quasi isometry and deformations of calabi yau manifolds we prove several formulas related to hodge theory and the kodaira spencer kuranishi deformation theory of kahler manifolds as applications we present a construction of globally convergent power series of integrable beltrami differentials on calabi yau manifolds and also a construction of global canonical family of holomorphic n 0 forms on the deformation spaces of calabi yau manifolds similar constructions are also applied to the deformation spaces of compact kahler manifolds

the geometry of three forms in six dimensions we study the special algebraic properties of alternating 3 forms in 6 dimensions and introduce a diffeomorphism invariant functional on the space of differential 3 forms on a closed 6 manifold m restricting the functional to a de rham cohomology class in h3 m r we find that a critical point which is generic in a suitable sense defines a complex threefold with trivial canonical bundle this approach gives a direct method of showing that an open set in h3 m r is a local moduli space for this structure and introduces in a natural way the special pseudo kahler structure on it

unified lasso estimation by least squares approximation we propose a method of least squares approximation lsa for unified yet simple lasso estimation our general theoretical framework includes ordinary least squares generalized linear models quantile regression and many others as special cases specifically lsa can transfer many different types of lasso objective functions into their asymptotically equivalent least squares problems thereafter the standard asymptotic theory can be established and the lars algorithm can be applied in particular if the adaptive lasso penalty and a bayes information criterion type tuning parameter selector are used the resulting lsa estimator can be as efficient as the oracle extensive numerical studies confirm our theory

topological invariants of o grady s six dimensional irreducible symplectic variety we study o grady examples of irreducible symplectic varieties we establish that both of them can be deformed into lagrangian fibrations we analyze in detail the topology of the six dimensional example in particular we compute its euler characteristic and determine its beauville form

kodaira spencer theory of gravity and exact results for quantum string amplitudes we develop techniques to compute higher loop string amplitudes for twistedn 2 theories with 3 i e the critical case an important ingredient is the discovery of an anomaly at every genus in decoupling of brst trivial states captured to all orders by a master anomaly equation in a particular realization of then 2 theories the resulting string field theory is equivalent to a topological theory in six dimensions the kodaira spencer theory which may be viewed as the closed string analog of the chern simons theory using the mirror map this leads to computation of the number of holomorphic curves of higher genus curves in calabi yau manifolds it is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the correspondingn 2 theory relations withc 1 strings are also pointed out

twisted fourier mukai transforms for holomorphic symplectic four folds we apply the methods of c a ldararu to construct a twisted fourier mukai transform between a pair of holomorphic symplectic four folds which are fibred by lagrangian abelian surfaces more precisely we obtain an equivalence between the derived category of coherent sheaves on a certain lagrangian fibration and the derived category of twisted sheaves on its mirror partner as a corollary we extend the original fourier mukai transform to degenerations of abelian surfaces another consequence of the general theory is that the holomorphic symplectic four fold and its mirror are connected by a one parameter family of deformations through lagrangian fibrations

the moduli space of asymptotically cylindrical calabi yau manifolds we prove that the deformation theory of compactifiable asymptotically cylindrical calabi yau manifolds is unobstructed this relies on a detailed study of the dolbeault hodge theory and its description in terms of the cohomology of the compactification we also show that these calabi yau metrics admit a polyhomogeneous expansion at infinity a result that we extend to asymptotically conical calabi yau metrics as well we then study the moduli space of calabi yau deformations that fix the complex structure at infinity there is a weil petersson metric on this space which we show is kahler by proving a local families l 2 index theorem we exhibit its kahler form as a multiple of the curvature of a certain determinant line bundle

collinearity and optimal restrictions on regression parameters for estimating responses collinearity among independent variables in multiple linear regression can have severe effects on the precision of response estimation for some region of interest of independent variables collinearity is shown to be a situation in which there exist some linear restrictions on the regression parameters that might yield better response estimators than the ordinary least squares estimators in the mean squared error context this paper studies restrictions and formulates optimal restrictions in the sense of mean squared error it is shown that the least squares estimator of under the optimal restrictions is identical to a principal component estimator of

