kahlerian twistor spaces the work of r penrose has shown the deep relationship between the conformal structure of minkowski space and the complex geometry of lines in projective three space this transformation applies to a more general class of conformal structures and in particular there is a riemannian version described in 5 which is itself of interest to mathematical physicists basically to each oriented riemannian 4manifold x one associates canonically a 6 manifold z the twistor space of x together with an almost complex structure if this structure is integrable then z becomes a complex 3 manifold with a distinguished family of projective lines on it whose geometry describes the conformal geometry of the manifold x it is natural to ask what sort of complex manifold one obtains by this process in this paper we ask the more specific question which compact 4c manifolds have ka hlerian twistor spaces 1 the answer rather surprisingly is that there are just two examples the 4 sphere s and the complex projective plane p2 c each with their standard homogeneous conformal structures the twistor space of s 4 is the 3 dimensional projective space p3 c and that of p 2 q is the manifold f2 c of flags in c 3 the essential point of the proof of this result is the remark that if z is a twistor space with a kahler metric then the canonical bundle k is negative using vanishing theorems and the riemann roch theorem we then narrow down the possibilities for z to four cases projective space the flag manifold the intersection of two quadrics in p5 and the double covering of p3 branched over a non singular quartic surface the last two candidates cannot be realized however because the value of their euler characteristic is incompatible with their being twistor spaces throughout the proof we make essential use of a real structure on z which reduces considerably the occurrence of singularities at various stages aside from this our methods are the standard ones of algebraic geometry the four examples to which the proof leads us are all fano threefolds if we drop the requirement of compactness on x then it is quite possible for an open set of a fano threefold to be a twistor space in particular we show that the family of conies lying on the intersection of two

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

robustifying bayesian nonparametric mixtures for count data our motivating application stems from surveys of natural populations and is characterized by large spatial heterogeneity in the counts which makes parametric approaches to modeling local animal abundance too restrictive we adopt a bayesian nonparametric approach based on mixture models and innovate with respect to popular dirichlet process mixture of poisson kernels by increasing the model flexibility at the level both of the kernel and the nonparametric mixing measure this allows to derive accurate and robust estimates of the distribution of local animal abundance and of the corresponding clusters the application and a simulation study for different scenarios yield also some general methodological implications adding flexibility solely at the level of the mixing measure does not improve inferences since its impact is severely limited by the rigidity of the poisson kernel with considerable consequences in terms of bias however once a kernel more flexible than the poisson is chosen inferences can be robustified by choosing a prior more general than the dirichlet process therefore to improve the performance of bayesian nonparametric mixtures for count data one has to enrich the model simultaneously at both levels the kernel and the mixing measure

bayesian kernel mixtures for counts although bayesian nonparametric mixture models for continuous data are well developed the literature on related approaches for count data is limited a common strategy is to use a mixture of poissons which unfortunately is quite restrictive in not accounting for distributions with variance less than the mean other approaches include mixing multinomials which requires finite support and using a dirichlet process prior with a poisson base measure which does not allow for smooth deviations from the poisson we propose broad class of alternative models nonparametric mixtures of rounded continuous kernels we develop an efficient gibbs sampler for posterior computation and perform a simulation study to assess performance focusing on the rounded gaussian case we generalize the modeling framework to account for multivariate count data joint modeling with continuous and categorical variables and other complications we illustrate our methods through applications to a developmental toxicity study and m

twistor theory of hyper kahler metrics with hidden symmetries we review the hierarchy for the hyper kahler equations and define a notion of symmetry for solutions of this hierarchy a four dimensional hyper kahler metric admits a hidden symmetry if it embeds into a hierarchy with a symmetry it is shown that a hyper kahler metric admits a hidden symmetry if it admits a certain killing spinor we show that if the hidden symmetry is tri holomorphic then this is equivalent to requiring symmetry along a higher time and the hidden symmetry determines a twistor group action as introduced by bielawski twistor quotients of hyper kahler manifolds world scientific river edge nj 2001 this leads to a construction for the solution to the hierarchy in terms of linear equations and variants of the generalized legendre transform for the hyper kahler metric itself given by ivanov and rocek commun math phys 182 291 1996 we show that the ale spaces are examples of hyper kahler metrics admitting three tri holomorphic killing spinors these metrics are in this sense

