least squares reverse time migration using controlled order multiple reflections abstractreverse time migration rtm using multiples generates inherent crosstalk artifacts due to the interference among multiples of different orders we have developed a method to remove such crosstalk this approach first separates the recorded seismic data into primary reflections and multiples using the surface related multiples elimination algorithm and then isolates the multiples into different orders we can take any specified say the nth order of multiples data as the incident wave and the next higher order multiples data n 1 th order as the corresponding primary reflection data for imaging we have applied the least squares migration scheme to these two successive orders of multiples our method is denoted as least squares rtm using controlled order multiples lsrtm cm our numerical tests demonstrated that lsrtm cm can significantly improve imaging quality compared with straightforward seismic imaging using multiples without multiples separation

adaptive surface related multiple elimination the major amount of multiple energy in seismic data is related to the large reflectivity of the surface a method is proposed for the elimination of all surface related multiples by means of a process that removes the influence of the surface reflectivity from the data an important property of the proposed multiple elimination process is that no knowledge of the subsurface is required on the other hand the source signature and the surface reflectivity do need to be provided as a consequence the proposed process has been implemented adaptively meaning that multiple elimination is designed as an inversion process where the source and surface reflectivity properties are estimated and where the multiple free data equals the inversion residue results on simulated data and field data show that the proposed multiple elimination process should be considered as one of the key inversion steps in stepwise seismic inversion

some properties of the injective tensor product of lp 0 1 and a banach space abstract let x be a real or complex banach space and 1 l p 0 1 x the injective tensor product of lp 0 1 and x has the radon nikodym property resp the analytic radon nikodym property the near radon nikodym property contains no copy of c0 is weakly sequentially complete if and only if x has the same property and each continuous linear operator from lp 0 1 to x is compact

an inverse scattering series method for attenuating multiples in seismic reflection data we present a multidimensional multiple attenuation method that does not require any subsurface information for either surface or internal multiples to derive these algorithms we start with a scattering theory description of seismic data we then introduce and develop several new theoretical concepts concerning the fundamental nature of and the relationship between forward and inverse scattering these include 1 the idea that the inversion process can be viewed as a series of steps each with a specific task 2 the realization that the inverse scattering series provides an opportunity for separating out subseries with specific and useful tasks 3 the recognition that these task specific subseries can have different and more favorable data requirements convergence and stability conditions than does the original complete inverse series and most importantly 4 the development of the first method for physically interpreting the contribution that individual terms and pieces of terms in the inv

geometrical implications of certain infinite dimensional decompositions we investigate the connections between the global structure of a banach space i e the existence of certain finite and infinite dimensional de compositions and the geometrical properties of the closed convex bounded sub sets of such a space i e the existence of extremal and other topologically distin guished points the global structures of various supposedly pathological examples of banach spaces constructed by r c james turn out to be more universal than expected for instance james tree type resp james matrix type decompositions characterize banach spaces with the point of continuity property resp the radon nikodym property moreover the convex point of continuity property is stable under the formation of james infinitely branching tree type sums of infinite dimensional factors we also give several counterex amples to various questions relating some topological and geometrical concepts in banach spaces

the bochner schoenberg eberlein property for commutative banach algebras especially fourier and fourier stieltjes algebras the classical bochner schoenberg eberlein theorem characterizes the continuous functions on the dual group of a locally compact abelian group g which arise as fourier stieltjes transforms of elements of the measure algebra m g of g this has led to the study of the algebra of bse functions on the spectrum of an arbitrary commutative banach algebra and of the concept of a bse algebra as introduced by takahasi and hatori since then bse algebras have been studied by several authors in this paper we investigate bse algebras in the general context on the one hand and on the other hand we specialize to fourier and fourier stieltjes algebras of locally compact groups

unwinding the hairball graph pruning algorithms for weighted complex networks empirical networks of weighted dyadic relations often contain noisy edges that alter the global characteristics of the network and obfuscate the most important structures therein graph pruning is the process of identifying the most significant edges according to a generative null model and extracting the subgraph consisting of those edges here we focus on integer weighted graphs commonly arising when weights count the occurrences of an event relating the nodes we introduce a simple and intuitive null model related to the configuration model of network generation and derive two significance filters from it the marginal likelihood filter mlf and the global likelihood filter glf the former is a fast algorithm assigning a significance score to each edge based on the marginal distribution of edge weights whereas the latter is an ensemble approach which takes into account the correlations among edges we apply these filters to the network of air traffic volume between us airports and recover a geographically faithful representation of the graph furthermore compared with thresholding based on edge weight we show that our filters extract a larger and significantly sparser giant component

