotropy of images modeled as stationary or intrinsically stationary random fields on a lattice is developed the test is based on the wavelet theory and can operate on the horizontal and vertical scale of choice or on any combination of scales scale is introduced through the wavelet variances sometimes called as the wavelet power spectrum which decompose the variance over different horizontal and vertical spatial scales the method is more general than existing tests for isotropy since it handles intrinsically stationary random fields as well as second order stationary fields the performance of the method is demonstrated on samples from different random fields and compared with three existing methods it is competitive with or outperforms existing methods since it consistently rejects close to the nominal level for isotropic fields while having a rejection rate for anisotropic fields comparable with the existing methods in the stationary case and superior in the intrinsic case as practical examples paper density images of handsheets and mammogram images are analyzed