reproducing formulas for generalized translation invariant systems on locally compact abelian groups in this paper we connect the well established discrete frame theory of generalized shift invariant systems to a continuous frame theory to do so we let j j 2 j be a countable family of closed co compact subgroups of a sec ond countable locally compact abelian group g and study systems of the form j2jfgj p g 2 j p2pj with generators gj p in l 2 g and with each pj being a countable or an uncountable index set we refer to systems of this form as generalized translation invariant gti systems many of the familiar transforms e g the wavelet shearlet and gabor transform both their discrete and continu ous variants are gti systems under a technical local integrability condition lic we characterize when gti systems constitute tight and dual frames that yield reproducing formulas for l 2 g this generalizes results on generalized shift invariant systems where each pj is assumed to be countable and each j is a uni form lattice in g to the case of uncountably many generators and not necessarily discrete closed co compact subgroups furthermore even in the case of uniform lattices j our characterizations improve known results since the class of gti systems satisfying the lic is strictly larger than the class of gti systems sat isfying the previously used local integrability condition as an application of our characterization results we obtain new characterizations of translation invariant continuous frames and gabor frames for l 2 g in addition we will see that the admissibility conditions for the continuous and discrete wavelet and gabor trans form in l 2 r n are special cases of the same general characterizing equations

quasi orthogonal decompositions of structured frames a decomposition of a hilbert space h into a quasi orthogonal family of closed subspaces is introduced we shall investigate conditions in order to derive bounded families of corresponding quasi projectors or resolutions of the identity operator given a local family of atoms or generalized stable basis for each subspace we show that the union of the local atoms can generate a global frame for the hilbert space corresponding duals can be calculated in a flexible way by means of systems of quasi projectors an application to gabor frames is presented as example of the use of this technique for calculation of duals and explicit estimates of lattice constants

spatiotemporal analysis of event related fmri data using partial least squares partial least squares pls has proven to be a important multivariate analytic tool for positron emission tomographic and more recently event related potential erp data the application to erp incorporates the ability to analyze space and time together a feature that has obvious appeal for event related functional magnetic resonance imaging fmri data this paper presents the extension of spatiotemporal pls st pls to fmri explaining the theoretical foundation and application to an fmri study of auditory and visual perceptual memory analysis of activation effects with st pls was compared with conventional univariate random effects analysis showing general consensus for both methods but several unique observations by st pls including enhanced statistical power the application of st pls for assessment of task dependent brain behavior relationships is also presented singular features of st pls include 1 no assumptions about the shape of the hemodynamic response functions hrfs 2 robust statistical assessment at the image level through permutation tests 3 protection against outlier influences at the voxel level through bootstrap resampling 4 flexible analytic configurations that allow assessment of activation difference brain behavior relations and functional connectivity these features enable st pls to act as an important complement to other multivariate and univariate approaches used in neuroimaging research

operator valued frames we develop a natural generalization of vector valued frame theory we term operator valued frame theory using operator algebraic methods this extends work of the second author and d han which can be viewed as the mul tiplicity one case and extends to higher multiplicity their dilation approach we prove several results for operator valued frames concerning duality dis jointeness complementarity and composition of operator valued frames and the relationship between the two types of similarity left and right of such frames a key technical tool is the parametrization of parseval operator val ued frames in terms of a class of partial isometries in the hilbert space of the analysis operator we apply these notions to an analysis of multiframe gener ators for the action of a discrete group g on a hilbert space one of the main results of the han larson work was the parametrization of the parseval frame generators in terms of the unitary operators in the von neumann algebra gen erated by the group representation and the resulting norm path connectedness of the set of frame generators due to the connectedness of the group of unitary operators of an arbitrary von neumann algebra in this paper we general ize this multiplicity one result to operator valued frames however both the parameterization and the proof of norm path connectedness turn out to be necessarily more complicated and this is at least in part the rationale for this paper our parameterization involves a class of partial isometries of a different von neumann algebra these partial isometries are not path connected in the norm topology but only in the strong operator topology we prove that the set of operator frame generators is norm pathwise connected precisely when the von neumann algebra generated by the right representation of the group has no minimal projections as in the multiplicity one theory there are analogous results for general non parseval frames

green currents for holomorphic automorphisms of compact kahler manifolds and some additional regularity properties very likely the currents t will describe the distribution of invariant manifolds of codimension s corresponding to the small est lyapounov exponents let dp denote the dynamical degree of order p of it describes the growth under iteration of the volume of p dimensional manifolds when d 1 it is natural to introduce first a positive closed 1 l current as ifnyoj 7 lim

hyperbolic polynomial diffeomorphisms of c2 ii hubbard trees this paper is a sequel to part i y ishii hyperbolic polynomial diffeomorphisms of i a non planar map adv math 218 2 2008 417 464 in the current article we construct an object analogous to a hubbard tree consisting of a pair of trees decorated with loops and a pair of maps between them for a hyperbolic polynomial diffeomorphism f of key notions in the construction are the pinching disks and the pinching locus which determine how local dynamical pieces are glued together to obtain a global picture it is proved that the shift map on the orbit space of a hubbard tree is topologically conjugate to f on its julia set several examples of hubbard trees are also given