fano varieties of cubic fourfolds containing a plane we prove that the fano variety of lines of a generic cubic fourfold containing a plane is isomorphic to a moduli space of twisted stable complexes on a k3 surface on the other hand we show that the fano varieties are always birational to moduli spaces of twisted stable coherent sheaves on a k3 surface the moduli spaces of complexes and of sheaves are related by wall crossing in the derived category of twisted sheaves on the corresponding k3 surface

decay of solutions of some nonlinear wave equations abstract we study the large time behaviour of solutions to the initial value problem for the korteweg de vries equation and for the regularized long wave equation with a dissipative term appended using energy estimates a maximum principle and a transformation of cole hopf type sharp rates of temporal decay of certain norms of the solution are obtained

on the weil petersson volume and the first chern class of the moduli space of calabi yau manifolds in this paper we proved that the weil petersson volume of calabi yau moduli is a rational number we also proved that the integrations of the invariants of the ricci curvature of the weli petersson metric with respect to the weil petersson volume form are all rational numbers

enriques surfaces analytic discriminants and borcherds s φ function in bor 96 borcherds constructed a non vanishing weight 4 modular form on the moduli space of marked polarized enriques surface of degree 2 by considering the twisted denominator function of the fake monster lie algebra associated to an automorphism of order 2 of the leech lattice fixing an 8 dimensional subspace in jt 94 and jt 96 we defined and studied a meromorphic multi valued modular form of weight 2 which we call the k3 analytic discriminant on the moduli space of marked polarized k3 surfaces of degree 2d in certain cases including when where p k are distinct primes our meromorphic form is actually a holomorphic form our construction involves a determinant of the laplacian on a polarized k3 surface with respect to the calabi yau metric together with the l 2 norm of the image of the period map with respect to a properly scaled holomorphic two form since the universal cover of any enriques surface is a k3 surface we can restrict the k3 analytic discriminant to the moduli space of degree 2 enriques surfaces the main result of this paper is the observation that the square of our degree 2 analytic discriminant viewed as a function on the moduli space of degree 2 enriques surfaces is equal to the borcherd s function up to a universal multiplicative constant this result generalizes known results in the study of generalized kac moody algebras and elliptic curves and suggests further connections with higher dimensional calabi yau varieties specifically those which can be realized as complete intersections in some possibly weighted projective space

generalized hodge metrics and bcov torsion on calabi yau moduli we establish an unexpected relation among the weil petersson metric the generalized hodge metrics and the bcov torsion using this relation we prove that certain kind of moduli spaces of polarized calabi yau manifolds do not admit complete subvarieties that is there is no complete family for certain class of polarized calabi yau manifolds we also give an estimate of the complex hessian of the bcov torsion using the relation after establishing a degenerate version of the schwarz lemma of yau we prove that the complex hessian of the bcov torsion is bounded by the poincare metric

asymptotic behavior of solutions toward the rarefaction waves to the cauchy problem for the scalar diffusive dispersive conservation laws abstract in this paper we investigate the asymptotic behavior of solutions to the cauchy problem for the scalar diffusive dispersive conservation laws where the far field states are prescribed especially we deal with the generalized models for korteweg de vries burgers kuramoto equation when the corresponding riemann problem for the hyperbolic part admits a riemann solution which consists of single rarefaction wave it is proved that the solution of the cauchy problem tends toward the rarefaction wave as time goes to infinity

frequentist prediction intervals and predictive distributions summary we consider parametric frameworks for the prediction of future values of a random variable y based on previously observed data x simple pivotal methods for obtaining calibrated prediction intervals are presented and illustrated frequentist predictive distri butions are defined as confidence distributions and their utility is demonstrated a simple pivotal based approach that produces prediction intervals and predictive distributions with well calibrated frequentist probability interpretations is introduced and efficient simulation methods for producing predictive distributions are considered properties related to an average kullback leibler measure of goodness for predictive or estimated distributions are given the predictive distributions here are shown to be optimal in certain settings with invariance structure and to dominate plug in distributions under certain conditions

learning to classify ordinal data the data replication method classification of ordinal data is one of the most important tasks of relation learning this paper introduces a new machine learning paradigm specifically intended for classification problems where the classes have a natural order the technique reduces the problem of classifying ordered classes to the standard two class problem the introduced method is then mapped into support vector machines and neural networks generalization bounds of the proposed ordinal classifier are also provided an experimental study with artificial and real data sets including an application to gene expression analysis verifies the usefulness of the proposed approach

