a class of multiplicity adjusted tests for spatial clustering based on case control point data a class of tests with quadratic forms for detecting spatial clustering of health events based on case control point data is proposed it includes cuzick and edwards s test statistic 1990 journal of the royal statistical society series b 52 73 104 although they used the property of asymptotic normality of the test statistic we show that such an approximation is generally poor for moderately large sample sizes instead we suggest a central chi square distribution as a better approximation to the asymptotic distribution of the test statistic furthermore not only to estimate the optimal value of the unknown parameter on the scale of cluster but also to adjust for multiple testing due to repeating the procedure by changing the parameter value we propose the minimum of the profile p value of the test statistic for the parameter as an integrated test statistic we also provide a statistic to estimate the areas or cases which make large contributions to significant clustering the proposed methods are illustrated with a data set concerning the locations of cases of childhood leukemia and lymphoma and another on early medieval grave site locations consisting of affected and nonaffected grave sites

tests to detect clustering of infected individuals within families a new simple test to detect within family clustering of infected individuals is proposed the test is derived as the score test for several different parametric models designed to allow an increased within family infectivity the new test is compared with other tests proposed to detect the same type of clustering caused by increased within family infectivity applications of household disease data and simulations are used to illustrate the theory

l2 analytic torsion abstract in this paper we introduce a new differential invariant called l2 analytic torsion for closed manifolds with positive decay and whose universal covers have trivial l2 cohomology l2 analytic torsion can be thought of as a suitable generalization of the ray singer analytic torsion we establish various functorial properties of l2 analytic torsion and also compute it for odd dimensional closed hyperbolic manifolds with the help of results from fried

spectral flow eta invariants and von neumann algebras abstract in this paper we prove that the spectral flow of a path of tangential signature operators on a closed odd dimensional manifold parametrized by unitary representations of the fundamental group is a homotopy invariant of the manifold and the path in the space of unitary representations for a large class of fundamental groups with the help of results due to weinberger proc nat acad sci u s a 85 1988 5362 5363 we also prove that an eta invariant for normal covering spaces introduced by cheeger and gromov j differential geom 21 1985 1 34 and defined using the von neumann trace is a homotopy invariant for bieberbach groups finally we compute this invariant for closed locally symmetric spaces and obtain the surprising result that the eta invariant for such spaces is a differential invariant

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

realistic power simulations compare point and area based disease cluster tests one can roughly divide disease cluster tests into area based using regional data and point based using exact locations we have compared the power of two area based methods moran s i and i pop a new method to that of two point based methods the cuzick edwards test and grimson s test using three realistic simulations of disease fox rabies in england childhood leukaemia in north humberside england and lyme disease in georgia the naive belief that point based methods should be better is not supported for the complex data simulated here i pop and the cuzick edwards test had higher power than grimson s method or moran s i i pop capitalizes on high inter region variability while moran s i cannot

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

clustering of rare events the clustering of cases of a rare disease is considered the number of events observed for each unit is assumed to have a poisson distribution the mean of which depends upon the population size and the cluster membership of that unit here a cluster consists of those units that are homogeneous in their rate of occurrence of the rare events under study a sample of units is modeled by a mixture of poisson distributions one for each cluster the mixing parameters being the proportions of all units represented by the components of the mixture maximum likelihood and bayes approaches are employed to determine criteria for separating a sample into groups of units with homogeneous rates a likelihood ratio test for the significance of a two component mixture is presented as an example the performance of the criteria is illustrated with data on the spatial occurrence of sudden infant deaths sids in north carolina counties over a four year period the results suggest that the practice of dividing the counties into high and low risk categories on the basis of the ordered rates alone should be questioned tests based upon combinatorial methods are also presented to examine the significance of the number of contiguous counties among those with high rates

