a network algorithm for performing fisher s exact test in r c contingency tables abstract an exact test of significance of the hypothesis that the row and column effects are independent in an r c contingency table can be executed in principle by generalizing fisher s exact treatment of the 2 2 contingency table each table in a conditional reference set of r c tables with fixed marginal sums is assigned a generalized hypergeometric probability the significance level is then computed by summing the probabilities of all tables that are no larger on the probability scale than the observed table however the computational effort required to generate all r c contingency tables with fixed marginal sums severely limits the use of fisher s exact test a novel technique that considerably extends the bounds of computational feasibility of the exact test is proposed here the problem is transformed into one of identifying all paths through a directed acyclic network that equal or exceed a fixed length some interesting new optimization theorems are developed in the process the numer

computation theory of cellular automata self organizing behaviour in cellular automata is discussed as a computational process formal language theory is used to extend dynamical systems theory descriptions of cellular automata the sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages many examples are given the sizes of the minimal grammars for these languages provide measures of the complexities of the sets this complexity is usually found to be non decreasing with time the limit sets generated by some classes of cellular automata correspond to regular languages for other classes of cellular automata they appear to correspond to more complicated languages many properties of these sets are then formally non computable it is suggested that such undecidability is common in these and other dynamical systems

the attractor basin portrait of a cellular automaton local space time structures such as domains and the intervening dislocations dominate a wide class of cellular automaton ca behavior for such spatially extended dynamics regular domains vicinities and attractors are introduced as organizing principles to identify the discretized analogs of attractors basins and separatrices structures used in classifying dissipative continuous state dynamical systems we describe the attractor basin portrait of nonlinear elementary ca rule 18 whose global dynamics is largely determined by a single regular attracting domain the latter s basin is analyzed in terms of subbasin and portal structures associated with particle annihilation the conclusion is that the computational complexity of such ca is more apparent than real transducer machines are constructed that automatically identify domain and dislocation structures in space time count the number of dislocations in a spatial pattern and implement an isomorphism between rule 18 and rule 90 we use a transducer to trace dislocation trajectories and confirm that in rule 18 isolated dislocation trajectories as well as a dislocation gas agree extremely well with the classical model of annihilating diffusive particles the ca efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space time

on inverting permutation tests abstract polynomial time algorithms are presented for inverting permutation tests the one sample permutation test is inverted to make confidence statements about a location parameter and the two sample permutation test is inverted to make confidence statements concerning a shift in location or scale these algorithms require polynomial time as opposed to complete enumeration algorithms which require exponential time a computational method for the inversion of rank tests is also suggested the algorithms extend to stratified experiments

discrete series representations for the orbit spaces arising from two involutions of real reductive lie groups leth gbe real reductive lie groups a discrete series representation for a homogeneous spaceg his an irreducible representation ofgrealized as a closedg invariant subspace ofl2 g h the condition for the existence of discrete series representations forg hwas not known in general except for reductive symmetric spaces this paper offers a sufficient condition for the existence of discrete series representations forg hin the setting thatg his a homogeneous submanifold of a symmetric space g hwhereg g h we prove that discrete series representations are non empty for a number of non symmetric homogeneous spaces such assp 2n r sp n0 c gl n1 c gl nk c nj n ando 4m n u 2m j 0 2j n

the kink of cellular automaton rule 18 performs a random walk we give an exact characterization of the movement of a single kink in the elementary cellular automaton rule 18 it is a random walk with independent increments as well as independent delay times its statistical parameters are computed to confirm the earlier simulation results by grassberger

kink movements and percolation in the binary additive cellular automaton we show that under the bernoulli initial condition two kinks in the cellular automaton ca 18 256 will annihilate each other with probability one it turns out that there is an equivalent statement in terms of percolation in the simple binary additive ca namely under the bernoulli initial condition l s do not percolate in the binary additive ca

approximately exact inference for the common odds ratio in several 2 2 tables abstract the conditional maximum likelihood estimator mle of the common odds ratio in a sequence of independent 2 2 tables is known to be superior to the mantel haenszel estimator in terms of asymptotic efficiency and has the further advantage that its exact distribution is known however a long standing barrier to the widespread use of this estimator has been computational intractability in particular the calculation of significance levels confidence sets and power based on the exact distribution requires fast and efficient algorithms an important class of such algorithms form the basis of statxact a software package able to solve various aspects of the exact inference problem for a sequence of several 2 2 tables in real time we provide an alternative methodology by developing several useful saddlepoint approximations to the exact distribution of the conditional mle the approximations are derived from an interesting representation for hypergeometric random variables as a sum of independent