stability of g frames g frames are natural generalizations of frames which cover many other recent generalizations of frames e g bounded quasi projectors frames of subspaces outer frames oblique frames pseudo frames and a class of time frequency localization operators moreover it is known that g frames are equivalent to stable space splittings in this paper we study the stability of g frames we first present some properties for g bessel sequences then we prove that g frames are stable under small perturbations we also study the stability of dual g frames

abundance of strange attractors in 1976 he h non performed a numerical study of the family of diffeomorphisms of the plane ha b x y 1 ax2 y bx and detected for parameter values a l 4 b 0 3 what seemed to be a non trivial attractor with a highly intricate geometric structure this family has since then been the subject of intense research both numerical and theoretical but its dynamics is still far from being completely understood in particular one could not exclude the possibility that the attractor observed by h6non were just a periodic orbit with a very high period recently in a remarkable paper bc2 benedicks and carleson were able to show that this is not the case at least for a positive lebesgue measure set of parameter values near a 2 b o more precisely they showed that if b 0 is small enough then for a positive measure set of a values near a 2 the corresponding diffeomorphism ha b exhibits a strange attractor their argument is a very creative extension of the techniques they had previously developed in bull for the study of the quadratic family on the real line and no doubt it will be important for the understanding of several other situations of complicated nonhyperbolic dynamics when acquainted in 1985 with the work by benedicks and carleson then in progress palls suggested that one should in this context think of the h6non family as a particular although important model for the creation of a horseshoe and that the emphasis should be put on the occurrence of unfoldings of homoclinic tangencies he proposed that the correct setting for benedicks carleson s results is within this more general framework of homoclinic bifurcations and stated the following

some properties of g frames in hilbert c modules in this paper we give some new results for g frames in hilbert c modules and then we introduce a bounded a linear operator l by means of this operator l we character the properties of the g frames and g riesz basis in hilbert c modules finally we establish some important equalities and inequalities for frames and g frames in hilbert c modules

analysis of neurotransmitter receptor distribution patterns in the cerebral cortex abstract the concentration of transmitter receptors varies between different locations in the human cerebral cortex but also between the different cortical layers within the same area analyzing the regional differences in the laminar distribution patterns of various neurotransmitter receptor binding sites by means of quantitative receptor autoradiography may thus provide a functionally relevant insight into the organization of the cortex here we introduce an approach to the analysis of in vitro receptor autoradiographic data providing a framework for the assessment of differences in both mean concentration and laminar distribution patterns across multiple subjects initially laminar receptor distribution patterns for cortical areas are quantified by sampling density profiles in a series of regions of interest rois from digitalized autoradiographs and computing a mean profile per roi these roi mean profiles are then corrected for distortions in the laminar pattern introduced by cortical folding and averaged to yield a mean profile per area receptor and hemisphere differences in mean binding site concentration between areas are quantified by the asymmetry coefficient which is the difference of the mean concentrations divided by their sum to quantify differences in laminar receptor distribution patterns between areas the effects of absolute binding site concentration are first removed by dividing each profile by its mean value differences in the laminar pattern were then quantified by calculating the euclidean distance between these mean corrected profiles for single subject analysis we propose a permutation test comparing the differences between the mean profiles for two areas to differences between groups of profiles randomly assembled from all rois sampled in either area group inference can then be based on a between subject conjunction analysis after correcting p values to control for multiple comparisons the feasibility of the presented approach is demonstrated by an exemplary analysis of the neurochemical differences between the ventral parts of the second and the third visual area

dynamics of bimeromorphic maps of surfaces we classify bimeromorphic self maps f x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of compact kahler surfaces x in terms of their actions f h 1 1 x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i on cohomology we observe that the growth rate of f n is invariant under bimeromorphic conjugacy and that by conjugating one can always arrange that f n f n we show that the sequence f n can be bounded grow linearly grow quadratically or grow exponentially in the first three cases we show that after conjugating f is an automorphism virtually isotopic to the identity f preserves a rational fibration or f preserves an elliptic fibration respectively in the last case we show that there is a unique up to scaling expanding eigenvector for f that is nef and that f is bimeromorphically conjugate to an automorphism if and only if 2 0 we go on in this case to construct a dynamically natural positive current representing and we study the growth rate of periodic orbits of f we conclude by illustrating our results with a particular family of examples

on the duality of fusion frames the fusion frames were considered recently by p g casazza g kutyniok and s li in connection with distributed processing and are related to the construction of global frames from local frames in this paper we give new results on the duality of fusion frames in hilbert spaces