hyper kahler metrics and a generalization of the bogomolny equations we generalize the bogomolny equations to field equations on 3 n and describe a twistor correspondence we consider a general hyper kahler metric in dimension 4n with an action of the torustn compatible with the hyper kahler structure we prove that such a metric can be described in terms of thetn solution of the field equations coming from the twistor space of the metric

controlling the reinforcement in bayesian non parametric mixture models summary the paper deals with the problem of determining the number of components in a mixture model we take a bayesian non parametric approach and adopt a hierarchical model with a suitable non parametric prior for the latent structure a commonly used model for such a problem is the mixture of dirichlet process model here we replace the dirichlet process with a more general non parametric prior obtained from a generalized gamma process the basic feature of this model is that it yields a partition structure for the latent variables which is of gibbs type this relates to the well known exchangeable product partition models if compared with the usual mixture of dirichlet process model the advantage of the generalization that we are examining relies on the availability of an additional parameter belonging to the interval 0 1 it is shown that such a parameter greatly influences the clustering behaviour of the model a value of that is close to 1 generates a large number of clusters most of which are of small size then a reinforcement mechanism which is driven by acts on the mass allocation by penalizing clusters of small size and favouring those few groups containing a large number of elements these features turn out to be very useful in the context of mixture modelling since it is difficult to specify a priori the reinforcement rate it is reasonable to specify a prior for hence the strength of the reinforcement mechanism is controlled by the data

hierarchical mixture modeling with normalized inverse gaussian priors in recent years the dirichlet process prior has experienced a great success in the context of bayesian mixture modeling the idea of overcoming discreteness of its realizations by exploiting it in hierarchical models combined with the development of suitable sampling techniques represent one of the reasons of its popularity in this article we propose the normalized inverse gaussian n ig process as an alternative to the dirichlet process to be used in bayesian hierarchical models the n ig prior is constructed via its finite dimensional distributions this prior although sharing the discreteness property of the dirichlet prior is characterized by a more elaborate and sensible clustering which makes use of all the information contained in the data whereas in the dirichlet case the mass assigned to each observation depends solely on the number of times that it occurred for the n ig prior the weight of a single observation depends heavily on the whole number of ties in the sample moreover expressio

hyper kahler hierarchies and their twistor theory a twistor construction of the hierarchy associated with the hyper kahler equations on a metric the anti self dual einstein vacuum equations asdve in four dimensions is given the recursion operator r is constructed and used to build an infinite dimensional symmetry algebra and in particular higher flows for the hyper kahler equations it is shown that r acts on the twistor data by multiplication with a rational function the structures are illustrated by the example of the sparling tod eguchi hansen solution

a semiparametric bayesian model for randomised block designs summary a model is proposed for a bayesian semiparametric analysis of randomised block experiments the model is a hierarchical model in which a dirichlet process is inserted at the middle stage for the distribution of the block effects this model allows an arbitrary distribution of block effects and it results in effective estimates of treatment contrasts block effects and the distribution of block effects an effective computational strategy is presented for describing the posterior distribution

multiresolution transmission of the correlation modes between bivariate time series based on complex network theory abstract this study introduces an approach to study the multiscale transmission characteristics of the correlation modes between bivariate time series the correlation between the bivariate time series fluctuates over time the transmission among the correlation modes exhibits a multiscale phenomenon which provides richer information to investigate the multiscale transmission of the correlation modes this paper describes a hybrid model integrating wavelet analysis and complex network theory to decompose and reconstruct the original bivariate time series into sequences in a joint time frequency domain and defined the correlation modes at each time frequency domain we chose the crude oil spot and futures prices as the sample data the empirical results indicate that the main duration of volatility 32 64 days for the strongly positive correlation between the crude oil spot price and the futures price provides more useful information for investors moreover the weighted degree weighted indegree and weighted outdegree of the correlation modes follow power law distributions the correlation fluctuation strengthens the extent of persistence over the long term whereas persistence weakens over the short and medium term the primary correlation modes dominating the transmission process and the major intermediary modes in the transmission process are clustered both in the short and long term