fast computation of exact confidence limits for the common odds ratio in a series of 2 2 tables abstract the odds ratio is widely used as a measure of association in epidemiologic studies and clinical trials we consider calculation of exact confidence limits for the common odds ratio in a series of independent 2 2 tables and propose three modifications of the network algorithm of mehta patel and gray 1 formulating and dealing with the problem in algebraic instead of graph theoretic terms 2 performing convolutions on the natural scale instead of the logarithmic scale and 3 using the secant method instead of binary search to compute roots of polynomial equations enhancement of computational efficiency exceeding an order of magnitude afforded by these modifications is empirically demonstrated we also compare the modified method with one based on the fast fourier transform fft further we show that the fft method can also result in considerable loss of numerical accuracy the modifications proposed in this article yield an algorithm that is not only fast and accurate but that combine

noisy collective behaviour in deterministic cellular automata we investigate cellular automata in four and five dimensions for which chate and manneville recently have found nontrivial collective behaviour more precisely though being fully deterministic the average magnetization seems to be periodic respectively quasiperiodic with superimposed noise whose amplitude decreases with system size we confirm this behaviour on very large systems and over very large times we analyse in detail the statistical properties of the noise systems on small lattices and or subject to additional external noise are metastable arguments by grinstein et al suggest that in the periodic case the infinite deterministic systems should be metastable too these arguments are generalized to quasiperiodic systems we find evidence that they do indeed apply but we find no direct evidence for metastability of large systems

statistical analysis of digital images of periodic fibrous structures using generalized hurst exponent distributions abstract distinction of diverse two dimensional periodic structures can be based on a large number of methods and parameters while the quantitative description of differences between similar samples is usually difficult this article aims by the use of statistical random walk in a generalized q order dimensional space at introducing a methodology to qualify the networked structures on the basis of exemplary textile samples the presented results were obtained at 1 bit monochromatic maps obtained from optical microscopic pictures significant features of samples were represented by the obtained distributions of hurst exponents and shannon entropy calculations

on the prediction of local patterns in cellular automata abstract the class of deterministic one dimensional cellular automata studied recently by wolfram are considered we represent a state of an automaton as probability distribution of patterns of a fixed size in this way information is lost but it is possible to approximate the stepwise action of the automaton by the iteration of an analytic mapping of the set of probability distributions to itself such nonlinear analytic mappings generally have nontrivial attrators and in the most interesting cases wolfram class iii these are single points the point attractors under appropriate circumstances provide good approximations to the frequencies of local patterns generated by the discrete rules from which they were derived two appropriate settings for such approximation are transient patterns generated from random starts and patterns generated in a noisy environment in the case with noise improvement is found by correction of the analytic mappings for the effects of noise examples of both types of approximation are considered

localization and standard modules for real semisimple lie groups i the duality theorem in this paper we relate two constructions of representations of semisimple lie groups constructions that appear quite different at first glance homogeneous vector bundles are one source of representations if a real semisimple lie group go acts on a vector bundle e m over a quotient space m go ho then go acts also on the space of sections c m e and on any subspace vcc m e defined by a go invariant system of differential equations ordinary induction so called cohomological induction and the construction of representations by quantizat ion all fit into the framework of homogeneous vector bundles for any complex semisimple lie algebra g there is an equivalence of categories due to beilinson bernstein 1 between modules on the one hand and sheaves of modules over the flag variety x of g on the other in the context of real semisimple lie groups this equivalence of categories associates infinitesimal representations to orbits in the flag variety of the complexified lie algebra orbits not of the group go itself but of the complexification of maximal compact subgroup ko c go we shall show that these beilinson bernstein modules are naturally dual to modules attached to certain homogeneous vector bundles in the special case of a compact group both the beilinson bernstein construction and the construction via homogeneous vector bundles reduce to the borel weil bott theorem our duality theorem is then a particular instance of serre duality

efficient monte carlo methods for conditional logistic regression abstract exact inference for the logistic regression model is based on generating the permutation distribution of the sufficient statistics for the regression parameters of interest conditional on the sufficient statistics for the remaining nuisance parameters despite the availability of fast numerical algorithms for the exact computations there are numerous instances where a data set is too large to be analyzed by the exact methods yet too sparse or unbalanced for the maximum likelihood approach to be reliable what is needed is a monte carlo alternative to the exact conditional approach which can bridge the gap between the exact and asymptotic methods of inference the problem is technically hard because conventional monte carlo methods lead to massive rejection of samples that do not satisfy the linear integer constraints of the conditional distribution we propose a network sampling approach to the monte carlo problem that eliminates rejection entirely its advantages over alternative saddlepoint

restrictions of quaternionic representations in a paper by gross and wallach 1996 j reine angew math 481 73 123 the k types of the continuations of the quaternionic discrete series of a quaternionic lie group g are associated with projective orbits o of certain subgroups in g c in this paper we will show that the restrictions of the representations to quaternionic subgroups are closely related with the intersection of the zariski closure of o with hyperplanes we apply this to the minimal representations of the exceptional groups of real rank 4 and investigate the correspondences of certain compact dual pairs

chaos and diffusion in deterministic cellular automata abstract it is shown that some of the deterministic one dimensional cellular automata studied recently by wolfram exhibit a kind of spontaneous symmetry breaking the associated kinks bloch walls perform annihilating diffusive walks for infinite lattices and large times in addition close analogies between these automata and strange attractors are exhibited by mapping the automata onto dynamical systems defined by iterations of the unit square