dilations of operator valued measures with bounded p variations and framings on banach spaces abstract the dilations for operator valued measures ovms and bounded linear maps indicate that the dilation theory is in general heavily dependent on the banach space nature of the dilation spaces this naturally led to many questions concerning special type of dilations in particular it is not known whether ultraweakly continuous normal maps can be dilated to ultraweakly continuous homomorphisms we answer this question affirmatively for the case when the domain algebra is an abelian von neumann algebra it is well known that completely bounded hilbert space operator valued measures correspond to the existence of orthogonal projection valued dilations in the sense of naimark and stinespring and ovms with bounded total variations are completely bounded but not the vice versa with the aim of classifying ovms from the dilation point of view we introduce the concept of total p variations for ovms we prove that any completely bounded ovm has finite 2 variation and any ovm with finite p variation can be dilated to a but usually non hilbertian projection valued measure of the same type with the help of framing induced ovms we prove that conventional minimal dilation space of a non trivial framing contains c 0 then does not have bounded p variation

experimental design and the relative sensitivity of bold and perfusion fmri this paper compares the statistical power of bold and arterial spin labeling perfusion fmri for a variety of experimental designs within and across subjects based on theory and simulations we predict that perfusion data are composed of independent observations in time under the null hypothesis in contrast to bold data which possess marked autocorrelation we also present a method sinc subtraction of generating perfusion data from its raw source signal that minimizes the presence of oxygen sensitive signal changes and can be used with any experimental design empirically we demonstrate the absence of autocorrelation in perfusion noise examine the shape of the hemodynamic response function for bold and perfusion and obtain a measure of signal to noise for each method this information is then used to generate a model of relative sensitivity of the bold and perfusion methods for within subject experimental designs of varying temporal frequency it is determined that perfusion fmri provides superior sensitivity for within subject experimental designs that concentrate their power at or below approximately 0 009 hz corresponding to a blocked experimental design of 60 s epochs additionally evidence is presented that across subject hypothesis tests may be more sensitive when conducted using perfusion imaging despite the better within subject signal to noise obtained in some cases with bold

orthogonality of a pair of frames over locally compact abelian groups abstract in this article we provide necessary and sufficient conditions for the orthogonality of two bessel families when such families have the form of generalized translation invariant gti systems over a second countable locally compact abelian lca group g the work is motivated by the utility of a recent notion given by jakobsen and lemvig on gti systems in l 2 g and the concept of the orthogonality or strongly disjointness of a pair of frames studied by balan han and larson consequently we deduce similar results for several function systems including the case of ti systems and gti systems on compact abelian groups we apply our results to the bessel families having wave packet structure combination of wavelet as well as gabor structure and hence a characterization for pairwise orthogonal wave packet frame systems over lca groups is obtained in addition we relate the well established theory from literature with our results by observing several deductions in the context of wavelet and gabor systems over lca groups with g r d z d etc

dynamics of polynomial mappings of c 2 we study the dynamics of polynomial self mappings f of c 2 we construct for a large class of mappings an invariant measure which is mixing and of maximal entropy h f max log d t f log 1 f where d t f is the topological degree of f and 1 f its first dynamical degree to achieve this we look at the meromorphic extensions of f to smooth minimal compactifications of c 2 when a good compactification is found we construct an f invariant green current t which contains many dynamical informations when d t f 1 f 1 the measure is obtained as p dd c vt where v is a partial green function defined on the support of t when 1 t t where t is a globally defined f invariant current

p y operator frames for a banach space abstract in this paper p y bessel operator sequences operator frames and p y riesz bases for a banach space x are introduced and discussed as generalizations of the usual concepts for a hilbert space and of the g frames it is proved that the set b x p y of all p y bessel operator sequences for a banach space x is a banach space and isometrically isomorphic to the operator space b x l p y some necessary and sufficient conditions for a sequence of operators to be a p y bessel operator sequence are given also a characterization of an independent p y operator frame for x is obtained lastly it is shown that an independent p y operator frame for x is just a p y riesz basis for x and has a unique dual q y operator frame for x

quasiconformal homeomorphisms and dynamics i solution of the fatou julia problem on wandering domains on demontre un resultat dynamique sur l iteration d une application analytique complexe sur la sphere de riemann

dynamical compactifications of c 2 we find good dynamical compactifications for arbitrary polynomial mappings of c 2 and use them to show that the degree growth sequence satisfies a linear integral recursion formula for maps of low topological degree we prove that the green function is well behaved for maps of maximum topological degree we give normal forms

on fatou bieberbach domains a fatou bieberbach domain is a domain in c2 which is a biholomorphic image of c2 and is not all of c2 the existence of such domains has been known for a long time there are several papers dealing with fatou bieberbach domains bf bs de e fs gl k n1 n2 rr1 rr2 s nevertheless they remain quite misterious objects and there are many open questions about them one of them is the following rr1 q 11 p 79 if is a fatoubieberbach domain and l is a complex line is it possible that a l is connected b l has finitely many components c l is a circular disc let be the open unit disc in c and let p suppose one wants to obtain a fatou bieberbach domain whose intersection with the z axis z 0 z c is approximately the unit disc one would try to find such that

hyperbolic polynomial diffeomorphisms of c2 iii iterated monodromy groups abstract this paper is a sequel to part i 13 and part ii 14 15 in the current article we relate several combinatorial descriptions of the julia sets for hyperbolic polynomial diffeomorphisms of c 2 quotients of solenoids 3 automata 22 and hubbard trees 14 15 the notion of iterated monodromy groups are defined for such diffeomorphisms and are used to construct automata from hubbard trees