von neumann algebra invariants of dirac operators abstract in this paper we define and study certain von neumann algebra invariants associated to the dirac operator acting on l 2 spinors on the universal covering space of a compact riemannian spin manifold we first study a novikov shubin type invariant which is a conformal invariant but which is not independent of the choice of metric however we prove results which give evidence that this invariant may always be positive when the novikov shubin type invariant is positive we can define the von neumann algebra determinant of the dirac laplacian and the corresponding element in the determinant line of the space of l 2 harmonic spinors on the universal covering space which we also compute for certain locally symmetric spaces finally we study a von neumann algebra eta invariant associated to the dirac operator and we show that it is sometimes an obstruction to the existence of metrics of positive scalar curvature

second order analysis of inhomogeneous spatial point processes using case control data methods for the statistical analysis of stationary spatial point process data are now well established methods for nonstationary processes less so one of many sources of nonstationary point process data is a case control study in environmental epidemiology in that context the data consist of a realization of each of two spatial point processes representing the locations within a specified geographical region of individual cases of a disease and of controls drawn at random from the population at risk in this article we extend work by baddeley moller and waagepetersen 2000 statistica neerlandica54 329 350 concerning estimation of the second order properties of a nonstationary spatial point process first we show how case control data can be used to overcome the problems encountered when using the same data to estimate both a spatially varying intensity and second order properties second we propose a semiparametric method for adjusting the estimate of intensity so as to take account of explanatory variables attached to the cases and controls our primary focus is estimation but we also propose a new test for spatial clustering that we show to be competitive with existing tests we describe an application to an ecological study in which juvenile and surviving adult trees assume the roles of controls and cases

detection of spatial disease clusters with lisa functions detection of disease clusters is an important tool in epidemiology that can help to identify risk factors associated with the disease and in understanding its etiology in this article we propose a method for the detection of spatial clusters where the locations of a set of cases and a set of controls are available the method is based on local indicators of spatial association functions lisa functions particularly on the development of a local version of the product density which is a second order characteristic of spatial point processes the behavior of the method is evaluated and compared with kulldorff s spatial scan statistic by means of a simulation study it is shown that the lisa method yields high sensitivity and specificity when it is used to detect simulated clusters of different sizes and shapes it also performs better than the spatial scan statistic when they are used to detect clusters of irregular shape however it presents relatively high type i error in situations where the number of cases is high both methods are applied for detecting spatial clusters of kidney disease in the city of valencia spain in the year 2008

methods for analysing spatial processes of several types of points two approaches are described to the analysis of spatial patterns consisting of several types of points the first approach uses a method of asymptotically unbiased estimation of the second moment distribution the second uses methods based on regions of empty space in the patterns some distributional results are given in each case and a method of monte carlo testing conditional on the marginal structure is described the methods are illustrated by being applied to some physiological data

heat kernels on covering spaces and topological invariants it is well known that there are relationships between the heat flow acting on differential forms on a closed oriented manifold m and the topology of m from hodge theory one can recover the betti numbers of m from the heat flow furthermore ray and singer 42 defined an analytic torsion a smooth invariant of acyclic flat bundles on m and conjectured that it equals the classical reidemeister torsion this conjecture was proved to be true independently by cheeger 7 and muller 40 the analytic torsion is nonzero only on odd dimensional manifolds and behaves in some ways as an odd dimensional counterpart of the euler characteristic 20 if m is not simply connected then there is a covering space analog of the betti numbers using the heat flow on the universal cover m one can define the l2 betti numbers of m 1 by taking the trace of the heat kernel not in the ordinary sense but as an element of a certain type ii von neumann algebra more concretely this amounts to integrating the local trace of the heat kernel over a fundamental domain in m in 11 we summarize this theory we consider the covering space analog of the analytic torsion this i analytic torsion has the same relation to the i cohomology as the ordinary analytic torsion bears to de rham cohomology in 111 we define the i analytic torsion 9 m under a technical assumption which we discuss later and prove its basic properties we show that m is a smooth invariant of manifolds whose l2 betti numbers vanish the proof is similar to that of the analogous statement for the ordinary analytic torsion but requires some care because of the possible slow decay of the heat kernels for large time in order to know if there are interesting examples of m we compute it in the case where m admits a hyperbolic metric it is clear that is proportionate to the volume of the hyperbolic metric which is

