asymptotics for configural location estimators keywords robustness challenges optimality reference stap article 1986 001 record created on 2006 04 04 modified on 2017 05 12

conformal blocks and generalized theta functions let yp be the moduli space of rank r vector bundles with trivial determinant on a riemann surface x this space carries a natural line bundle the determinant line bundle s we describe a canonical isomorphism of the space of global sections of sk with the space of conformal blocks defined in terms of representations of the lie algebra 5 c z it follows in particular that the dimension of h yk is given by the verlinde formula

on the correlation structure of continuous and discrete point rainfall 1 this paper proposes new analytical results based on the theory of stochastic processes that establish a theoretical dependence of point rainfall variance on the scale of observation under somewhat general assumptions it is shown that power law scaling commonly assumed by analyses and models of point rainfall cannot hold over all scales of observation and that an inner regime exists for small sampling intervals where the variance is a quadratic function of interval length a power law scaling regime is shown to exist for larger aggregation intervals whose characteristics depend on the memory of the continuous rainfall process the presence of a transition regime between the inner and the scaling regime is also shown and may explain the deviations from a power law scaling behavior in observed rainfall reported in the literature furthermore the application of the theory to rainfall data from a representative variety of climate types shows that fractal and multifractal analysis techniques and models may indeed fail to capture observed rainfall properties over wide ranges of aggregation scales finally correlation structures with short and long term memory are considered and different theoretical relationships expressing rainfall variance as a function of aggregation interval are derived and tested against rainfall observed at different locations with aggregation timescales ranging from 15 min to 2 days the theoretical and observational analyses show that both finite and infinite memory rainfall processes may be observed in nature

reliability of different depth duration frequency equations for estimating short duration design storms 1 the design storm depth is defined as the rainfall depth that is expected to occur in the considered site for a given probability of occurrence and a given duration of the storm it is generally estimated by using parametric depth duration frequency ddf equations in particular this article considers the frequent case when one needs to estimate the design storm depth for very short durations typically from 5 to 45 min while observed rainfall extremes for calibrating the ddf parameters are only available for longer durations in this case the ddf curves are generally extrapolated below the range of durations that were used for estimating their parameters it is well known that this procedure induces estimation errors that depend on the type of ddf equation that is used the aim of this study is to test the capability of seven different ddf curves characterized by two or three parameters to provide an estimate of the design rainfall for storm durations shorter than 1 hour when their parameterization is performed by using data referred to longer storms the results point out that a proper choice of the ddf curve may improve the reliability of the design storm depth estimation significantly in particular ddf curves with three parameters provide a conservative estimation with an average relative error which never exceeded 20 for all the storm duration considered here

process dependent persistence in precipitation records abstract whether long term persistence ltp exists in precipitation process has been studied for several decades and it is still an open question in this study the precipitation records of hourly and daily resolutions are applied to estimate the persistence of precipitation over a wider range of scales mainly by means of detrended fluctuation analysis dfa the results show that precipitation persistence can be described as a varying rather than a universal scaling behavior two distinct scaling regimes are determined by their associated power law behavior f s s f s is the fluctuation function s is the time scale is the scaling exponent and they are process dependent a regime of frontal systems with stronger ltp s is less than around 200 h 0 74 and a regime of random nature of weather system and climate variability with weaker ltp s is larger than around 200 h 0 54 this result indicates that when we simulate the precipitation process it is necessary to take the different persistent properties over the corresponding scale range into account to select the appropriate model

algebro geometric analogues of donaldson s polynomials donaldson 5 has introduced polynomials on the second homology of any simply connected closed four manifold m with b odd at least 3 which up to are invariant under orientation preserving diffeomorphisms for every c ibm there is a polynomial 7c m syma h2 s where d c 4c z2 b 1 to define it one considers j c the set which is in a natural way a manifold of gauge equivalence classes of connections on the su 2 bundle on m with c2 c antiself dual with respect to a generic metric on m there is a natural map h2 m h2 j c namely slant product with 88 where p is the universal so 3 principal bundle on m x j c one way of defining 7c m 10 is to construct a compactification of r xc carrying a fundamental class xc one proves that extends to a map h2 m h2 xc then one defines