isomorphisms between lp function spaces when p 1 we prove a number of results concerning isomorphisms between spaces of the type lp x where x is a separable p banach space and 0 p 1 our results imply that the quotient of lp 0 1 0 1 by the subspace of functions depending only on the first variable is not isomorphic to lp answering a question of n t peck more generally if b0 is a sub algebra of the borel sets of 0 1 then lp 0 1 lp 0 1 b0 is isomorphic to lp if and only if lp 0 1 b0 is complemented we also show that lp has up to isomorphism at most one complemented subspace non isomorphic to lp and classify completely those spaces x for which lp x lp in particular if l lp x 0 and lp x lp then x lp or is finite dimensional if x has trivial dual and lp x lp then x lp

identification of image artifacts from internal multiples first order internal multiples are a source of coherent noise in seismic images because they do not satisfy the single scattering assumption fundamental to most seismic processing there are a number of techniques to estimate internal multiples in data in many cases these algorithms leave some residual multiple energy in the data this energy produces artifacts in the image and the location of these artifacts is unknown because the multiples wereestimatedinthedatabeforetheimagewasformed toavoid this problem we propose a method by which the artifacts caused by internal multiples are estimated directly in the image we use ideas from the generalized bremmer series and the lippmannschwinger scattering series to create a forward scattering series to model multiples and an inverse scattering series to describe

on the near differentiability property of banach spaces abstract let be a scalar measure of bounded variation on a compact metrizable abelian group g suppose that has the property that for any measure whose fourier stieltjes transform vanishes at the measure has radon nikod m derivative with respect to the haar measure on g then l pigno and s saeki showed that itself has radon nikod m derivative such property is not shared by vector measures in general we say that a banach space x has the near differentiability property if every x valued measure of bounded variation shares the above property we prove that banach spaces with the radon nikod m property have the near differentiability property while banach spaces with the near differentiability property enjoy the near radon nikod m property we also show that the banach spaces l 1 0 1 and l 1 h 0 1 have the near differentiability property lastly we show that banach spaces with the near differentiability property have type ii radon nikod m property whenever is a riesz subset of type 0 of g

configuration model for correlation matrices preserving the node strength correlation matrices are a major type of multivariate data to examine properties of a given correlation matrix a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices such as those derived from random matrix theory that partially preserve properties of the original matrix we propose a model to generate such reference correlation and covariance matrices for the given matrix correlation matrices are often analyzed as networks which are heterogeneous across nodes in terms of the total connectivity to other nodes for each node given this background the present algorithm generates random networks that preserve the expectation of total connectivity of each node to other nodes akin to configuration models for conventional networks our algorithm is derived from the maximum entropy principle we will apply the proposed algorithm to measurement of clustering coefficients and community detection both of which require a null model to assess the statistical significance of the obtained results

the analytic complete continuity property abstract we introduce the notion of the analytic complete continuity property of banach spaces we give different characterizations of this property we show that this property is different from known related properties such as the complete continuity property and the analytic radon nikod m property

proportional thresholding in resting state fmri functional connectivity networks and consequences for patient control connectome studies issues and recommendations graph theoretical analysis has become an important tool in the examination of brain dysconnectivity in neurological and psychiatric brain disorders a common analysis step in the construction of the functional graph or network involves thresholding of the connectivity matrix selecting the set of edges that together form the graph on which network organization is evaluated to avoid systematic differences in absolute number of edges studies have argued against the use of an absolute threshold in case control studies and have proposed the use of proportional thresholding instead in which a pre defined number of strongest connections are selected as network edges ensuring equal network density across datasets here we systematically studied the effect of proportional thresholding on the construction of functional matrices and subsequent graph analysis in patient control functional connectome studies in a few simple experiments we show that differences in overall strength of functional connectivity fc as often observed between patients and controls can have predictable consequences for between group differences in network organization in individual networks with lower overall fc the proportional thresholding algorithm has to select more edges based on lower correlations which have on average a higher probability of being spurious and thus introduces a higher degree of randomness in the resulting network we show across both empirical and artificial patient control datasets that lower levels of overall fc in either the patient or control group will most often lead to differences in network efficiency and clustering suggesting that differences in fc across subjects will be artificially inflated or translated into differences in network organization based on the presented case control findings we inform about the caveats of proportional thresholding in patient control studies in which groups show a between group difference in overall fc we make recommendations on how to examine report and to take into account overall fc effects in future patient control functional connectome studies

removal of internal multiples with the common focus point cfp approach part 1 explanation of the theory removal of surface and internal multiples can be formulated by removing the influence of downward scattering boundaries and downward scattering layers the involved algorithms can be applied in a model driven or a data driven way a unified description is proposed that relates both types of algorithms based on wave theory the algorithm for the removal of surface multiples shows that muted shot records play the role of multichannel prediction filters the algorithm for the removal of internal multiples shows that muted cfp gathers play the role of multichannel prediction filters the internal multiple removal algorithm is illustrated with numerical examples the conclusion is that the layer related version of the algorithm has significant practical advantages

estimation of multiple scattering by iterative inversion part i theoretical considerations a review has been given of the surface related multiple problem by making use of the so called feedback model from the resulting equations it has been concluded that the proposed solution does not require any properties of the subsurface however source detector and reflectivity properties of the surface need be specified those properties have been quantified in a surface operator and this operator is estimated as part of the multiple removal problem the surface related multiple removal algorithm has been formulated in terms of a neumann series and in terms of an iterative equation the neumann formulation requires a nonlinear optimization process for the surface operator while the iterative formulation needs a number of linear optimizations the iterative formulation also has the advantage that it can be integrated easily with another multiple removal method an algorithm for the removal of internal multiples has been proposed as well this algorithm is an extension of the surface related method removal of internal multiples requires knowledge of the macro velocity model between the surface and the upper boundary of the multiple generating layer in part ii also published in this issue the success of the proposed algorithms has been demonstrated on numerical experiments and field data examples

age related changes in modular organization of human brain functional networks graph theory allows us to quantify any complex system e g in social sciences biology or technology that can be abstractly described as a set of nodes and links here we derived human brain functional networks from fmri measurements of endogenous low frequency correlated oscillations in 90 cortical and subcortical regions for two groups of healthy young and older participants we investigated the modular structure of these networks and tested the hypothesis that normal brain aging might be associated with changes in modularity of sparse networks newman s modularity metric was maximised and topological roles were assigned to brain regions depending on their specific contributions to intra and inter modular connectivity both young and older brain networks demonstrated significantly non random modularity the young brain network was decomposed into 3 major modules central and posterior modules which comprised mainly nodes with few inter modular connections and a dorsal fronto cingulo parietal module which comprised mainly nodes with extensive inter modular connections the mean network in the older group also included posterior superior central and dorsal fronto striato thalamic modules but the number of intermodular connections to frontal modular regions was significantly reduced whereas the number of connector nodes in posterior and central modules was increased

extracting the multiscale backbone of complex weighted networks a large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength in recent years the study of an increasing number of large scale networks has highlighted the statistical heterogeneity of their interaction pattern with degree and weight distributions that vary over many orders of magnitude these features along with the large number of elements and links make the extraction of the truly relevant connections forming the network s backbone a very challenging problem more specifically coarse graining approaches and filtering techniques come into conflict with the multiscale nature of large scale systems here we define a filtering method that offers a practical procedure to extract the relevant connection backbone in complex multiscale networks preserving the edges that represent statistically significant deviations with respect to a null model for the local assignment of weights to edges an important aspect of the method is that it does not belittle small scale interactions and operates at all scales defined by the weight distribution we apply our method to real world network instances and compare the obtained results with alternative backbone extraction techniques

multiple subtraction using an expanded multichannel matching filter an expanded multichannel matching emcm filter is proposed for the adaptive subtraction in seismic multiple attenuation for a normal multichannel matching filter where an original seismic trace is matched by a group of multiple model traces the lateral coherency of adjacent traces is likely to be exploited to discriminate the overlapped multiple and primary reflections in the proposed emcm filter a seismic trace is matched by not only a group of the ordinary multiple model traces but also their adjoints generated mathematically the adjoints of a multiple model trace include its first derivative its hilbert transform and the derivative of the hilbert transform the convolutional coefficients associated with the normal multichannel filter can be represented as a 2d operator in the time space domain this 2d operator is expanded with an additional spatial dimension in the emcm filter to improve the robustness of the adaptive subtraction the multiple model traces are generated using moveout equations to afford efficiency in the multiple attenuation application

surface related multiple elimination on wide tow marine data surface related multiples typically correspond to the largest component of multiple energy on marine seismic data because the surface is an almost perfect reflector with a reflectivity close to unity and thus their elimination is a major goal of seismic processing recent work has shown surface related multiple elimination srme to be effective in attenuating surface related multiples particularly in complex geology which may include diffracting features figure 1 shows the basic idea behind srme a surface related multiple is recorded at receiver x r due to a shot at location xs the event is a surface related multiple because it undergoes at least one downward reflection at the surface in this case at a during its propagation one readily sees that this surface related multiple event is the composition of two events one recorded at a due to a shot at xs and a second recorded at xr due to a shot at a thus the basic operation in srme is a spatio temporal convolution of the data with itself this gives the correct kinematics of the surface related multiples but not their amplitudes the exact prediction is given by a cross convolution of the data with the surface related multiple free version of the data and with proper accounting for directivity ghosts and the obliquity factor in an iterative formulation the i 1 th estimate of the multiples is the cross convolution of the data u with the ith estimate of the multiple free data u i figure 1 basic concept behind srme srme does not require any subsurface information nor does it make any assumptions about seismic events such as hyperbolicity or moveout separation between primaries and multiples as a result srme can handle arbitrarily complex multiples including in particular diffracted multiples in fact srme appears to be the only effective approach to attenuating diffracted multiples and this

free surface multiple attenuation for blended data abstractblended data sets are now being acquired because of improved efficiency and reduction in cost compared with conventional seismic data acquisition we have developed two methods for blended data free surface multiple attenuation the first method is based on an extension of surface related multiple elimination srme theory in which free surface multiples of the blended data can be predicted by a multidimensional convolution of the seismic data with the inverse of the blending operator a least squares inversion method is used which indicates that crosstalk noise existed in the prediction result due to the approximate inversion an adaptive subtraction procedure similar to that used in conventional srme is then applied to obtain the blended primary this can damage the energy of primaries the second method is based on inverse data processing idp theory adapted to blended data we derived a formula similar to that used in conventional idp and we attenuated free surface multiples by simple mut

improving adaptive subtraction in seismic multiple attenuation in seismic multiple attenuation once the multiple models have been built the effectiveness of the processing depends onthesubtractionstep usuallytheprimaryenergyispartially attenuated during the adaptive subtraction if an l 2 norm matching filter is used to solve a least squares problem the expandedmultichannelmatchingemcmfiltergenerallyis effective but conservative parameters adopted to preserve theprimarycouldleadtosomeremainingmultiples wehave managed to improve the multiple attenuation result through aniterativeapplicationoftheemcmfiltertoaccumulatethe effect of subtraction a butterworth type masking filter based on the multiple model can be used to preserve most of the primary energy prior to subtraction and then subtraction canbeperformedontheremainingparttobettersuppressthe multiples without affecting the primaries meanwhile subtraction can be performed according to the orders of the multiples as a single subtraction window usually covers different order multiples with different amplitudes theoretical analyses and synthetic and real seismic data set demonstrations provedthatacombinationofthesethreestrategiesiseffective in improving the adaptive subtraction during seismic multipleattenuation

applications of the theory of semi embeddings to banach space theory let x and y be banach spaces and t x y an injective bounded linear operator t is called a semi embedding if t maps the closed unit ball of x to a closed subset of y this concept was introduced by lotz peck and porta proc edinburgh math soc 22 1979 233 240 it is proved that if x semi embeds in y and x is separable then x has the radon nikodym property provided y does it is shown that if l1 semi embeds in y then y fails the schur property and contains a subspace isomorphic to l1 as a consequence of the proof it is shown that if x is a subspace of l1 either l1 embeds in x or l1 embeds in l1x the simpler result that l1 does not semi embed in c0 is treated separately this result is used to deduce the classic result of menchoff that there exists a singular probability measure on the circle with fourier coefficients vanishing at infinity some generalizations of the notion of semi embedding are given and several complements and open questions are discussed

decompositions of banach lattices into direct sums we consider the problem of decomposing a banach lattice z as a direct sum z x y where x and y are complemented subspaces satisfying a condition of incomparability e g every operator from y to x is strictly singular we treat both the atomic and nonatomic cases in particular we answer a question of wojtaszczyk by showing that l1 ffll2 has unique structure as a nonatomic banach lattice one of the most important problems in the theory of banach lattices which is still open is whether any complemented subspace of a banach lattice must be linearly isomorphic to a banach lattice the main difficulty seems to lie in the fact that most of the criteria for a banach space to be isomorphic to a lattice do not really distinguish between lattices and their complemented subspaces we do not actually treat this question in the present paper but rather consider the situation z x d3 y where z is a banach lattice and x and y two complemented subspaces which are assumed to satisfy different conditions that make them distinct in some or another sense this line of research was initiated by p wojtaszczyk 128 and also by i s edelstein and p wojtaszczyk 3 who proved that if z has a normalized unconditional basis zn n l i e it is a separable atomic lattice so that every linear operator from y into x is compact then zn n l splits into two disjoint parts which are respectively equivalent to bases of x and y in particular both x and y have unconditional bases the proof of this result is based on a fundamental theorem from 28 and 3 which is mentioned below as theorem a we give here a different proof which does not make use of theorem a but instead is based on a simple change of signs result from 2 which is described below as theorem b we also consider the case when the compactness assumption above is replaced by the total incomparability of x and y for which we prove a similar result provided x and y have unconditional bases unfortunately the most interesting case when every operator from y into x is assumed to be strictly singular which was raised as an open problem in 28 remains unsolved we conclude the section devoted to the atomic case with a simple theorem on block bases of a space with unconditional basis zn 1 whose span is complemented such a block basis splits into two disjoint parts the first equivalent to a subsequence of zn n received by the editors september 5 1986 1980 mathematics subject classification 1985 revision primary 46b30 46b15 secondary 46a40 this research was supported by grant no 84 00210 from the united states israel binational science foundation bsf jerusalem israel the research of the first author was also supported in part by nsf grant dms 8500938 the research of the second author was also supported in part by nsf grant dms 8601401 r 1987 american mathematical society ooo2 9947 87 1 00 25 per page

some characterizations of the analytic radon nikodým property in banach spaces the analytic radon nikod m property for a complex banach space x is characterized in several ways analogous to the common characterizations of the radon nikod m property for example the banach space x has the analytic radon nikod m property if and only if any operator from l1 to x that factors through l1h01 is representable the characterizations are used to study complemented subspaces of l1h01 and to define the analytic radon nikod m property for real banach spaces

the three space problem for l 1 we construct a subspace x of l1 such that x is an 1 sum of spaces isomorphic to 11 but such that l1 x does not contain a copy of l1 we also construct two banach spaces e1 e2 that do not contain a copy of li but such that e1 x e2 contains a copy of l1 moreover the projections this content downloaded from 207 46 13 150 on thu 28 jul 2016 05 31 04 utc all use subject to http about jstor org terms the three space problem for l 29 of li on each factor are one to one and the images of the unit ball of l1 are closed these examples settle questions of j lindenstrauss p pelczynski j bourgain and h p rosenthal equipe d analyse tour 46 u a au c n r s n0 754 universitt paris vi 4 place jussieu 75230 paris cedex 05 department of mathematics ohio state university 231 w 18th avenue columbus ohio 43210 this content downloaded from 207 46 13 150 on thu 28 jul 2016 05 31 04 utc all use subject to http about jstor org terms

scale free brain functional networks functional magnetic resonance imaging is used to extract functional networks connecting correlated human brain sites analysis of the resulting networks in different tasks shows that a the distribution of functional connections and the probability of finding a link versus distance are both scale free b the characteristic path length is small and comparable with those of equivalent random networks and c the clustering coefficient is orders of magnitude larger than those of equivalent random networks all these properties typical of scale free small world networks reflect important functional information about brain states

multidimensional inverse scattering series internal multiple prediction in the coupled plane wave domain the inverse scattering series internal multiple prediction and attenuation algorithm predicts multiples using certain combinations of input seismic reflection data events which are computed in the wavenumber pseudo depth or plane wave vertical travel time i e p domains significant differences can arise in the algorithms output and computational expense depending on which domain is used many of these are traceable to the response of the algorithm to the users choice of the search limiting parameter the question of which domain is optimal can be addressed with benchmark synthetics the compactness of the input to the plane wave domain algorithm leads to the expectation that it will have a reduced computational expense also the lack of increase in the dominant period i e width of input events as the horizontal slowness increases leads to the expectation that it will respond well to a constant both of these expectations are borne out with a 1 5d benchmark example a 2d plane wave pred

information filtering in complex weighted networks many systems in nature society and technology can be described as networks where the vertices are the system s elements and edges between vertices indicate the interactions between the corresponding elements edges may be weighted if the interaction strength is measurable however the full network information is often redundant because tools and techniques from network analysis do not work or become very inefficient if the network is too dense and some weights may just reflect measurement errors and need to be be discarded moreover since weight distributions in many complex weighted networks are broad most of the weight is concentrated among a small fraction of all edges it is then crucial to properly detect relevant edges simple thresholding would leave only the largest weights disrupting the multiscale structure of the system which is at the basis of the structure of complex networks and ought to be kept in this paper we propose a weight filtering technique based on a global null model global statistical significance gloss filter keeping both the weight distribution and the full topological structure of the network the method correctly quantifies the statistical significance of weights assigned independently to the edges from a given distribution applications to real networks reveal that the gloss filter is indeed able to identify relevant connections between vertices

multiple prediction through inversion theoretical advancements and real data application wave equation based multiple attenuation seismic methods may be divided into the two distinct phases of multiple modeling and multiple subtraction these two are interrelated and must be optimized in order to produce an optimal final result the multiple prediction through inversion mpi scheme updates the multiple model iteratively as we usually do in a linearized inverse problem the scheme models the multiple wavefield without an explicit knowledge of surface and subsurface structures or of the source signature both are generally unknown in seismic surveys however compared to a conventional surface related multiple attenuation method the accuracy of the multiple model is improved both kinematically and dynamically it is because the mpi scheme implicitly takes account of the spatial variation of the surface reflectivity the source signature the detector patterns and receiver ghosts and other effects included in the so called surface operator when the mpi scheme is used in the first phase it also significantly reduces the nonlinearity of the problem in the second phase that involves attenuating multiples without removing or altering primaries the effectiveness of the mpi scheme is demonstrated by examples involving real marine seismic data

imaging of multiple reflections current multiple removal algorithms in seismic processing use either differential moveout or predictability if the differential moveout between primaries and multiples is small prediction is the only option available in the last decade multidimensional prediction error filtering by weighted convolution such as surface related multiple elimination srme have proved to be very successful in practice so far multiples have been considered as noise and have been discarded after the removal process in this paper we argue that multiple reflections contain a wealth of information that can be used in seismic processing to improve the resolution of reservoir images beyond current capability in the near future one may expect that the so called weighted crosscorrelation wcc concept may offer an attractive alternative in approaching the multiple problem wcc creates an option to avoid the adaptive subtraction process as applied in prediction error algorithms moreover it allows the transformation of multiples into primaries the latter means that seismic imaging with primaries and multiples nonlinear process can be implemented by a sequence of linear processes including the transformation of multiples into primaries and the imaging of primaries

radon nikodym property for the projective tensor product of kothe function spaces abstract let e be an order continuous kothe function space or an order continuous banach lattice and x be a dual banach space then e x the projective tensor product of e and x has the radon nikodym property if and only if both e and x do

multiple elimination using a pattern recognition technique standard prestack multiple elimination techniques such as predictive deconvolution or radon transforms fail in the presence of complex structures

on the representation of order continuous operators by random measures using the representation tf y if dvy where vy is a random mea sure we characterize some interesting bands in the lattice of all order continuous operators on a space of measurable functions for example an operator t is lattice orthogonal to all integral operators i e all cv are singular or belongs to the band generated by all riesz homomorphisms i e all r are atomic if and only if t satisfies certain properties which are modeled after the riesz homomorphism property 31 and continuity with respect to convergence in measure on the other hand for operators orthogonal to all riesz homomorphisms i e all vy are diffuse we give characterizations analogous to the characterizations of dunford and pettis and buhvalov for integral operators the latter results are related to enflo operators to a result of j bourgain on dunford pettis operators and martingale representa tions of operators

transport in weighted networks partition into superhighways and roads transport in weighted networks is dominated by the minimum spanning tree mst the tree connecting all nodes with the minimum total weight we find that the mst can be partitioned into two distinct components having significantly different transport properties characterized by centrality the number of times a node or link is used by transport paths one component superhighways is the infinite incipient percolation cluster for which we find that nodes or links with high centrality dominate for the other component roads which includes the remaining nodes low centrality nodes dominate we find also that the distribution of the centrality for the infinite incipient percolation cluster satisfies a power law with an exponent smaller than that for the entire mst the significance of this finding is that one can improve significantly the global transport by improving a tiny fraction of the network the superhighways

simultaneous inversion of multiples and primaries inversion versus subtraction in this article we propose an inversion scheme to replace the adaptive subtraction approaches which are widely used in conventional two step prediction subtraction multiple elimination methods this new method named simp simultaneous inversion for multiples and primaries inverts seismic data using constraints e g modeled multiples and or geologic discriminants for multiples and primaries simultaneously simp incorporates pattern recognition and shaping filters into one concise and practically solvable formulation its main advantages are that no orthogonality between multiples and primaries is assumed and that wavelet information is not necessary for the inversion

probabilistic thresholding of functional connectomes application to schizophrenia abstract functional connectomes are commonly analysed as sparse graphs constructed by thresholding cross correlations between regional neurophysiological signals thresholding generally retains the strongest edges correlations either by retaining edges surpassing a given absolute weight or by constraining the edge density the latter more widely used method risks inclusion of false positive edges at high edge densities and exclusion of true positive edges at low edge densities here we apply new wavelet based methods which enable construction of probabilistically thresholded graphs controlled for type i error to a dataset of resting state fmri scans of 56 patients with schizophrenia and 71 healthy controls by thresholding connectomes to fixed edge specific p value we found that functional connectomes of patients with schizophrenia were more dysconnected than those of healthy controls exhibiting a lower edge density and a higher number of dis connected components furthermore many participants connectomes could not be built up to the fixed edge densities commonly studied in the literature 5 30 while controlling for type i error additionally we showed that the topological randomisation previously reported in the schizophrenia literature is likely attributable to non significant edges added when thresholding connectomes to fixed density based on correlation finally by explicitly comparing connectomes thresholded by increasing p value and decreasing correlation we showed that probabilistically thresholded connectomes show decreased randomness and increased consistency across participants our results have implications for future analysis of functional connectivity using graph theory especially within datasets exhibiting heterogenous distributions of edge weights correlations between groups or across participants

on the structure of non weakly compact operators on banach lattices in this paper we study extensions of theorems of hagler and stegall on lp spaces 11 and of rosenthal 24 25 and pelczynski 21 on c k spaces to more general banach spaces with some lattice structure which do not contain complemented copies of i r we show that i fx is a separable banach space such that co does not embed into x and t is a bounded linear operator from x into some banach space y such that t y is not separable then i if x has local unconditional structure h la gordon and lewis 7

wave propagation in heterogeneous media effects of fine scale heterogeneity we study the multiple scattering effects caused by fine scale heterogeneity for this purpose it is unreasonable to rely on a linearization of the dependency of the wavefield in the parameters that describe the medium therefore the only tools that correctly model wave propagation are based on the numerical solution of the two way wave equation by finite differences or finite elements a fine grid provides a straightforward approach to account for fine scale heterogeneity in this situation there is no need for high order schemes variational methods allow us to exhibit a numerical scheme that accounts for heterogeneity and that is by construction stable provided a stability condition is fulfilled this condition is a sufficient stability condition contrary to the classical necessary stability conditions in addition general mathematical results prove the finite difference solution is close to the solution of the wave equation when the grid is fine enough the multiple scattering effects caused by fine scale heterogeneity are very important in particular we observe that imaging the so computed synthetic data by standard migration techniques that assume a linearization of the above mentioned dependency shows a strongly noise corrupted image this illustrates the importance of preprocessing data to remove the effect of multiple scattering we try to improve the signal to noise ratio by removing multiples related to the free surface although significant noise reduction is achieved even more sophisticated preprocessing is required to obtain a clear image of the subsurface

explosive percolation in thresholded networks abstract explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges although extensively studied in random network models and reconstructed real networks explosive percolation has not been observed in a more realistic scenario where a network is generated by thresholding a similarity matrix describing between node associations in this report i examine construction schemes of such thresholded networks and demonstrate that explosive percolation can be observed by introducing edges in a particular order

gδ embeddings in hilbert space ii in this paper which is a continuation of 10 we exhibit some topological conditions on a banach space which ensure that it contains isometric copies of infinite dimensional conjugate spaces this result is used to identify a large class of banach spaces that are hereditarily separable duals a method of defining a jamestree sum of a countable number of banach spaces is given it is used to construct various counterexamples for instance there exists for each integer n a banach space that can be mapped into hilbert space via the composition of n but not n 1 g embeddings we also continue the investigation of the global structure of some geometrically defined banach spaces for example it is shown that a separable banach space x with the radon nikodym property r n p has a subspace y with a boundedly complete finite dimensional decomposition f d d such that xy has an f d d and the r n p

radon nikodým properties associated with subsets of countable discrete abelian groups with any subset of a countable discrete abelian we associate with it three banach space properties these properties are radon nikodym type properties the relationship between these properties is investigated the results are applied to give new characterizations of riesz subsets and rosenthal subsets of countable discrete abelian groups

gδ embeddings in hilbert space abstract it is shown that a separable banach space x has the point of weak to norm continuity property resp the radon nikodym property if and only if there exists a compact g embedding resp an h embedding from x into l2 this solves several questions of j bourgain and h p rosenthal j funct anal 52 1983 it is also shown that every non relatively compact sequence in a banach space with property pc has a difference subsequence which is a boundedly complete basic sequence this solves a question of pelczynski and extends some results of w b johnson and h p rosenthal studia math 43 1972 77 92 various related questions asked in the above bourgain rosenthal reference and by g a edgar and r f wheeler pac j math 115 1984 and n ghoussoub and h p rosenthal math ann 264 1983 321 332 are also settled

the in stability of functional brain network measures across thresholds the large scale organization of the brain has features of complex networks that can be quantified using network measures from graph theory however many network measures were designed to be calculated on binary graphs whereas functional brain organization is typically inferred from a continuous measure of correlations in temporal signal between brain regions thresholding is a necessary step to use binary graphs derived from functional connectivity data however there is no current consensus on what threshold to use and network measures and group contrasts may be unstable across thresholds nevertheless whole brain network analyses are being applied widely with findings typically reported at an arbitrary threshold or range of thresholds this study sought to evaluate the stability of network measures across thresholds in a large resting state functional connectivity dataset network measures were evaluated across absolute correlation based and proportional sparsity based thresholds and compared between sex and age groups overall network measures were found to be unstable across absolute thresholds for example the direction of group differences in a given network measure may change depending on the threshold network measures were found to be more stable across proportional thresholds these results demonstrate that caution should be used when applying thresholds to functional connectivity data and when interpreting results from binary graph models

operators l1 r x and the norm continuity problem for semigroups we present a new method for constructing c0 semigroups for which properties of the resolvent of the generator and continuity properties of the semigroup in the operator norm topology are controlled simultaneously it allows us to show that a there exists a c0 semigroup which is continuous in the operator norm topology for no t 0 1 such that the resolvent of its generator has a logarithmic decay at infinity along vertical lines b there exists a c0 semigroup which is continuous in the operator norm topology for no t r such that the resolvent of its generator has a decay along vertical lines arbitrarily close to a logarithmic one these examples rule out any possibility of characterizing norm continuity of semigroups on arbitrary banach spaces in terms of resolvent norm decay on vertical lines

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

seismic trace interpolation in the f x y domain seismic trace interpolation is implemented as a 2 d x y spatial prediction performed separately on each frequency f slice this so called f x y domain trace interpolation method is based on the relation that the linear prediction lp operator estimated at a given frequency may be used to predict data at a higher frequency but a smaller trace spacing the relationship originally given for thef x domain trace interpolation is successfully extended to the f x y domain the extension is achieved by masking the data samples selectively from the input frequency slice to design the lp operators two interpolation algorithms using the full step and the fractional step predictions respectively are developed both methods use an all azimuth prediction in the x y domain but the fractional step prediction method is computationally more efficient while the interpolation method can be applied to a common offset cube of 3 d seismic it can also be applied to 2 d seismic traces for prestack data processing sy

removal of internal multiples with the common focus point cfp approach part 2 application strategies and data examples in the past the surface multiple removal method based on the feedback model has been successfully applied to many different field data sets the extension of surface to internal multiples can be made by replacing shot records with common focus point cfp gathers a cfp gather representing focused data with one source in the subsurface and all receivers at the surface or vice versa for a receiver gather the internal multiple removal algorithm can be formulated in terms of boundary related and layer related versions in the boundary related version the internal multiples are removed for one downward scattering reflector at a time in the layer related version the internal multiples are removed for a sequence of downward scattering reflectors at a time an exact velocity model is not required but proper muting is critical muting becomes straightforward in the cfp domain the strategy for applying the two versions of the multiple removal algorithm is demonstrated on physical model and field data one can conclude that the layer related version is the most appropriate in most situations because it requires less user action and does not need exact knowledge of the multiple generating boundary

consistency based thresholding of the human connectome densely seeded probabilistic tractography yields weighted networks that are nearly fully connected hence containing many spurious fibers it is thus necessary to prune spurious connections from probabilistically derived networks to obtain a more reliable overall estimate of the connectivity a standard method is to threshold by weight keeping only the strongest edges here by measuring the consistency of edge weights across subjects we propose a new thresholding method that aims to reduce the rate of false positives in group averaged connectivity matrices close inspection of the relationship between consistency weight and distance suggests that the most consistent edges are in fact those that are strong for their length rather than simply strong overall hence retaining the most consistent edges preserves more long distance connections than traditional weight based thresholding which penalizes long connections for being weak regardless of anatomy by comparing our thresholded networks to mouse and macaque tracer data we also show that consistency based thresholding exhibits the species invariant exponential decay of connection weights with distance while weight based thresholding does not we also show that consistency based thresholding can be used to identify highly consistent and highly inconsistent subnetworks across subjects enabling more nuanced analyses of group level connectivity than just the mean connectivity

statistical properties of randomly broken objects and of multivalley structures in disordered systems the statistical properties of the multivalley structure of disordered systems and of randomly broken objects have many features in common for all these problems if w denotes the weight of the sth piece we show that the probability distributions pi w of the largest piece w p2 w of the second largest piece and n y of y 1 wi always have singularities at w l n w2 l n and y ijn n 1 2 3

multiple prediction through inversion a fully data driven concept for surface related multiple attenuation this paper introduces a fully data driven concept multiple prediction through inversion mpi for surface related multiple attenuation sma it builds the multiple model not by spatial convolution as in a conventional sma but by updating the attenuated multiple wavefield in the previous iteration to generate a multiple prediction for the new iteration as is usually the case in an iterative inverse problem because mpi does not use spatial convolution it is able to minimize the edge effect that appears in conventional sma multiple prediction and to eliminate the need to synthesize near offset traces required by a conventional scheme so that it can deal with a seismic data set with missing near offset traces the mpi concept also eliminates the need for an explicit surface operator which is required by conventional sma and is comprised of the inverse source signature and other effects this method accounts implicitly for the spatial variation of the surface operator in multiple model building and attempts to predict multiples which are not only accurate kinematically but are also accurate in phase and amplitude

conjugate operators that preserve the nonconvergence of bounded martingales we show that the conjugate t of an operator t x y with x and y banach spaces satisfies the following dichotomy either t preserves the nonconvergence of bounded martingales in y or there exists a compact operator k x y such that the kernel n t k fails the radon nikod m property

adaptive overburden elimination with the multidimensional marchenko equation abstractiterative substitution of the multidimensional marchenko equation has been introduced recently to integrate internal multiple reflections in the seismic imaging process in so called marchenko imaging a macro velocity model of the subsurface is required to meet this objective the model is used to back propagate the data during the first iteration and to truncate integrals in time during all successive iterations in case of an erroneous model the image will be blurred akin to conventional imaging and artifacts may arise from inaccurate integral truncations however the scheme is still successful in removing artifacts from internal multiple reflections inspired by these observations we rewrote the marchenko equation such that it can be applied early in a processing flow without the need of a macro velocity model instead we have required an estimate of the two way traveltime surface of a selected horizon in the subsurface we have introduced an approximation such that adaptive subtracti