essential self adjointness for semi bounded magnetic schrodinger operators on non compact manifolds abstract we prove essential self adjointness for semi bounded below magnetic schrodinger operators on complete riemannian manifolds with a given positive smooth measure which is fixed independently of the metric some singularities of the scalar potential are allowed this is an extension of the povzner wienholtz simader theorem the proof uses the scheme of wienholtz but requires a refined invariant integration by parts technique as well as the use of a family of cut off functions which are constructed by a non trivial smoothing procedure due to karcher

the spinor heat kernel in maximally symmetric spaces the heat kernelk x x t of the iterated dirac operator on ann dimensional simply connected maximally symmetric riemannian manifold is calculated on the odd dimesional hyperbolic spacesk is a minakshisundaram dewitt expansion which terminates to the coefficientan 1 2 and is exact on the odd spheres the heat kernel may be written as an image sum of wkb kernels each term corresponding to a classical path geodesic in the even dimensional case the wkb approximation is not exact but a closed form ofk is derived both in terms of spherical eigenfunctions and of a sum over classical paths the spinor plancherel measure and function in the hyperbolic case are also calculated a simple relation between the analytic structure of onhn and the degeneracies of the dirac operator onsn is found

an optimal inequality between scalar curvature and spectrum of the laplacian for a riemannian closed spin manifold and under some topological assumption non zero a genus or enlargeability in the sense of gromov lawson we give an optimal upper bound for the infimum of the scalar curvature in terms of the first eigenvalue of the laplacian the main difficulty lies in the study of the odd dimensional case on the other hand we study the equality case for the closed spin riemannian manifolds with non zero a genus this work improves an inequality which was first proved by k ono in 1988

the choice of test for detecting raised disease risk near a point source this paper considers the problem of testing for excess risk near a point source of risk s as might be postulated to exist near a nuclear installation for example the data are assumed to be in the form of counts in small areas for which expected numbers of cases have also been calculated by reference to national rates it is shown how to derive the most powerful test against any given alternative hypothesis such linear risk score tests are further considered particularly that which scores each case according to the reciprocal of the rank of the distance from s these tests are compared with two tests due to stone for general ordered alternatives and the important distinction is drawn between conditional and unconditional versions of the tests their behaviour is illustrated by application to data on childhood leukaemia in relation to nuclear installations in britain

the detection of disease clustering in time this paper presents a new index for the level of disease clustering in time which is devised to the case where the data are grouped into several equally spaced intervals this index is applicable to both temporal and cyclical clustering the asymptotic distribution of this index is derived under the null hypothesis of no clustering in time monte carlo simulation studies show that the asymptotic results are good approximations when the sample size is as small as the number of intervals an average of one per interval the powers of the test based on this index for both types of clustering are compared with those of several existing procedures tables of upper percentage points of this index are given

a test to detect clusters of disease summary a test is given to detect clustering in disease incidence or mortality data the test statistic is the mean distance between all pairs of disease cases its null mean and variance and its asymptotic normality are derived under assumptions that accommodate differences in population distribution among demographic subgroups at different disease risk the test is illustrated on 63 cases of anal and rectal squamous cell carcinoma in san francisco during 1973 1981 patterns of disease incidence and mortality over time space or occupational categories can provide clues to the cause of the disease an aetiologic agent can produce a spatial temporal or occupational cluster of disease cases it is seldom difficult to detect clusters of rare diseases like angiosarcoma of the liver among men occupationally exposed to polyvinyl chloride however more common diseases present two problems first clusters may be obscured by the scattered occurrence of cases unrelated to the cause of the clusters secondly clusters may be produced by factors unrelated to the disease process such as variations in the overall population distribution or variations in the distributions of demographic subgroups at high disease risk it is therefore useful to have a method for detecting clusters that will adjust for such factors previous tests for clustering for example pinkel nefzger 1959 knox 1964 mantel 1967 are not satisfactory for the study of chronic disease such as cancer those tests are designed to determine whether cases are clustered both in space and in time simultaneously however cases of chronic disease caused by a spatially localized agent may be close in space but they are unlikely to be close in time because of long and variable time periods between exposure and diagnosis thus there is need for alternative methods to detect spatial clusters in regional disease incidence or mortality data consider the set x xl xk of points called census tracts with nk cases of disease called cancer in tract xk under the hypothesis ho of no clustering the nk are independent poisson variables with the mean of nk proportional to the population size ek in tract xk