supersymmetric sigma models twistors and the atiyah hitchin metric the legendre transform and its generalizations originally found in supersymmetric models are techniques that can be used to givelocal constructions of hyperkahler metrics we give a twistor space interpretation to the generalizations of the legendre transform construction the atiyah hitchin metric on the moduli space of two monopoles is used as a detailed example

are gibbs type priors the most natural generalization of the dirichlet process discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in bayesian inference here we focus on the family of gibbs type priors a recent elegant generalization of the dirichlet and the pitman yor process priors these random probability measures share properties that are appealing both from a theoretical and an applied point of view i they admit an intuitive predictive characterization justifying their use in terms of a precise assumption on the learning mechanism ii they stand out in terms of mathematical tractability iii they include several interesting special cases besides the dirichlet and the pitman yor processes the goal of our paper is to provide a systematic and unified treatment of gibbs type priors and highlight their implications for bayesian nonparametric inference we deal with their distributional properties the resulting estimators frequentist asymptotic validation and the construction of time dependent versions applications mainly concerning mixture models and species sampling serve to convey the main ideas the intuition inherent to this class of priors and the neat results they lead to make one wonder whether it actually represents the most natural generalization of the dirichlet process

the self duality equations on a riemann surface in this paper we shall study a special class of solutions of the self dual yang mills equations the original self duality equations which arose in mathematical physics were defined on euclidean 4 space the physically relevant solutions were the ones with finite action the so called instantons the same equations may be dimensionally reduced to euclidean 3 space by imposing invariance under translation in one direction these equations also have physical relevance the solutions which have finite action in three dimensions are the magnetic monopoles if we take the reduction process one step further and consider solutions which are invariant under two translations we obtain a set of equations in the plane here however there is no clear physical meaning and indeed attempts to find finite action solutions have failed nevertheless these are the equations we shall consider despite the lack of interesting solutions in r2 the equations have the important property conformal invariance which allows them to be defined on manifolds modelled on r2 by conformal maps namely riemann surfaces we shall consider here solutions of the self duality equations defined on a compact riemann surface there are in fact solutions as we shall show and the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure which will be the focus of our study it brings together in a harmonious way the subjects of riemannian geometry topology algebraic geometry and symplectic geometry illuminating all these facets of the same object accounts for the length of this paper the self duality equations are equations from gauge theory geometrically they are defined in terms of connections on principal bundles while the group of the principal bundle may be chosen arbitrarily for the equations to make sense we restrict attention here to the simplest case of su 2 or so 3 there are two reasons for this the first and most obvious is that it simplifies calculations and avoids the use of inductive processes which are inherent in the consideration of a general lie group of higher rank the second reason is that solutions for su 2 have an intimate relationship with the internal structure of the riemann surface as a consequence of results we shall prove about solutions to the self duality equations we learn something about the moduli space of complex structures on the surface itself namely teichmuller space

inverses of 2 2 block matrices abstract in this paper the authors give explicit inverse formulae for 2 2 block matrices with three different partitions then these results are applied to obtain inverses of block triangular matrices and various structured matrices such as hamiltonian per hermitian and centro hermitian matrices

gravitational instantons of type d k and a generalization of the gibbons hawking ansatz we describe a quaternionic based ansatz generalizing the gibbons hawking ansatz to a class of hyperkahler metrics with hidden symmetries we then apply it to obtain explicit expressions for gravitational instanton metrics of type d k

