on the curvature of piecewise flat spaces we consider analogs of the lipschitz killing curvatures of smooth riemannian manifolds for piecewise flat spaces in the special case of scalar curvature the definition is due to t regge considerations in this spirit date back to j steiner we show that if a piecewise flat space approximates a smooth space in a suitable sense then the corresponding curvatures are close in the sense of measures

correlations between zeros of a random polynomial we obtain exact analytical expressions for correlations between real zeros of the kac random polynomial we show that the zeros in the interval 1 1 are asymptotically independent of the zeros outside of this interval and that the straightened zeros have the same limit translation invariant correlations then we calculate the correlations between the straightened zeros of theo 1 random polynomial

universal fluctuations of zeros of chaotic wavefunctions wavefunctions of one and two dimensional quantum systems can be parametrized by a finite number of zeros lying in phase space we study correlations of these zeros for fully chaotic systems in terms of a statistical model based on random polynomials excellent agreement is found for the two point correlation function and nearest neighbour spacing distribution of this model and the results obtained for wavefunctions of dynamical systems we conjecture that these correlation functions are valid for any chaotic system after rescaling the phase space distances unfolding some consequences for the distribution of zeros due to time reversal symmetry are also discussed

nonstationary cluster size inference with random field and permutation methods because of their increased sensitivity to spatially extended signals cluster size tests are widely used to detect changes and activations in brain images however when images are nonstationary the cluster size distribution varies depending on local smoothness clusters tend to be large in smooth regions resulting in increased false positives while in rough regions clusters tend to be small resulting in decreased sensitivity worsley et al proposed a random field theory rft method that adjusts cluster sizes according to local roughness of images worsley k j 2002 nonstationary fwhm and its effect on statistical inference of fmri data presented at the 8th international conference on functional mapping of the human brain june 2 6 2002 sendai japan available on cd rom in neuroimage 16 2 779 780 hum brain mapp 8 1999 98 in this paper we implement this method in a permutation test framework which requires very few assumptions is known to be exact j cereb blood flow metab 16 1996 7 and is robust neuroimage 20 2003 2343 we compared our method to stationary permutation stationary rft and nonstationary rft methods using simulated data we found that our permutation test performs well under any setting examined whereas the nonstationary rft test performs well only for smooth images under high df we also found that the stationary rft test becomes anticonservative under nonstationarity while both nonstationary rft and permutation tests remain valid under nonstationarity on a real pet data set we found that though the nonstationary tests have reduced sensitivity due to smoothness estimation variability these tests have better sensitivity for clusters in rough regions compared to stationary cluster size tests we include a detailed and consolidated description of worsley nonstationary rft cluster size test

the derivatives of homotopy theory we construct a functor of spaces mn and show that its multilinearization is equivalent to the nth layer of the taylor tower of the identity functor of spaces this allows us to identify the derivatives of the identity functor and determine their homotopy type the calculus of homotopy functors developed by goodwillie gi g2 g3 establishes that a homotopy functor f satisfying certain connectivity conditions has associated to it a tower of functors pf pn f these functors act like a taylor series approximation to f in the sense that for a space x there is a map pnf x f x k pnf x for each n and the connectivity of this map increases with n this theory has been applied to the study of the functor a waldhausen s algebraic k theory of spaces in this paper we turn our attention to the taylor tower of the identity functor of spaces i the ultimate goal is to identify the taylor tower of i and use it to study homotopy theory in this paper we construct a collection of symmetric functors mn and show that the multilinearization of mn is equivalent to the nth layer fiber pni pn i of the taylor tower of i this construction also allows us to identify the nth derivative of i this is a spectrum with l action which is equivalent to the functor fiber pni k pni the paper is organized as follows in section 1 we summarize the basic results and terminology of calculus that will be used throughout the paper in section 2 we describe the problem of finding the taylor tower of i in more detail and state the main results in section 3 we outline the method by which the nth derivative of a functor is determined in section 4 we construct the functor mn and a natural transformation tn used to establish the equivalence between the multilinearization of mn and fiber pnf pnf in section 5 we determine the homotopy type of the derivatives and in section 6 we show that t is sufficiertly connected to induce an equivalence between the multilinearization of mn and fiber p f pif l the results in this paper come from the author s thesis written uncler the direction of tom goodwillie at brown university the author wishes to thank him for his guidance and for many insightful discussions the author alsq wishes to thank randy mccarthy for his helpful suggestions during the writing of this paper received by the editors february 10 1994 1991 mathematics subject clqssification primary 55p65 1995 american mathematical society 0002 9947 95 1 00 25 per page

statistical analyses of brain surfaces using gaussian random fields on 2 d manifolds interest in the morphometric analysis of the brain and its subregions has recently intensified because growth or degeneration of the brain in health or illness affects not only the volume but also the shape of cortical and subcortical brain regions and new image processing techniques permit detection of small and highly localized perturbations in shape or localized volume with remarkable precision an appropriate statistical representation of the shape of a brain region is essential however for detecting localizing and interpreting variability in its surface contour and for identifying differences in volume of the underlying tissue that produce that variability across individuals and groups of individuals our statistical representation of the shape of a brain region is defined by a reference region for that region and by a gaussian random field grf that is defined across the entire surface of the region we first select a reference region from a set of segmented brain images of healthy individuals the grf is then estimated as the signed euclidean distances between points on the surface of the reference region and the corresponding points on the corresponding region in images of brains that have been coregistered to the reference correspondences between points on these surfaces are defined through deformations of each region of a brain into the coordinate space of the reference region using the principles of fluid dynamics the warped coregistered region of each subject is then unwarped into its native space simultaneously bringing into that space the map of corresponding points that was established when the surfaces of the subject and reference regions were tightly coregistered the proposed statistical description of the shape of surface contours makes no assumptions other than smoothness about the shape of the region or its grf the description also allows for the detection and localization of statistically significant differences in the shapes of the surfaces across groups of subjects at both a fine and coarse scale we demonstrate the effectiveness of these statistical methods by applying them to study differences in shape of the amygdala and hippocampus in a large sample of normal subjects and in subjects with attention deficit hyperactivity disorder adhd

chaos revealing multiplicative representation of quantum eigenstates the quantisation of the two dimensional toric and spherical phase spaces is considered in analytic coherent state representations every pure quantum state admits therein a finite multiplicative parametrisation by the zeros of its husimi function for eigenstates of quantised systems this description explicitly reflects the nature of the underlying classical dynamics in the semiclassical regime the distribution of the zeros in the phase space becomes one dimensional for integrable systems and highly spread out conceivably uniform for chaotic systems this multiplicative representation thereby acquires a special relevance for semiclassical analysis in chaotic systems

the triple rotation method for constructing t norms given an involutive negator n and a left continuous t norm t that either has no zero divisors or is rotation invariant we build a rotation invariant t norm from a rescaled version of t and its left right and front rotation depending on the involutive negator n and the set of zero divisors of t some reshaping of the rescaled version of t may occur during the rotation process the rescaled version of t itself can be understood as the b zoom of the newly constructed rotation invariant t norm with b the unique fixpoint of n starting with a rotation invariant t norm t there is however one important restriction the triple rotation method based on the involutive negator n will yield a t norm if and only if the companion q of t is commutative on 0 1 2 when q is not commutative on 0 1 2 there even does not exist a rotation invariant t norm with b zoom equal to t

nirs spm statistical parametric mapping for near infrared spectroscopy near infrared spectroscopy nirs is a non invasive method to measure brain activity via changes in the degree of hemoglobin oxygenation through the intact skull as optically measured hemoglobin signals strongly correlate with bold signals simultaneous measurement using nirs and fmri promises a significant mutual enhancement of temporal and spatial resolutions although there exists a powerful statistical parametric mapping tool in fmri current public domain statistical tools for nirs have several limitations related to the quantitative analysis of simultaneous recording studies with fmri in this paper a new public domain statistical toolbox known as nirs spm is described it enables the quantitative analysis of nirs signal more specifically nirs data are statistically analyzed based on the general linear model glm and sun s tube formula the p values are calculated as the excursion probability of an inhomogeneous random field on a representation manifold that is dependent on the structure of the error covariance matrix and the interpolating kernels nirs spm not only enables the calculation of activation maps of oxy deoxy hemoglobin and total hemoglobin but also allows for the super resolution localization which is not possible using conventional analysis tools extensive experimental results using finger tapping and memory tasks confirm the viability of the proposed method

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

on fuzzy type theory this paper is a generalization of classical simple type theory we have developed a formal system of fuzzy type theory which differs from the classical one essentially in extension of truth values from two to infinitely many the structure of truth values is assumed to be an imtl algebra residuated lattice with prelinearity and double negation extended by the baaz delta operation various properties of fuzzy type theory are proved including its completeness

distribution of zeros of random and quantum chaotic sections of positive line bundles we study the limit distribution of zeros of certain sequences of holomorphic sections of high powers m n of a positive holomorphic hermitian line bundle l over a compact complex manifold m our first result concerns random sequences of sections using the natural probability measure on the space of sequences of orthonormal bases s n j of h 0 m l n we show that for almost every sequence s n j the associated sequence of zero currents 1 n z s n j tends to the curvature form of l thus the zeros of a sequence of sections s n h 0 m l n chosen independently and at random become uniformly distributed our second result concerns the zeros of quantum ergodic eigenfunctions where the relevant orthonormal bases s n j of h 0 m l n consist of eigensections of a quantum ergodic map we show that also in this case the zeros become uniformly distributed

simplicial structures on model categories and functors we produce a highly structured way of associating a simplicial category to a model category which improves on work of dwyer and kan and answers a question of hovey we show that model categories satisfying a certain axiom are quillen equivalent to simplicial model categories a simplicial model category provides higher order structure such as composable mapping spaces and homotopy colimits we also show that certain homotopy invariant functors can be replaced by weakly equivalent simplicial or continuous functors this is used to show that if a simplicial model category structure exists on a model category then it is unique up to simplicial quillen equivalence

conic aggregation functions inspired by the notion of conic t norms we introduce conic aggregation functions such aggregation functions are completely characterized by their zero set special classes of binary conic aggregation functions such as conic quasi copulas and conic copulas are considered we provide the necessary and sufficient conditions on the boundary curve of the zero set of a conic aggregation function to obtain a conic quasi copula and conclude that the class of conic copulas is a proper subclass of the class of conic quasi copulas moreover we characterize the class of singular conic copulas we investigate some aggregations of conic quasi copulas some examples are also provided

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

phase space approach to quantum dynamics replaces the schrodinger equation for the time propagation of states of a quantized 2d spherical phase space by the dynamics of a system of n particles lying in phase space this is done through factorization formulae of an analytic function theory arising in a coherent state representation the particles being the zeroes of the quantum state for linear hamiltonians like a spin in a uniform magnetic field the motion of the particles is classical however nonlinear terms induce interactions between the particles their time propagation is studied and it is shown that contrary to integrable systems for chaotic maps they tend to fill as their classical counterpart the whole phase space in a uniform way

poincare lelong approach to universality and scaling of correlations between zeros this note is concerned with the scaling limit as n of n point correlations between zeros of random holomorphic polynomials of degree n in m variables more generally we study correlations between zeros of holomorphic sections of powers ln of any positive holomorphic line bundle l over a compact kahler manifold distances are rescaled so that the average density of zeros is independent of n our main result is that the scaling limits of the correlation functions and more generally of the correlation forms are universal i e independent of the bundle l manifold m or point on m

chaotic analytic zero points exact statistics for those of a random spin state a natural statistical ensemble of 2j points on the unit sphere can be associated via the majorana representation with a random quantum state of spin j and an exact expression is obtained here for the general k point correlation function in this ensemble the pair correlation in the large j limit takes the relatively simple form where and is the angular separation of the pair of points on the sphere it appears from the numerical work of others that in this limit these statistics are typical of the zero points of analytic functions associated with chaotic quantum dynamical systems

distribution of roots of random polynomials we consider polynomials of high degree with random coefficients which appear in the context of quantum chaotic dynamics and investigate various conditions under which their roots tend to concentrate near the unit circle in the complex plane correlation functions of roots are computed analytically we also investigate a certain class of random polynomials whose roots cover in a uniform way the riemann sphere special emphasis is devoted to the influence of symmmetries

an improved theoretical p value for spms based on discrete local maxima abstract we present a new continuity correction to the p value for local maxima of a statistical parametric map that bridges the gap between small fwhm when the bonferroni correction is accurate and large fwhm when random field theory is accurate the new method based on discrete local maxima is always an upper bound like the bonferroni but lower and hence more accurate for large fwhm without increasing false positives it resulted in p values that were 43 lower than the best of bonferroni or random field theory methods when applied to a typical fmri data set

triangular norms position paper i basic analytical and algebraic properties we present the basic analytical and algebraic properties of triangular norms we discuss continuity as well as the important classes of archimedean strict and nilpotent t norms triangular conorms and de morgan triples are also mentioned finally a brief historical survey on triangular norms is given

the goodwillie tower of the identity functor and the unstable periodic homotopy of spheres we investigate goodwillie s taylor tower of the identity functor from spaces to spaces more specifically we reformulate johnson s description of the goodwillie derivatives of the identity and prove that in the case of an odd dimensional sphere the only layers in the tower that are not contractible are those indexed by powers of a prime moreover in the case of a sphere the tower is finite in v k periodic homotopy

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

generalizations to the constructions of t norms rotation annihilation construction in this paper the constructions of triangular norms are investigated specially based on weak negations which are not necessarily involutive the rotation and the rotation annihilation constructions are extended by means of these methods we can get new families of left continuous t norms compatible with weak negations given however not all weak negations are suitable for those generalized constructions to highlight it some counterexamples are given

generalized continuous and left continuous t norms arising from algebraic semantics for fuzzy logics this paper focuses on the issue of how generalizations of continuous and left continuous t norms over linearly ordered sets should be from a logical point of view taking into account recent results in the scope of algebraic semantics for fuzzy logics over chains with a monoidal residuated operation we advocate linearly ordered bl algebras and mtl algebras as adequate generalizations of continuous and left continuous t norms respectively in both cases the underlying basic structure is that of linearly ordered residuated lattices although the residuation property is equivalent to left continuity in t norms continuous t norms have received much more attention due to their simpler structure we review their complete description in terms of ordinal sums and discuss the problem of describing the structure of their generalization to bl chains in particular we show the good behavior of bl algebras over a finite or complete chain and discuss the partial knowledge of rational bl chains then we move to the general non continuous case corresponding to left continuous t norms and mtl chains the unsolved problem of describing the structure of left continuous t norms is presented together with a fistful of construction decomposition techniques that apply to some distinguished families of t norms and finally we discuss the situation in the general study of mtl chains as a natural generalization of left continuous t norms

classical wave experiments on chaotic scattering we review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves inasmuch as these experiments use antennas or transducers to couple waves into or out of the systems scattering theory has to be applied for a quantitative interpretation of the measurements most experiments concentrate on tests of predictions from random matrix theory and the random plane wave approximation in all studied examples a quantitative agreement between experiment and theory is achieved to this end it is necessary however to take absorption and imperfect coupling into account concepts that were ignored in most previous theoretical investigations classical phase space signatures of scattering are being examined in a small number of experiments

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

rotation invariant t norms where triple rotation and rotation annihilation meet generalizing the notion of a zoom of a t norm not only allows to extend the triple rotation method and its corresponding decomposition but also allows to describe the interface between the triple rotation method and the rotation annihilation method an alternative view on the partition behind the rotation annihilation method is required to make both methods compatible besides zooms we also use contour lines and the companion of a t norm to concisely formulate the results

van melle s combining function in mycin is a representable uninorm an alternative proof abstract recently tsadiras and margaritis have shown that the function implemented in the expert system mycin for combining certainty factors is a uninorm in this paper we present a compact alternative to the given direct and lengthy proof based on the construction of representable uninorms by means of an additive generator consequently we show that van melle s combining function is a representable uninorm in fact it is a rescaled version of the representable uninorm on the unit interval constructed from the algebraic product and the probabilistic sum

the detection of local shape changes via the geometry of hotelling s t 2 fields this paper is motivated by the problem of detecting local changes or differences in shape between two samples of objects via the nonlinear deformations required to map each object to an atlas standard local shape changes are then detected by high values of the random field of hotelling s t 2 statistics for detecting a change in mean of the vector deformations at each point in the object to control the null probability of detecting a local shape change we use the recent result of adler that the probability that a random field crosses a high threshold is very accurately approximated by the expected euler characteristic ec of the excursion set of the random field above the threshold we give an exact expression for the expected ec of a hotelling s t 2 field and we study the behavior of the field near local extrema this extends previous results for gaussian random fields by adler and x 2 t and f fields by worsley and cao for illustration these results are applied to the detection of differences in brain shape between a sample of 29 males and 23 females

equivariant stable homotopy and sullivan s conjecture let g be a p group and let x be a g complex let eg denote a contractible space on which g acts freely by the homotopy fixed point set of x we mean the fixed point set f eg x g where f eg x denotes the function space of all maps eg x equipped with a g action by 9f 9f9 1 if we let denote the one point space with trivial g action we may also consider the g space f x it is canonically g homeomorphic to x the g map e g induces a map x g f x g in 19 d sullivan proposed the following

distribution of nearest distances between nodal points for the berry function in two dimensions according to berry a wave chaotic state may be viewed as a superposition of monochromatic plane waves with random phases and amplitudes here we consider the distribution of nodal points associated with this state using the property that both the real and imaginary parts of the wave function are random gaussian fields we analyze the correlation function and densities of the nodal points using two approaches the poisson and bernoulli we derive the distribution of nearest neighbor separations furthermore the distribution functions for nodal points with specific chirality are found comparison is made with results from numerical calculations for the berry wave function

operadic multiplications in equivariant spectra norms and transfers we study homotopy coherent commutative multiplicative structures on equivariant spaces and spectra we define n operads equivariant generalizations of e operads algebras in equivariant spectra over an n operad model homotopically commutative equivariant ring spectra that only admit certain collections of hill hopkins ravenel norms determined by the operad analogously algebras in equivariant spaces over an n operad provide explicit constructions of certain transfers this characterization yields a conceptual explanation of the structure of equivariant infinite loop spaces to explain the relationship between norms transfers and n operads we discuss the general features of these operads linking their properties to families of finite sets with group actions and analyzing their behavior under norms and geometric fixed points a surprising consequence of our study is that in stark contract to the classical setting equivariantly the little disks and linear isometries operads for a general incomplete universe u need not determine the same algebras our work is motivated by the need to provide a framework to describe the flavors of commutativity seen in recent work of the second author and hopkins on localization of equivariant commutative ring spectra

saddles singularities and extrema in random phase fields four simple topological rules are derived that constrain the arrangement of critical points saddles singularities and extrema in a random phase field these rules relate the signs of the singularities to the nature of the extrema maxima or minima and the topology of the saddles once the latter is fixed only a single degree of freedom remains and if for example some extremum is chosen to be a maximum this choice automatically determines the nature of all other extrema and the signs of all singularities thus even in a random wave field there are extensive topologically mandated correlations between all critical points higher order gradient fields derived from the phase are considered and the rules and their induced correlations are shown to apply also to these fields other aspects of the phase field are discussed and it is shown for example that the number of saddles very nearly but not necessarily exactly equals the number of singularities plus the number of extrema and that during the evolution of the wave field large numbers of different specific features must appear simultaneously

spectral mackey functors and equivariant algebraic k theory i abstract spectral mackey functors are homotopy coherent versions of ordinary mackey functors as defined by dress we show that they can be described as excisive functors on a suitable category and we use this to show that universal examples of these objects are given by algebraic k theory more importantly we introduce the unfurling of certain families of waldhausen categories bound together with suitable adjoint pairs of functors this construction completely solves the homotopy coherence problem that arises when one wishes to study the algebraic k theory of such objects as spectral mackey functors finally we employ this technology to introduce fully functorial versions of a theory upside down a theory and the algebraic k theory of derived stacks we use this to give what we think is the first general construction of 1 et equivariant algebraic k theory for profinite etale fundamental groups this is key to our approach to the mackey functor case of a sequence of conjectures of gunnar carlsson

density and correlation functions of vortex and saddle points in open billiard systems we present microwave measurements for the density and spatial correlation of current critical points in an open billiard system and compare them with new and previous predictions of the random wave model rwm in particular due to an improvement of the experimental setup we determine experimentally the spatial correlation of saddle points of the current field an asymptotic expression for the vortex saddle and saddle saddle correlation functions based on the rwm is derived with experiment and theory agreeing well we also derive an expression for the density of saddle points in the presence of a straight boundary with general mixed boundary conditions in the rwm and compare with experimental measurements of the vortex and saddle density in the vicinity of a straight wall satisfying dirichlet conditions

statistics of nodal lines and points in chaotic quantum billiards perimeter corrections fluctuations curvature for real time reversal symmetric quantum billiards the mean length l of nodal line is calculated for the nth mode n 1 with wavenumber k using a gaussian random wave model adapted locally to satisfy dirichlet or neumann boundary conditions the leading term is of order k i e n and the first perimeter correction dominated by an unanticipated long range boundary effect is of order log k i e log n with the same sign negative for both boundary conditions the leading order state to state fluctuations l are of order log k for the curvature of nodal lines and 2 are of order k but 3 and higher moments diverge for complex e g aharonov bohm billiards the mean number n of nodal points phase singularities in the mode has a leading term of order k2 i e n the perimeter correction again a long range effect is of order klog k i e nlog n and positive notwithstanding nodal depletion near the boundary and the fluctuations n are of order k log k generalizations of the results for mixed robin boundary conditions are stated

the topology of spaces of knots cosimplicial models we present two models for the space of knots which have endpoints at fixed boundary points in a manifold with boundary one model defined as an inverse limit of spaces of maps between configuration spaces and another which is cosimplicial these models build on the calculus of isotopy functors and are weakly homotopy equivalent to knot spaces when the ambient dimension is greater than three the mapping space model and the evaluation map on which it builds is suitable for analysis through differential topology the cosimplicial model gives rise to spectral sequences which converge to ohomology and homotopy groups of spaces of knots when they are connected we explicitly identify and establish vanishing lines in these spectral sequences

screening of charged singularities of random fields many types of point singularity have a topological index or charge associated with them for example the phase of a complex field depending on two variables can either increase or decrease on making a clockwise circuit around a simple zero enabling the zeros to be assigned charges of 1 in random fields we can define a correlation function for the charge weighted density of singularities for many types of topologically charged singularity this correlation function satisfies an identity which shows that the singularities screen each other perfectly a positive singularity is surrounded by an excess of concentration of negatives which exactly cancel its charge and vice versa this paper gives a simple and widely applicable derivation of this result a counterexample where screening is incomplete is also exhibited

signed zeros of gaussian vector fields density correlation functions and curvature we calculate correlation functions of the signed density of zeros of gaussian distributed vector fields we are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract riemann cartan or riemannian manifold as an application we discuss one and two point functions the zeros of a two dimensional gaussian vector field model the distribution of topological defects in the high temperature phase of two dimensional systems with orientational degrees of freedom such as superfluid films thin superconductors and liquid crystals

statistics of nodal points of in plane random waves in elastic media we consider the nodal points nps u 0 and v 0 of the in plane vectorial displacements u u v which obey the navier cauchy equation similar to the berry conjecture of quantum chaos we present the in plane eigenstates of chaotic billiards as the real part of the superposition of longitudinal and transverse plane waves with random phases by an average over random phases we derive the mean density and correlation function of nps consequently we consider the distribution of the nearest distances between nps

universality and scaling of correlations between zeros on complex manifolds we study the limit as n of the correlations between simultaneous zeros of random sections of the powers l n of a positive holomorphic line bundle l over a compact complex manifold m when distances are rescaled so that the average density of zeros is independent of n we show that the limit correlation is independent of the line bundle and depends only on the dimension of m and the codimension of the zero sets we also provide some explicit formulas for pair correlations in particular we prove that hannay s limit pair correlation function for su 2 polynomials holds for all compact riemann surfaces

calculus of functors and model categories the category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure b chorny w g dwyer homotopy theory of small diagrams over large categories preprint 2005 in this paper we construct various localizations of the projective model structure and also give a variant for functors from simplicial sets to spectra we apply these model categories in the study of calculus of functors namely for a classification of polynomial and homogeneous functors in the n homogeneous model structure the nth derivative is a quillen functor to the category of spectra with sn action after taking into account only finitary functors which may be done in two different ways the above quillen map becomes a quillen equivalence this improves the classification of finitary homogeneous functors by t g goodwillie t g goodwillie calculus iii taylor series geom topol 7 2003 645 711 electronic

co rotation annihilations of residuated semigroups two new ways to construct involutive residuated semigroups are introduced in this paper namely connected and disconnected co rotation annihilations co rotation annihilations utilizes two particular kinds of residuated semigroups to construct a third one the method is suitable for constructing a large class of examples of negative rank involutive fl e algebras that is where the unit element of the algebra is smaller than the falsum constant which defines the involution in the algebra

tilted euler characteristic densities for central limit random fields with application to bubbles local increases in the mean of a random field are detected con servatively by thresholding a field of test statistics at a level u chosen to control the tail probability or p value of its maximum this p value is approximated by the expected euler characteristic ec of the ex cursion set of the test statistic field above u denoted e au under isotropy one can use the expansion e au p k vkk u where vk is an intrinsic volume of the parameter space andk is an ec density of the field ec densities are available for a number of pro cesses mainly those constructed from multivariate gaussian fields via smooth functions using saddlepoint methods we derive an ex pansion fork u for fields which are only approximately gaussian but for which higher order cumulants are available we focus on linear combinations of n independent non gaussian fields whence a central limit theorem is in force the threshold u is allowed to grow with the sample size n in which case our expression has a smaller relative asymptotic error than the gaussian ec density several illustrative examples including an application to bubbles data accompany the theory

the construction of left continuous t norms a geometric approach in two dimensions abstract each t norm can be identified with its cayley tomonoid which consists of pairwise commuting order preserving functions from the real unit interval to itself cayley tomonoids provide an easily manageable yet versatile tool for the construction of t norms to give evidence to this claim we review and reformulate several construction methods that are known in the literature we adopt on the one hand a geometric point of view manipulations with t norms have often been inspired by their three dimensional graphs by means of cayley tomonoids the process gains the character of putting together the pieces of a jigsaw puzzle we consider on the other hand construction methods in their algebraic context we show that those constructions that correspond to certain tomonoid extensions can be described on the basis of cayley tomonoids in a particularly transparent way

on the nonexistence of elements of kervaire invariant one we show that the kervaire invariant one elements j 2j 1 2s exist only for j 6 by browder s theorem this means that smooth framed manifolds of kervaire invariant one exist only in dimensions 2 6 14 30 62 and possibly 126 except for dimension 126 this resolves a longstanding problem in algebraic topology

real coextensions as a tool for constructing triangular norms we present in this paper a universal method of constructing left continuous triangular norms l c t norms the starting point is an arbitrary possibly finite totally ordered monoid fulfilling the conditions that are characteristic for l c t norms commutativity negativity and quanticity we show that under suitable conditions we can extend this structure by substituting each element for a real interval the process can be iterated and if the final structure obtained in this way is order isomorphic to a closed real interval its monoidal operation can up to isomorphism be identified with a l c t norm we specify the constituents needed for the construction in an explicit way we furthermore illustrate the method on the basis of a number of examples

co rotation constructions of residuated semigroups abstract a construction method called connected co rotation is introduced in this paper the precursor of its disconnected version has been introduced by r k meyer both co rotation constructions result in residuated semigroups among them non positive rank involutive fl e algebras these constructions can be considered as skew dual to their rotation counterparts those without the co syllable the classes of residuated semigroups for which the connected co rotation construction results in associative operations are characterized since the constructions are suitable to construct non positive rank involutive fl e algebras co rotations provide a better insight into the algebraic semantic of the substructural logic iul

associativity of triangular norms characterized by the geometry of their level sets associativity of triangular norms is an algebraic property which unlike for example their commutativity is usually understood as hardly visually interpretable this problem has been studied intensively in the last decade and as a result geometric symmetries of triangular norms with involutive level sets have been revealed the presented paper intends to introduce a different approach which gives more general results the inspiration is taken from web geometry a branch of differential geometry and its concept of reidemeister closure condition which is known to provide a geometric characterization of associativity of loops the paper shows that this concept can be adopted successfully for triangular norms so that it characterizes their associativity in a similar way moreover the offered adaptation preserves the beneficial transparency and simplicity of the reidemeister closure condition this way a visual characterization of the associativity based on the geometry of the level sets is provided for general continuous and continuous archimedean triangular norms

increasing power for voxel wise genome wide association studies the random field theory least square kernel machines and fast permutation procedures imaging traits are thought to have more direct links to genetic variation than diagnostic measures based on cognitive or clinical assessments and provide a powerful substrate to examine the influence of genetics on human brains although imaging genetics has attracted growing attention and interest most brain wide genome wide association studies focus on voxel wise single locus approaches without taking advantage of the spatial information in images or combining the effect of multiple genetic variants in this paper we present a fast implementation of voxel and cluster wise inferences based on the random field theory to fully use the spatial information in images the approach is combined with a multi locus model based on least square kernel machines to associate the joint effect of several single nucleotide polymorphisms snp with imaging traits a fast permutation procedure is also proposed which significantly reduces the number of permutations needed relative to the standard empirical method and provides accurate small p value estimates based on parametric tail approximation we explored the relation between 448 294 single nucleotide polymorphisms and 18 043 genes in 31 662 voxels of the entire brain across 740 elderly subjects from the alzheimer s disease neuroimaging initiative adni structural mri scans were analyzed using tensor based morphometry tbm to compute 3d maps of regional brain volume differences compared to an average template image based on healthy elderly subjects we find method to be more sensitive compared with voxel wise single locus approaches a number of genes were identified as having significant associations with volumetric changes the most associated gene was grin2b which encodes the n methyl d aspartate nmda glutamate receptor nr2b subunit and affects both the parietal and temporal lobes in human brains its role in alzheimer s disease has been widely acknowledged and studied suggesting the validity of the approach the various advantages over existing approaches indicate a great potential offered by this novel framework to detect genetic influences on human brains

analytic representations in quantum mechanics various euclidean hyperbolic and elliptic analytic representations are introduced and relations among them are discussed the bargmann analytic representation in the complex plane is considered and its relation to other phase space methods for the harmonic oscillator is reviewed the general theory that relates the growth of analytic functions with the density of their zeros is applied to bargmann functions and it leads to theorems on the completeness of sequences of glauber coherent states two hyperbolic analytic representations in the unit disc based on su 1 1 coherent states and also on phase states are introduced a third analytic representation in the complex plane based on barut girardello states is also considered and transformations which relate it to the other ones are studied in the case of systems with finite dimensional hilbert space an elliptic analytic representation in the extended complex plane and also another analytic representation based on theta functions are introduced the berezin formalism in the euclidean hyperbolic and elliptic cases is discussed contour analytic representations in these three cases are also presented

higher equivariant excision abstract we develop a theory of goodwillie calculus for functors between g equivariant homotopy theories where g is a finite group we construct j excisive approximations for any finite g set j these combine into a poset the goodwillie tree that extends the classical goodwillie tower we prove convergence results for the tree of a functor on pointed g spaces that commutes with fixed points and we reinterpret the tom dieck splitting as an instance of a more general splitting phenomenon that occurs for the fixed points of the equivariant derivatives of these functors as our main example we describe the layers of the tree of the identity functor in terms of the equivariant spanier whitehead duals of the partition complexes

a characterization theorem on the rotation construction for triangular norms the rotation construction for t norms is introduced in j appl non classical logics 10 2000 83 92 in the present paper we characterize the widest class of operators with which the rotation construction results in left continuous t norms with involutive associated negations

continuity of left continuous triangular norms with special associated negations abstract first we show that the class of left continuous triangular norms whose associated negations are discontinuous only at one point is not generally continuous except for the trivial case second we find the strongest left continuous triangular norm with a given associated negation and shows that there is no weakest left continuous triangular norm with a given associated negation

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

correlations and screening of topological charges in gaussian random fields two point topological charge correlation functions of several types of geometric singularity in gaussian random fields are calculated explicitly using a general scheme zeros of n dimensional random vectors signed by the sign of their jacobian determinant critical points gradient zeros of real scalars in two dimensions signed by the hessian and umbilic points of real scalars in two dimensions signed by their index the functions in each case depend on the underlying spatial correlation function of the field these topological charge correlation functions are found to obey the first stillinger lovett sum rule for ionic fluids

the monge metric on the sphere and geometry of quantum states topological and geometrical properties of the set of mixed quantum states in the n dimensional hilbert space are analysed assuming that the corresponding classical dynamics takes place on the sphere we use the vector su 2 coherent states and the generalized husimi distributions to define the monge distance between two arbitrary density matrices the monge metric has a simple semiclassical interpretation and induces a non trivial geometry among all pure states the distance from the maximally mixed state proportional to the identity matrix admits the largest value for the coherent states while the delocalized chaotic states are close to this contrasts the geometry induced by the standard trace hilbert schmidt or bures metrics for which the distance from is the same for all pure states we discuss possible physical consequences including unitary time evolution and the process of decoherence we introduce also a simplified monge metric defined in the space of pure quantum states and more suitable for numerical computation

unified univariate and multivariate random field theory we report new random field theory p values for peaks of canonical correlation spms for detecting multiple contrasts in a linear model for multivariate image data this completes results for all types of univariate and multivariate image data analysis all other known univariate and multivariate random field theory results are now special cases so these new results present a true unification of all currently known results as an illustration we use these results in a deformation based morphometry dbm analysis to look for regions of the brain where vector deformations of nonmissile trauma patients are related to several verbal memory scores to detect regions of changes in anatomical effective connectivity between the trauma patients and a group of age and sex matched controls and to look for anatomical connectivity in cortical thickness

exact statistical properties of the zeros of complex random polynomials the zeros of complex gaussian random polynomials with coefficients such that the density in the underlying complex space is uniform are known to have the same statistical properties as the zeros of the coherent state representation of one dimensional chaotic quantum systems we extend the interpretation of these polynomials by showing that they also arise as the wavefunction for a quantum particle in a magnetic field constructed from a random superposition of states in the lowest landau level a study of the statistical properties of the zeros is undertaken using exact formulae for the one and two point distribution functions attention is focused on the moments of the two point correlation in the bulk the variance of a linear statistic and the asymptotic form of the two point correlation at the boundary a comparison is made with the same quantities for the eigenvalues of complex gaussian random matrices

structure of left continuous triangular norms with strong induced negations iii construction and decomposition this paper is the continuation of jenei j appl non classical logics 10 2000 83 92 11 2001 351 366 where the rotation construction and the rotation annihilation construction have been presented respectively both constructions produce left continuous but not continuous triangular norms with strong induced negations here we show that these two constructions allow us to define indecomposability and that each decomposable left continuous triangular norm with strong induced negation can be derived as result of one of the above constructions in this way two general decomposition theorems arise in addition the decomposition of left continuous triangular norms with strong induced negations can be defined in a unique way namely when the decomposition is done by the minimal decomposition point

chaotic eigenfunctions in phase space we study individual eigenstates of quantized area preserving maps on the 2 torus which are classically chaotic in order to analyze their semiclassical behavior we use the bargmann husimi representations for quantum states as well as their stellar parametrization which encodes states through a minimal set of points in phase space the constellation of zeros of the husimi density we rigorously prove that a semiclassical uniform distribution of husimi densities on the torus entails a similar equidistribution for the corresponding constellations we deduce from this property a universal behavior for the phase patterns of chaotic bargmann eigenfunctions which is reminiscent of the wkb approximation for eigenstates of integrable systems though in a weaker sense in order to obtain more precise information on chaotic eigenconstellations we then model their properties by ensembles of random states generalizing former results on the 2 sphere to the torus geometry this approach yields statistical predictions for the constellations which fit quite well the chaotic data we finally observe that specific dynamical information e g the presence of high peaks like scars in husimi densities can be recovered from the knowledge of a few long wavelength fourier coefficients which therefore appear as valuable order parameters at the level of individual chaotic eigenfunctions