quiver generalization of a conjecture of king tollu and toumazet abstract stretching the parameters of a littlewood richardson coefficient of value 2 by a factor of n results in a coefficient of value n 1 12 9 19 we give a geometric proof of a generalization for representations of quivers

the stringy e function of the moduli space of rank 2 bundles over a riemann surface of genus 3 we compute the stringy e function or the motivic integral of the moduli space of rank 2 bundles over a riemann surface of genus 3 in doing so we answer a question of batyrev about the stringy e functions of the git quotients of linear representations

a functorial construction of moduli of sheaves we show how natural functors from the category of coherent sheaves on a projective scheme to categories of kronecker modules can be used to construct moduli spaces of semistable sheaves this construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions about which more complete results can be proved

a point process model for rainfall further developments a stochastic model for rainfall at a single site is studied in which storms arrive in a poisson process each storm consisting of a cluster of a random number of rain cells each cell having random duration and depth a model studied in an earlier paper is extended to provide a better fit to empirical experience the extension being based on the attachment of a single random variable to each storm to achieve in particular some correlation between the durations of the cells within a single storm the properties of the new model are developed its fitting to two sets of empirical data is described and the examination of adequacy of fit is studied in some detail via properties not used in the fitting procedure finally a theoretical study is made of short term prediction from the model

robust confidence intervals for a location parameter the configural approach abstract a conditional approach to robustness is described and applied to interval estimation for a location parameter two new types of confidence interval estimators using two dimensional numerical integrations within location and scale configurations emerge strong confidence intervals have robust conditional coverage probabilities bioptimal confidence intervals are as short as possible and have robust overall coverage probabilities robust intervals compromising the gaussian and the slash distributions serve as examples a comparison with a variety of other confidence intervals shows the nonrobustness of rank based interval estimators for samples of size 10 robust intervals based on m estimators are clearly superior tuning constants must be chosen carefully for interval estimation an interval based on tukey s biweight for example should be used with tuning constants of about 7 8 and 11 for samples of size 20 10 and 5 respectively

generalized scale invariance in the atmosphere and fractal models of rain in recent years there has been considerable interest in stochastic rain models by developing new ideas about scale invariance and intermittency we argue that the scope of such models can be greatly extended the notions of scale invariance intermittency and the associated idea of fractal dimension have lately gained considerable ground particularly in the context of extremely variable phenomena such as those found in the mesoscale and in hydrodynamic turbulence we review some relevant work and argue that the atmosphere respects a symmetry principle that we call generalized scale invariance in which the statistical properties of the small and large scale are related to each other by a magnification coupled with a differential stratification due to gravity and differential rotation due to the coriolis force we further argue that the extremely erratic intermittent nature of the atmosphere is characterized by scale invariant fractal measures leading to hyperbolic fat tailed probability distributions of the fluctuations the standard statistical methods based on exponential fall offs in both correlations and probability distributions are inappropriate when the variability is of this type we show how both the scaling and intermittency may be exploited to develop extremely variable stochastic models of rain although the models examined here are the simplest of a family of extremely variable processes depending on only two radar determined parameters they lead to realizations possessing many realistic features of the rainfield including complexity of form clustering and bands at all scales as well as differential stratification and rotation finally we point to weaknesses in the models in particular their monodimensional nature and suggest possible improvements