mixture of regression models for large spatial datasets abstractwhen a spatial regression model that links a response variable to a set of explanatory variables is desired it is unlikely that the same regression model holds throughout the domain when t

inverse monoids trees and context free languages this paper is concerned with a study of inverse monoids presented by a set x subject to relations of the form e i f i i i where e i and f i are dyck words i e idempotents of the free inverse monoid on x some general results of stephen are used to reduce the word problem for such a presentation to the membership problem for a certain subtree of the cayley graph of the free group on x in the finitely presented case the word problem is solved by using rabin s theorem on the second order monadic logic of the infinite binary tree some connections with the theory of rational subsets of the free group and the theory of context free languages are explored

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

the word problem for inverse monoids presented by one idempotent relator abstract we study inverse monoids presented by a finite set of generators and one relation e 1 where e is a word representing an idempotent in the free inverse monoid and 1 is the empty word we show that 1 the word problem is solvable by a polynomial time algorithm 2 every congruence class in the free monoid with respect to such a presentation is a deterministic context free language such congruence classes can be viewed as generalizations of parenthesis languages and 3 the word problem is solvable by a linear time algorithm in the more special case where e is a positively labeled idempotent

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

the higson roe exact sequence and l2 eta invariants abstract the goal of this paper is to solve the problem of existence of an l 2 relative eta morphism on the higson roe structure group using the cheeger gromov l 2 eta invariant we construct a group morphism from the higson roe maximal structure group constructed in 35 to the reals when we apply this morphism to the structure class associated with the spin dirac operator for a metric of positive scalar curvature we get the spin l 2 rho invariant when we apply this morphism to the structure class associated with an oriented homotopy equivalence we get the difference of the l 2 rho invariants of the corresponding signature operators we thus get new proofs for the classical l 2 rigidity theorems of keswani obtained in 41

l2 topological invariants of 3 manifolds we give results on thel2 betti numbers and novikov shubin invariants of compact manifolds especially 3 manifolds we first study the betti numbers and novikov shubin invariants of a chain complex of hilbert modules over a finite von neumann algebra we establish inequalities among the novikov shubin invariants of the terms in a short exact sequence of chain complexes our algebraic results along with some analytic results on geometric 3 manifolds are used to compute thel2 betti numbers of compact 3 manifolds which satisfy a weak form of the geometrization conjecture and to compute or estimate their novikov shubin invariants

a new proposal to adjust moran s i for population density we analyse the effect of using prevalence rates based on populations with different sizes in the power of spatial independence tests we compare the well known spatial correlation moran s index to three indexes obtained after adjusting for population density one proposed by oden another proposed by waldhor and a third proposed by us in this paper we find an effect of spatially correlated populations in the type i error probability on the test based on moran s and waldhor s indexes we conclude also that the test proposed by oden is powerful to test risk heterogeneity but it has disadvantages when the interest is solely on the spatial correlation of morbidity risks in this latter case we recommend using our proposed test which is more powerful than the usual moran s index applied directly to the rates

log linear logistic model fitting and local score statistics for cluster detection with covariate adjustments the standard method for p value computation of spatial scan statistics with adjustments for covariate effects is to conduct monte carlo simulations with these effects estimated under the null hypothesis of no clustering however when the covariates are geographically unbalanced the proposed monte carlo p value estimates are too conservative with corresponding loss of power due to excessive adjustments for confounding between covariates and location we show that the use of an alternative procedure that involves local score statistics with parameters fitted on a log linear or logistic model addresses this problem we also discuss extensions of the procedure when there are multiple or continuous covariates