the weil petersson geometry of the moduli space of su n 3 calabi yau manifolds i the weil petersson metric is defined on the moduli space of calabi yau manifolds the curvature of this weil petersson metrics is computed and its potential is explicitely defined it is proved that the moduli space of calabi yau manifolds is unobstructed see tian

on the stability of riemannian manifold with parallel spinors inspired by the recent work hhm03 we prove two stability results for compact riemannian manifolds with nonzero parallel spinors our first result says that ricci flat metrics which also admit nonzero parallel spinors are stable in the direction of changes in conformal structures as the critical points of the total scalar curvature functional our second result which is a local version of the first one shows that any metric of positive scalar curvature cannot lie too close to a metric with nonzero parallel spinor we also prove a rigidity result for special holonomy metrics in the case of su m holonomy the rigidity result implies that scalar flat deformations of calabi yau metric must be calabi yau finally we explore the connection with a positive mass theorem of d03 which presents another approach to proving these stability and rigidity results

the tangent bundle of a calabi yau manifold deformations and restriction to rational curves the tangent bundle x of a calabi yau threefoldx is the only known example of a stable bundle with non trivial restriction to any rational curve onx by deforming the direct sum of x and the trivial line bundle one can try to obtain new examples we use algebro geometric techniques to derive results in this direction the relation to the finiteness of rational curves on calabi yau threefolds is discussed

mirror symmetry and rational curves on quintic threefolds a guide for mathematicians we give a mathematical account of a recent string theory calcula tion which predicts the number of rational curves on the generic quintic three fold our account involves the interpretation of yukawa couplings in terms of variations of hodge structure a new q expansion principle for functions on the moduli space of calabi yau manifolds and the mirror symmetry phe nomenon recently observed by string theorists department of mathematics duke university durham north carolina 27706 e mail address drm math duke edu this content downloaded from 157 55 39 224 on wed 14 dec 2016 04 59 36 utc all use subject to http about jstor org terms

analytic torsion for calabi yau threefolds after bershadsky cecotti ooguri vafa we introduce an invariant of calabi yau threefolds which we call the bcov invariant and which we obtain using analytic torsion we give an explicit formula for the bcov invariant as a function on the compactified moduli space when it is isomorphic to a projective line as a corollary we prove the formula for the bcov invariant of quintic mirror threefolds conjectured by bershadsky cecotti ooguri vafa

strict and nonstrict positivity of direct image bundles this paper is a sequel to berndtsson in ann math 169 531 560 2009 in that paper we studied the vector bundle associated to the direct image of the relative canonical bundle of a smooth kahler morphism twisted with a semipositive line bundle we proved that the curvature of a such vector bundles is always semipositive in the sense of nakano here we address the question if the curvature is strictly positive when the kodaira spencer class does not vanish we prove that this is so provided the twisting line bundle is strictly positive along fibers but not in general

on quasi isomorphic dgbv algebras one of the methods to obtain frobenius manifold structures is via differential gerstenhaber batalin vilkovisky dgbv algebra construction an important problem as motivated from mirror symmetry is how to identify frobenius manifold structures constructed from two different dgbv algebras for dgbv algebras with suitable conditions we show the functorial property of a construction of deformations of the multiplicative structures of their cohomology in particular we show that quasi isomorphic dgbv algebras yield equivalent formal frobenius manifold structures

geometry of formal kuranishi theory abstract the principle ambient cohomology of a kaehler manifold annihilates obstructions has been known and exploited since pioneering work of kodaira this paper unifies and modestly extends known results in the context of abstract deformations of compact kaehler manifolds and submanifolds