modeling unobserved sources of heterogeneity in animal abundance using a dirichlet process prior in surveys of natural populations of animals a sampling protocol is often spatially replicated to collect a representative sample of the population in these surveys differences in abundance of animals among sample locations may induce spatial heterogeneity in the counts associated with a particular sampling protocol for some species the sources of heterogeneity in abundance may be unknown or unmeasurable leading one to specify the variation in abundance among sample locations stochastically however choosing a parametric model for the distribution of unmeasured heterogeneity is potentially subject to error and can have profound effects on predictions of abundance at unsampled locations in this article we develop an alternative approach wherein a dirichlet process prior is assumed for the distribution of latent abundances this approach allows for uncertainty in model specification and for natural clustering in the distribution of abundances in a data adaptive way we apply this approach in an analysis of counts based on removal samples of an endangered fish species the okaloosa darter results of our data analysis and simulation studies suggest that our implementation of the dirichlet process prior has several attractive features not shared by conventional fully parametric alternatives

main memory triangle computations for very large sparse power law graphs finding counting and or listing triangles three vertices with three edges in massive graphs are natural fundamental problems which have recently received much attention because of their importance in complex network analysis here we provide a detailed survey of proposed main memory solutions to these problems in a unified way we note that previous authors have paid surprisingly little attention to space complexity of main memory solutions despite its both fundamental and practical interest we therefore detail space complexities of known algorithms and discuss their implications we also present new algorithms which are time optimal for triangle listing and beats previous algorithms concerning space needs they have the additional advantage of performing better on power law graphs which we also detail we finally show with an experimental study that these two algorithms perform very well in practice allowing us to handle cases which were previously out of reach

the construction of ale spaces as hyper kahler quotients on decrit la construction d une famille particuliere de 4 varietes hyper kahler les espaces asymptotiquement localement euclidiens ale on decrit une 4 variete de riemann avec juste une extremite qui a l infini ressemble au quotient r 4 de l espace euclidien r 4 par un groupe fini d identifications

the two parameter poisson dirichlet distribution derived from a stable subordinator the two parameter poisson dirichlet distribution denoted mathsf pd alpha theta is a probability distribution on the set of decreasing positive sequences with sum 1 the usual poisson dirichlet distribution with a single parameter theta introduced by kingman is mathsf pd 0 theta known properties of mathsf pd 0 theta including the markov chain description due to vershik shmidt and ignatov are generalized to the two parameter case the size biased random permutation of mathsf pd alpha theta is a simple residual allocation model proposed by engen in the context of species diversity and rediscovered by perman and the authors in the study of excursions of brownian motion and bessel processes for 0 alpha 1 mathsf pd alpha 0 is the asymptotic distribution of ranked lengths of excursions of a markov chain away from a state whose recurrence time distribution is in the domain of attraction of a stable law of index alpha formulae in this case trace back to work of darling lamperti and wendel in the 1950s and 1960s the distribution of ranked lengths of excursions of a one dimensional brownian motion is mathsf pd 1 2 0 and the corresponding distribution for a brownian bredge is mathsf pd 1 2 1 2 the mathsf pd alpha 0 and mathsf pd alpha alpha distributions admit a similar interpretation in terms of the ranked lengths of excursions of a semistable markov process whose zero set is the range of a stable subordinator of index alpha

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

mass in kahler geometry we prove a simple explicit formula for the mass of any asymptotically locally euclidean ale kahler manifold assuming only the sort of weak fall off conditions required for the mass to actually be well defined for ale scalar flat kahler manifolds the mass turns out to be a topological invariant depending only on the underlying smooth manifold the first chern class of the complex structure and the kahler class of the metric when the metric is actually ae asymptotically euclidean our formula not only implies a positive mass theorem for kahler metrics but also yields a penrose type inequality for the mass