testing for changes in spatial relative risk the spatial relative risk function is a useful tool for describing geographical variation in disease incidence we consider the problem of comparing relative risk functions between two time periods with the idea of detecting alterations in the spatial pattern of disease risk irrespective of whether there has been a change in the overall incidence rate using case control datasets for each period we use kernel smoothing methods to derive a test statistic based on the difference between the log relative risk functions which we term the log relative risk ratio for testing a null hypothesis of an unchanging spatial pattern of risk we show how p values can be computed using both randomization methods and an asymptotic normal approximation the methodology is applied to data on campylobacteriosis from 2006 to 2013 in a region of new zealand we find clear evidence of a change in the spatial pattern of risk between those years which can be explained in differences by response to a public health initiative between urban and rural communities copyright 2017 john wiley sons ltd

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

primary decomposition and the fractal nature of knot concordance for each sequence mathcal p p 1 t p 2 t dots of polynomials we define a characteristic series of groups called the derived series localized at mathcal p these group series yield filtrations of the knot concordance group that refine the n solvable filtration we show that the quotients of successive terms of these refined filtrations have infinite rank the new filtrations allow us to distinguish between knots whose classical alexander polynomials are coprime and even to distinguish between knots with coprime higher order alexander polynomials this provides evidence of higher order analogues of the classical p t primary decomposition of the algebraic concordance group we use these techniques to give evidence that the set of smooth concordance classes of knots is a fractal set

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

a test for spatial disease clustering adjusted for multiple testing tango 1995 proposed a test statistic c for detecting spatial disease clusters however like most other methods it requires a value of the scale parameter which adjusts for the size of cluster to be detected in advance of its use when an appropriate size of cluster cannot be predicted and many clustered areas are expected we usually repeat the procedure by changing the size parameter but this practice clearly faces a multiple testing problem in this paper to ameliorate this problem we propose an extended test statistic which searches the minimum of the profile p value of c for the parameter on cluster size which varies continuously from a small value near zero upwards until it reaches to about half the size of the whole study area monte carlo simulation study shows that the power of the proposed method is shown to be reasonably high compared with the best power attained by c unadjusted for multiple testing in all the cluster models considered the proposed procedure is illustrated with some disease maps simulated in the tokyo metropolitan area

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

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

knot concordance and von neumann rho invariants we present new results announced in t on the classical knot concordance group c we establish the nontriviality at all levels of the n solvable filtration fn f1 f0 c introduced in cot1 recall that this filtration is significant due to its intimate connection to tower constructions arising in work of a casson and m freedman on the topological classification problem for 4 manifolds and due to the fact that all previously known concordance invariants are reflected in the first few terms in the filtration in cot1 nontriviality at the first new level n 3 was established here we prove the nontriviality of the filtration for all n hence giving the ultimate justification to the theory a broad range of techniques is employed in our proof including cut and paste topology and analytical estimates we use the cheeger gromov estimate for von neumann invariants a deep analytic result we also introduce a number of new algebraic arguments involving noncommutative localization and blanchfield forms we have attempted to make this article accessible to readers with only passing knowledge of cot1

inverse monoids decidability and complexity of algebraic questions this paper investigates the word problem for inverse monoids generated by a set c subject to relations of the form e f where e and f are both idempotents in the free inverse monoid generated by c it is shown that for every fixed monoid of this form the word problem can be solved both in linear time on a ram as well as in deterministic logarithmic space which solves an open problem of margolis and meakin for the uniform word problem where the presentation is part of the input exptime completeness is shown for the cayley graphs of these monoids it is shown that the first order theory with regular path predicates is decidable regular path predicates allow to state that there is a path from a node x to a node y that is labeled with a word from some regular language as a corollary the decidability of the generalized word problem is deduced

spatial clustering for inhomogeneous populations a new method for detecting spatial clustering of events in populations with non uniform density is proposed the method is based on selecting controls from the population at risk and computing interpoint distances for the combined sample nonparametric tests are developed which are based on the number of cases among the k nearest neighbours of each case and the number of cases nearer than the k nearest control the performance of these tests is evaluated analytically and by simulation and the method is applied to a data set on the locations of cases of childhood leukaemia and lymphoma in a defined geographical area