convergence rate of solutions toward traveling waves for the cauchy problem of generalized korteweg de vries burgers equations abstract in this paper we investigate the exponential time decay rate of solutions toward traveling waves for the cauchy problem of generalized korteweg de vries burgers equations e u t u x x x u x x f u x 0 t 0 x r with prescribed initial data i u x 0 u 0 x u as x here 0 and 0 are real constants u u are two given constants and the smooth nonlinear function f u is assumed to be either convex or concave an exponential time decay rate of its global solution toward traveling wave solutions is obtained by employing the space time weighted energy method which was initiated by kawashima and matsumura s kawashima a matsumura asymptotic stability of traveling wave solutions of systems for one dimensional gas motion comm math phys 101 1985 97 127 and later elaborated by matsumura nishihara a matsumura k nishihara asymptotic stability of traveling waves for scalar viscous conservation laws with non convex nonlinearity comm math phys 165 1994 83 96 and nishikawa m nishikawa convergence rates to the traveling wave for viscous conservation laws funkcial ekvac 41 1998 107 132

mirror symmetry via logarithmic degeneration data i this paper lays the foundations of a program to study mirror symmetry by studying the log structures of illusie fontaine and kato on degenerations of calabi yau manifolds the basic idea is that one can associate to certain sorts of degenerations of calabi yau manifolds a log calabi yau space which is a log structure on the degenerate fibre the log cy space captures essentially all the information of the degeneration and hence all mirror statements for the large complex structure limit given by the degeneration can already be derived from the log cy space in this paper we begin by discussing affine manifolds with singularities given such an affine manifold along with a polyhedral decomposition we show how to construct a scheme consisting of a union of toric varieties in certain non degenerate cases we can also construct log structures on these schemes conversely given certain sorts of degenerations one can build an affine manifold with singularities structure on the dual intersection complex of the degeneration mirror symmetry is then obtained as a discrete legendre transform on these affine manifolds thus providing an algebro geometrization of the strominger yau zaslow conjecture the deepest result of this paper shows an isomorphism between log complex moduli of a log cy space and log kahler moduli of its mirror

flops motives and invariance of quantum rings for ordinary ops the correspondence dened by the graph closure is shown to give equivalence of chow motives and to preserve the poincar e pairing in the case of simple ordinary ops this correspondence preserves the big quantum cohomology ring after an analytic continuation over the

mukai flops and deformations of symplectic resolutions we prove that two projective symplectic resolutions of open image in new window are connected by mukai flops in codimension 2 for a finite sub group g sp 2n it is also shown that two projective symplectic resolutions of open image in new window are deformation equivalent

decay rates for the solutions of model equations for bore propagation we study the large time behaviour of solutions to the korteweg de vries burgers equation with bore like initial data this work relies on the methods of amick bona and schonbeck to obtain sharp rates of temporal decay of certain norms of the solution thus obtaining an improvement over results of naumkin and shishmarev

sparse kernel machine regression for ordinal outcomes ordinal outcomes arise frequently in clinical studies when each subject is assigned to a category and the categories have a natural order classification rules for ordinal outcomes may be developed with commonly used regression models such as the full continuation ratio cr model fcr which allows the covariate effects to differ across all continuation ratios and the cr model with a proportional odds structure pcr which assumes the covariate effects to be constant across all continuation ratios for settings where the covariate effects differ between some continuation ratios but not all fitting either fcr or pcr may lead to suboptimal prediction performance in addition these standard models do not allow for non linear covariate effects in this paper we propose a sparse cr kernel machine km regression method for ordinal outcomes where we use the km framework to incorporate non linearity and impose sparsity on the overall differences between the covariate effects of continuation ratios to control for overfitting in addition we provide data driven rule to select an optimal kernel to maximize the prediction accuracy simulation results show that our proposed procedures perform well under both linear and non linear settings especially when the true underlying model is in between fcr and pcr models we apply our procedures to develop a prediction model for levels of anti ccp among rheumatoid arthritis patients and demonstrate the advantage of our method over other commonly used methods

gauss bonnet chern theorem on moduli space in this paper we prove a gauss bonnet chern type theorem in full generality for the chern weil forms of hodge bundles that is the chern weil forms compute the corresponding chern classes this settles a long standing problem second we apply the result to calabi yau moduli and proved the corresponding gauss bonnet chern type theorem in the setting of weil petersson geometry as an application of our results in string theory we prove that the number of flux vacua of type ii string compactified on a calabi yau manifold is finite and their number is bounded by an intrinsic geometric quantity