spinor bundles on quadrics we define some stable vector bundles on the complex quadric hypersurface qn of dimension n as the natural generalization of the universal bundle and the dual of the quotient bundle on q4 gr l 3 we call them spinor bundles when n 2fc 1 there is one spinor bundle of rank 2k 1 when n 2k there are two spinor bundles of rank 2k 1 their behavior is slightly different according as n 0 mod 4 or n 2 mod 4 as an application we describe some moduli spaces of rank 3 vector bundles on q5 and qe introduction let qn be the smooth quadric hypersurface of the complex pro jective space pn 1 in this paper we define in a geometrical way some vector bundles on the quadric qn as the natural generalization of the universal bundle and the dual of the quotient bundle on q4 gr l 3 we call them spinor bundles on q4 this definition is equivalent to the usual one spinor bundles are homogeneous and stable according to the definition of mum ford takemoto we study their first properties using the geometrical description given and some standard techniques available in oss we also use a theorem of ramanan see um about the stability of homoge neous bundles induced by irreducible representations when n is odd there is only one spinor bundle while when n is even there are two nonisomorphic spinor bun dles when n is even the behavior of spinor bundles is slightly different according as n 0 mod4 or n 2 mod4 in ot2 we have given a cohomological splitting criterion for vector bundles on quadrics involving spinor bundles qn spin n 2 p cty st is a homogeneous manifold and the semisimple part of the lie algebra of p ai is o n at the level of lie algebras spinor bundles are defined from the spin and half spin representations of o n the paper is divided into three sections in 1 we give some preliminary results and we define the spinor bundles in 2 we study the first properties of spinor bundles in 3 as an application we describe some moduli spaces of rank 3 vector bundles on q5 and qq

some easy t statistics abstract this article explores the use of t statistics based on two or four order statistics the functions of the order statistics which are used to define the t statistics are the pivots and bipivots the pivots are exact order statistics while the bipivots are the means of two adjacent order statistics two t statistics based on the pivots and bipivots are examined and compared to other t statistics including student s t under various sampling situations we conclude that the proposed t statistics are not only simple to use but are robust and perform quite well in terms of the lengths of their confidence intervals we recommend that these t statistics be used for sample sizes between 4 and 20 because they perform well and are easy to use tables of percentage points are provided to facilitate the use of the t statistics

groupe de picard des varietes de modules de fibres semi stables sur les courbes algebriques soient x une courbe algebrique projective lisse de genre g 2 sur r d des entiers avec r 2 on note u r d la variete de modules des fibres algebriques semi stables sur x de rang r et de degre d us r d l ouvert de u r d correspondant aux fibres stables on sait que u r d est une variete algebrique projective irreductible et normale si r et d ne sont pas premiers entre eux u r d n est pas lisse sauf dans une exception le cas ou g 2 r 2 et d est pair on supposera dans cet article qu on n est pas dans ce cas on a alors codimu r d u r d us r d 2 et u r d us r d est le lieu des points singuliers de u r d si l est un fibre en droites de degre d sur x on note u r l la sous variete fermee de u r d correspondant aux fibres vectoriels de determinant isomorphe a l on etudie dans cet article les groupes de picard pic u r d et pic u r l on montre d abord que les varietes u r d et u r l sont localement factorielles on calcule ensuite pic u r d et pic u r l qui sont decrits au moyen des diviseurs thetas generalises

plucker forms and the theta map let rm su x r 0 be the moduli space of semistable vector bundles of rank r and trivial determinant over a smooth irreducible complex projective curve x the theta map theta r rm su x r 0 rightarrow bbb p n is the rational map defined by the ample generator of rm pic rm su x r 0 the main result of the paper is that theta r is generically injective if g gg r and x is general this partially answers the following conjecture proposed by beauville theta r is generically injective if x is not hyperelliptic the proof relies on the study of the injectivity of the determinant map d e wedge r h 0 e rightarrow h 0 det e for a vector bundle e on x and on the reconstruction of the grassmannian g r rm from a natural multilinear form associated to it defined in the paper as the pl ucker form the method applies to other moduli spaces of vector bundles on a projective variety x