the dynamics of the henon map the purpose of this paper is to develop machinery which is suitable for a study of the long time behavior of systems such as the henon map with expansion combined with strong contraction our study is modeled on the treatment of the one dimensional system x 1 ax 2 and we study the perturbation of a from the value a 2 and b small a surprising number of complications arise when b 0 the computer simulations give some indication of the complicated structure of the attractor but it can safely be stated that the real difficulties do not show up the central aim of the paper is to introduce what we consider the relevant concepts and techniques needed to study mappings such as the henon one

duality in reconstruction systems we consider the notion of finite dimensional reconstructions systems rs s which includes the fusion frames as projective rs s we study erasures some geometrical properties of these spaces the spectral picture of the set of all dual systems of a fixed rs the spectral picture of the set of rs operators for the projective systems with fixed weights and the structure of the minimizers of the joint potential in this setting we give several examples

frames and bases of subspaces in hilbert spaces abstract in this paper we develop the frame theory of subspaces for separable hilbert spaces we will show that for every parseval frame of subspaces w i i i for a hilbert space h there exists a hilbert space k h and an orthonormal basis of subspaces n i i i for k such that w i p n i where p is the orthogonal projection of k onto h we introduce a new definition of atomic resolution of the identity in hilbert spaces in particular we define an atomic resolution operator for an atomic resolution of the identity which even yield a reconstruction formula

hyperbolic polynomial diffeomorphisms of c2 i a non planar map abstract in this paper we develop a general framework for verifying hyperbolicity of holomorphic dynamical systems in c 2 our framework in particular enables us to construct the first example of a hyperbolic henon map of c 2 which is non planar i e which is not topologically conjugate on its julia set to a small perturbation of any expanding polynomial in one variable the key ideas in its proof are the poincare box which is a building block to apply our criterion for hyperbolicity an operation called fusion to merge two polynomials in one variable to obtain essentially two dimensional dynamics and rigorous computation by using interval arithmetic some conjectures and problems are also presented

functional mri using sensitivity encoded echo planar imaging sense epi parallel imaging methods become increasingly available on clinical mr scanners to investigate the potential of sensitivity encoded single shot epi sense epi for functional mri five imaging protocols at different sense reduction factors r and matrix sizes were compared with respect to their noise characteristics and their sensitivity toward functional activation in a motor task examination at constant echo times sense epi was either used to shorten the single volume acquisition times trmin at matrix size 128 100 22 slices from 3 9 s no sense to 2 0 s at r 3 or to increase the matrix size to 192 153 22 slices resulting in trmin 5 3 s for r 2o r trmin 3 4 s for r 3 at the lower resolution the bisection of echo train length r 2 substantially reduced distortions and blurring while signal to noise and statistical power measured by cluster size and maximum t value per unit time were hardly reduced at r 3 the additional gain in speed and distortion reduction was quite small while signal to noise and statistical power dropped significantly with enhanced spatial resolution the time course signal to noise was better than expected from theory for purely thermal noise because of a reduced contribution of physiological noise and statistical power almost reached that of the regular low resolution single shot epi with a slight drop off toward r 3 thus sense epi allows to substantially increase speed and spatial resolution in fmri at sense reduction factors up to r 2 the potential drawbacks regarding signal to noise and statistical power are almost negligible

dynamics of horizontal like maps in higher dimension we study the regularity of the green currents and of the equilibrium measure associated to a horizontal like map in under a natural assumption on the dynamical degrees we estimate the speed of convergence towards the green currents the decay of correlations for the equilibrium measure and the lyapounov exponents we show in particular that the equilibrium measure is hyperbolic we also show that the green currents are the unique invariant vertical and horizontal positive closed currents the results apply in particular to henon like maps to regular polynomial automorphisms of and to their small perturbations

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

pfaff systems currents and hulls let s be a pfaff system of dimension 1 on a compact complex manifold m we prove that there is a positive partial overline partial closed current t of bidimension 1 1 and of mass 1 directed by the pfaff system s there is no integrability assumption we also show that local singular solutions always exist under a transversality assumption of s on the boundary of an open set u we prove the existence in u of positive partial overline partial closed currents directed by s in u using i partial overline partial negative currents we discuss jensen measures local maximum principle and hulls with respect to a cone mathcal p of smooth functions in the euclidean complex space subharmonic in some directions the case where mathcal p is the cone of plurisubharmonic functions is classical we use the results to describe the harmonicity properties of the solutions of equations of homogeneous monge ampere type we also discuss extension problems of positive directed currents

stability and bifurcations for dissipative polynomial automorphisms of mathbb c 2 we study stability and bifurcations in holomorphic families of polynomial automorphisms of mathbb c 2 we say that such a family is weakly stable over some parameter domain if periodic orbits do not bifurcate there we first show that this defines a meaningful notion of stability which parallels in many ways the classical notion of j stability in one dimensional dynamics define the bifurcation locus to be the complement of the weak stability locus in the second part of the paper we prove that under an assumption of moderate dissipativity the parameters displaying homoclinic tangencies are dense in the bifurcation locus this confirms one of palis conjectures in the complex setting the proof relies on the formalism of semi parabolic bifurcation and the construction of critical points in semi parabolic basins which makes use of the classical denjoy carleman ahlfors and wiman theorems