algebraic elliptic cohomology theory and flops i we define the algebraic elliptic cohomology theory coming from krichever s elliptic genus as an oriented cohomology theory on smooth varieties over an arbitrary perfect field we show that in the algebraic cobordism ring with rational coefficients the ideal generated by differences of classical flops coincides with the kernel of krichever s elliptic genus this generalizes a theorem of b totaro in the complex analytic setting

curvature and characteristic numbers of hyper kahler manifolds it is perhaps surprising to see this norm expressed solely in terms of the volume andpontryagin classes in fact the context for this formula is the work of rozansky andwitten who showed in 10 how one could associate to each compact hyperk ahlermanifold a three manifold invariant in more abstract terms what they show is that

l 1 penalized continuation ratio models for ordinal response prediction using high dimensional datasets health status and outcomes are frequently measured on an ordinal scale for high throughput genomic datasets the common approach to analyzing ordinal response data has been to break the problem into one or more dichotomous response analyses this dichotomous response approach does not make use of all available data and therefore leads to loss of power and increases the number of type i errors herein we describe an innovative frequentist approach that combines two statistical techniques l1 penalization and continuation ratio models for modeling an ordinal response using gene expression microarray data a simulation study was conducted to assess the performance of two computational approaches and two model selection criterion for fitting frequentist l1 penalized continuation ratio models moreover the approaches were empirically compared using three application datasets each of which seeks to classify an ordinal class using microarray gene expression data as the predictor variables we conclude that the l1 penalized constrained continuation ratio model is a useful approach for modeling an ordinal response for datasets where the number of covariates p exceeds the sample size n and the decision of whether to use aic or bic for selecting the final model should depend upon the similarities between the pathologies underlying the disease states to be classified

algebraic deformations of compact kahler surfaces ii in the first version of this paper a short proof was given of kodaira s result that every compact kahler surface is a deformation of an algebraic surface under the extra assumption that the infinitesimal deformations of the surface were unobstructed in this paper the extra assumption is removed

predicting future responses based on possibly mis specified working models summary under a general regression setting we propose an optimal unconditional prediction procedure for future responses the resulting prediction intervals or regions have a desirable average cov erage level over a set of covariate vectors of interest when the working model is not correctly specified the traditional conditional prediction method is generally invalid on the other hand one can empirically calibrate the above unconditional procedure and also obtain its crossvalidated counterpart various large and small sample properties of these unconditional methods are ex amined analytically and numerically we find that the ic fold crossvalidated procedure performs exceptionally well even for cases with rather small sample sizes the new proposals are illustrated with two real examples one with a continuous response and the other with a binary outcome

theta functions and hodge numbers of moduli spaces of sheaves on rational surfaces we compute generating functions for the hodge numbers of the moduli spaces of h stable rank 2 sheaves on a rational surface s in terms of theta functions for indefinite lattices if h lies in the closure of the ample cone and has self intersection 0 it follows that the generating functions are jacobi forms in particular the generating functions for the euler numbers can be expressed in terms of modular forms and their transformation behaviour is compatible with the predictions of s duality we also express the generating functions for the signatures in terms of modular forms it turns out that these generating functions are also with respect to another developing parameter the generating function for the donaldson invariants of s evaluated on all powers of the point class

on the influence of the kernel on the consistency of support vector machines in this article we study the generalization abilities of several classifiers of support vector machine svm type using a certain class of kernels that we call universal it is shown that the soft margin algorithms with universal kernels are consistent for a large class of classification problems including some kind of noisy tasks provided that the regularization parameter is chosen well in particular we derive a simple sufficient condition for this parameter in the case of gaussian rbf kernels on the one hand our considerations are based on an investigation of an approximation property the so called universality of the used kernels that ensures that all continuous functions can be approximated by certain kernel expressions this approximation property also gives a new insight into the role of kernels in these and other algorithms on the other hand the results are achieved by a precise study of the underlying optimization problems of the classifiers furthermore we show consistency for the maximal margin classifier as well as for the soft margin svm s in the presence of large margins in this case it turns out that also constant regularization parameters ensure consistency for the soft margin svm s finally we prove that even for simple noise free classification problems svm s with polynomial kernels can behave arbitrarily badly