on the restriction of zuckerman s derived functor modules a q λ to reductive subgroups in this article we study the restriction of zuckerman s derived functor g k modules aq to gfor symmetric pairs of reductive lie algebras g g when the restriction decomposes into irreducible g k modules we give an upper bound for the branching law in particular we prove that each g k module occurring in the restriction is isomorphic to a submodule of aq for a parabolic subalgebra qof g and determine their associated varieties for the proof we realize aq on complex partial flag varieties by using d modules 1 introduction our object of study is branching laws of zuckerman s derived functor modules aq with respect to symmetric pairs of real reductive lie groups let g0 be a real reductive lie group with lie algebra g0 fix a cartan invo lution of g0 so that the fixed set k0 g0 is a maximal compact subgroup of g0 write k for the complexification of k0 g0 k0 p0 for the cartan de composition with respect to and g g0 rc for the complexification similar notation will be used for other lie algebras the cohomologically induced module aq is a g k module defined for a stable parabolic subalgebra q of g and a character t he g k module aq is unitarizable under certain conditions on the parameter and therefore plays a large part in the study of the unitary dual of real reductive lie groups one of the fundamental problems in representation theory is to decompose a given representation into irreducible constituents to begin with we consider the restriction of g k modules to k or equivalently to the compact group k0 i n this case it is known that any irreducible g k module decomposes as a direct sum of irreducible representations of k and each k type occurs with finite multi plicity for aq the following formula gives an upper bound for the multiplici ties

aperiodicity in one dimensional cellular automata abstract cellular automata are a class of mathematical systems characterized by discreteness in space time and state values determinism and local interaction a certain class of one dimensional binary site valued nearest neighbor automata is shown to generate infinitely many aperiodic temporal sequences from arbitrary finite initial conditions on an infinite lattice the class of automaton rules that generate aperiodic temporal sequences are characterized by a particular form of injectivity in their interaction rules included are the nontrivial linear automaton rules that is rules for which the superposition principle holds certain nonlinear automata with injectivity properties similar to those of linear automata and a wider subset of nonlinear automata whose interaction rules satisfy a weaker form of injectivity together with certain symmetry conditions the evolution of this last subset of automata can be viewed as consisting of multiple domains within which behavior exactly mimics that of a linear automaton a linearization technique is used to establish that these domains coalesce in finite time to produce at most two domains and thereby to assert the aperiodicity of their temporal sequences

discrete decomposability of the restriction of a_q λ with respect to reductive subgroups ii micro local analysis and asymptotic k support let g c g be real reductive lie groups this paper offers a criterion on the triplet g g ir that the irreducible unitary representation ir of g splits into a discrete sum of irreducible unitary representations of a subgroup g when restricted to g each of finite multiplicity furthermore we shall give an upper estimate of the multiplicity of an irreducible unitary representation of g occurring in wrig

methods for exact goodness of fit tests abstract numerous goodness of fit tests with asymptotic chi squared distributions have been proposed for discrete multivariate data and there has been much discussion about using asymptotic results for computing critical values when there are small expected cell values although exact methods would be preferred in these situations it generally is believed that such methods are computationally intractable we propose methods for calculating exact distributions and significance levels for goodness of fit statistics that are computationally feasible over a wide range of models in particular the distribution for a simple multinomial model can be evaluated in polynomial time for composite null hypotheses we calculate the distribution conditional on the sufficient statistics for the nuisance parameters we calculate the characteristic function of a distribution and invert the characteristic function using the fast fourier transform fft our approach emphasizes the relationship between exact methods and

differential operators on homogeneous spaces iii characteristic varieties of harish chandra modules and of primitive ideals letg be a semi simple complex algebraic group with lie algebra and flag varietyx g b for each primitive idealj with trivial central character in the enveloping algebrau we define a characteristic variety in the cotangent bundle ofx which projects under the springer resolution mapt x onto the closure of a nilpotent orbit we prove that this characteristic variety is theg saturation of the characteristic variety of a highest weight module with annihilatorj we conjecture that it is irreducible forg sl n our conjecture would provide a geometrical explanation for the classification of primitive ideals in terms of weyl group representations as achieved by a joseph the presentation of these ideas here is simultaneously used to some extent as an opportunity to continue our more general systematic discussion of differential operators on a complete homogeneous space and to study more generally characteristic varieties of harish chandra modules

