stable trace formula cuspidal tempered terms consider a connected reductive group g over a number field f for technical reasons we assume that the derived group of g is simply connected see l1 in l3 langlands partially stabilizes the trace formula for g after making certain assumptions he writes the elliptic regular part of the trace formula for g as a linear combination of the elliptic g regular parts of the stable trace formulas for the elliptic endoscopic groups h of g the function f used in the stable trace formula forh is obtained from the function f used in the trace formula for g by transferring orbital integrals

power of the scan statistic in detecting a changed segment in a bernoulli sequence summary fu curnow 1990 derive recursive equations to find the level of significance and power of a likelihood ratio test for a changed segment of specified length based on the scan statistic the maximum number of successes within the specified length their method is computationally feasible for segment lengths of 20 or less we present and evaluate highly accurate approximations as well as bounds for the power function of this test that are computationally feasible even for very large segment lengths we also evaluate power when the duration of the increased length used in the test statistic does not correspond to the actual length scientists dealing with data sequences modelled by independent bernoulli trials frequently seek criteria to detect changes in the underlying process certain criteria have been developed to be sensitive to situations in which the probability of success on an individual trial changes at a point in the sequence fu curnow 1990 consider a version of a two change point problem with known distance m between the change points and with the trial probability of success at the two ends being equal they give recurrence relations for the probability of type i error and the power computational difficulties arise on even large computers when the number of trials is large in the present paper we derive highly accurate approximations that allow computation of power for all segment lengths consider a sequence of n independent 0 1 random variables x1 x2 xn let 1 denote success with pr x 1 i t we wish to test the null hypothesis of a constant probability of success ho i t i t 1 n against the alternative that some contiguous sequence of m events starting at an unknown trial z has a higher probability of success fu curnow 1990 note that the generalized likelihood ratio test for this alternative rejects ho for large values of the scan statistic

galois representations arising from some compact shimura varieties our aim is to establish some new cases of the global langlands correspondence for glm along the way we obtain a new result on the description of the cohomology of some compact shimura varieties let f be a cm eld with complex conjugation c and

approximating the distribution of the scan statistic using moments of the number of clumps abstract let x 1 x 2 xn be randomly distributed points on the unit interval let nx x d be the number of these points contained in the interval x x d the scan statistic nd is defined as the maximum number of points in a window of length d that is nd sup x nx x d this statistic is used to test for the presence of nonrandom clustering we say that m points form an m d clump if these points are all contained in some interval of length d let y denote the number of m d clumps in this article we show how to compute the lower order moments of y and we use these moments to obtain approximations and bounds for the distribution of the scan statistic nd our approximations are based on using the methods of moments technique to approximate the distribution of y we try two basic types of methods of moments approximations one involving a simple markov chain model and others using various different compound poisson approximations our results compare favorably with other approximations and bounds

on the distributions of scan statistics abstract this article considers the distribution of the scan statistic over some interval of the real line both for a fixed number of independent uniform points and for a poisson process it provides a new series method of calculating this distribution in the poisson case and a simple self contained recursive approximation in the fixed case these results work best at low densities which is precisely the case when the closed formulas are computationally impractical the results are compared with values tabulated by neff and naus 1980 and with a recent approximation due to naus 1982 there is also an explanation of why naus s approximation is good in the poisson case and a derivation of recursive bounds in the fixed case

automorphism invariant representations of real reductive groups we characterize representations of a connected real reductive group which are invariant under an automorphism of finite order the intertwining operators constructed in this characterization are then used to prove a paley wiener theorem for a class of real reductive groups twisted by involutions

approximations for the tail probabilities and moments of the scan statistic the scan statistic is used to test the hypothesis that the observed events occur at random uniformly distributed in time or space versus the hypothesis that they cluster within a moving window of size w to implement the testing procedure based on the scan statistic its tail probabilities have to be effectively evaluated in this article a survey of results on the approximations of the distribution of the scan statistic and its moments is presented numerical results comparing these approximations are also given numerous references with applications in epidemiological studies using the scan statistics are mentioned related scan statistics that have been used in many other interesting applications are listed in the reference section the article concludes with the presentation of unsolved problems related to the scan statistic