higher order alexander invariants and filtrations of the knot concordance group we establish certain nontriviality results for several filtrations of the smooth and topological knot concordance groups first as regards the n solvable filtration of the topological knot concordance group c defined by k orr p teichner and the first author 0 f n 5 f n f 1 5 f 1 0 f 0 5 f 0 c we refine the recent nontriviality results of cochran and teichner by including information on the alexander modules these results also extend those of c livingston and the second author we exhibit similar structure in the closely related symmetric grope filtration ofc we also show that the grope filtration of the smooth concordance group is nontrivial using examples that cannot be distinguished by the ozsvath szabo invariant nor by j rasmussen s s invariant our broader contribution is to establish in the relative case the key homological results whose analogues cochran orr teichner established in the absolute case we say two knots k 0 and k 1 are concordant modulo n solvability if k o k 1 f n our main result is that for any knot k whose classical alexander polynomial has degree greater than 2 and for any positive integer n there exist infinitely many knots k i that are concordant to k modulo n solvability but are all distinct modulo n 5 solvability moreover the k i and k share the same classical seifert matrix and alexander module as well as sharing the same higher order alexander modules and seifert presentations up to order n 1

higher rho invariants and the moduli space of positive scalar curvature metrics abstract given a closed smooth manifold m which carries a positive scalar curvature metric one can associate an abelian group p m to the space of positive scalar curvature metrics on this manifold the group of all diffeomorphisms of the manifold naturally acts on p m the moduli group p m of positive scalar curvature metrics is defined to be the quotient abelian group of this action i e the coinvariant of the action p m measures the size of the moduli space of positive scalar curvature metrics on m in this paper we use the higher rho invariant and the finite part of the k theory of the group c algebra of 1 m to give a lower bound of the rank of the moduli group p m the key idea of our proof is the use of higher rho invariant this is a secondary invariant associated to dirac operators and in particular depends on the choice of riemannian metric we show that the higher rho invariant remains unchanged in a certain k theory group under the action of the diffeomorphism group allowing us to distinguish elements in p m

spatial cluster detection for ordinal outcome data in geographical disease surveillance spatial scan statistics are used to identify areas having unusually high or low rates of disease outcomes and to determine the statistical significance of detected clusters the spatial scan statistic for ordinal data such as stage of cancer has been developed to detect clusters representing areas with high rates of more serious stages compared with the surrounding areas such areas were expressed using likelihood ratio ordering which is a rather strict order restriction and hence the method might fail to detect spatial clusters with high rates of worse categories e g later stage in this paper we relax the order restriction using stochastic ordering and examine differences between the two approaches in detecting spatial clusters through simulation studies we show that the stochastic ordering based approach has higher power sensitivity and positive predictive value under several scenarios we illustrate the two methods with the use of a real data example copyright 2012 john wiley sons ltd

disease clusters exact distributions of maxima and p values this paper presents combinatorial exact methods that are useful in the analysis of disease cluster data obtained from small environments such as buildings and neighbourhoods maxwell boltzmann and fermi dirac occupancy models are compared in terms of appropriateness of representation of disease incidence patterns space and or time in these environments the methods are illustrated by a statistical analysis of the incidence pattern of bone fractures in a setting wherein fracture clustering was alleged to be occurring one of the methodological results derived in this paper is the exact distribution of the maximum cell frequency in occupancy models language en

an index theorem on open manifolds ii on decrit et on applique un nouveau theoreme d indice pour des operateurs elliptiques sur certaines varietes non compactes on calcule un indice a valeur reelle pour des operateurs de type dirac sur des varietes non compactes de geometrie bornee

twisted alexander polynomials and symplectic structures let n be a closed oriented 3 manifold a folklore conjecture states that s 1 n admits a symplectic structure only if n admits a fibration over the circle the purpose of this paper is to provide evidence to this conjecture studying suitable twisted alexander polynomials of n and showing that their behavior is the same as of those of fibered 3 manifolds in particular we will obtain new obstructions to the existence of symplectic structures and to the existence of symplectic forms representing certain cohomology classes of s 1 n as an application of these results we will show that s 1 n p does not admit a symplectic structure where n p is the 0 surgery along the pretzel knot p 5 3 5 answering a question of peter kronheimer

rationality of geometric signatures of complete 4 manifolds according to cg4 and cfg the complete manifolds with bounded sectional curvature and finite volume admit positive rank f structures near infinity in this paper we show that in dimension four if the manifolds also have bounded covering geometry near infinity then there exist f structures with special topological properties f structures with these properties cannot be constructed solely by means of the general methods in cg4 and cfg using these special properties we prove a conjecture of cheeger gromov on the rationality of the geometric signatures in the four dimensional case