analysis of overdispersed count data by mixtures of poisson variables and poisson processes count data often show overdispersion compared to the poisson distribution overdispersion is typically modeled by a random effect for the mean based on the gamma distribution leading to the negative binomial distribution for the count this paper considers a larger family of mixture distributions including the inverse gaussian mixture distribution it is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures the same approach can be used to generate counting processes from poisson processes where the rate or the time is random a random rate corresponds to variation between patients whereas a random time corresponds to variation within patients

bayesian nonparametric estimation of the probability of discovering new species summary we consider the problem of evaluating the probability of discovering a certain number of new species in a new sample of population units conditional on the number of species recorded in a basic sample we use a bayesian nonparametric approach the different species proportions are assumed to be random and the observations from the population exchangeable we provide a bayesian estimator under quadratic loss for the probability of discovering new species which can be compared with well known frequentist estimators the results we obtain are illustrated through a numerical example and an application to a genomic dataset concerning the discovery of new genes by sequencing additional single read sequences of cdna fragments

new hyperkahler metrics and new supermultiplets we present new constructions of hyperkahler metrics along with the three new classes ofn 4 supermultiplets that they derive from further we provide a general setting for understanding the constructions and give a detailed description of the multiplets inn 2 andn 4 superspace

nahm s equations and hyperkahler geometry the geometry of certain moduli spaces of solutions to nahm s equations is studied and a family of gravitational instationsj is shown to arise as a deformation of theh atiyah hitchin maniford

a new estimator of the discovery probability summary species sampling problems have a long history in ecological and biological studies and a number of issues including the evaluation of species richness the design of sampling experiments and the estimation of rare species variety are to be addressed such inferential problems have recently emerged also in genomic applications however exhibiting some peculiar features that make them more challenging specifically one has to deal with very large populations genomic libraries containing a huge number of distinct species genes and only a small portion of the library has been sampled sequenced these aspects motivate the bayesian nonparametric approach we undertake since it allows to achieve the degree of flexibility typically needed in this framework based on an observed sample of size n focus will be on prediction of a key aspect of the outcome from an additional sample of size m namely the so called discovery probability in particular conditionally on an observed basic sample of size n we derive a novel estimator of the probability of detecting at the n m 1 th observation species that have been observed with any given frequency in the enlarged sample of size n m such an estimator admits a closed form expression that can be exactly evaluated the result we obtain allows us to quantify both the rate at which rare species are detected and the achieved sample coverage of abundant species as m increases natural applications are represented by the estimation of the probability of discovering rare genes within genomic libraries and the results are illustrated by means of two expressed sequence tags datasets

a torelli type theorem for gravitational instantons on montre que chaque 4 variete hyper kahler asymptotiquement localement euclidienne et isometrique a un membre d une des familles obtenues dans un article precedent

hyperkahler metrics and supersymmetry we describe two constructions of hyperkahler manifolds one based on a legendre transform and one on a sympletic quotient these constructions arose in the context of supersymmetric nonlinear models but can be described entirely geometrically in this general setting we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience

finding the multipath propagation of multivariable crude oil prices using a wavelet based network approach the globalization and regionalization of crude oil trade inevitably give rise to the difference of crude oil prices the understanding of the pattern of the crude oil prices mutual propagation is essential for analyzing the development of global oil trade previous research has focused mainly on the fuzzy long or short term one to one propagation of bivariate oil prices generally ignoring various patterns of periodical multivariate propagation this study presents a wavelet based network approach to help uncover the multipath propagation of multivariable crude oil prices in a joint time frequency period the weekly oil spot prices of the opec member states from june 1999 to march 2011 are adopted as the sample data first we used wavelet analysis to find different subseries based on an optimal decomposing scale to describe the periodical feature of the original oil price time series second a complex network model was constructed based on an optimal threshold selection to describe the structural feature of multivariable oil prices third bayesian network analysis bna was conducted to find the probability causal relationship based on periodical structural features to describe the various patterns of periodical multivariable propagation finally the significance of the leading and intermediary oil prices is discussed these findings are beneficial for the implementation of periodical target oriented pricing policies and investment strategies