the distribution of maxima of approximately gaussian random fields motivated by the problem of testing for the existence of a signal of known parametric structure and unknown location as explained below against a noisy background we obtain for the maximum of a centered smooth random field an approximation for the tail of the distribution for the motivating class of problems this gives approximately the significance level of the maximum score test the method is based on an application of a likelihood ratio identity followed by approximations of local fields numerical examples illustrate the accuracy of the approximations

false discovery rate for scanning statistics the false discovery rate is a criterion for controlling type i error in simultaneous testing of multiple hypotheses for scanning statistics due to local dependence clusters of neighbouring hypotheses are likely to be rejected together in such situations it is more intuitive and informative to group neighbouring rejections together and count them as a single discovery with the false discovery rate defined as the proportion of clusters that are falsely declared among all declared clusters assuming that the number of false discoveries under this broader definition of a discovery is approximately poisson and independent of the number of true discoveries we examine approaches for estimating and controlling the false discovery rate and provide examples from biological applications copyright 2011 oxford university press

quantum enveloping superalgebras and link invariants corresponding to each finite dimensional simple basic classical lie superalgebra a new quantum enveloping superalgebra is introduced which has the structure of a braided quasi hopf superalgebra in the case of osp 1 2n this quantum enveloping superalgebra is shown to be isomorphic to the standard drinfeld jimbo quantum superalgebra uq osp 1 2n as braided quasi hopf superalgebras the new quantum enveloping superalgebras are applied to construct link invariants from which vassiliev invariants can be readily extracted this in particular provides a useful construction for the vassiliev invariants associated with uq osp 1 2n

universal tangle invariant and commutants of quantum algebras we construct a universal tangle invariant on a quantum algebra we show that the invariant maps tangle to commutants of the algebra every 1 1 tangle is mapped to a casimir operator of the algebra the eigenvalue of the casimir operator in an irreducible representation of the algebra is a link polynomial for the closure of the tangle this result is applied to a discussion of the alexander conway polynomial and quantum holonomy in chern simons theory in three dimensions

braid group representations arising from quantum supergroups with arbitrary q and link polynomials the theory of quantum supergroups is applied to the construction of braid group representations and link invariants a method developed in an earlier publication is reviewed which produces link polynomials from braid group representations generated by quantum supergroup invariant r matrices when q is a generic complex parameter this method applied to the universal r matrices yields hierarchies of link polynomials associated with different irreps of quantum supergroups when q is a root of unity suitable constraints are imposed on quantum supergroups to turn them into finite dimensional quasitriangular z2 graded hopf algebras the corresponding universal r matrices are obtained which in turn lead to series of link polynomials upon using the above mentioned method as concrete examples the link polynomials related to the vector irreps of the quantum supergroups uq osp m 2n all the irreps of uq osp 1 2 with generic q and a class of doubly atypical irreps of uq gl 2 1 with q a root of unity

statistical properties of local extrema in two dimensional gaussian random fields this paper is concerned with the statistical properties of the local extrema and local maxima of two dimensional 2d gaussian random fields grfs a grf may be represented by a linear filtering operation on a white noise field the spatial properties of the grf are then determined by the shape of the filter kernel function new expressions are derived for the mean spatial density of local extrema and for the distribution of local extrema in a 2 d random field the work is motivated by the problem of detecting known structures in images using 2d matched filters the new results enable accurate performance predictions to be made of the reliability of such filters in the presence of noise case studies are presented for several well known 2 d filter kernel functions

analysis of observer performance in known location tasks for tomographic image reconstruction we consider the task of detecting a statistically varying signal of known location on a statistically varying background in a reconstructed tomographic image we analyze the performance of linear observer models in this task we show that if one chooses a suitable reconstruction method a broad family of linear observers can exactly achieve the optimal detection performance attainable with any combination of a linear observer and linear reconstructor this conclusion encompasses several well known observer models from the literature including models with a frequency selective channel mechanism and certain types of internal noise interestingly the optimal reconstruction methods are unregularized and in some cases quite unconventional these results suggest that for the purposes of designing regularized reconstruction methods that optimize lesion detectability known location tasks are of limited use

pairwise likelihood methods for inference in image models summary we consider parameter estimation for certain random set models for image data for the spatial models considered here a full likelihood based approach to this problem is often difficult since the likelihood generally cannot be computed for images of typical size this has motivated the consideration of various less computationally demanding parameter estimation techniques we discuss one method based on likelihoods for small subsets of the data consideration of the basic technique within the framework of the theory of estimating functions leads to a weighted version of the basic approach results of a simulation study are reported for some variants of the boolean model and excursion sets of random fields the methods are illustrated for some data on the spatial incidence of heather