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

delocalized l2 invariants abstract we define extensions of the l 2 analytic invariants of closed manifolds called delocalized l 2 invariants these delocalized invariants are constructed in terms of a nontrivial conjugacy class of the fundamental group we show that in many cases they are topological in nature we show that the marked length spectrum of an odd dimensional hyperbolic manifold can be recovered from its delocalized l 2 analytic torsion there are technical convergence questions

hadamard states for the klein gordon equation on lorentzian manifolds of bounded geometry we consider the klein gordon equation on a class of lorentzian manifolds with cauchy surface of bounded geometry which is shown to include examples such as exterior kerr kerr de sitter spacetime and the maximal globally hyperbolic extension of the kerr outer region in this setup we give an approximate diagonalization and a microlocal decomposition of the cauchy evolution using a time dependent version of the pseudodifferential calculus on riemannian manifolds of bounded geometry we apply this result to construct all pure regular hadamard states and associated feynman inverses where regular refers to the state s two point function having cauchy data given by pseudodifferential operators this allows us to conclude that there is a one parameter family of elliptic pseudodifferential operators that encodes both the choice of pure regular hadamard state and the underlying spacetime metric

likelihood based tests for spatial randomness many different methods have been proposed to test the spatial randomness of a point pattern adjusting for an inhomogeneous background population these tests can be classified into cluster detection tests concerned with the detection and inference of local clusters and global clustering tests which collect evidence for clustering throughout the study region this paper is mainly concerned about global clustering tests some tests for spatial randomness are based on likelihoods which include the spatial and space time scan statistics with variable window size and gangnon and clayton s weighted average likelihood ratio tests both of these tests perform well compared to other tests for cluster detection and global clustering respectively in this study we develop other likelihood based tests for global clustering and we explore the use of different weight functions with these tests the power of these tests is evaluated using simulated data set and compared with existing methods

ends of finite volume nonpositively curved manifolds we study complete finite volume n manifolds m of bounded nonpositive sectional curvature a classical theorem of m gromov says that if such m has negative curvature then it is homeomorphic to the interior of a compact manifold with boundary and we denote this boundary partial m if n ge 3 we prove that the universal cover of the boundary widetilde partial m and also the pi 1m cover of the boundary partial widetilde m have vanishing n 2 dimensional homology for n 4 the first of these recovers a result of nguy tilde hat mathrm e n phan saying that each component of the boundary partial m is aspherical for any n ge 3 the second of these implies the vanishing of the first group cohomology group with group ring coefficients h 1 b pi 1m mathbb z pi 1m 0 a consequence is that pi 1m is freely indecomposable these results extend to manifolds m of bounded nonpositive curvature if we assume that m is homeomorphic to the interior of a compact manifold with boundary our approach is a form of homological collapse for ends of finite volume manifolds of bounded nonpositive curvature this paper is very much influenced by earlier yet still unpublished work of nguy tilde hat mathrm e n phan

case control isotonic regression for investigation of elevation in risk around a point source stone s isotonic regression method for analysing count data to estimate disease risk in relation to a point source of environmental pollution is now routinely used this paper develops the corresponding procedure for case control data consisting of the locations of individual cases with controls with associated covariate information in this setting the generalized likelihood ratio statistic to test the null hypothesis of constant risk against the alternative that risk is a monotone non increasing function of distance from the point source is intractable an approximate monte carlo test is described extending an exact test proposed by bithell for the situation in which there are no covariates interval estimates of risk as a function of distance from the point source are constructed by simulation of the sampling distribution of the isotonic regression estimator the methodology is illustrated by two applications one to the relative risk of larynx cancers and lung cancers near a now disused industrial incinerator the other to the risk of asthma in children in relation to distance of residence from the nearest main road