on space time scaling of cumulated rainfall fields in the study of space time rainfall it is particularly important to establish characteristic properties to guide both theoretical and modeling research efforts in the present paper new observational analyses on the scaling properties of time evolving cumulated rainfall fields are presented and a theoretical framework for their interpretation is introduced it is found that the time evolution of the spatial organization of a cumulated rainfall field produces scaling relationships of spatial variance versus time and characteristic values for the scaling exponent the reproduction of these values constitutes a basic requirement for spatial temporal field generators in order to model important properties of real rainfall fields it is then shown on theoretical grounds what properties the instantaneous rainfall intensity fields must obey in order to reproduce the experimental observations and how the size of the observation domain affects the scaling relationships some current stochastic models of space time precipitation are finally discussed and analyzed in the light of the tools introduced to show under what circumstances the models considered give acceptable results furthermore it is shown that the assumption of an exponential time correlation function used in many current rainfall models is not compatible with observations

multiscaling properties of rainfall and bounded random cascades the connection among different types of exponents characterizing multiscaling properties of rainfall and a criterion for stationarity of random fields are discussed and a new phenomenological model for rainfall time series simulation is proposed the bounded random cascade model presented here is a generalization of the well known model with the multiplicative weights of the generator converging to unity as the cascade proceeds to smaller scales this allows one to directly simulate a multiscaling random field with an energy spectrum exponent 1 which is typical for rainfall time series data but which cannot be produced by a standard model a procedure is proposed for estimating the cascade parameters of this new bounded model from observed data parameters are estimated from two data sets with different degrees of intermittency and different spectral exponents the bounded model simulations using these parameters produced realistic rainfall time series with spectral exponents similar to their observed counterparts

a theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall generating fine scale time series of intermittent rainfall that are fully consistent with any given coarse scale totals is a key and open issue in many hydrological problems we propose a stationary disaggregation method that simulates rainfall time series with given dependence structure wet dry probability and marginal distribution at a target finer lower level time scale preserving full consistency with variables at a parent coarser higher level time scale we account for the intermittent character of rainfall at fine time scales by merging a discrete stochastic representation of intermittency and a continuous one of rainfall depths this approach yields a unique and parsimonious mathematical framework providing general analytical formulations of mean variance and autocorrelation function acf for a mixed type stochastic process in terms of mean variance and acfs of both continuous and discrete components respectively to achieve the full consistency between variables at finer and coarser time scales in terms of marginal distribution and coarse scale totals the generated lower level series are adjusted according to a procedure that does not affect the stochastic structure implied by the original model to assess model performance we study rainfall process as intermittent with both independent and dependent occurrences where dependence is quantified by the probability that two consecutive time intervals are dry in either case we provide analytical formulations of main statistics of our mixed type disaggregation model and show their clear accordance with monte carlo simulations an application to rainfall time series from real world is shown as a proof of concept

the mathematical structure of rainfall representations 1 a review of the stochastic rainfall models this is the first of a three part series on the mathematical structure of rainfall models several important attempts at modeling rainfall are reviewed special attention is given to the mathematical structures that arise in the rainfall descriptions a general overview of the three part series is given as preface to this part

intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a riemann surface let n and d be coprime positive integers and define m n d to be the moduli space of semi stable holomorphic vector bundles of rank n degree d and fixed determinant on a compact riemann surface e this moduli space is a compact kifhler manifold which has been studied from many different points of view for more than three decades see for instance narasimhan and seshadri 41 the subject of this article is the characterization of the intersection pairings in the cohomology ring1 h m n d a set of generators of this ring was described by atiyah and bott in their seminal 1982 paper 2 on the yangmills equations on riemann surfaces where in addition inductive formulas for the betti numbers of m n d obtained earlier using number theoretic methods 13 25 were rederived by poincare duality knowledge of the intersection pairings between products of these generators or equivalently knowledge of the evaluation on the fundamental class of products of the generators completely determines the structure of the cohomology ring in 1991 donaldson 15 and thaddeus 47 gave formulas for the intersection pairings between products of these generators in h m 2 1 in terms of bernoulli numbers then using physical methods witten 50 found formulas for generating functions from which could be extracted the intersection pairings between products of these generators in h m n d for general rank n these generalized his rigorously proved formulas 49 for the symplectic volume of m n d for instance the symplectic volume of m 2 1 is given by

the level rank duality for non abelian theta functions we prove that the strange duality conjecture of beauville donagi tu holds for all curves we establish first a more extended level rank duality interesting in its own right from which the standard level rank duality follows by restriction

factorisation of generalised theta functions i we prove a version of factorisation relating the space of sections of theta bundles on the moduli spaces of parabolic rank 2 vector bundles on curves of genusg andg 1

the strange duality conjecture for generic curves let sux r be the moduli space of semi stable vector bundles of rank r with trivial determinant over a connected smooth projective algebraic curve x of genus g 1 over c recall that a vector bundle e on x is called semi stable if for any subbundle v deg v rk v deg e rk e points of sux r correspond to isomorphism classes of semi stable rank r vector bundles with trivial determinant up to an equivalence relation for any line bundle l of degree g 1 onx define l e sux r h e l 1 this turns out be a non zero cartier divisor whose associated line bundle l o l does not depend upon l it is known that l generates the picard group of sux r for this and the precise definition of l in terms of determinant of cohomology see dn let u x k be the moduli space of semi stable rank k and degree k g 1 bundles on x recall that on u x k there is a canonical non zero theta cartier divisor k whose underlying set is f u x k h x f 0 put m o k consider the natural map k r sux r u x k u x kr given by tensor product from the theorem of the square it follows that k rm is isomorphic to l m the canonical element kr h0 u x kr m and the kunneth theorem give a map well defined up to scalars

on the hitchin system 1 1 what is known as the hitchin system is a completely integrable hamiltonian system cihs involving vector bundles over algebraic curves identified by hitchin in h1 h2 it was recently generalized by faltings f in this paper we only consider the case of ranktwo vector bundles with trivial determinant in that case the hitchin system corresponding to a curve c of genus g is obtained as follows let

statistical modeling of daily rainfall occurrences in this paper likelihood based inference procedures for discrete point process models are developed and a new family of discrete point process models for daily rainfall occurrences is proposed the model which is termed a markov bernoulli process can be viewed as a sequence of bernoulli trials with randomized success probabilities contained within the family of markov bernoulli models are markov chain and bernoulli trial models asymptotic properties of maximum likelihood estimators of markov bernoulli model parameters are derived these results provide the basis for assessing standard errors and correlation of parameter estimators and for developing likelihood ratio tests to choose among markov bernoulli markov chain and bernoulli trial models inference procedures are applied to a data set from washington d c

coordinate rings for the moduli stack of sl2 c quasi parabolic principal bundles on a curve and toric fiber products abstract we continue the program started in manon 2010 m1 to understand the combinatorial commutative algebra of the projective coordinate rings of the moduli stack m c p sl 2 c of quasi parabolic sl 2 c principal bundles on a generic marked projective curve we find general bounds on the degrees of polynomials needed to present these algebras by studying their toric degenerations in particular we show that the square of any effective line bundle on this moduli stack yields a koszul projective coordinate ring this leads us to formalize the properties of the polytopes used in proving our results by constructing a category of polytopes with term orders we show that many of results on the projective coordinate rings of m c p sl 2 c follow from closure properties of this category with respect to fiber products

gv sheaves fourier mukai transform and generic vanishing we prove a formal criterion for generic vanishing in the sense originated by green and lazarsfeld and pursued further by hacon but in the context of an arbitrary fourier mukai correspondence for smooth projective varieties we apply this to deduce a kodaira type generic vanishing theorem for adjoint bundles associated to nef line bundles and in fact a more general generic nadel type vanishing theorem for multiplier ideal sheaves still in the context of the picard variety the same method gives various other generic vanishing results by reduction to standard vanishing theorems we further use our criterion in order to address some examples related to generic vanishing on higher rank moduli spaces

descent of coherent sheaves and complexes to geometric invariant theory quotients abstract fix a scheme x over a field of characteristic zero that is equipped with an action of a reductive algebraic group g we give necessary and sufficient conditions for a g equivariant coherent sheaf on x or a bounded above complex of g equivariant coherent sheaves on x to descend to a good quotient x g this gives a description of the coherent derived category of x g as an admissible subcategory of the equivariant derived category of x

hecke correspondence stable maps and the kirwan desingularization we prove that the moduli space m0 0 n 2 of stable maps of degree 2 to the moduli space n of rank 2 stable bundles of flxed odd determinant ox ix over a smooth projective curve x of genus g 3 has two irreducible components which intersect transversely one of them is kirwan s partial desingularization e mx of the moduli space mx of rank 2 semistable bundles with determinant isomorphic to ox yix for some y 2 x the other component is the partial desingularization of the git quotient phom sl 2 w pgl 2 for a vector bundle w r 1 l i2 ix of rank g over the jacobian of x we also show that the hilbert scheme h the chow scheme c of conics in n and m0 0 n 2 are related by explicit contractions

moduli of vector bundles frobenius splitting and invariant theory let x be an irreducible projective curve of genus g over an algebraically closed field of positive characteristic 2 3 in part i we prove adapting the degeneration arguments of n tr that moduli spaces of rank two parabolic bundles on x are frobenius split m r for generic smooth x a similar result holds for x nodal a consequence is the verlinde formula in positive characteristic in part ii we give a direct proof of the fact that the local rings of the moduli spaces are f split and further that they are cohen macaulay this involves showing that the ring of invariants of g copies of 2 x 2 matrices under the adjoint action of sl 2 is f split and cohen macaulay

non power law scale properties of rainfall in space and time 1 the identification of general relationships linking statistical properties of rainfall aggregated at different temporal and spatial scales possesses clear theoretical and practical relevance among other properties it is important to characterize the scale dependence of rainfall variability which may for many purposes be summarized by its variance this paper presents theoretical results and observational analyses connecting the variance of temporal and spatial rainfall to the scale of observation under an assumption of second order stationarity previous results regarding the theoretical form of the temporal variance as a function of aggregation are refined and extended to the spatial case it is shown that the variance of aggregated rainfall exhibits an overall nonscaling form within the range of scales of usual hydrological interest it is further shown that the theoretically derived form of the variance as a function of scale is incompatible with power law relations usually assumed for the second order statistical moment within multiscaling approaches to rainfall modeling predictions of the theoretical derivations are validated by use of observations representing a wide variety of resolutions from 2 s to 1 hour in time and 4 km in space climates and measurement instruments the validation shows a good agreement between observations and the theoretically predicted forms of the variance as a function of aggregation the proposed theoretical framework thus provides a useful context for rainfall analysis modeling and downscaling in space and time and suggests careful reexaminations of usual multiscaling assumptions

strange duality of verlinde spaces for g_2 and f_4 we prove that the pull back of the canonical theta divisor for e 8 bundles at level one induces a strange duality between verlinde spaces for g 2 and f 4 at level one on smooth curves of genus g we also prove a parabolic generalization in terms of conformal blocks and write down identities between conformal blocks divisors in text pic overline text m g n mathbb q

probabilistic representation of the temporal rainfall process by a modified neyman scott rectangular pulses model parameter estimation and validation the capability of the neyman scott clustered stochastic point process model of rainfall to preserve various observed statistics is considered randomization of the cell duration parameter from storm to storm is shown to considerably improve the wet dry period joint distribution and extreme value statistics a simple procedure for parameter estimation is introduced and applied

projective normality of the moduli space of rank 2 vector bundles on a generic curve we prove that the embedding to the projective space by the generalized theta divisors of the moduli space of rank 2 vector bundles on a generic curve is projective normal