geometric quantization and multiplicities of group representations the heisenberg uncertainty principle says that it is impossible to determine simultaneously the position and momentum of a quantum mechanical particle this can be rephrased as follows the smallest subsets of classical phase space in which the presence of a quantum mechanical particle can be detected are its lagrangian submanifolds for this reason it makes sense to regard the lagrangian submanifolds of phase space as being its true points see weinstein 17 now let g be a compact lie group and g x x x a hamiltonian action of g on x see w for definitions it is well known that the fixed points of this action form a symplectic submanifold of x see for instance guillemin and sternberg 5 however what can one say about the fixed points of g we will show that they are also the points of a symplectic manifold xc this manifold is the marsden weinstein reduction of x with respect to the zero orbit in g and will be described in sect 2 it was introduced in a completely different context fl om ours by marsden and weinstein 12 problems in classical mechanics can often be reduced to the study of hamiltonian systems on symplectic manifolds and problems in quantum mechanics to the study of linear operators on hilbert space this fact has inspired a number of efforts to quantize symplectic geometry by devising schemes for associating hilbert space to symplectic manifolds the no go theorems of groenwald and van hove impose some embarrassing limitations on all such schemes however it seems to be a useful idea heuristically to think of every symplectic manifold x a ic 1 as being symbiotically associated with a hilbert space xq a t in such a way that the classical observables on the first space correspond to quantum observables on the second space the heuristics further suggests that if g is a group of symmetries of x la i j it should also be a group of symmetries of xq a tum in this heuristic spirit we will state the main conjecture of this paper

outlier tests for logistic regression a conditional approach summary we consider exact conditional methods for identifying outliers in logistic regression data tests for a single outlier and multiple outliers are developed assuming a logistic slippage model the p values for these tests are determined using an explicit enumeration of all possible responses consistent with the observed value of the sufficient statistic justifications are given for preferring this computationally intensive approach to standard methods based on asymptotic approximations the techniques are applied to two examples

sur la notion faiblement propre dans la conjecture de duflo in this article we verify duflo s conjecture for su 2 1 with respect to a borel subgroup it turns out that the non standard notion weakly proper faiblement propre in the formulation of duflo s conjecture is more reasonable than the standard notions proper and proper over image

computing distributions for exact logistic regression abstract logistic regression is a commonly used technique for the analysis of retrospective and prospective epidemiological and clinical studies with binary response variables usually this analysis is performed using large sample approximations when the sample size is small or the data structure sparse the accuracy of the asymptotic approximations is in question on other occasions singularity of the covariance matrix of parameter estimates precludes asymptotic analysis under these circumstances use of exact inferential procedures would seem to be a prudent alternative cox 1970 showed that exact inference on the parameters of a logistic model with binary response requires consideration of the distribution of sufficient statistics for these parameters to date however resorting to the exact method has not been computationally feasible except in a few special situations this article presents an efficient recursive algorithm that generates the joint and conditional distributions of the sufficient

kirillov s orbit method the case of discrete series representations let be a discrete series representation of a real reductive lie group g and let g be a reductive subgroup of g in this paper we give a geometric expression of the g multiplicities in g when the representation is g admissible

thermodynamics of systems of finite sequences it is proposed that the hamming distance between bit strings plays the role of interaction energy the statistical sum and thermodynamic functions are calculated for the canonical ensemble of bit sequences the method is illustrated with an ensemble of two sequence systems which evolve according to cellular automata rules

intriguing properties of global structure in some classes of finite cellular automata abstract the simplest one dimensional cellular automata introduced recently by wolfram are analyzed particularly the finite cellular automata with two special evolution rules are studied non trivial correspondence in global structure is found between the state transition diagrams under the two rules correspondence of cycle structure basin volume of each cycle and structure of transient trees etc origin of the correspondence is explored on the basis of local properties of the evolution rules it is shown that this correspondence becomes exact in the thermodynamic limit

permutation distributions via generating functions with applications to sensitivity analysis of discrete data abstract generating functions provide a simple and elegant way to describe probability or frequency distributions of discrete statistics and in particular permutation distributions they are also a computational tool many efficient algorithms including those described as fast fourier transform methods network methods and multiple shift methods are different implementations of the recursions needed to evaluate generating functions efficiently our goals here are twofold first we make the relationship between these efficient methods and generating functions explicit this establishes a language for looking at other questions in randomization exact inference and may help in finding more efficient implementations second we propose methods to examine the sensitivity of results of exact analysis of discrete data to small perturbations in the data specifically we consider two settings how the analysis would change if one outcome changed and how the analysis would change if one observation was adde

branching laws for verma modules and applications in parabolic geometry i abstract we initiate a new study of differential operators with symmetries and combine this with the study of branching laws for verma modules of reductive lie algebras by the criterion for discretely decomposable and multiplicity free restrictions of generalized verma modules t kobayashi 2012 22 we are brought to natural settings of parabolic geometries for which there exist unique equivariant differential operators to submanifolds then we apply a new method f method relying on the fourier transform to find singular vectors in generalized verma modules which significantly simplifies and generalizes many preceding works in certain cases it also determines the jordan holder series of the restriction for singular parameters the f method yields an explicit formula of such unique operators for example giving an intrinsic and new proof of juhl s conformally invariant differential operators juhl 2009 16 and its generalizations to spinor bundles this article is the first in the series and the next ones include their extension to curved cases together with more applications of the f method to various settings in parabolic geometries

exact inference for categorical data recent advances and continuing controversies methods for exact small sample analyses with categorical data have been increasingly well developed in recent years a variety of exact methods exist primarily using the approach that eliminates unknown parameters by conditioning on their sufficient statistics in addition a variety of algorithms now exist for implementing the methods this paper briefly summarizes the exact approaches and describes recent developments controversy continues about the appropriateness of some exact methods primarily relating to their conservative nature because of discreteness this issue is examined for two simple problems in which discreteness can be severe interval estimation of a proportion and the odds ratio in general adjusted exact methods based on the mid p value seem a reasonable way of reducing the severity of this problem

harmonically induced representations of solvable lie groups soit un groupe de lie g d algebre de lie g et h une polarisation pour l orbite on etudie la representation obtenue quand h est totalement complexe non necessairement positive et g resoluble

branching problems in reproducing kernel spaces for a semisimple lie group g satisfying the equal rank condition the most basic family of unitary irreducible representations is the discrete series found by harish chandra in our work here we study some of the branching laws for discrete series when restricted to a subgroup h of the same type by combining classical results with recent work of kobayashi in particular we prove discrete decomposability under harish chandra s condition of cusp form on the reproducing kernel we show a relation between discrete decomposability and representing certain intertwining operators in terms of differential operators

long range effects in an elementary cellular automaton we present evidence that one of the elementary one dimensional cellular automata in the sense of wolfram rule 22 in wolfram s notation involves very complex long range effects similar to a critical phenomenon this is in contrast to superficial evidence that would suggest that this rule leads to fairly simple behavior

finite multiplicity theorems for induction and restriction abstract we find upper and lower bounds of the multiplicities of irreducible admissible representations of a semisimple lie group g occurring in the induced representations ind h g from irreducible representations of a closed subgroup h as corollaries we establish geometric criteria for finiteness of the dimension of hom g ind h g induction and of hom h h restriction by means of the real flag variety g p and discover that uniform boundedness property of these multiplicities is independent of real forms and characterized by means of the complex flag variety

on obtaining permutation distributions in polynomial time abstract polynomial time algorithms are presented for finding the permutation distribution of any statistic that is a linear combination of some function of either the original observations or the ranks this class of statistics includes the original fisher two sample location statistic and such common nonparametric statistics as the wilcoxon ansari bradley savage and many others the algorithms are presented for the two sample problem and it is shown how to extend them to the multisample problem for example to find the distribution of the kruskal wallis and other extensions of the wilcoxon and to the single sample situation stratification ties and censored observations are also easily handled by the algorithms the algorithms require polynomial time as opposed to complete enumeration algorithms which require exponential time this savings is effected by first calculating and then inverting the characteristic function of the statistic

computing exact distributions for polytomous response data abstract this article presents an efficient method for computing exact conditional distributions of the sufficient statistics for the parameters of four polytomous response models for nominal response two baseline category logit models and for ordinal response two adjacent categories logit models are considered the method consists of recursive generation of the joint distribution of the sufficient statistics augmented by a technique to slice off portions of the evolving sample space so as to eventually yield the required conditional distribution two actual data sets are analyzed to illustrate the method

pattern dynamics in spatiotemporal chaos pattern selection diffusion of defect and pattern competition intermettency abstract a class of coupled map lattices is investigated as a model for the spatiotemporal chaos as the parameters are changed phase transitions among the patterns are observed pattern selection through the chaotic motion of domain is observed chaos is suppressed by the selection selection of the zigzag pattern is studied where localized defects which separate the two anti phase domains are found they change chaotically in time and move randomly in space the diffusion of defect is related with its chaotic motion collapse of zigzag pattern and the defect turbulence are studied in connection with the crisis in high dimensional dynamical systems pattern selection with longer wavelengths is found in the stronger coupling regime transition from pattern selection phase to fully developed turbulence occurs via the intermittency selective flicker like noise and the pareto distribution of lifetime of pattern are observed at the intermittency regime for the quantitative characterization of each phase pattern distributions pattern transition matrix static and dynamical entropies lifetime distribution of pattern spatiotemporal power spectra and lyapunov spectra are calculated phase transition from the pattern selection to fully developed turbulence is investigated with the use of these quantifiers where some order parameters and critical indeces are introduced

monte carlo study of infinite dimensional cellular automata abstract the well known one dimensional elementary cellular automata are generalized to an infinite number of dimensions the generalization of the most interesting automaton in 1d rule 22 is studied in detail by means of monte carlo as well as enumeration methods it is shown that monte carlo data extrapolate very smoothly to infinite system size numerical deviation from mean field theory is analyzed

cellular automata as a paradigm for ecological modeling we review cellular automata as a modeling formalism and discuss how it can be used for modeling spatial ecological processes the implications of this modeling paradigm for ecological observation are stressed finally we discuss some shortcomings of the cellular automaton formalism and mention some extensions and generalizations which may remedy these shortcomings

analysis on the minimal representation of o p q abstract for the group o p q we give a new construction of its minimal unitary representation via euclidean fourier analysis this is an extension of the q 2 case where the representation is the mass zero spin zero representation realized in a hilbert space of solutions to the wave equation the group o p q acts as the mobius group of conformal transformations on r p 1 q 1 and preserves a space of solutions of the ultrahyperbolic laplace equation on r p 1 q 1 we construct in an intrinsic and natural way a hilbert space of solutions so that o p q becomes a continuous irreducible unitary representation in this hilbert space we also prove that this representation is unitarily equivalent to the representation on l2 c where c is the conical subvariety of the nilradical of a maximal parabolic subalgebra obtained by intersecting with the minimal nilpotent orbit in the lie algebra of o p q

an algorithm for exact logistic regression abstract an efficient algorithm is given for the exact logistic analysis of a single parameter hypothesis tests and confidence intervals for a logistic regression parameter are obtained the method provides for the control of the effect of a stratification factor when making inferences concerning the regression parameter

geometric realization of discrete series for semisimple symmetric spaces let g be a connected semisimple lie group a an involution of g and h the connected component of the fixed point set of a containing the identity then g h is a semisimple symmetric space we assume g is a real form of a complex lie group and rank g h rank k k c h where k is a a stable maximal compact subgroup of g flensted jensen using his duality principle and poisson transform constructed countably many discrete series in u g h f j i then using deep results of hyperfunction theory and microlocal analysis oshima and matsuki gave a detailed characterization of these discrete series including a proof of flensted jensen s conjecture c 0 om based on these results we give the discrete series a geometric interpretation in locally symmetric spaces f c where g k and f cg is a cocompact discrete group such that f c h c h is cocompact our geometric interpretation is the following first of all to a flensted jensen function which is the generating function of a discrete series v we associate a harmonic form cb z on g with values in a finite dimensional g module v right g translates of coefficients of 5z realizes the contragredient t of r and tba is left invariant under h and under right k action it transforms according to the minimal k type with highest weight of 3 is the pull back of a v valued from coz on and v determines a locally constant bundle e on f so that if convergence holds

wave front sets of reductive lie group representations iii abstract let g be a real reductive algebraic group and let x be a homogeneous space for g with a non zero invariant density we give an explicit description of a zariski open dense subset of the asymptotics of the tempered support of l 2 x under additional hypotheses this result remains true for vector bundle valued harmonic analysis on x these results follow from an upper bound on the wave front set of an induced lie group representation under a uniformity condition

two dimensional cellular automata a largely phenomenological study of two dimensional cellular automata is reported qualitative classes of behavior similar to those in one dimensional cellular automata are found growth from simple seeds in two dimensiona cellular automata can produce patterns with complicated boundaries characterized by a variety of growth dimensions evolution from disordered states can give domains with boundaries that execute effectively continuous motions some global properties of cellular automata can be described by entropies and lyapunov exponents others are undecidable

the topological skeleton of cellular automaton dynamics abstract we have developed statistical techniques to study the structure of the state transition graphs of cellular automata with periodic boundary conditions in the limit of large system size we organize our results around the concept of a topological skeleton the topological skeleton is the set of physically relevant states covering this skeleton is a surface typically thin and dense which contains the bulk of the set of states states in the skeleton have some long histories states on the surface by contrast have only short histories they are reached only near the beginning of cellular automaton evolution we study in detail a sequence of rules which exhibit mostly skeletal to mostly surface structure

the equality of fractional dimensions for certain cellular automata abstract a study is made of the development of certain cellular automata with apparently chaotic behavior results are obtained for cellular automata arising from additive rules modulo 2 for the corresponding limit sets it is shown that the growth rate dimension the kolmogorov dimensions and the hausdorff dimensions all coincide this dimension is moreover independent of the choice of finite initial seed and the sampling times used these cellular thus provide test cases for the production of fractals by local processes

automatic filters for the detection of coherent structure in spatiotemporal systems most current methods for identifying coherent structures in spatially extended systems rely on prior information about the form which those structures take here we present two approaches to automatically filter the changing configurations of spatial dynamical systems and extract coherent structures one local sensitivity filtering is a modification of the local lyapunov exponent approach suitable to cellular automata and other discrete spatial systems the other local statistical complexity filtering calculates the amount of information needed for optimal prediction of the system s behavior in the vicinity of a given point by examining the changing spatiotemporal distributions of these quantities we can find the coherent structures in a variety of pattern forming cellular automata without needing to guess or postulate the form of that structure we apply both filters to elementary and cyclical cellular automata eca and cca and find that they readily identify particles domains and other more complicated structures we compare the results from eca with earlier ones based upon the theory of formal languages and the results from cca with a more traditional approach based on an order parameter and free energy while sensitivity and statistical complexity are equally adept at uncovering structure they are based on different system properties dynamical and probabilistic respectively and provide complementary information

defect particle kinematics in one dimensional cellular automata let a z be the cantor space of bi infinite sequences in a finite alphabet a and let s be the shift map on a z a cellular automaton is a continuous s commuting self map f of a z and a f invariant subshift is a closed f s invariant subset s a z suppose a a z is s admissible everywhere except for some small region we call a defect it has been empirically observed that such defects persist under iteration of f and often propagate like particles we characterize the motion of these particles and show that it falls into several regimes ranging from simple deterministic motion to generalized random walks to complex motion emulating turing machines or pushdown automata one consequence is that some questions about defect behaviour are formally undecidable

long range correlations in chaotic cellular automata abstract one dimensional cellular automata of class 3 are studied as models for spatially extended chaotic systems their irreversible dynamics can generate weak but long range spatial correlations the one labelled 22 by wolfram is treated in an exemplary way its stationary state is approximated by a markov chain the regular grammar underlying the markov chain is chosen with care so that it includes a maximum amount of information on the stationary state the approximation can be performed without simulating the dynamics of the cellular automaton 22 and reproduces its long range correlations qualitatively their origin is explained intuitively and they are argued to be a frequent feature of cellular automata with more complicated rules

unitary highest weight modules the unitary highest weight modules of a semisimple lie group g have been classified s 93 unfortunately this classification does not fit well with a more general picture of the unitary dual of g we give such a classification for g a classical group using derived functors and the philosophy of unipotent representations in particular these representations are associated to coadjoint orbits of g let 8 lie g 0 a cartan involution of 6 8 c a derived functor module is defined by the data q i u a o stable parabolic subalgebra of 0 and 17 an irreducible unitary representation of l the stabilizer of l in g considering z7 as a representation of i write z7 a rc where a e c c center of i denotes dual and rt z7l r we define a rc i rc cf definition 6 1 now fix n and vary 1 under certain restrictions on i which amount to a positivity condition on the corresponding bundle over g l a i rr is known to be irreducible and unitary as ii varies within this range the langlands parameters of a a rr vary smoothly however one cannot obtain all unitary highest weight modules under these restrictions the orbit method suggests how to obtain the remaining unitary highest weight modules the modules a rr are associated to coadjoint orbits as follows if rc is trivial we say a rr is associated to the elliptic orbit 0 g ii not all unitary highest weight modules may be obtained with rc trivial an example of which is the oscillator representation of 2n r the metapletic group we define 2n irreducible unitary highest weight modules rc 1 2 n k r is 113 oool 8708 87 7 50

analysis on the minimal representation of o p q i realization via conformal geometry abstract this is the first in a series of papers devoted to an analogue of the metaplectic representation namely the minimal unitary representation of an indefinite orthogonal group this representation corresponds to the minimal nilpotent coadjoint orbit in the philosophy of kirillov kostant we begin by applying methods from conformal geometry of pseudo riemannian manifolds to a general construction of an infinite dimensional representation of the conformal group on the solution space of the yamabe equation by functoriality of the constructions we obtain different models of the unitary representation as well as giving new proofs of unitarity and irreducibility the results in this paper play a basic role in the subsequent papers where we give explicit branching formulae and prove unitarization in the various models

convexity properties of the moment mapping ii be its associated momen t mapping see w for definitions the set x is the union of co adjoint orbits the main result of this paper is a description of the orbit structure of this set to describe this result we first note that the coadjoint orbits in q can be parametr ized as follows let t be a caf tan subalgebra of g and let b be a positive definite g invariant bilinear form on by means of b we get a g equivariant identification q let t be the subspace of q corresponding to t then every co adjoint orbit intersects i in a weyl group orbit so there is a one one correspondence between co adjoint orbits in q and weyl group orbits in t to get an even sharper parametrization let t be a weyl chamber in then every weyl group orbit intersects t in a single point so t is a modul i space for the co adjoint orbits two orbits in x are said to be of the same type if they are isomorphic as homogeneous g spaces since x is compact there are at most a finite number of different types of orbits see 1113 let h be a closed subgroup of t of codimension r and let cit be the set of all orbits in x of type g h

cellular automata in fuzzy backgrounds abstract the main purpose of this work is to understand some limitations introduced by the classical definitions of cellular automata ca to this end we have defined a new model of cas fuzzy ca s which allows the observation of interesting chaotic properties of elementary cas to date neither a formal nor a precise definition of chaos in cas exists we believe that the proposed model provides a sharper tool to detect which properties can be associated to a chaotic behavior we also define a measure rule entropy which gives information about the ca s dynamics solely on the basis of the rule table and provides theoretical explanations to some of the empirical observations

discrete decomposability of the restriction of aq λ with respect to reductive subgroupsiii restriction of harish chandra modules and associated varieties let h g be real reductive lie groups and an irreducible unitary representation of g we introduce an algebraic formulation discretely decomposable restriction to single out the nice class of the branching problem breaking symmetry in physics in the sense that there is no continuous spectrum in the irreducible decomposition of the restriction h this paper offers basic algebraic properties of discretely decomposable restrictions especially for a reductive symmetric pair g h and for the zuckerman vogan derived functor module and proves that the sufficient condition invent math 94 is in fact necessary a finite multiplicity theorem is established for discretely decomposable modules which is in sharp contrast to known examples of the continuous spectrum an application to the restriction h of discrete series for a symmetric space g h is also given

classification of discretely decomposable aq λ with respect to reductive symmetric pairs abstract we give a classification of the triples g g q such that zuckerman s derived functor g k module a q for a stable parabolic subalgebra q is discretely decomposable with respect to a reductive symmetric pair g g the proof is based on the criterion for discretely decomposable restrictions by the first author and on berger s classification of reductive symmetric pairs

discrete decomposability of the restriction of a q λ with respect to reductive subgroups and its applications letg g be real reductive lie groups and q a stable parabolic subalgebra of lie g this paper offers a sufficient condition on g g q that the irreducible unitary representation mathop a q limits ofg with non zero continuous cohomology splits into a discrete sum of irreducible unitary representations of a subgroupg each of finite multiplicity as an application to purely analytic problems new results on discrete series are also obtained for some pseudo riemannian non symmetric spherical homogeneous spaces which fit nicely into this framework some explicit examples of a decomposition formula are also found in the cases wherea q is not necessarily a highest weight module

analysis on the minimal representation of o p q ii branching laws this is a second paper in a series devoted to the minimal unitary representation of o p q by explicit methods from conformal geometry of pseudo riemannian manifolds we find the branching law corresponding to restricting the minimal unitary representation to natural symmetric subgroups in the case of purely discrete spectrum we obtain the full spectrum and give an explicit parseval plancherel formula and in the general case we construct an infinite discrete spectrum r 2003 published by elsevier science usa msc 22e45 22e46 53a30 43a85

duflo s conjecture for the branching problem to the iwasawa an subgroup of a semisimple lie group the purpose of this paper is to prove duflo s conjecture for g pi an where g is a real connected simple lie group of hermitian type and pi is a discrete series of g and an is the maximal exponential solvable subgroup for an iwasawa decomposition g kan this is essentially deduced from the following general theorem which we prove in this paper let g be a real connected semisimple lie group with lie algebra mathfrak g then a strongly elliptic g coadjoint orbit mathcal o is holomorphic if and only if text p mathcal o is an open an coadjoint orbit here text p mathfrak g longrightarrow mathfrak a oplus mathfrak n is the natural projection

distinguished nilpotent orbits kostant pairs and normalizers of lie algebras abstract a pair of lie algebras g g 1 will be called a kostant pair if g is semisimple g 1 is reductive in g and the restriction of the killing form b g to g 1 is nondegenerate we study the class of such nonsymmetric pairs and obtain some useful and new structural results we study the structure of the normalizers n g g 1 and as a consequence we obtain some corresponding worthy results about algebraic groups in particular we consider an interesting case when g 1 is a distinguished sl 2 subalgebra of g combined with the research due to v l popov we observe that the notions of self normalizing reductive subalgebras of a semisimple lie algebra and projective self dual algebraic subvarieties of the usual nilpotent cones are closely related

fock model and segal bargmann transform for minimal representations of hermitian lie groups abstract for any hermitian lie group g of tube type we construct a fock model of its minimal representation the fock space is defined on the minimal nilpotent k c orbit x in p c and the l 2 inner product involves a k bessel function as density here k g is a maximal compact subgroup and g c k c p c is a complexified cartan decomposition in this realization the space of k finite vectors consists of holomorphic polynomials on x the reproducing kernel of the fock space is calculated explicitly in terms of an i bessel function we further find an explicit formula of a generalized segal bargmann transform which intertwines the schrodinger and fock model its kernel involves the same i bessel function using the segal bargmann transform we also determine the integral kernel of the unitary inversion operator in the schrodinger model which is given by a j bessel function

dual pair correspondences for non linear covers of orthogonal groups abstract in this paper we study compact dual pair correspondences arising from smallest representations of non linear covers of odd orthogonal groups we identify representations appearing in these correspondences with subquotients of cohomologically induced representations

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

efficient calculation of the permutation distribution of trimmed means abstract the permutation distribution of the trimmed mean in matched pairs designs is studied this statistic is important since it is robust to both outliers and distributional assumptions a polynomial time algorithm for this inherently exponential time problem is presented the characteristic function of the distribution provides both the basis for the algorithm and a vehicle for calculating the asymptotic permutation distribution

geometric analysis on small unitary representations of gl n r abstract the most degenerate unitary principal series representations i r z 2 z of g gl n r attain the minimum of the gelfand kirillov dimension among all irreducible unitary representations of g this article gives an explicit formula of the irreducible decomposition of the restriction i h branching law with respect to all symmetric pairs g h for n 2 n with n 2 the restriction i h remains irreducible for h sp n r if 0 and splits into two irreducible representations if 0 the branching law of the restriction i h is purely discrete for h gl n c consists only of continuous spectrum for h gl p r gl q r p q n and contains both discrete and continuous spectra for h o p q p q 1 our emphasis is laid on geometric analysis which arises from the restriction of small representations to various subgroups