a weighted average likelihood ratio test for spatial clustering of disease we consider methods proposed for detecting localized spatial clustering we propose a new test statistic the weighted average likelihood ratio test as an alternative to the spatial scan maximum likelihood ratio test statistic two different types of weights are considered we propose an unbiased cluster selection criterion and evaluate the bias of the tests through simulation we also examine the power of the tests through simulations and apply the methods to the well known new york leukaemia data

segregation indices for disease clustering spatial clustering has important implications in various fields in particular disease clustering is of major public concern in epidemiology in this article we propose the use of two distance based segregation indices to test the significance of disease clustering among subjects whose locations are from a homogeneous or an inhomogeneous population we derive the asymptotic distributions of the segregation indices and compare them with other distance based disease clustering tests in terms of empirical size and power by extensive monte carlo simulations the null pattern we consider is the random labeling rl of cases and controls to the given locations along this line we investigate the sensitivity of the size of these tests to the underlying background pattern e g clustered or homogenous on which the rl is applied the level of clustering and number of clusters or to differences in relative abundances of the classes we demonstrate that differences in relative abundances have the highest influence on the empirical sizes of the tests we also propose various non rl patterns as alternatives to the rl pattern and assess the empirical power performances of the tests under these alternatives we observe that the empirical size of one of the indices is more robust to the differences in relative abundances and this index performs comparable with the best performers in literature in terms of power we illustrate the methods on two real life examples from epidemiology

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

nilpotent structures and invariant metrics on collapsed manifolds let mn be a complete riemannian manifold of bounded curvature say iki 0 we put mn w n c u fn c where 1n e consists of those points at which the injectivity radius of the exponential map is e the complementary set n c is called the e collapsed part of mn if x e 4 n r e then the metric ball bx r is quasi isometric with small distortion to the flat ball b0 r in the euclidean space rn after slightly

power of the scan statistic for detection of clustering the scan statistic is the maximum number of events in an interval of fixed length w as the subinterval moves over the entire time frame previous research derived the null distribution of the scan statistic under the conditional model which assumed that the total number of events was fixed and under the unconditional model which let the total number of events be a random variable this paper derives approximations for the power of the scan test for a pulse alternative under this alternative the relative risk of disease on a subinterval tau tau w tau unknown is theta fold as high as it is for other subintervals of length w two sets of approximations are given for each model the first approximation gives highly accurate results but requires use of a personal computer the second procedure can be performed on a hand held calculator and appears very accurate for the cases examined

statistical methods for the detection of spatial clustering in case control data in this paper i develop new approaches for the detection of spatial clustering in case control data one method is based upon drawing thiessen polygons around each control it is unnecessary to actually draw or compute the boundaries of the polygons it is sufficient to count for each control the number of cases that are closer to that control than to any other control a second method is similar to the cuzick edwards method which is based on counts of cases that are among the k nearest neighbours of cases but is instead based upon the number of cases within a specified distance of cases these first two methods are global methods in the sense that they provide a single statistic that measures the degree of spatial clustering the third method suggests a local statistic for tests of the null hypothesis of no spatial clustering around a prespecified focus the method is based upon the cumulative chi2 test which is typically used to test whether cases are more prevalent than expected around a prespecified location this is also extended to the case where all observational locations are considered as potential cluster locations and multiple testing is carried out each of the new methods is illustrated using data on childhood leukaemia and lymphoma cases in north humberside

l2 torsion invariants we discuss a generalisation of reidemeister franz torsion which applies to infinite dimensional representations of the fundamental group by utilising the theory of finite von neumann algebras our results apply to a class of closed oriented manifolds which are l2 acyclic in the sense of having trivial l2 cohomology evidence is presented for equality of the essentially combinatorial torsion introduced here with an analytic l2 ray singer torsion defined by the second named author

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