the k dual bessel generators for unitary groups of hilbert spaces abstract structured frames have interested many mathematicians and engineers due to their potential applications this paper addresses the theory of k frames associated with unitary groups let u be a unitary group for a separable hilbert space h given a k frame generator for u we present an explicit expression of all k dual bessel generators of for u under two cases and simultaneously prove that its canonical k dual bessel generator corresponds to the most economic presentation of the element from the range of k

regularity of dynamical green s functions for meromorphic maps of complex manifolds ergodic theory and pluripotential theory are closely related in nice enough situations dynamically defined green s functions give rise to invariant currents which intersect to yield measures of maximal entropy nice enough is often a condition on the regularity of the green s function in this paper we look at a variety of regularity properties that have been considered for dynamical green s functions we simplify and extend some known results and prove several others which are new we also give some examples indicating the limits of what one can hope to achieve in complex dynamics by relying solely on the regularity of a dynamical green s function

multipliers for von neumann schatten bessel sequences in separable banach spaces abstract in this paper we introduce the concept of von neumann schatten bessel multipliers in separable banach spaces and obtain some of their properties we study their behavior when the symbol belongs to l p also we investigate the continuous dependency of hilbert schmidt bessel multipliers on their parameters special attention is devoted to the study of invertible hilbert schmidt frame multipliers which is an extensive class of ordinary frame multipliers and includes g frame multipliers and fusion frame multipliers as elementary examples among other things the invertibility of hilbert schmidt riesz multipliers is completely characterized in particular we show that all the existing frames in hilbert spaces is uniquely determined by the set of its dual frames

the processing and representation of fractions within the brain an fmri investigation little is known about how adults process fractions and how fractions are represented in the brain the intraparietal sulcus is assumed to host an analogue representation of number magnitude it is unknown however how the magnitude of fractions is represented in the brain fraction magnitude might be represented by the numerical value of the fraction as a whole or might involve separate representations of the values of the fractions denominator and numerator the present fmri study investigated brain areas involved in fraction comparison as a diagnostic for fraction processing the numerical distance effect reaction times and error rates increase as the distance between the numbers being compared decreases was evaluated if fractions are represented as their numerical value a distance effect is expected for the distance between the numerical values of the two fractions being compared if fractions are represented in parts however that is as the separate values of their denominators and numerators a distance effect is expected for the distances between the two fractions numerators and denominators respectively although both types of distance effects were observed in the behavioral data only the distance between the numerical values of the two fractions was observed to modulate activation within the intraparietal sulcus ips this indicates that within the ips a fraction might be represented by its numerical value as a whole rather than by the numerical values of its numerator and denominator

complex projective structures lyapunov exponent degree and harmonic measure we study several new invariants associated to a holomorphic projective struc ture on a riemann surface of finite analytic type the lyapunov exponent of its holonomy which is of probabilistic dynamical nature and was introduced in our previous work the degree which measures the asymptotic covering rate of the developing map and a family of harmonic measures on the riemann sphere previously introduced by hussenot we show that the degree and the lyapunov exponent are related by a simple formula and give estimates for the hausdorff dimension of the harmonic measures in terms of the lyapunov exponent in accordance with the famous sullivan dictionary this leads to a descrip tion of the space of such projective structures that is reminiscent of that of the space of polynomials in holomorphic dynamics

symmetric approximation of frames and bases in hilbert spaces we introduce the symmetric approximation of frames by normalized tight frames extending the concept of the symmetric orthogonalization of bases by orthonormal bases in hilbert spaces we prove existence and uniqueness results for the symmetric approximation of frames by normalized tight frames even in the case of the symmetric orthogonalization of bases our techniques and results are new a crucial role is played by whether or not a certain operator related to the initial frame or basis is hilbert schmidt

excess of a class of g frames abstract in this paper we study the relationship between frames for the super hilbert space h h and g frames for h with respect to c 2 we show that a g frame associated with a frame for h h remains a g frame whenever any one of its elements is removed furthermore we show that the excess of such a g frame is at least dim h

ergodic properties of rational mappings with large topological degree let x be a projective manifold and f x x a rational mapping with large topological degree dt ek 1 f the k 1 th dynamical degree of f we give an elementary construction of a probability measure ef such that d n t fn ef for every smooth probability measure on x we show that every quasiplurisubharmonic function is ef integrable in particular ef does not charge either points of indeterminacy or pluripolar sets hence ef is f invariant with constant jacobian f ef dt ef we then establish the main ergodic properties of ef it is mixing with positive lyapunov exponents preimages of hmost h points as well as repelling periodic points are equidistributed with respect to ef moreover when dimc x 3 or when x is complex homogeneous ef is the unique measure of maximal entropy