type i quantum superalgebras q supertrace and two variable link polynomials a new general eigenvalue formula for the eigenvalues of casimir invariants for the type i quantum superalgebras is applied to the construction of link polynomials associated with any finite dimensional unitary irrep for these algebras this affords a systematic construction of new two variable link polynomials associated with any finite dimensional irrep with a real highest weight for the type i quantum superalgebras in particular infinite families of nonequivalent two variable link polynomials are determined in fully explicit form

detecting sparse signals in random fields with an application to brain mapping brain mapping data have been modeled as gaussian random fields and local increases in mean are detected by local maxima of a random field of test statistics derived from these data accurate p values for local maxima are readily available for isotropic data based on the expected euler characteristic of the excursion set of the test statistic random field in this article we give a simple method for dealing with nonisotropic data our approach has connections to the model of sampson and guttorp for nonisotropy in which there exists an unknown mapping of the support of the data to a space in which the random fields are isotropic heuristic justification for our approach comes from the nash embedding theorem formally we show that our method gives consistent unbiased estimators for the true p values based on new results of taylor and adler for random fields on manifolds which replace the euclidean metric by the variogram the results are used to detect gender differences in the cortical thickness of the b

structure and representations on the quantum supergroup ospq 2 2n the structure and representations of the quantum supergroup ospq 2 2n are studied systematically the algebra of functions on the quantum supergroup which specifies the quantum supergroup itself is taken to be the superalgebra generated by the matrix elements of the vector representation of the quantized universal superalgebra uq osp 2 2n it is shown that the algebra of functions is dense in the full dual uq osp 2 2n of uq osp 2 2n and possesses a hopf superalgebra structure the left integral and right integral on the quantum supergroup are discussed induced representations are developed using the noncommutative geometry of quantum homogeneous supervector bundles and a geometric realization of irreducible representations is obtained

false discovery control for random fields this article extends false discovery rates to random fields for which there are uncountably many hypothesis tests we develop a method for finding regions in the field s domain where there is a significant signal while controlling either the proportion of area or the proportion of clusters in which false rejections occur the method produces confidence envelopes for the proportion of false discoveries as a function of the rejection threshold from the confidence envelopes we derive threshold procedures to control either the mean or the specified tail probabilities of the false discovery proportion an essential ingredient of this construnction is a new algorithm to compute a confidence superset for the set of all true null locations we demonstrate our method with applications to scan statistics and functional neuroimaging

branes and supergroups extending previous work that involved d3 branes ending on a fivebrane with theta mathrm ym neq 0 we consider a similar two sided problem this construction in case the fivebrane is of ns type is associated to the three dimensional chern simons theory of a supergroup rm u m n or rm os rm p m 2n rather than an ordinary lie group as in the one sided case by s duality we deduce a dual magnetic description of the supergroup chern simons theory a slightly different duality in the orthosymplectic case leads to a strong weak coupling duality between certain supergroup chern simons theories on mathbb r 3 and a further t duality leads to a version of khovanov homology for supergroups some cases of these statements are known in the literature we analyze how these dualities act on line and surface operators

tests for a change point summary the problem considered is that of testing a sequence of independent normal random variables with constant known or unknown variance for no change in mean versus alternatives with a single change point various tests such as those based on the likelihood ratio and recursive residuals are studied power approximations are developed by integrating approximations for conditional boundary crossing probabilities a comparison of several tests is made

parameterizing quasi periodicity generalized poisson summation and its application to modified fibonacci antenna arrays the fairly recent discovery of quasi crystals whose x ray diffraction patterns reveal certain peculiar features which do not conform with spatial periodicity has motivated studies of the wave dynamical implications of aperiodic order within the context of the radiation properties of antenna arrays an instructive novel canonical example of wave interactions with quasi periodic order is illustrated here for one dimensional array configurations based on the modified fibonacci sequence with utilization of a two scale generalization of the standard poisson summation formula for periodic arrays this allows for a quasi floquet analytic parameterization of the radiated field which provides instructive insights into some of the basic wave mechanisms associated with quasi periodic order highlighting similarities and differences with the periodic case examples are shown for quasi periodic infinite and spatially truncated arrays with brief discussion of computational issues and potential applications

some characteristics of radiation from linearly phased sequentially excited periodic rectangular arrays of dipoles floquet wave and element by element summation representations are implemented to investigate the radiation from a periodic rectangular array of linearly phased sequentially pulsed dipoles in the frequency and time domains a synthetic aperture type formulation for floquet wave representation and an asymptotic formulation for the element by element summation representation are developed numerical results are presented to demonstrate the efficiency of the floquet wave representation in terms of radiating non radiating and diffracted wave constituents and then validated via comparison with direct summation over the contributions of individual dipole radiations

time domain green s function for an infinite sequentially excited periodic planar array of dipoles the present paper is a continuation of previous explorations by the authors aimed at gaining a basic understanding of the time domain td behavior of large periodic phased i e sequentially turned on array antennas and related configurations our systematic investigation of the relevant canonical td dipole excited green s functions has so far included those for infinite and truncated sequentially pulsed line periodic arrays parameterized in terms of radiating propagating and nonradiating evanescent conical td floquet waves fw and truncation induced td fw modulated tip diffractions the present contribution extends these investigations to an infinite periodic sequentially pulsed planar array which generates pulsed plane propagating and evanescent fw starting from the familiar frequency domain fd transformation of the linearly phased element by element summation synthesis into summations of propagating and evanescent fws we access the time domain by fourier inversion the inversion integrals are manipulated in a unified fashion into exact closed forms which are parameterized by the single nondimensional quantity spl eta c v sup p sub u1 where v sup p sub u1 and c are the excitation phase speed along a preferred phasing direction u sub 1 in the array plane and the ambient wave speed respectively the present study deals with the practically relevant rapidly phased propagating case spl eta 1 regime for a future manuscript numerical reference data generated via element by element summation over the fields radiated by the individual dipoles with ultrawide band limited excitation are compared with results obtained much more efficiently by inclusion of a few td fws physical interpretation of the formal td fw solutions is obtained by recourse to asymptotics instantaneous frequencies and wavenumbers and related constructs of special interest is the demonstration that the td fws emerge along equal delay ellipses from the array plane this furnishes a novel and physically appealing interpretation of the planar array td fw phenomenology

gaussian processes kinematic formulae and poincare s limit we consider vector valued unit variance gaussian processes defined over stratified manifolds and the geometry of their excursion sets in particular we develop an explicit formula for the expectation of all the lipschitz killing curvatures of these sets whereas our motivation is primarily probabilistic with statistical applications in the background this formula has also an interpretation as a version of the classic kinematic fundamental formula of integral geometry all of these aspects are developed in the paper particularly novel is the method of proof which is based on a an approximation to the canonical gaussian process on the n sphere the n limit which gives the final result is handled via recent extensions of the classic poincare limit theorem

a quantum group structure in integrable conformal field theories we discuss a quantization prescription of the conformal algebras of a class ofd 2 conformal field theories which are integrable we first give a geometrical construction of certain extensions of the classical virasoro algebra known as classicalw algebras in which these algebras arise as the lie algebra of the second hamiltonian structure of a generalized korteweg de vries hierarchy this fact implies that thew algebras obtained as a reduction with respect to the nilpotent subalgebras of the kac moody algebra describe the integrability of a toda field theory subsequently we determine the coadjoint operators of thew algebras and relate these to classical yang baxter matrices the quantization of these algebras can be carried out using the concept of a so called quantum group we derive the condition under which the representations of these quantum groups admit a hilbert space completion by exploring the relation with the braid group then we consider a modification of the miura transformation which we use to define a quantumw algebra this leads to an alternative interpretation of the coset construction for kac moody algebras in terms of nonlinear integrable hierarchies subsequently we use the connection between the induced braid group representations and the representations of the mapping class group of riemann surfaces to identify an action of thew algebras on the moduli space of stable curves and we give the invariants of this action this provides a generalization of the situation for the virasoro algebra where such as invariant is given by the so called mumford form which describes the partition function of the bosonic string

testing for a signal with unknown location and scale in a stationary gaussian random field we suppose that our observations can be decomposed into a fixed signal plus random noise where the noise is modelled as a particular stationary gaussian random field in n dimensional euclidean space the signal has the form of a known function centered at an unknown location and multiplied by an unknown amplitude and we are primarily interested in a test to detect such a signal there are many examples where the signal scale or width is assumed known and the test is based on maximising a gaussian random field over all locations in a subset of n dimensional euclidean space the novel feature of this work is that the width of the signal is also unknown and the test is based on maximising a gaussian random field in n 1 dimensions n dimensions for the location plus one dimension for the width two convergent approaches are used to approximate the null distribution one based on the method of knowles and siegmund which uses a version of weyl s tube formula for manifolds with boundaries and the other based on some recent work by worsley which uses the hadwiger characteristic of excursion sets as introduced by adler finally we compare the power of our method with one based on a fixed but perhaps incorrect signal width

geometry and representations of the quantum supergroup ospq 1 2n the quantum supergroup ospq 1 2n is studied systematically a haar functional is constructed and an algebraic version of the peter weyl theory is extended to this quantum supergroup quantum homogeneous superspaces and quantum homogeneous supervector bundles are defined following the strategy of connes theory parabolic induction is developed by employing the quantum homogeneous supervector bundles quantum frobenius reciprocity and a generalized borel weil theorem are established for the induced representations

analysis of fmri time series revisited again friston et al 1995 neuroimage 2 45 53 presented a method for detecting activations in fmr1 time series based on the general linear model and a heuristic analysis of the effective degrees of freedom in this communication we present corrected results that replace those of the previous paper and solve the same problem without recourse to heuristic arguments specifically we introduce a proper and unbiased estimator for the error terms and provide a more generally correct expression for the effective degrees of freedom the previous estimates of error variance were biased and in some instances could have led to a 10 20 overestimate of z values although the previous results are almost correct for the random regressors chosen for validation the present theoretical results are exact for any covariate or waveform we comment on some aspects of experimental design and data analysis in the light of the theoretical framework discussed here

random fields of multivariate test statistics with applications to shape analysis our data are random fields of multivariate gaussian observations and we fit a multivariate linear model with common design matrix at each point we are interested in detecting those points where some of the coefficients are nonzero using classical multivariate statistics evaluated at each point the problem is to find the p value of the maximum of such a random field of test statistics we approximate this by the expected euler characteristic of the excursion set our main result is a very simple method for calculating this which not only gives us the previous result of cao and worsley ann statist 27 1999 925 942 for hotelling s t 2 but also random fields of roy s maximum root maximum canonical correlations ann appl probab 9 1999 1021 1057 multilinear forms ann statist 29 2001 328 371 x 2 statist probab lett 32 1997 367 376 ann statist 25 1997 2368 2387 and x 2 scale space adv in appl probab 33 2001 773 793 the trick involves approaching the problem from the point of view of roy s union intersection principle the results are applied to a problem in shape analysis where we look for brain damage due to nonmissile trauma

frequency domain green s function for a planar periodic semi infinite phased array i truncated floquet wave formulation this two part sequence deals with the derivation and physical interpretation of a uniform high frequency solution for the field radiated at finite distance by a planar semi infinite phased array of parallel elementary electric dipoles the field obtained by direct summation over the contributions from the individual radiators is restructured into a double series of wavenumber spectral integrals whose asymptotic reduction yields a series encompassing propagating and evanescent floquet waves fws together with corresponding diffracted rays which arise from scattering of the fw at the edge of the array the formal aspects of the solution are treated in the present paper they involve a sequence of manipulations in the complex spectral wavenumber planes that prepare the integrands for subsequent efficient and physically incisive asymptotics based on the method of steepest descent different species of spectral poles define the various species of propagating and evanescent fw their interception by the steepest descent path sdp determines the variety of shadow boundaries for the edge truncated fw the uniform asymptotic reduction of the sdp integrals performed by the van der waerden 1951 procedure and yielding a variety of edge diffracted fields completes the formal treatment

a truncated floquet wave diffraction method for the full wave analysis of large phased arrays ii generalization to 3 d cases for pt i see ibid vol 48 no 3 p 594 600 2000 this paper deals with the generalization to three dimensional 3 d arrays of the truncated floquet wave tfw diffraction method for the full wave analysis of large arrays this generalization potentially includes arrays consisting of microstrip excited slots cavity backed apertures and patches the formulation is carried out first by deriving an appropriate fringe integral equation ie and next by defining entire domain basis functions in terms of global array functions shaped as tfw diffracted rays whose analytical expression is derived on the basis of prototype canonical problems the efficiency and the accuracy of this method is demonstrated by comparison with the results of an element by element full wave approach for a rectangular slot array

diffusion based spatial priors for functional magnetic resonance images we recently outlined a bayesian scheme for analyzing fmri data using diffusion based spatial priors harrison l m penny w ashburner j trujillo barreto n friston k j 2007 diffusion based spatial priors for imaging neuroimage 38 677 695 the current paper continues this theme applying it to a single subject functional magnetic resonance imaging fmri study of the auditory system we show that spatial priors on functional activations based on diffusion can be formulated in terms of the eigenmodes of a graph laplacian this allows one to discard eigenmodes with small eigenvalues to provide a computationally efficient scheme furthermore this formulation shows that diffusion based priors are a generalization of conventional laplacian priors penny w d trujillo barreto n j friston k j 2005 bayesian fmri time series analysis with spatial priors neuroimage 24 350 362 finally we show how diffusion based priors are a special case of gaussian process models that can be inverted using classical covariance component estimation techniques like restricted maximum likelihood patterson h d thompson r 1974 maximum likelihood estimation of components of variance paper presented at 8th international biometrics conference constanta romania the convention in spm is to smooth data with a fixed isotropic gaussian kernel before inverting a mass univariate statistical model this entails the strong assumption that data are generated smoothly throughout the brain however there is no way to determine if this assumption is supported by the data because data are smoothed before statistical modeling in contrast if a spatial prior is used smoothness is estimated given non smoothed data explicit spatial priors enable formal model comparison of different prior assumptions e g that data are generated from a stationary i e fixed throughout the brain or non stationary spatial process indeed for the auditory data we provide strong evidence for a non stationary process which concurs with a qualitative comparison of predicted activations at the boundary of functionally selective regions

numerical computation of the incomplete lipschitz hankel integral je o a z abstract two factorial neumann series expansions are derived for the incomplete lipschitz hankel integral je 0 a z these expansions are used together with the neumann series expansion given by agrest in an algorithm which efficiently computes je 0 a z to a user defined number of significant digits other expansions for je 0 a z which are found in the literature are also discussed but these expansions are found to offer no significant computational advantages when compared with the expansions used in the algorithm

network oriented dyadic time domain green s function for a sequentially excited infinite planar array of dipoles in free space during the past few years we have performed an effective wideband analysis for characterizing the electrodynamic behavior of phased array antennas infinite periodic structures frequency selective surfaces and related applications with emphasis on gaining physical insight into the phenomenology of short pulse radiation the present contribution shows the current status of our network oriented dyadic time domain green s function td gf for a planar array of sequentially excited dipoles that constitutes a prototype study of sequentially short pulsed radiation by infinite periodic arrays the dispersive effects of the td floquet waves fw and the consequences of a te and tm field decomposition are discussed in details in this network formulation the equivalent td transmission line tl voltages and currents excited by equivalent td current generators are determined an expression for the tm voltage tl gf is provided for the first time in terms of incomplete lipschitz hankel integrals and bessel functions together with some remarks for its evaluation as shown in previous publications for the scalar potentials real td physical observables are determined by pairing td floquet waves with positive and negative indices it is shown that the vectorial td radiated field is reconstructed at any time with the superposition of a few td fws

time harmonic and transient scattering by finite periodic flat strip arrays hybrid ray floquet mode mom algorithm a frequency and short pulse sp time domain td study of two dimensional plane wave scattering from a finite periodic array of thin flat coplanar perfectly conducting strips is presented rigorous analytical numerical reference solutions are established by spatial spectral wave number decomposition and the method of moments mom followed by frequency inversion the analytical portion is approximated so as to yield via high frequency asymptotics for a sufficiently large number of strips a hybrid ray floquet mode mom algorithm that not only explains the phenomena in physical terms but is also numerically efficient and reasonably accurate when compared with the reference solution of special interest are the td floquet modes with their space time dependent frequencies and wave numbers by superposition they can synthesize the highly resolved pulse train return under sp conditions attention is given also to direct sp td synthesis and to processing options for sp td data

new solutions of the yang baxter equation based on root of 1 representations of the para bose superalgebra new solutions of the quantum yang baxter equation depending in general on three arbitrary parameters are written down they are based on the root of unity representations of the quantum orthosymplectic superalgebra which were found recently representations of the braid group are defined within any nth tensorial power of root of 1 modules

a truncated floquet wave diffraction method for the full wave analysis of large phased arrays i basic principles and 2 d cases this two part sequence deals with the formulation of an efficient method for the full wave analysis of large phased array antennas this is based on the method of moments mom solution of a fringe integral equation ie in which the unknown function is the difference between the exact solution of the finite array and that of the associated infinite array the unknown currents can be interpreted as produced by the field diffracted at the array edge which is excited by the floquet waves fws pertinent to the infinite configuration following this physical interpretation the unknown in the ie is efficiently represented by a very small number of basis functions with domain on the entire array aperture in order to illustrate the basic concepts the first part of this sequence deals with the two dimensional example of a linearly phased slit array it is shown that the dominant phenomenon fur describing the current perturbation with respect to the infinite array is accurately represented in most cases by only three diffracted ray shaped unknown functions this also permits a simple interpretation of the element by element current oscillation which was described by other authors

combining spatial extent and peak intensity to test for activations in functional imaging within the framework of statistical mapping there are up to now only two tests used to assess the regional significance in functional images one is based on the magnitude of the foci and tends to detect high intensity signals while the second is based on the spatial extent of regions defined by a simple thresholding of the statistical map a test that is more sensitive to extended signals the aim of this paper is to combine the two tests into a single test that is more sensitive to a wider range of signals this combined test is based on an analytical approximation of the distribution of these two parameters size and height and is applied in the context of statistical maps the risk of error in noise only 2d or 3d volumes is assessed under a wide range of experimental conditions obtained by varying both the resolution of the map and the threshold at which clusters are defined in addition we have investigated this new test on simulated signals and applied it to an experimental pet dataset the experimental risk of error is close to the predicted one and the overall sensitivity increases when analyzing a volume containing different types of signals

periodicity induced generalized fourier transform pair the field radiated by an infinite periodic structure can be expressed in terms of floquet waves fws both in the frequency domain fd and time domain td see felsen l b and capolino f ieee trans antennas propagat vol 48 p 921 31 2000 a new periodicity induced generalized fourier transform ft pair is derived relating fd fws to td fws and vice versa based on tabulated transforms and physical conditions at infinity the new fts are directly related to the simple canonical problem of a line array of sequentially excited dipoles that is a basic building block for more general phased periodic structures

scale space spatio temporal random fields spatio temporal statistical models have been receiving increasing attention in a variety of image processing applications notably for detecting noisy patterns or shapes during their temporal evolutions space time models are however still limited to detect accurately spatio temporal patterns of multiresolution properties to this end the present paper addresses the detection of spatio temporal patterns from multitemporal images at multiple scales we propose a new stochastic model that incorporates scale space and space time models based on random fields specifically a scale space spatio temporal gaussian random field thereby a statistical test to assess the null hypothesis noise only is computed by the expected euler characteristic ec approach a validation of our approach is investigated on synthetic examples using one dimensional signals then a real application is carried out for detection of growing microorganisms from surface roughness acquired at multiple time points based on the detection results microbial colonies are thereafter discriminated through their scale and growth evolution the results show the possibility of investigating robust and complete analysis in the context of precocious pattern detection highlightsspatio temporal statistical modelling of surface roughness acquired at multiple time points scale space analysis of multitemporal surface measurements statistical threshold based on scale space spatio temporal random field model detection of spatiotemporal patterns of unknown scales discrimination of spatiotemporal patterns based on the growth evolution

penalized discriminant analysis of sup 15 o water pet brain images with prediction error selection of smoothness and regularization hyperparameters the authors propose a flexible comprehensive approach for analysis of sup 15 o water positron emission tomography pet brain images using a penalized version of linear discriminant analysis pda they applied it to scans from 20 subjects eight scans subject performing a finger movement task and analyzed 1 two classes to obtain a covariance normalized baseline activation image and 2 eight classes for the mean within subject temporal structure which contained baseline activation and time dependent changes in a two dimensional canonical subspace the authors imposed spatial smoothness on the resulting image s by expanding it in five tensor product b spline tps bases of varying smoothness and further regularized with a ridge type penalty on the noise covariance matrix the discrimination approach of pda provides a probabilistic framework within which prediction error pe estimates are derived the authors used these to optimize over tps bases and a ridge hyperparameter expressed as equivalent degrees of freedom edf they obtained unbiased low variance pe estimates using modern resampling tools 632 bootstrap and cross validation and compared pda of 1 tps projected mean normalized and unnormalized scans and 2 mean normalized scans with and without additional presmoothing by examining the tradeoffs between pe and edf as a function of basis selection and image smoothing the authors demonstrate the utility of pda the pe framework and the relationship between singular value decomposition and smooth tps bases in the analysis of functional neuroimages

a conservative test for multiple comparison based on highly correlated test statistics in genetics we often encounter a large number of highly correlated test statistics the most famous conservative bound for multiple comparison is bonferroni s bound which is suitable when the test statistics are independent but not when the test statistics are highly correlated this article proposes a new conservative bound that is easily calculated without multiple integration and is a good approximation when the test statistics are highly correlated the performance of the proposed method is evaluated by simulation and real data analysis

an accurate and efficient analysis for transient plane waves obliquely incident on a conductive half space te case we develop a method for the analytical evaluation of the inverse laplace transform representations for transient transverse magnetic tm plane wave obliquely incident on a conductive half space we assume that the permittivity and conductivity of the dispersive half space are independent of frequency the time domain expressions for the reflected and transmitted waves are first represented as inverse laplace transforms the transient fields are then shown to consist of two canonical integrals the canonical integrals in turn are solved analytically thereby yielding close form solutions involving incomplete lipschitz hankel integrals ilhis the ilhis are computed numerically using efficient convergent and asymptotic series expansions thus enabling the efficient computation of the transient fields the exact closed form expressions are verified by comparing with previously published results and with results obtained using standard numerical integration and fast fourier transform fft algorithms an asymptotic series representation for the ilhis is also employed to obtain a relatively simple late time approximation for the transient fields this approximate late time expression is shown to accurately model the fields over a large portion of its time history

universal r matrices and invariants of quantum supergroups a general method is developed for constructing invariants of quantum supergroups using universal r matrices applied to uq gl 2 1 this method yields the invariants of this quantum supergroup in explicit form the eigenvalues of these invariants in arbitrary irreducible highest weight representations are computed

graded representations of the temperley lieb algebra quantum supergroups and the jones polynomial it is shown that from each self dual representation of a quantum supergroup with nonvanishing q superdimension a graded representation of the temperley lieb algebra can be constructed which in turn gives rise to a solution of the graded yang baxter equation as examples the vector irrep of uq osp m 2n and all the finite dimensional irreps of uq osp 1 2 are studied and the corresponding graded matrices are obtained explicitly a general method is also given to obtain link polynomials from graded matrices applied to the ones associated with graded representations of the temperley lieb algebra the method yields the jones polynomial

complex time representation of the sommerfeld type integrals and its application to 1 d periodic structures the concept of complex time is employed to derive the time domain representation of the green s function of a periodic structure for the first time the spatial domain green s function of the periodic structure in the frequency domain is separated into singular and nonsingular terms the nonsingular terms are approximated by using exponential functions resulting in the well known complex time representation of the time domain green s function in order to find a closed form expression for the singular terms a novel time domain representation of the sommerfeld type integrals is derived the proposed procedure is applied to the computation of the time domain green s function of a one dimensional periodic structure numerical experiments demonstrate the high accuracy of this method

structure and representations of the quantum general linear supergroup the structure and representations of the quantum general linear supergroup gl q m n are studied systematically by investigating the hopf superalgebra g q of its representative functions g q is factorized into g q pi g q bar pi and a peter weyl basis is constructed for each factor parabolic induction for the quantum supergroup is developed the underlying geometry of induced representations is discussed and an analog of frobenius reciprocity is obtained a quantum borel weil theorem is proven for the irreducible covariant and contravariant tensorial representations and explicit realizations are given for classes of irredducible tensorial representatins in terms of sections of quantum super vector bundles over quantum projective superspaces

analytic properties and covariance functions for a new class of generalized gibbs random fields spartan spatial random fields ssrfs are generalized gibbs random fields equipped with a coarse graining kernel that acts as a low pass filter for the fluctuations ssrfs are defined by means of physically motivated spatial interactions and a small set of free parameters interaction couplings this paper focuses on the fluctuation gradient curvature fgc ssrf model henceforth referred to as fgc ssrf this model is defined on the euclidean space r by means of interactions proportional to the squares of the field realizations as well as their gradient and curvature the permissibility criteria of fgc ssrfs are extended by considering the impact of a finite bandwidth kernel it is proved that the fgc ssrfs are almost surely differentiable in the case of finite bandwidth asymptotic explicit expressions for the spartan covariance function are derived for d 1 and d 3 both known and new covariance functions are obtained depending on the value of the fgc ssrf shape parameter nonlinear dependence of the covariance integral scale on the fgc ssrf characteristic length is established and it is shown that the relation becomes linear asymptotically the results presented in this paper are useful in random field parameter inference and in spatial interpolation of irregularly spaced samples

analysis of the rayleigh pulse seismologists make frequent use of wavelets also referred to as signals signatures or pulses particularly in such fields as seismic filtering wavelet processing wave propagation modeling and trace inversion whenever possible the actual seismic wavelet of the real source should be considered hosken 1988 however frequently particularly in wave propagation modeling one must consider a synthetic source wavelet this should if possible be given by a simple mathematical formula and possess an easy description for its most important spectral properties e g amplitude and phase spectrum main frequency hilbert transform etc moreover the mathematical expression should be such that with a minimum number of parameters a large flexibility in the form of the wavelet can be obtained

twisting invariance of link polynomials derived from ribbon quasi hopf algebras the construction of link polynomials associated with finite dimensional representations of ribbon quasi hopf algebras is discussed in terms of the formulation of an appropriate markov trace we then show that this markov trace is invariant under twisting of the quasi hopf structure which in turn implies twisting invariance of the associated link polynomials

weighted fourier series representation and its application to quantifying the amount of gray matter we present a novel weighted fourier series wfs representation for cortical surfaces the wfs representation is a data smoothing technique that provides the explicit smooth functional estimation of unknown cortical boundary as a linear combination of basis functions the basic properties of the representation are investigated in connection with a self adjoint partial differential equation and the traditional spherical harmonic spharm representation to reduce steep computational requirements a new iterative residual fitting irf algorithm is developed its computational and numerical implementation issues are discussed in detail the computer codes are also available at http www stat wisc edu mchung softwares weighted spharm weighted spharm html as an illustration the wfs is applied in quantifying the amount of gray matter in a group of high functioning autistic subjects within the wfs framework cortical thickness and gray matter density are computed and compared

solutions of the graded classical yang baxter equation and integrable models linear superalgebraic equations giving rise to solutions of the graded classical yang baxter equation are developed and solved explicitly the connection of these equations with the theory of lie bi superalgebras is pointed out and the possibility of using the solutions of the graded classical yang baxter equation to construct integrable supersymmetric models is discussed

rotation space random fields with an application to fmri data siegmund and worsley considered the problem of testing for a signal with unknown location and scale in a gaussian random field defined on r n the test statistic was the maximum of a gaussian random field in an n 1 dimensional scale space n dimensions for location and one dimension for the scale of a smoothing kernel siegmund and worsley used two methods one involving the expected euler characteristic of the excursion set and the other involving the volume of tubes to derive an approximate null distribution the purpose of this paper is to extend the scale space result to the rotation space random field when n 2 where the maximum is taken over all rotations of the filter as well as scales we apply this result to the problem of searching for activation in brain images obtained by functional magnetic resonance imaging fmri

multiparameter link invariants from quantum supergroups a method is developed for constructing multiparameter link invariants for a class of representations of the quantum supergroups uq gl m n the cases uq gl 1 1 and uq gl 2 1 are studied in detail in the former we obtain a multiparameter generalization of the alexander conway invariants

universal l operator and invariants of the quantum supergroup uq gl m n a spectral parameter dependent solution of the graded yang baxter equation is obtained which is universal in the sense that it lives in uq gl m n end v with v the vector module of uq gl m n the invariants of this quantum supergroup are constructed using this solution

a q superdimension formula for irreps of type i quantum superalgebras we derive a closed formula for the q superdimensions of a wide class of irreps including all unitary irreps of the type i quantum superalgebras

estimating the number of peaks in a random field using the hadwiger characteristic of excursion sets with applications to medical images excursion sets has been studied by adler who defined the ig integral geometry characteristic of excursion sets as a multidimensional analogue of the number of upcrossings of the threshold by a unidimensional process the ig characteristic equals the euler characteristic of an excursion set provided that the set does not touch the boundary of the volume and adler found the expected ig characteristic for a stationary random field inside a fixed volume worsley evans marrett and neelin used the ig characteristic as an estimator of the number of regions of activation of positron emission tomography pet images of blood flow in the brain unfortunately the ig characteristic is only defined on intervals it is not invariant under rotations and it can fail to count connected regions that touch the boundary this is important since activation often occurs in the cortical regions near the boundary of the brain in this paper we study the hadwiger characteristic which is defined on arbitrary sets is invariant under rotations and does count connected regions whether they touch the boundary or not our main result is a simple expression for the expected hadwiger characteristic for an isotropic stationary random field in two and three dimensions and on a smooth surface embedded in three dimensions results are applied to pet studies of pain perception and word recognition

frequency and time domain green s functions for a phased semi infinite periodic line array of dipoles we extend a previous prototype study of felsen and capolino see ibid vol 48 p 921 931 june 2000 of frequency domain fd and time domain td green s functions for an infinite periodic phased line array of dipoles to account for the effects of truncation as modeled by a semi infinite array these canonical problems are to be used eventually for the systematic analysis and synthesis of actual rectangular td plane phased arrays in the presentation we rely on the analytic results and phenomenologies pertaining to the infinite array which are reviewed major emphasis is then placed on the modifications introduced by the truncation finite poisson summation is used to convert the individual dipole radiations into collective truncated wavefields the fd and td floquet waves fw in the td exact closed form solutions are obtained and are examined asymptotically to extract fd and td periodicity matched conical truncated fw fields both propagating and nonpropagating corresponding tip diffracted periodicity matched spherical waves and uniform transition functions connecting both across the fd and td fw truncation boundaries these new effects can again be incorporated in a fw modulated geometrical theory of diffraction a numerical example of radiation from a finite phased td dipole array with band limited excitation demonstrates the accuracy and efficiency of the fw diffracted field asymptotic algorithm when compared with an element by element summation reference solution

hermite rodriguez uwb circular arrays pulsed circular arrays are collecting growing interest in radar applications such as automotives and indoor navigations this contribution presents the analytic derivation of the space time and energy patterns of pulsed circular arrays in terms of geometrical and electrical parameters as well as of the signal distortion produced by the antennas response it is shown that the field emitted by circular arrays with many elements can be represented as a summation of a practically finite set of high order hermite rodriguez waveforms while the energy pattern is a generalized hypergeometric function the angular and temporal resolutions are finally related through handy formulas to the array size the input signals and to the antenna types

quantum group invariants and link polynomials a general method is developed for constructing quantum group invariants and determining their eigenvalues applied to the universal matrix this method leads to the construction of a closed formula for link polynomials to illustrate the application of this formula the quantum groups uq es uq so 2m 1 and uq gl m are considered as examples and corresponding link polynomials are obtained

time domain weyl s identity and the causality trick based formulation of the time domain periodic green s function time domain floquet modes for analyzing scattering radiation from periodically arranged planar scatterers sources have been presented recently in a series of papers by felsen and capolino in these papers they have investigated phenomenological details of transient scattering radiation by such structures typically time domain floquet modes are derived either by fourier transforming their frequency domain counterparts or using spatial synthesis using poisson summation this paper proposes an alternative means to develop similar expressions and is motivated by the possibility of easily extending the method to the analysis of periodic structures in a layered medium as will be shown the time domain weyl s identity can be used to construct the periodic green s function using both homogeneous and inhomogeneous plane waves we will also derive expressions using the causality trick this technique involves using time symmetric non causal signals however it yields much simpler expressions that involve only homogeneous time domain plane waves and the results are identical to those obtained using the time domain weyl s identity for the time region of interest finally we will use the whittaker formulation which relies on real signals to derive time domain floquet modes this formulation is applicable for simultaneous excitation only

euler characteristics for gaussian fields on manifolds we are interested in the geometric properties of real valued gaussian random fields defined on manifolds our manifolds m are of class c3 and the random fields f are smooth our interest in these fields focuses on their excursion sets f 1 u and their geometric properties specifically we derive the expected euler characteristic ee f 1 u of an excursion set of a smooth gaussian random field part of the motivation for this comes from the fact that ee f 1 u relates global properties of m to a geometry related to the covariance structure of f of further interest is the relation between the expected euler characteristic of an excursion set above a level u and pp supp mf p u our proofs rely on results from random fields on rrn as well as differential and riemannian geometry