quantum function algebra at roots of 1 abstract we introduce a form of the quantum function algebra on a drinfeld jimbo quantum group over the ring z q q 1 specializing q to a root of 1 we show that over the cyclotomic field this algebra is a projective module over its central sub algebra which is the usual coordinate algebra of the group we study the induced poisson lie structure of the group a bundle of algebras on a complex simply connected lie group with hamiltonian flows in the bundle is constructed some representations of the quantum function algebra in a root of 1 are constructed as an application an estimate of the dimension of an arbitrary representation is given

rigid analytic quantum groups and quantum arens michael envelopes abstract we introduce a rigid analytification of the quantized coordinate algebra of a semisimple algebraic group and a quantized arens michael envelope of the enveloping algebra of the corresponding lie algebra working over a non archimedean field and when q is not a root of unity we show that these analytic quantum groups are topological hopf algebras and frechet stein algebras we then introduce an analogue of the bgg category o for the quantum arens michael envelope and show that it is equivalent to the category o for the corresponding quantized enveloping algebra

local multiplicity adjustment for the spatial scan statistic using the gumbel distribution the spatial scan statistic is an important and widely used tool for cluster detection it is based on the simultaneous evaluation of the statistical significance of the maximum likelihood ratio test statistic over a large collection of potential clusters in most cluster detection problems there is variation in the extent of local multiplicity across the study region for example using a fixed maximum geographic radius for clusters urban areas typically have many overlapping potential clusters while rural areas have relatively few the spatial scan statistic does not account for local multiplicity variation we describe a previously proposed local multiplicity adjustment based on a nested bonferroni correction and propose a novel adjustment based on a gumbel distribution approximation to the distribution of a local scan statistic we compare the performance of all three statistics in terms of power and a novel unbiased cluster detection criterion these methods are then applied to the well known new york leukemia dataset and a wisconsin breast cancer incidence dataset

tests of spatial randomness adjusted for an inhomogeneity a general framework in many applications it is of interest to test whether a spatial point pattern is randomly generated after adjusting for an underlying spatial inhomogeneity a great variety of different test statistics have been proposed for this purpose by scientists in different fields these are reviewed in this article despite apparent dissimilarities in terms of their original formulations most of these statistics can be placed into one general framework of which they are special cases this makes it easier to see exactly how they relate to one another and also to determine which test to use for a particular application the general framework can also be used for proposing new tests by combining properties of existing tests for developing theoretical foundations for these types of test statistics for doing structured comparative evaluations and for software development

weighted normal spatial scan statistic for heterogeneous population data in geographical spatial epidemiology and disease surveillance all the existing spatial scan methods for cluster detection using continuous data are designed for evaluating clusters of individuals and analyzing individual level data motivated by growing demands to study the spatial heterogeneity of continuous measures in population data such as mortality rates survival rates average body mass indexes and pollution at state county and census tract levels we propose a weighted normal scan statistic for investigating the clusters of the cells geographic units such as counties with unusual high low continuous regional measures where the weights reflect the uncertainty of the regional measures or sample size number of observed cases in the cells power precision the effect of the weights and the sensitivity of the proposed test statistic to data from various distributions are investigated through intensive simulation the method is applied to 1988 2002 stage i and ii lung cancer survival data in

d modules on rigid analytic spaces i we introduce a sheaf of infinite order differential operators d on smooth rigid analytic spaces that is a rigid analytic quantisation of the cotangent bundle we show that the sections of this sheaf over sufficiently small affinoid varieties are frechet stein algebras and use this to define co admissible sheaves of d modules we prove analogues of cartan s theorems a and b for co admissible d modules