groupwise independent component decomposition of eeg data and partial least square analysis this paper focuses on two methodological developments for analysis of neuroimaging data the first is the derivation of robust spatiotemporal activity patterns across a group of subjects using a combination of principal component analysis pca and independent component analysis ica in applications to erp data the space dimension is typically represented in terms of scalp electrodes the signal recorded by high density electrode caps is known to be highly correlated due in part to volume conduction consequently this redundancy is also reflected in spatiotemporal patterns characterizing signal differences across experimental conditions we present an alternative spatial representation and signal compression based on pca for dimensionality reduction and ica conducted across all subjects and conditions simultaneously the second advancement is the use of partial least squares pls analysis to assess task dependent changes in the expression of the independent components in an application to empirical erp data we derive an efficient number of independent component maps comparative pls analysis on the independent components versus original electrode data shows that task effects are not only preserved under compression but also enhanced statistically

valid population inference for information based imaging from the second level t test to prevalence inference in multivariate pattern analysis of neuroimaging data second level inference is often performed by entering classification accuracies into a t test vs chance level across subjects we argue that while the random effects analysis implemented by the t test does provide population inference if applied to activation differences it fails to do so in the case of classification accuracy or other information like measures because the true value of such measures can never be below chance level this constraint changes the meaning of the population level null hypothesis being tested which becomes equivalent to the global null hypothesis that there is no effect in any subject in the population consequently rejecting it only allows to infer that there are some subjects in which there is an information effect but not that it generalizes rendering it effectively equivalent to fixed effects analysis this statement is supported by theoretical arguments as well as simulations we review possible alternative approaches to population inference for information based imaging converging on the idea that it should not target the mean but the prevalence of the effect in the population one method to do so permutation based information prevalence inference using the minimum statistic is described in detail and applied to empirical data

exact g frames in hilbert spaces g frames which were considered recently as generalized frames in hilbert spaces have many properties similar to those of frames but not all the properties are similar for example exact frames are equivalent to riesz bases but exact g frames are not equivalent to g riesz bases in this paper we firstly give a characterization of an exact g frame in a complex hilbert space we also obtain an equivalent relation between an exact g frame and a g riesz basis under some conditions lastly we consider the stability of an exact g frame for a hilbert space under perturbation these properties of exact g frames for hilbert spaces are not similar to those of exact frames

fusion frames and g frames fusion frames and g frames were considered recently as generalizations of frames in hilbert spaces in this paper we generalize some of the known results in frame theory to fusion frames and g frames we obtain new g frames by considering g frames for its components we also obtain some results about alternate dual g frames excess of g frames and stability of g frames under small perturbations

properties of finite dual fusion frames abstract a new notion of dual fusion frame has been recently introduced by the authors in this article that notion is further motivated and it is shown that it is suitable to deal with questions posed in a finite dimensional real or complex hilbert space reinforcing the idea that this concept of duality solves the question about an appropriate definition of dual fusion frames it is shown that for overcomplete fusion frames there always exist duals different from the canonical one conditions that assure the uniqueness of duals are given the relation of dual fusion frame systems with dual frames and dual projective reconstruction systems is established optimal dual fusion frames for the reconstruction in case of erasures of subspaces and optimal dual fusion frame systems for the reconstruction in case of erasures of local frame vectors are determined examples that illustrate the obtained results are exhibited

multisubject fmri studies and conjunction analyses abstract in this paper we present an approach to making inferences about generic activations in groups of subjects using fmri in particular we suggest that activations common to all subjects reflect aspects of functional anatomy that may be typical of the population from which that group was sampled these commonalities can be identified by a conjunction analysis of the activation effects in which the contrasts testing for an activation are specified separately for each subject a conjunction is the joint refutation of multiple null hypotheses in this instance of no activation in any subject the motivation behind this use of conjunctions is that fixed effect analyses are generally more sensitive than equivalent random effect analyses this is because fixed effect analyses can harness the large degrees of freedom and small scan to scan variability relative to the variability in responses from subject to subject when assessing the significance of an estimated response the price one pays for the apparent sensitivity of fixed effect analyses is that the ensuing inferences pertain to and only to the subjects studied however a conjunction analysis using a fixed effect model allows one to infer i that every subject studied activated and ii that at least a certain proportion of the population would have shown this effect the second inference depends upon a meta analytic formulation in terms of a confidence region for this proportion this approach retains the sensitivity of fixed effect analyses when the inference that only a substantial proportion of the population activates is sufficient

time frequency partitions and characterizations of modulation spaces with localization operators abstract we study families of time frequency localization operators and derive a new characterization of modulation spaces this characterization relates the size of the localization operators to the global time frequency distribution as a by product we obtain a new proof for the existence of multi window gabor frames and extend the structure theory of gabor frames

complex henon maps and discrete groups abstract consider the standard family of complex henon maps h x y p x a y x where p is a quadratic polynomial and a is a complex parameter let u be the set of points that escape to infinity under forward iterations the analytic structure of the escaping set u is well understood from previous work of j hubbard and r oberste vorth as a quotient of c d c by a discrete group of automorphisms isomorphic to z 1 2 z on the other hand the boundary j of u is a complicated fractal object on which the henon map behaves chaotically we show how to extend the group action to s 1 c in order to represent the set j as a quotient of s 1 c by an equivalence relation we analyze this extension for henon maps that are perturbations of hyperbolic polynomials with connected julia set or polynomials with a parabolic fixed point