parabolic transfer for real groups this paper is the second of two articles in real harmonic analysis in the first paper a14 we established asymptotic formulas for some natural distributions on a real group in this paper we shall establish important relationships among the distributions as the group varies the group is the set of real points of a connected reductive group g over r the distributions are weighted orbital integrals jm f on g r and their invariant counterparts im f here m g is a levi subgroup of g while mg reg r is a strongly g regular conjugacy class in m r the relationships are defined by the invariant transfer of functions on g r to functions attached to endoscopic groups of g this necessitates our working with the invariant distributions im f we refer the reader to the introduction of a14 for some general remarks on these objects the distributions im f are the generic archimedean terms in the invariant trace formula we cannot review the trace formula here the reader might consult the introductions to a13 and its two predecessors for a brief summary the purpose of the paper a13 was to stabilize the invariant trace formula subject to a condition on the fundamental lemma that has been established in some special cases the stable trace formula is a milestone of sorts it is expected to lead to reciprocity laws which relate fundamental arithmetic data attached to automorphic representations on different groups the stable trace formula of a13 relies upon the results of this paper as well as a paper a16 in preparation this has been our guiding motivation the relevant identities among the nonarchimedean forms of the distributions im f were actually established in a13 they were a part of the global argument that culminated in the stable trace formula as such they are subject to the condition on the fundamental lemma mentioned above our goal here is to establish the outstanding archimedean identities we shall do so by purely local means which are independent of the fundamental lemma to simplify the introducton we assume that the derived group of g is simply connected the identities then relate the invariant distributions ong r with stable distributions on endoscopic groups g r we recall that a stable distribution on g r depends only on the average values assumed by a test function over strongly regular stable conjugacy classes in greg r which is to say intersections of g reg r

probability inequalities for multivariate distributions with dependence structures abstract let x 1 xn be a sequence of random variables with a given positive or negative dependence structure in this article we exploit the assumed dependence structure to construct a sequence of bounds for the p xi e ci i 1 n where ci are infinite intervals of the same type these bounds are superior to the well known product bounds that are based solely on the marginal probabilities moreover the new bounds can serve as respectable approximations for the p xi e ci i 1 n

a useful upper bound for the tail probabilities of the scan statistic when the sample size is large abstract although a number of approximations to the distribution under uniformity of the scan statistic are known they are when the sample size is large either difficult to compute or numerically unstable a simple upper bound for the upper tail of the distribution based on a result of hunter 1976 is derived it is found that for large sample sizes and a reasonably wide range of window widths this bound gives a numerically stable approximation that is sufficiently accurate for hypothesis testing purposes

continuous testing for poisson process intensities a new perspective on scanning statistics summarywe propose a continuous testing framework to test the intensities of poisson processes that allows a rigorous definition of the complete testing procedure from an infinite number of hypotheses to joint error rates our work extends procedures based on scanning windows by controlling the familywise error rate and the false discovery rate in a non asymptotic manner and in a continuous way we introduce the p value process on which the decision rule is based our method is applied in neuroscience via the standard homogeneity and two sample tests

ultradiffusion the relaxation of hierarchical systems the authors show that the dynamics of relaxation in hierarchical structures leads to an anomalous decay process which they term ultradiffusion using renormalisation group techniques they explicitly calculate the behaviour of the autocorrelation function in a one dimensional hierarchical system and show its universal power law decay as a function of temperature the authors also demonstrate analytically the emergence of a hierarchy of time scales this phenomenon is relevant to systems ranging from macromolecules to computing structures

nonoverlapping clusters approximate distribution and application to molecular biology summary an approach is developed for the screening of genomic sequence data to identify gene regulatory regions this approach is based on deciding if putative transcription factor binding sites are clustered together to a greater extent than one would expect by chance given n events occurring on an interval of width l l base pairs an r w cluster is defined as r 1 consecutive events all contained within a window of length wl accurate and easily computable approximations are derived for the distribution of the number of nonoverlapping r w clusters under the model that the positions of the n events have a uniform distribution simulations demonstrate that these approximations have greater accuracy than existing methods the approximation is applied to detect erythroid specific regulatory regions in genomic dna sequences first in an artificial case where r is specified a priori and then as part of an exploratory approach

local global compatibility and the action of monodromy on nearby cycles we strengthen the local global compatibility of langlands correspondences for gln in the case when n is even and l 6d p let l be a cm field and let be a cuspidal automorphic representation of gln al which is conjugate self dual assume that 1 is cohomological and not slightly regular as defined by shin in this case chenevier and harris constructed an l adic galois representationrl and proved the local global compatibility up to semisimplification at primes v not dividing l we extend this compatibility by showing that the frobenius semisimplification of the restriction of rl to the decomposition group at v corresponds to the image of v via the local langlands correspondence we follow the strategy of taylor and yoshida where it was assumed that is square integrable at a finite place to make the argument work we study the action of the monodromy operator n on the complex of nearby cycles on a scheme which is locally etale over a product of strictly semistable schemes and we derive a generalization of the weight spectral sequence in this case we also prove the ramanujan petersson conjecture for as above

dynamics of simple computer networks we consider a simple two dimensional layered automaton each processor in the automaton performs the same nonlinear thresholdlike operation so that the row to row evolution of the array can also be seen as the time development of a one dimensional automaton one row of the machine is reserved for input another is singled out as output we study the output space in detail as restricted by the very wiring of the array enumerating the output configurations and characterizing them statistically we demonstrate that input configurations flow to a set of zero measure in output space the variations in output that are to be expected when input is subjected to perturbations are also examined

a proof of langland s conjecture on plancherel measures complementary series of p adic groups analysis of p adic reductive groups our first result theorem 7 9 proves a conjecture of langlands on normalization of intertwining operators by means of local langlands root numbers and l functions at least when the group is quasi split and the inducing representation is generic assuming two natural conjectures in harmonic analysis of p adic groups we also prove the validity of the conjecture in general theorem 9 5 as our second result we obtain all the complementary series and special representations of quasi split p adic groups coming from rank one parabolic subgroups and generic supercuspidal represen

matching rectangles in d dimensions algorithms and laws of large numbers abstract for each point of the integer lattice zd let x and y be independent identically distributed random variables with p x y p 0 1 let s n be the volume of the largest d dimensional cube in 1 n d with the property that x y at every point of the cube r n is similarly defined to be the maximum volume of perfectly matching rectangles it is proved that if all possible shifts of the x lattice relative to the y lattice are allowed p lim n s n log n lim n r n log n 2d 1 where log is to base 1 p the corresponding limit without shifts is d algorithms to find largest squares and rectangles with and without shifts are also given

rigid inner forms of real and p adic groups we dene a new cohomology set h 1 u w z g for an ane algebraic group g and a nite central subgroup both dened over a local eld of characteristic zero which is an enlargement of the usual rst galois cohomology set of g we show how this set can be used to give a precise conjectural description of the internal structure and endoscopic transfer of tempered l packets for arbitrary connected reductive groups that extends the well known conjectural description for quasi split groups in the case of real groups we show that this description is correct using shelstad s work

level raising and symmetric power functoriality iii we apply automorphy lifting techniques to establish new cases of symmetric power functoriality for hilbert modular forms of regular algebraic weight the proof is based on a novel application of an automorphy lifting theorem for residually reducible galois representations

scan statistics with weighted observations we examine scan statistics for one dimensional marked poisson processes such statistics tabulate the maximum weighted count of event occurrences within a window of predetermined width over all windows within an observed interval we derive analytical formulas and also give an importance sampling method for approximating the tail probabilities of scan statistics because high throughput genomic sequencing has led to the availability of massive amounts of biomolecular sequence data it is often of interest to search long dna or protein sequences for local regions that are enriched for a certain characteristic thus scan statistics have become a useful tool in modern computational biology we illustrate the application of our p value approximations with such examples

one dimensional ising chain with competing interactions exact results and connection with other statistical models we study the ground state properties of a one dimensional ising chain with a nearest neighbor ferromagnetic interactionj1 and akth neighboranti ferromagnetic interactionjk whenjk j1 1 k there exists a highly degenerate ground state with a residual entropy per spin for the finite chain with free boundary conditions we calculate the degeneracy of this state exactly and find that it is proportional to the n k 1 th term in a generalized fibonacci sequence defined by fn k fn 1 k fn k k in addition we show that this one dimensional model is closely related to the following problems a a fully frustrated two dimensional ising system with a periodic arrangement of nearest neighbor ferro and antiferromagnetic bonds b close packing of dimers on a ladder a 2 strip of the square lattice and c directed self avoiding walks on finite lattice strips

characteristic cycles of holomorphic discrete series the characteristic cycles of standard modules arising from closed at orbits in a flag variety are studied and those of holomorphic discrete series are determined explicitly also the asymptotic expansion of the distribution characters of holomorphic discrete series are computed the result verifies a conjecture of d vogan in this special case suppose gr is a linear semisimple lie group and ar a maximal compact subgroup of gr in case the symmetric space gr ar carries a hermitian structure gr has a family of holomorphic discrete series representations let be the underlying harish chandra module of an arbitrary holomorphic dis crete series representation and o be the corresponding distribution character on the group the associated cycle 2 7 of is an algebraic cycle defined al gebraically on n the dual to the complexification of the lie algebra or of gr on the other hand according to barbasch vogan the fourier transform of the leading term of the asymptotics of 8 near the identity is a linear combination of canonical invariant measures on coadjoint gr orbits in g r it therefore de termines a cycle on gm in this paper we determine both invariants attached to the holomorphic discrete series it then verifies in this special case a conjecture of d vogan which asserts that the major part of both invariants coincide under the orbit correspondence of sekiguchi the complexified tangent space of gr a r at the identity coset is naturally identified to a quotient of q therefore via the invariant nondegenerate killing form the holomorphic tangent space is identified to a subspace in g here the holomorphic structure is the one chosen to define then the associated cycle 2 7 is the holomorphic tangent space with multiplicity the dimension of the lowest a r type of i 2 13 the computation is made through the corre sponding 2 module on the flat variety x of 9 and the moment map from the cotangent bundle t x to g generally modules giving rise to the discrete series are supported on closed a orbits on x k is the complexification of ar the normal derivatives then induce a good filtration on these modules this then computes the associated graded modules as sheaves of coherent cf modules on t x although in general the moment map is quite complicated on the support of the associated graded module in the situation where holo

a double scan statistic for clusters of two types of events we develop a scan type statistic to measure the unusualness of the clustering of two types of events over time the statistic allows for a lagged effect between the two types of events we derive the expected number of nonoverlapping clumps of clusters under retrospective and prospective chance models of no association results are derived and approaches are given to handle both uniform and more general distributions of events over time we investigate the power of the statistic against an alternative where the observed data is a mixture of linked and unassociated clusters the statistic is applied to data on homicide suicide clusters over a 7 year period for several counties and several sex race combinations

local coefficients as artin factors for real groups introduction the purpose of this paper is to prove the equality of certain local coefficients of arithmetic significance which were attached to representations of quasi split real reductive algebraic groups in 27 with their corresponding artin factors attached by local class field theory 21 as a consequence we establish an identity satisfied by certain normalized intertwining operators it seems to be useful in applications of the trace formula 1 29 more precisely let g be the group of real points of a quasi split reductive algebraic group over r let a be the set of simple roots defined by a fixed minimal parabolic subgroup po m0a0u of g fix 6 c a and let p p9 be the corresponding standard parabolic subgroup of g and write p man for its langlands decomposition fix a nondegenerate character x f u i a h o be an irreducible admissible x gic banach in particular x generic unitary representation of m cf section 1 given v g a the complex dual of the lie algebra of a let i v o 0 be the continuously quasi unitarily if o is unitary induced representation indp ga e v 9 and let v v o 0 be its space section 0 then f a vfoo o now let w be the weyl group of ao in g choose w g w such that w 0 c a let n be the unipotent group opposite to n define n u c wn w where w is a representative of w in g for g f a 00 define

an approximation for the distribution of the scan statistic the scan statistic evaluates whether an apparent cluster of disease in time is due to chance the statistic employs a moving window of length w and finds the maximum number of cases revealed through the window as it scans or slides over the entire time period t computation of the probability of observing a certain size cluster under the hypothesis of a uniform distribution is infeasible when n the total number of events is large and w is of moderate or small size relative to t we give an approximation that is an asymptotic upper bound easy to compute and for the purposes of hypothesis testing more accurate than other approximations presented in the literature the approximation applies both when n is fixed and when n has a poisson distribution we illustrate the procedure on a data set of trisomic spontaneous abortions observed in a two year period in new york city

approximations for distributions of scan statistics abstract certain statistical applications deal with the extremal distributions of the number of points in a moving interval or window of fixed length this article gives an approximation that is highly accurate for several of these distributions applications include the maximum cluster of points on a line or circle multiple coverage by subintervals or subarcs of fixed size the length of the longest success run in bernoulli trials and the generalized birthday problem

boole bonferroni inequalities and linear programming we present a method to obtain sharp lower and upper bounds for the probability that at least one out of a number of events in an arbitrary probability space will occur the input data are some of the binomial moments of the occurrences such as the sum of the probabilities of the individual events or the sum of the joint probabilities of all pairs of events we develop a special very simple linear programming algorithm to obtain these bounds the method allows us to compute good bounds in an optimal way utilizing only the first few terms in the inclusion exclusion formula possible applications include obtaining bounds for the reliability of a stochastic system solving algorithmically some stochastic programming problems and approximating multivariate probabilities in statistics in a numerical example we approximate the probability that a gaussian process runs below a given level in a number of consecutive epochs

on geometric transfer in real twisted endoscopy we prove the existence of a transfer of orbital integrals in endoscopy for real reductive groups when there is twisting by an automorphism dened over the reals and by a character on the real points of the group our proof contains a relatively short self contained argument for the already known case of standard endoscopy

a twisted invariant paley wiener theorem for real reductive groups let g be the group of real points of a possibly disconnected linear reductive algebraic group defined over r which is generated by the real points of a connected component g let k be a maximal compact subgroup of the group of real points of the identity component of this algebraic group we characterize the space of maps 7 tr f where is an irreducible tempered representation of g and f varies over the space of smooth compactly supported functions on g which are leftand right k finite this work is motivated by applications to the twisted arthur selberg trace formula

multiple temporal cluster detection summary this article proposes a simple method to determine single or multiple temporal clustering on a variable size population by a transformation of the data set the method based on a regression model allows consideration of a variable population size during the time of study a model selection procedure and a resampling method are used to select the number of clusters the results have applications in epidemiological studies of rare diseases

harish chandra s method of descent 1 one of the main tools in the study of representation theory of reductive groups is harish chandra s method of descent let g be a real reductive group given a semisimple element s of g let h be the centralizer of s in g then the behavior of an invariant eigendistribution in a neighborhood of s may be described in terms of an invariant distribution of h in a neighborhood of the identity this leads to the notion of descent taking an invariant eigendistribution of g defined on a neighborhood of s to an invariant distribution of h defined in a neighborhood of the identity in h the descent of any standard character of

the residual entropy for a class of one dimensional classical lattice models the zero temperature limit of the characteristic equation of the transfer matrix is derived for one dimensional classical lattice systems with a finite one point configuration space and finite range interactions in this way the author obtains an explicit polynomial equation for the residual entropy which only involves the counting of some specific periodic ground state configurations the formula is applied to some well known models and compared with similar calculations in the literature

a stable trace formula iii proof of the main theorems this paper is the last of three articles designed to stabilize the trace formula our goal is to stabilize the global trace formula for a general connected group subject to a condition on the fundamental lemma that has been established in some special cases in the first article i we laid out the foundations of the process we also stated a series of local and global theorems which together amount to a stabilization of each of the terms in the trace formula in the second paper ii we established a key reduction in the proof of one of the global theorems in this paper we shall complete the proof of the theorems we shall combine the global reduction of ii with the expansions that were established in section 10 of i we refer the reader to the introduction of i for a general discussion of the problem of stabilization the introduction of ii contains further discussion of the trace formula with emphasis on the elliptic coefficients agll s these objects are basic ingredients of the geometric side of the trace formula

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

cellular automata and statistical mechanical models we elaborate on the analogy between the transfer matrix of usual lattice models and the master equation describing the time development of cellular automata transient and stationary properties of probabilistic automata are linked to surface and bulk properties respectively of restricted statistical mechanical systems it is demonstrated that methods of statistical physics can be successfully used to describe the dynamic and the stationary behavior of such automata some exact results are derived including duality transformations exact mappings disorder and linear solutions many examples are worked out in detail to demonstrate how to use statistical physics in order to construct cellular automata with desired properties this approach is considered to be a first step toward the design of fully parallel probabilistic systems whose computational abilities rely on the cooperative behavior of their components

approximations and bounds for the distribution of the scan statistic abstract the scan statistic is used in many areas of science to test the null hypothesis of uniformity against a clustering alternative this article derives approximations and bounds for the distribution of scan statistics an extensive simulation study is carried out to compare the approximations and the bounds derived in this article with other known approximations and bounds the new lower and upper bounds that have been derived are very useful in evaluating the approximations and the simulation a quantity of average number of points in the scanning interval of length d d is introduced to study the approximations for the distribution of the scan statistic for low values of d the approximation derived in this article is the most accurate one the importance of the scan statistics arises from their applications in many areas including nuclear physics geology radio optics photography and epidemiology