localization for quantum groups at a root of unity let c be the field of complex numbers and fix q g c let g be a semi simple lie algebra over c and let g be the corresponding simply connected algebraic group let uq be the quantized enveloping algebra of q let oq be the algebra of quantized functions on g let oq b be the quotient hopf algebra of oq corresponding to a borel subgroup b of g in the paper bk we defined categories of equivariant quantum o modules and pg modules on the quantum flag variety of g we proved that the beilinson bernstein localization theorem holds at a generic q namely the global section functor gives an equivalence between categories of modules and vq iaod es on the quantum flag variety thus one can translate questions about the represen tation theory of quantum groups to the study of the noncommutative geometry of the quantum flag variety in this paper we prove that a derived version of this theorem holds at the root of unity case using this equivalence we get that one can understand the representation theory of quantum groups at roots of unity through the now commutative geometry of the springer fibers we now recall the main results in bk the constructions given there are crucial for the present paper and a fairly detailed survey of the material there is given in the next section we defined an equivariant sheaf of quasi coherent modules over the quantum flag variety to be a left oq mod e equipped with a right q b comod ile structure satisfying certain compatibility conditions such objects form a category denoted ai q gq it contains certain line bundles oq for in the weight lattice we proved that oq x is ample for 0 holds for every q this implies that the category m bq gq is a proj category in the sense of serre

darboux theory of integrability in cn taking into account the multiplicity abstract darboux in 1878 provided a theory on the existence of first integrals of polynomial systems based on the existence of sufficient invariant algebraic hypersurfaces called now the darboux theory of integrability in 1979 jouanolou successfully improved the darboux theory of integrability characterizing the existence of rational first integrals for this he used sophisticated tools of algebraic geometry the aim of this paper is to improve the classical result of darboux and the new one of jouanolou taking into account the multiplicity of the invariant algebraic hypersurfaces additionally our proof of the improved result of jouanolou is much simpler and elementary than the original one some examples show that the improved darboux theory of integrability with multiplicity is much useful than the classical one

quantum flag varieties equivariant quantum d modules and localization of quantum groups abstract let o q g be the algebra of quantized functions on an algebraic group g and o q b its quotient algebra corresponding to a borel subgroup b of g we define the category of sheaves on the quantum flag variety of g to be the o q b equivariant o q g modules and prove that this is a proj category we construct a category of equivariant quantum d modules on this quantized flag variety and prove the beilinson bernstein s localization theorem for this category in the case when q is transcendental

a generalized linear models approach to spatial scan statistics for covariate adjustment the spatial scan statistic proposed by kulldorff commun statist theory methods 1997 26 1481 1496 is one of the most widely used methods for detecting spatial clusters and evaluating their statistical significance however it is not fully capable of adjusting for all types of confounding covariates in this article a generalized linear models glm approach to construct spatial scan statistics which is readily in a form for covariate adjustment is proposed using glm spatial scan statistics for different probability models can be formulated in a single framework the test statistic is based on the log likelihood ratio test statistic and evaluated using monte carlo hypothesis testing the proposed method is illustrated using texas female breast cancer data concerning late versus early stage cancer cases with covariates of race ethnicity and age group

fast subset scan for spatial pattern detection summary we propose a new fast subset scan approach for accurate and computationally efficient event detection in massive data sets we treat event detection as a search over subsets of data records finding the subset which maximizes some score function we prove that many commonly used functions e g kulldorff s spatial scan statistic and extensions satisfy the linear time subset scanning property enabling exact and efficient optimization over subsets in the spatial setting we demonstrate that proximity constrained subset scans substantially improve the timeliness and accuracy of event detection detecting emerging outbreaks of disease 2 days faster than existing methods

verma modules over p adic arens michael envelopes of reductive lie algebras abstract let k be a locally compact p adic field g a split reductive lie algebra over k and u g its universal enveloping algebra we investigate the category c g of coadmissible modules over the p adic arens michael envelope u g of u g let p g be a parabolic subalgebra the main result gives a canonical equivalence between the classical parabolic bgg category of g relative to p and a certain explicitly given highest weight subcategory of c g this completely clarifies the verma module theory over u g

invariant distributions on p adic analytic groups let p be a prime number let l be a finite extension of the field qp of p adic numbers let k be a spherically complete extension field of l and let g be the group of l rational points of a split reductive group over l we derive several explicit descriptions of the center of the algebra d g k of locally analytic distributions on g with values in k the main result is a generalization of an isomorphism of harish chandra which connects the center of d g k with the algebra of weyl invariant centrally supported distributions on a maximal torus of g this isomorphism is supposed to play a role in the theory of locally analytic representations of g as studied by p schneider and j teitelbaum

detection of an anomalous cluster in a network we consider the problem of detecting whether or not in a given sensor network there is a cluster of sensors which exhibit an unusual behavior formally suppose we are given a set of nodes and attach a random variable to each node we observe a realization of this process and want to decide between the following two hypotheses under the null the variables are i i d standard normal under the alternative there is a cluster of variables that are i i d normal with positive mean and unit variance while the rest are i i d standard normal we also address surveillance settings where each sensor in the network collects information over time the resulting model is similar now with a time series attached to each node we again observe the process over time and want to decide between the null where all the variables are i i d standard normal and the alternative where there is an emerging cluster of i i d normal variables with positive mean and unit variance the growth models used to represent the emerging cluster are quite general and in particular include cellular automata used in modelling epidemics in both settings we consider classes of clusters that are quite general for which we obtain a lower bound on their respective minimax detection rate and show that some form of scan statistic by far the most popular method in practice achieves that same rate within a logarithmic factor our results are not limited to the normal location model but generalize to any one parameter exponential family when the anoma lous clusters are large enough

a study on the use of gumbel approximation with the bernoulli spatial scan statistic the bernoulli version of the spatial scan statistic is a well established method of detecting localised spatial clusters in binary labelled point data a typical application being the epidemiological case control study a recent study suggests the inferential accuracy of several versions of the spatial scan statistic principally the poisson version can be improved at little computational cost by using the gumbel distribution a method now available in satscan tm www satscan org we study in detail the effect of this technique when applied to the bernoulli version and demonstrate that it is highly effective albeit with some increase in false alarm rates at certain significance thresholds we explain how this increase is due to the discrete nature of the bernoulli spatial scan statistic and demonstrate that it can affect even small p values despite this we argue that the gumbel method is actually preferable for very small p values furthermore we extend previous research by running benchmark trials on 12 000 synthetic datasets thus demonstrating that the overall detection capability of the bernoulli version i e ratio of power to false alarm rate is not noticeably affected by the use of the gumbel method we also provide an example application of the gumbel method using data on hospital admissions for chronic obstructive pulmonary disease

p value approximations for spatial scan statistics using extreme value distributions spatial scan statistics are widely applied to identify spatial clusters in geographic disease surveillance to evaluate the statistical significance of detected clusters monte carlo hypothesis testing is often used because the null distribution of spatial scan statistics is not known a drawback of the method is that we have to increase the number of replications to obtain accurate p values gumbel based p value approximations for spatial scan statistics have recently been proposed and evaluated for poisson and bernoulli models in this study we examine the use of a generalized extreme value distribution to approximate the null distribution of spatial scan statistics as well as the gumbel distribution through simulation p value approximations using extreme value distributions for spatial scan statistics are assessed for multinomial and ordinal models in addition to poisson and bernoulli models copyright 2014 john wiley sons ltd

the beilinson bernstein correspondence for quantized enveloping algebras theory of the quantized flag manifold as a quasi scheme non commutative scheme has been developed by lunts rosenberg 15 they have formulated an analogue of the beilinson bernstein correspondence using the q differential operators introduced in their earlier paper 14 in this paper we shall establish its modified version using a class of q differential operators which is possibly smaller than the one in 14

stable flatness of nonarchimedean hyperenveloping algebras let l be a completely valued nonarchimedean field and g a finite dimensional lie algebra over l we show that its hyperenveloping algebra f g agrees with its arens michael envelope and furthermore is a stably flat completion of its universal enveloping algebra as an application we prove that the taylor relative cohomology for the locally convex algebra f g is naturally isomorphic to the lie algebra cohomology of g

spatial scan statistics with overdispersion the spatial scan statistic has been widely used in spatial disease surveillance and spatial cluster detection for more than a decade however overdispersion often presents in real world data causing not only violation of the poisson assumption but also excessive type i errors or false alarms in order to account for overdispersion we extend the poisson based spatial scan test to a quasi poisson based test the simulation shows that the proposed method can substantially reduce type i error probabilities in the presence of overdispersion in a case study of infant mortality in jiangxi china both tests detect a cluster however a secondary cluster is identified by only the poisson based test it is recommended that a cluster detected by the poisson based scan test should be interpreted with caution when it is not confirmed by the quasi poisson based test copyright 2011 john wiley sons ltd

on the asymmetric may leonard model of three competing species in this paper we analyze the global asymptotic behavior of the asymmetric may leonard model of three competing species frac dx i dt x i 1 x i beta ix i 1 alpha ix i 1 x i 0 0 i 1 2 3 with x 0 x 3 x 4 x 1 under the assumption 0 b1b2b3 and p is a saddle point with one dimensional stable manifold gamma if a1a2a3 b1b2b3 then p is global asymptotically stable in int r3 ii if a1a2a3 b1b2b3 then for each initial condition x 0 not in gamma the solution v

fast detection of arbitrarily shaped disease clusters disease cluster detection and evaluation have commonly used spatial statistics methods that scan the map with a fixed circular window to locate candidate clusters recently there has been interest in searching for clusters with arbitrary shape the circular scan test retains high power of detecting a cluster but does not necessarily identify the exact regions contained in a non circular cluster particularly well we propose implement and evaluate a new procedure that is fast and produces clusters estimates of arbitrary shape in a rich class of possible cluster candidates we showed that our methods contain the so called upper level set method as a particular case we present a power study of our method and among other results the main conclusion is that the likelihood based arbitrarily shaped scan method is not appropriate to find a cluster estimate when the parameter space includes the set of all possible spatial clusters in a map a large and discrete parameter space maximum likely cluster estimates tend to overestimate the true cluster by a large extent this calls for a new approach different from the maximum likelihood method for this important public health problem

integrability of a class of n dimensional lotka volterra and kolmogorov systems abstract we study the integrability of an n dimensional differential kolmogorov systems of the form x j x j a j k 1 n a j k x k x j x 1 x n j 1 n where a j and a j k are constants for j k 1 n and x 1 x n is a homogeneous polynomial of degree n 2 with either one additional invariant hyperplane or with one exponential factor we also study the integrability of the n dimensional classical lotka volterra systems when x 1 x n 0 in particular we consider the integrability of the asymmetric may leonard systems

fast generalized subset scan for anomalous pattern detection we propose fast generalized subset scan fgss a new method for detecting anomalous patterns in general categorical data sets we frame the pattern detection problem as a search over subsets of data records and attributes maximizing a nonparametric scan statistic over all such subsets we prove that the nonparametric scan statistics possess a novel property that allows for efficient optimization over the exponentially many subsets of the data without an exhaustive search enabling fgss to scale to massive and high dimensional data sets we evaluate the performance of fgss in three real world application domains customs monitoring disease surveillance and network intrusion detection and demonstrate that fgss can successfully detect and characterize relevant patterns in each domain as compared to three other recently proposed detection algorithms fgss substantially decreased run time and improved detection power for massive multivariate data sets

an elliptic spatial scan statistic the spatial scan statistic is commonly used for geographical disease cluster detection cluster evaluation and disease surveillance the most commonly used shape of the scanning window is circular in this paper we explore an elliptic version of the spatial scan statistic using a scanning window of variable location shape eccentricity angle and size and with and without an eccentricity penalty the method is applied to breast cancer mortality data from northeastern united states and female oral cancer mortality in the united states power comparisons are made with the circular scan statistic

cluster detection of spatial regression coefficients popular approaches to spatial cluster detection such as the spatial scan statistic are defined in terms of the responses here we consider a varying coefficient regression and spatial clusters in the regression coefficients for varying coefficient regression such as the geographically weighted regression different regression coefficients are obtained for different spatial units it is often of interest to the practitioners to identify clusters of spatial units with distinct patterns in a regression coefficient but there is no formal statistical methodology for that rather cluster identification is often ad hoc such as by eyeballing the map of fitted regression coefficients and discerning patterns in this paper we develop new methodology for spatial cluster detection in the regression setting based on hypotheses testing we evaluate our methods in terms of power and coverages for true clusters via simulation studies for illustration our methodology is applied to a cancer mortality dataset copyright 2016 john wiley sons ltd

on irreducible representations of compact p adic analytic groups we prove that the canonical dimension of a coadmissible representation of a semisimple p adic lie group in a p adic banach space is either zero or at least half the dimension of a nonzero coadjoint orbit to do this we establish analogues for p adically completed enveloping algebras of bernstein s inequality for modules over weyl algebras the beilinson bernstein localisation theorem and quillen s lemma about the endomorphism ring of a simple module over an enveloping algebra