global dynamics of quadratic second order difference equation in the first quadrant we investigate the global behavior of a quadratic second order difference equation x n 1 ax n 2 bx n x n 1 cx n 1 2 dx n ex n 1 f n 0 1 with non negative parameters and initial conditions we find the global behavior for all ranges of parameters and determine the basins of attraction of all equilibrium points

analysis of fmri time series revisited abstract this paper presents a general approach to the analysis of functional mri time series from one or more subjects the approach is predicated on an extension of the general linear model that allows for correlations between error terms due to physiological noise or correlations that ensue after temporal smoothing this extension uses the effective degrees of freedom associated with the error term the effective degrees of freedom are a simple function of the number of scans and the temporal autocorrelation function a specific form for the latter can be assumed if the data are smoothed in time to accentuate hemodynamic responses with a neural basis this assumption leads to an expedient implementation of a flexible statistical framework the importance of this small extension is that in contradistinction to our previous approach any parametric statistical analysis can be implemented we demonstrate this point using a multiple regression analysis that tests for effects of interest activations due to word generation while taking explicit account of some obvious confounds

structure seeking multilinear methods for the analysis of fmri data in comprehensive fmri studies of brain function the data structures often contain higher order ways such as trial task condition subject and group in addition to the intrinsic dimensions of time and space while multivariate bilinear methods such as principal component analysis pca have been used successfully for extracting information about spatial and temporal features in data from a single fmri run the need to unfold higher order data sets into bilinear arrays has led to decompositions that are nonunique and to the loss of multiway linkages and interactions present in the data these additional dimensions or ways can be retained in multilinear models to produce structures that are unique and which admit interpretations that are neurophysiologically meaningful multiway analysis of fmri data from multiple runs of a bilateral finger tapping paradigm was performed using the parallel factor parafac model a trilinear model was fitted to a data cube of dimensions voxels by time by run similarly a quadrilinear model was fitted to a higher way structure of dimensions voxels by time by trial by run the spatial and temporal response components were extracted and validated by comparison to results from traditional svd pca analyses based on scenarios of unfolding into lower order bilinear structures

continuous and discrete wavelet transforms this paper is an expository survey of results on integral representations and discrete sum expansions of functions in l 2 bf r in terms of coherent states two types of coherent states are considered weyl heisenberg coherent states which arise from translations and modulations of a single function and affine coherent states called wavelets which arise as translations and dilations of a single function in each case it is shown how to represent any function in l 2 bf r as a sum or integral of these states most of the paper is a survey of literature most notably the work of i daubechies a grossmann and j morlet a few results of the authors are included

a study on the stability of g banach frames abdollahpour introduced the concept of g banach frames in this paper we study the stability of g banach frames under perturbations some conditions on the stability of g banach frames are obtained in particular the stability results by abdollahpour are the special case of ours

on commuting polynomial automorphisms of mathbb c k k 3 we characterize the polynomial automorphisms of mathbb c 3 which commute with a regular automorphism we use their meromorphic extension to mathbb p 3 and consider their dynamics on the hyperplane at infinity we conjecture the additional hypothesis under which the same characterization is true in all dimensions we give a partial answer to a question of s smale that in our context can be formulated as follows can any polynomial automorphism of mathbb c k be the uniform limit on compact sets of polynomial automorphisms with trivial centralizer i e c f simeq mathbb z

semi parabolic bifurcations in complex dimension two parabolic bifurcations in one complex dimension demonstrate a wide variety of interesting dynamical phenomena in this paper we consider the bifurcations of a holomorphic diffeomorphism in two complex dimensions with a semi parabolic semiattracting fixed point

dynamics of regular birational maps in p k abstract we develop the study of some spaces of currents of bidegree p p as an application we construct the equilibrium measure for a large class of birational maps of p k as intersection of green currents we show that these currents are extremal and that the corresponding measure is mixing

a structure theorem for semi parabolic henon maps abstract consider the parameter space p c 2 of complex henon maps h c a x y x 2 c a y a x a 0 which have a semi parabolic fixed point with one eigenvalue e 2 i p q in this paper we provide a complete topological description of the julia set and forward julia set within a family of semi parabolic henon maps i e those henon maps from the curve p which are perturbations of a quadratic polynomial p with a parabolic fixed point of multiplier we prove that there is an open disk of parameters in p for which the semi parabolic henon map has connected julia set j and is structurally stable on j and j the forward julia set j has a nice local description inside a certain bidisk it is a trivial fiber bundle over j p the julia set of the polynomial p with fibers biholomorphic to a disk the julia set j is homeomorphic to the quotient of a solenoid by an equivalence relation and j j the closure of the saddle periodic points

classification of recurrent domains for some holomorphic maps abstract riemann surface as in theorem 1 2 we show first that f is not constant on any component fl v l 0 hence we can assume using a diagonal process that for a subsequence fm fm h and h ld on ut of p c q g2 h q q consequently u of n is closed in t2 since fro ld on zn and since f is not of finite order see fm then f is conjugate to an irrational rotation on the riemann surface e we then show as in theorem 2 3 of fs3 that z is contained in f2 so e is closed in i2 the rest of the argument is as in theorem 1 2 or as in fs3 theorem 2 3 references b bbd bs cg fm fs1 fs2 fs3 fs4 g hi ko kr m in rr u beardon a iteration of rational functions springer verlag 1991 barrett d bedford e dadok j t actions on holomorphically separable complex manifolds math z 202 1989 65 82 bedford e smillie j polynomial diffeomorphisms of 2 ii amer j math 4 1991 657 679 carleson l gamelin t complex dynamics springer verlag 1993 friedland s milnor j dynamical properties of plane automorphisms ergodic theory and dynamical systems 9 1989 67 99 fornaess j e sibony n complex dynamics in higher dimension i asterisque 222 1994 201 231 fornaess j e sibony n complex dynamics in higher dimension ii to appear in ann math studies fornaess j e sibony n complex henon mappings in 2 and fatou bieberbach domains duke math j 65 1992 345 380 fornaess j e sibony n holomorphic dynamical systems to appear gavosto e to appear herman m recent results on some open questions on siegel s linearization kobayashi s hyperbolic manifolds and holomorphic mappings new york marcel dekker 1970 kruzhilin n g holomorphic automorphisms of hyperbolic reinhardt do mains math ussr izvestya 32 1989 15 38 milnor j dynamics in one complex variable introductory lectures suny stony brook institute for mathematical sciences preprint 1990 5 narashiman r several complex variables univ chicago press 1971 rosay j p rudin w holomorphic maps from ie n to c n tams 310 1988 47 86 ueda t fatou set in complex dynamics in projective spaces preprint

energy and invariant measures for birational surface maps given a birational self map of a compact complex surface it is useful to find an invariant measure that relates the dynamics of the map to its action on cohomology under a very weak hypothesis on the map we show how to construct such a measure the main point in the construction is to make sense of the wedge product of two positive closed 1 1 currents we are able to do this in our case because local potentials for each current have finite energy with respect to the other our methods also suffice to show that the resulting measure is mixing does not charge curves and has nonzero lyapunov exponents

screening for partial conjunction hypotheses summary we consider the problem of testing for partial conjunction of hypothesis which argues that at least u out of n tested hypotheses are false it offers an in between approach to the testing of the conjunction of null hypotheses against the alternative that at least one is not and the testing of the disjunction of null hypotheses against the alternative that all hypotheses are not null we suggest powerful test statistics for testing such a partial conjunction hypothesis that are valid under dependence between the test statistics as well as under independence we then address the problem of testing many partial conjunction hypotheses simultaneously using the false discovery rate fdr approach we prove that if the fdr controlling procedure in benjamini and hochberg 1995 journal of the royal statistical society series b 57 289 300 is used for this purpose the fdr is controlled under various dependency structures moreover we can screen at all levels simultaneously in order to display the findings on a superimposed map and still control an appropriate fdr measure we apply the method to examples from microarray analysis and functional magnetic resonance imaging fmri two application areas where the need for partial conjunction analysis has been identified

assessing the sensitivity of fmri group maps abstract group maps created from individual functional maps provide useful summaries of patterns of brain activation different methods for combining information have been proposed in the statistical literature and have been recently applied to fmri data since these group maps are statistics it is natural to ask how robust they are that is are they sensitive to the effects of unusual subjects unusual might be in terms of extent location or strength of activation our approach in this paper is to jackknife group maps formed by different combining procedures the jackknife method which involves deleting each observation subject in turn and recalculating the statistic the group map is commonly used for the purpose of assessing sensitivity we examine the theoretical properties of four combining methods in addition via a collection of measures defined on the difference between group maps based on the entire sample and based on the jackknifed samples we evaluate the robustness of these same methods on data from an fmri experiment results indicate that there is a type of tradeoff in the combining techniques we consider between robustness and conservativeness methods that are liberal in that they allow for the discovery of many active voxels tend also to be more sensitive to the influences of individual subjects

frames and semi frames loosely speaking a semi frame is a generalized frame for which one of the frame bounds is absent more precisely given a total sequence in a hilbert space we speak of an upper resp lower semi frame if only the upper resp lower frame bound is valid equivalently for an upper semi frame the frame operator is bounded but has an unbounded inverse whereas a lower semi frame has an unbounded frame operator with bounded inverse we study mostly upper semi frames both in the continuous case and in the discrete case and give some remarks for the dual situation in particular we show that reconstruction is still possible in certain cases

g frames and g riesz bases g frames are generalized frames which include ordinary frames bounded invertible linear operators as well as many recent generalizations of frames e g bounded quasi projectors and frames of subspaces g frames are natural generalizations of frames and provide more choices on analyzing functions from frame expansion coefficients we give characterizations of g frames and prove that g frames share many useful properties with frames we also give a generalized version of riesz bases and orthonormal bases as an application we get atomic resolutions for bounded linear operators

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics