ramification of local fields with imperfect residue fields we define two decreasing filtrations by ramification groups on the absolute galois group of a complete discrete valuation field whose residue field may not be perfect in the classical case where the residue field is perfect we recover the classical upper numbering filtration the definition uses rigid geometry and log structures we also establish some of their properties

multiscale methods for data on graphs and irregular multidimensional situations for regularly spaced one dimensional data wavelet shrinkage has proven to be a compelling method for non parametric function estimation we create three new multiscale methods that provide wavelet like transforms both for data arising on graphs and for irregularly spaced spatial data in more than one dimension the concept of scale still exists within these transforms but as a continuous quantity rather than dyadic levels further we adapt recent empirical bayesian shrinkage techniques to enable us to perform multiscale shrinkage for function estimation both on graphs and for irregular spatial data we demonstrate that our methods perform very well when compared with several other methods for spatial regression for both real and simulated data although we concentrate on multiscale shrinkage regression we present our new wavelet transforms as generic tools intended to be the basis of methods that might benefit from a multiscale representation of data either on graphs or for irregular spatial data

oversampled graph laplacian matrix for graph filter banks we describe a method of oversampling signals defined on a weighted graph by using an oversampled graph laplacian matrix the conventional method of using critically sampled graph filter banks has to decompose the original graph into bipartite subgraphs and a transform has to be performed on each subgraph because of the spectral folding phenomenon caused by downsampling of graph signals therefore the conventional method cannot always utilize all edges of the original graph in a single stage transformation our method is based on oversampling of the underlying graph itself and it can append nodes and edges to the graph somewhat arbitrarily we use this approach to make one oversampled bipartite graph that includes all edges of the original non bipartite graph we apply the oversampled graph with the critically sampled graph filter bank or the oversampled one for decomposing graph signals and show the performances on some experiments

a mixture theory with a director for linear elastodynamics of periodically laminated media abstract the asymptotic method of multiple scales is used to construct a continuum theory with microstructure for the linear elastodynamics of a periodically laminated medium the resulting theory is in the form of a homogeneous binary mixture theory of micromorphic materials with a common director oriented normal to the interfaces the model contains nine conservation equations six for the linear momenta of both constituents and three for the director momentum the asymptotically derived constitutive equations contain mixture properties which in contrast to phenomenological theories are determined solely from the properties of the individual constituents and their volume fractions the mixture conservation and constitutive equations are complemented by an appropriate set of boundary conditions determined by a variational procedure the efficacy of the model is assessed by comparison of predicted and exact phase velocity spectra for waves propagating at oblique incidence to the layers the excellent agreement observed indicates that the model is useful for studying the dynamic behavior of laminated composites further the method of multiple scales appears to provide an effective approach to the accurate determination of the large scale behavior of a material which exhibits small scale periodic heterogeneity

l espace symetrique de drinfeld et correspondance de langlands locale ii we study the geometry and the cohomology of the tamely ramified cover of drinfeld s p adic symmetric space over a p adic field k for this tame level we prove in a purely local way most of a conjecture of harris on the form of the ell adic cohomologies as well as the torsion freeness of the integral cohomology in this paper we also compute the ell adic cohomology of coxeter deligne lusztig variety associated to mathrm gl d and some results of independent interest on the coefficient systems over the bruhat tits building associated to mathrm gl d k have been established

weight monodromy conjecture for p adically uniformized varieties the aim of this paper is to prove the weight monodromy conjecture deligne s conjecture on the purity of monodromy filtration for varieties p adically uniformized by the drinfeld upper half spaces of any dimension the ingredients of the proof are to prove a special case of the hodge standard conjecture and apply a positivity argument of steenbrink m saito to the weight spectral sequence of rapoport zink as an application by combining our results with the results of schneider stuhler we compute the local zeta functions of p adically uniformized varieties in terms of representation theoretic invariants we also consider a p adic analogue by using the weight spectral sequence of mokrane

learning graphs with monotone topology properties and multiple connected components recent papers have formulated the problem of learning graphs from data as an inverse covariance estimation problem with graph laplacian constraints while such problems are convex existing methods cannot guarantee that solutions will have specific graph topology properties e g being a tree which are desirable for some applications the problem of learning a graph with topology properties is in general non convex in this paper we propose an approach to solve these problems by decomposing them into two sub problems for which efficient solutions are known specifically a graph topology inference gti step is employed to select a feasible graph topology then a graph weight estimation gwe step is performed by solving a generalized graph laplacian estimation problem where edges are constrained by the topology found in the gti step our main result is a bound on the error of the gwe step as a function of the error in the gti step this error bound indicates that the gti step should be solved using an algorithm that approximates the data similarity matrix by another matrix whose entries have been thresholded to zero to have the desired type of graph topology the gti stage can leverage existing methods which are typically based on minimizing the total weight of removed edges since the gwe stage is an inverse covariance estimation problem with linear constraints it can be solved using existing convex optimization methods we demonstrate that our approach can achieve good results for both synthetic and texture image data

discrete signal processing on graphs frequency analysis signals and datasets that arise in physical and engineering applications as well as social genetics biomolecular and many other domains are becoming increasingly larger and more complex in contrast to traditional time and image signals data in these domains are supported by arbitrary graphs signal processing on graphs extends concepts and techniques from traditional signal processing to data indexed by generic graphs this paper studies the concepts of low and high frequencies on graphs and low high and band pass graph signals and graph filters in traditional signal processing these concepts are easily defined because of a natural frequency ordering that has a physical interpretation for signals residing on graphs in general there is no obvious frequency ordering we propose a definition of total variation for graph signals that naturally leads to a frequency ordering on graphs and defines low high and band pass graph signals and filters we study the design of graph filters with specified frequency response and illustrate our approach with applications to sensor malfunction detection and data classification

compact support biorthogonal wavelet filterbanks for arbitrary undirected graphs this paper extends previous results on wavelet filterbanks for data defined on graphs from the case of orthogonal transforms to more general and flexible biorthogonal transforms as in the recent work the construction proceeds in two steps first we design one dimensional two channel filterbanks on bipartite graphs and then extend them to multi dimensional separable two channel filterbanks for arbitrary graphs via a bipartite subgraph decomposition we specifically design wavelet filters based on the spectral decomposition of the graph and state sufficient conditions for the filterbanks to be perfect reconstruction and orthogonal while our previous designs referred to as graph qmf filterbanks are perfect reconstruction and orthogonal they are not exactly k hop localized i e the computation at each node is not localized to a small k hop neighborhood around the node in this paper we relax the condition of orthogonality to design a biorthogonal pair of graph wavelets that are k hop localized with compact spectral spread and still satisfy the perfect reconstruction conditions the design is analogous to the standard cohen daubechies feauveau s cdf construction of factorizing a maximally flat daubechies half band filter preliminary results demonstrate that the proposed filterbanks can be useful for both standard signal processing applications as well as for signals defined on arbitrary graphs

canonical subgroups of barsotti tate groups let s be the spectrum of a complete discrete valuation ring with fraction field of characteristic 0 and perfect residue field of characteristic p 3 let g be a truncated barsotti tate group of level 1 over s if g is not too supersingular a condition that will be explicitly expressed in terms of the valuation of a certain determinant then we prove that we can canonically lift the kernel of the frobenius endomorphism of its special fiber to a subgroup scheme of g finite and flat over s we call it the canonical subgroup of g

application de hodge tate duale d un groupe de lubin tate immeuble de bruhat tits du groupe lineaire et filtrations de ramification

efficient sampling set selection for bandlimited graph signals using graph spectral proxies we study the problem of selecting the best sampling set for bandlimited reconstruction of signals on graphs a frequency domain representation for graph signals can be defined using the eigenvectors and eigenvalues of variation operators that take into account the underlying graph connectivity smoothly varying signals defined on the nodes are of particular interest in various applications and tend to be approximately bandlimited in the frequency basis sampling theory for graph signals deals with the problem of choosing the best subset of nodes for reconstructing a bandlimited signal from its samples most approaches to this problem require a computation of the frequency basis i e the eigenvectors of the variation operator followed by a search procedure using the basis elements this can be impractical in terms of storage and time complexity for real datasets involving very large graphs we circumvent this issue in our formulation by introducing quantities called graph spectral proxies defined using the powers of the variation operator in order to approximate the spectral content of graph signals this allows us to formulate a direct sampling set selection approach that does not require the computation and storage of the basis elements we show that our approach also provides stable reconstruction when the samples are noisy or when the original signal is only approximately bandlimited furthermore the proposed approach is valid for any choice of the variation operator thereby covering a wide range of graphs and applications we demonstrate its effectiveness through various numerical experiments

micromechanical modeling of transient waves from matrix cracking and fiber fracture in laminated beams abstract a micromechanical model for excitation of waves resulting from fiber fracture and matrix cracking in laminated beams is presented the source is described as a time dependent displacement discontinuity and the wave propagation in the beam is modeled by a higher order beam theory the equations of motion defined by the beam model are then formally solved by employing integral transforms asymptotically valid solutions are subsequently found using residue calculus and the stationary phase method as an example a 90 0 2 90 beam with a width to thickness ratio of 10 is considered the dispersion curves resulting from the beam theory and three dimensional finite element computations are compared and a maximum frequency for applicability of the beam theory is determined the time response from fiber fracture and transverse matrix cracking is presented the applications of the results to the analysis of acoustic emission experiments are also discussed

on the decomposition numbers of the finite general linear groups ii let g gl q q a prime power and let r be an odd prime not dividing q let s be a semisimple element of g of order prime to r and assume that r divides qdeg x 1 for all elementary divisors a of s relating representations of certain hecke algebras over symmetric groups with those of g we derive a full classification of all modular irreducible modules in the r block bh of g with semisimple part s the decomposition matrix d of bs may be partly described in terms of the decomposition matrices of the symmetric groups corresponding to the hecke algebras above moreover d is lower unitriangular this applies in particular to all r blocks of g if r divides q 1 thus in this case the r decomposition matrix of g is lower unitriangular introduction the modular representation theory of finite groups of lie type defined over a field of characteristic p is naturally divided into the cases of equal characteristic r p and unequal characteristic r p this paper begins the study of decomposition numbers in the unequal characteristic case of the finite general linear groups when r 2 let g be the full linear group of degree n over gf q and 2 r be a prime not dividing q let s c g be semisimple and consider the geometric conjugacy class s g of irreducible characters corresponding to the g conjugacy class of s using basic properties of the deligne lusztig operators introduced in 7 we will determine a parabolic subgroup p ps of g and a cuspidal irreducible character of x of p such that s g is just the set of constituents of xg the induced character let r r k be an r modular system for g and m a kp module affording x then end kg m is called the hecke algebra of m compare 5 and has been calculated in a more general context by r b howlett and g i lehrer in 12 it turns out that end kg m k w the hecke algebra of w where w wj denotes the weyl group of cg s the centralizer of s in g compare 1 2 4 13 in particular k w has a basis tw iw c w such that the structure constants of the multiplication are all contained in r c k so let r w be the r order in k w generated by wtiw ew and r w r r r w choosing a special rp lattice s in m and using the classification of the r blocks of rg given by p fong and b srinivasan in received by the editors july 25 1983 and in revised form october 18 1983 may 23 1984 and september 1 1984 1980 mathematics subject classification primary 20c20 secondary 20g40 this work was supported by the deutsche forschungsgemeinschaft 1985 american mathematical society 0002 9947 85 1 00 25 per page

m channel perfect recovery of coarsened graphs and graph signals with spectral invariance and topological preservation in this paper an m channel perfect reconstruction filter bank based on a coarsening algorithm is proposed compared with most of the designs of graph filter banks that do not consider the graph reconstruction our proposed design can provide the perfect graph reconstruction as well as perfect graph signal reconstruction in the analysis part the proposed filter bank provides a coarse version of the input graph as well as coarsened graph signal spectral invariant to the input signal in the synthesis part the filter bank perfectly reconstructs the input graph as well as input signal from their coarse version the spirit of the proposed design is to partition the spectral information of the input graph and input graph signal into every channel the partition method is adjustable and can be nonuniform two intuitive schemes named sort by eigenvalue and sort by intensity for uniform partition are introduced in the proposed design the coarsening operators are obtained through an existing coarsening algorithm while the recovery operators are defined by taking the conjugate transpose of the coarsening operators besides we address the relation between the proposed design and a framework of sampling graph signals based on the discrete sampling theory it is shown that the coarsening operator in the proposed design is actually a special case of the sampling operator in the framework based on the discrete sampling theory experimental results are presented to demonstrate the effectiveness of the proposed design of filter banks

floquet bloch decomposition for the computation of dispersion of two dimensional periodic damped mechanical systems floquet bloch theorem is widely applied for computing the dispersion properties of periodic structures and for estimating their wave modes and group velocities the theorem allows reducing computational costs through modeling of a representative cell while providing a rigorous and well posed spectral problem representing wave dispersion in undamped media most studies employ the floquet bloch approach for the analysis of undamped systems or for systems with simple damping models such as viscous or proportional damping in this paper an alternative formulation is proposed whereby wave heading and frequency are used to scan the k space and estimate the dispersion properties the considered approach lends itself to the analysis of periodic structures with complex damping configurations resulting for example from active control schemes the presence of damping materials or the use of shunted piezoelectric patches examples on waveguides with various levels of damping illustrate the performance and the characteristics of the proposed approach and provide insights into the properties of the obtained eigensolutions

downsampling of signals on graphs via maximum spanning trees downsampling of signals living on a general weighted graph is not as trivial as of regular signals where we can simply keep every other samples in this paper we propose a simple yet effective downsampling scheme in which the underlying graph is approximated by a maximum spanning tree mst that naturally defines a graph multiresolution this mst based method significantly outperforms the two previous downsampling schemes coloring based and svd based on both random and specific graphs in terms of computations and partition efficiency quantified by the graph cuts the benefit of using mst based downsampling for recently developed critical sampling graph wavelet transforms in compression of graph signals is demonstrated

attribute fusion in a latent process model for time series of graphs hypothesis testing on time series of attributed graphs has applications in diverse areas e g social network analysis wherein vertices represent individual actors or organizations connectome inference wherein vertices are neurons or brain regions and text processing wherein vertices represent authors or documents we consider the problem of anomaly change point detection given the latent process model for time series of graphs with categorical attributes on the edges presented in n h lee and c e priebe a latent process model for time series of attributed random graphs statist inference stoch process vol 14 pp 231 253 2011 various attributed graph invariants are considered and their power for detection as a function of a linear fusion parameter is presented our main result is that inferential performance in mathematically tractable first order and second order approximation models does provide guidance for methodological choices applicable to the exact realistic but intractable model furthermore to the extent that the exact model is realistic we may tentatively conclude that approximation model investigations have some bearing on real data applications

vanishing cycles for formal schemes let k be a non archimedean field and let x be a formal scheme locally finitely presented over the ring of integers k see 1 in this work we construct and study the vanishing cycles functor from the category of etale sheaves on the generic fibre x of x which is a k analytic space to the category of etale sheaves on the closed fibre xs of x which is a scheme over the residue field of k we prove that if x is the formal completion x of a scheme x finitely presented over k along the closed fibre then the vanishing cycles sheaves of x are canonically isomorphic to those of x as defined in sga7 exp xiii in particular the vanishing cycles sheaves of x depend only on x and any morphism x induces a homomorphism from the pullback of the vanishing cycles sheaves of x under s ys xs to those of y furthermore we prove that for each x one can find a nontrivial ideal of k such that if two morphisms x coincide modulo this ideal then the homomorphisms between the vanishing cycles sheaves induced by and coincide these facts were conjectured by p deligne in 1 we associate with a formal scheme x locally finitely presented over k a k analytic space x in the sense of ber1 and ber2 in 2 we find that the morphism y x which is induced by an etale morphism of formal schemes y x possesses a certain property morphisms of k analytic spaces with this property are called quasi etale and they give rise to a quasi etale site xqet of a k analytic space x there is a canonical morphism of sites xqet xet where xet is the etale site introduced in ber2 we show that the inverse image functor identifies the category of etale sheaves x et with a full subcategory of

techniques for constructing biorthogonal bipartite graph filter banks the processing of data defined on irregular discrete domains i e graph signals is becoming an emerging area with great application potential using spectral graph theory narang and ortega 2013 laid the framework for two channel filter banks with critical sampling for bipartite graph signals the bipartite graph filter bank can be extended to any arbitrary graph using the notion of separable filtering the design of the biorthogonal filter banks by narang and ortega 2013 is based on the factorization of a maximally flat polynomial the factorization technique does not allow much control of the spectral response of the graph filters resulting in response asymmetry in this paper we present a generic framework for constructing biorthogonal graph filter banks that does not require factorization we introduce the notion of polyphase representation and ladder structures for graph filter banks we show that filters having virtual spectral symmetry and almost energy preservation can be constructed without any sophisticated optimization fine control of the spectral response can also be achieved with ease

on ramification in transcendental extensions of local fields abstract let l k be an extension of complete discrete valuation fields and assume that the residue field of k is perfect and of positive characteristic the residue field of l is not assumed to be perfect in this paper we prove a formula for the swan conductor of the image of a character h 1 k q z in h 1 l q z for sufficiently ramified further we define generalizations l k ab and l k as of the classical function and prove a formula for l k ab t for sufficiently large t r

deformation spaces of one dimensional formal modules and their cohomology abstract let m m be the formal scheme which represents the functor of deformations of a one dimensional formal module over f p equipped with a level m structure by work of boyer in equal characteristic and harris and taylor the l adic etale cohomology of the generic fibre m m of m m realizes simultaneously the local langlands and jacquet langlands correspondences the proofs given so far use drinfeld modular varieties or shimura varieties to derive this local result in this paper we show without the use of global moduli spaces that the jacquet langlands correspondence is realized by the euler poincare characteristic of the cohomology under a certain finiteness assumption on the cohomology groups it is shown that the correspondence is realized in only one degree one main ingredient of the proof consists in analyzing the boundary of the deformation spaces and in studying larger spaces which can be considered as compactifications of the spaces m m

discrete signal processing on graphs sampling theory we propose a sampling theory for signals that are supported on either directed or undirected graphs the theory follows the same paradigm as classical sampling theory we show that perfect recovery is possible for graph signals bandlimited under the graph fourier transform the sampled signal coefficients form a new graph signal whose corresponding graph structure preserves the first order difference of the original graph signal for general graphs an optimal sampling operator based on experimentally designed sampling is proposed to guarantee perfect recovery and robustness to noise for graphs whose graph fourier transforms are frames with maximal robustness to erasures as well as for erd s renyi graphs random sampling leads to perfect recovery with high probability we further establish the connection to the sampling theory of finite discrete time signal processing and previous work on signal recovery on graphs to handle full band graph signals we propose a graph filter bank based on sampling theory on graphs finally we apply the proposed sampling theory to semi supervised classification of online blogs and digit images where we achieve similar or better performance with fewer labeled samples compared to previous work

tight wavelet frames on multislice graphs we present a framework for the design of wavelet transforms tailored to data defined on multislice graphs i e multiplex or dynamic graphs graphs with multiple types of interactions are ubiquitous in real life motivating the extension of wavelets to these complex domains our framework generalizes the recently proposed spectral graph wavelet transform sgwt d hammond p vandergheynst and r gribonval wavelets on graphs via spectral graph theory appl comput harmon anal vol 30 pp 129 150 mar 2011 which is designed in the spectral frequency domain of an arbitrary finite weighted graph we extend the sgwt to form a tight frame which conserves energy in the wavelet domain and define the relationship between conventional and spectral graph wavelets we then propose a design for multislice graphs that is based on the higher order singular value decomposition hosvd a powerful tool from multilinear algebra in particular the multiple adjacency matrices are stacked to form a tensor and the hosvd decomposition provides information about its third order structure analogous to that provided by matrix factorizations we obtain a set of eigennetworks and from these graph wavelets which exploit the variability across the graphs we demonstrate the feasibility of our method 1 by capturing different orientations of a gray scale image and 2 by decomposing brain signals from functional magnetic resonance imaging we show its effectiveness to identify variability across graph edges and provide meaningful decompositions

equivalences of tame blocks for p adic linear groups let p and ell be two distinct primes f a p adic field and n an integer we show that any level 0 block of the category of smooth overline mathbb z ell valued representations of mathrm gl n f is equivalent to the unipotent block of an appropriate product of mathrm gl n i f i more precisely we show that level 0 blocks of p adic general linear groups obey the functoriality principle for blocks introduced in dat contemp math 691 103 131 2017 the overall strategy is to use the jordan decomposition of blocks of finite general linear groups and the theory of coefficients systems on the relevant buildings as a bridge between the p adic and finite worlds to overcome the main technical difficulty we need fine properties of deligne lusztig cohomology proved in bonnafe et al ann math 185 2 609 670 2017

optimized update prediction assignment for lifting transforms on graphs transformations on graphs can provide compact representations of signals with many applications in denoising feature extraction or compression in particular lifting transforms have the advantage of being critically sampled and invertible by construction but the efficiency of the transform depends on the choice of a good bipartition of the graph into update mathcal u and prediction mathcal p nodes this is the update prediction mathcal u mathcal p assignment problem which is the focus of this paper we analyze this problem theoretically and derive an optimal mathcal u mathcal p assignment under assumptions about signal model and filters furthermore we prove that the best mathcal u mathcal p partition is related to the correlation between nodes on the graph and is not the one that minimizes the number of conflicts connections between nodes of same label or maximizes the weight of the cut we also provide experimental results in randomly generated graph signals and real data from image and video signals that validate our theoretical conclusions demonstrating improved performance over state of the art solutions for this problem

refined characteristic class and conductor formula in this article we prove a conductor formula in a geometric situation which is an analogue of the grothendieck ogg shafarevich formula our approach uses the ramification theory of abbes and saito and relies on tsushima s refined characteristic class

spectrum adapted tight graph wavelet and vertex frequency frames we consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs while the filters used in previous spectral graph wavelet constructions are only adapted to the length of the spectrum the filters proposed in this paper are adapted to the distribution of graph laplacian eigenvalues and therefore lead to atoms with better discriminatory power our approach is to first characterize a family of systems of uniformly translated kernels in the graph spectral domain that give rise to tight frames of atoms generated via generalized translation on the graph we then warp the uniform translates with a function that approximates the cumulative spectral density function of the graph laplacian eigenvalues we use this approach to construct computationally efficient spectrum adapted tight vertex frequency and graph wavelet frames we give numerous examples of the resulting spectrum adapted graph filters and also present an illustrative example of vertex frequency analysis using the proposed construction

signal adapted tight frames on graphs the analysis of signals on complex topologies modeled by graphs is a topic of increasing importance decompositions play a crucial role in the representation and processing of such information here we propose a new tight frame design that is adapted to a class of signals on a graph the construction starts from a prototype meyer type system of kernels with uniform subbands the ensemble energy spectral density is then defined for a given set of signals defined on the graph the prototype design is then warped such that the resulting subbands capture the same amount of energy for the signal class this approach accounts at the same time for graph topology and signal features the proposed frames are constructed for three different graph signal sets and are compared with non signal adapted frames vertex localization of a set of resulting atoms is studied the frames are then used to decompose a set of real graph signals and are also used in a setting of signal denoising the results illustrate the superiority of the designed signal adapted frames over frames blind to signal characteristics in representing data and in denoising

numerical modeling of acoustic emission in laminated tensile test specimens abstract acoustic emission from transverse matrix cracks and fiber fracture in typical laminated tensile test specimens is modeled the acoustic sources are described as time dependent displacement discontinuities which subsequently are translated to volume forces the transient waves are computed using a finite element model of the specimen s cross section the finite element modeling leads to a system of differential equations in the axial coordinate and time the differential equations are solved using fourier transforms and eigenmode superposition followed by inversion of the transforms through residue calculus and fft computed time histories for matrix cracking and fiber fracture are presented the highest frequency content in these signals corresponds typically to 300 khz a method to measure the average matrix crack propagation velocity is suggested

bipartite graph filter banks polyphase analysis and generalization the work by narang and ortega perfect reconstruction two channel wavelet filter banks for graph structured data ieee trans signal process vol 60 no 6 pp 2786 2799 jun 2012 compact support biorthogonal wavelet filterbanks for arbitrary undirected graphs ieee trans signal process vol 61 no 19 pp 4673 4685 oct 2013 laid the foundations for the two channel critically sampled perfect reconstruction filter bank for signals defined on undirected graphs this basic filter bank is applicable only to bipartite graphs but using the notion of separable filtering the basic filter bank can be applied to any arbitrary undirected graphs in this paper several new theoretical results are presented in particular the proposed polyphase analysis yields filtering structures in the downsampled domain that are equivalent to those before downsampling and thus can be exploited for efficient implementation these theoretical results also provide new insights that can be exploited in the design of these systems these insights allow us to generalize these filter banks to directed graphs and to using a variety of graph base matrices while also providing a link to the text dsp g framework of sandryhaila and moura discrete signal processing on graphs ieee trans signal process vol 61 no 7 pp 1644 1636 apr 2013 discrete signal processing on graphs frequency analysis ieee trans signal process vol 62 no 12 pp 3042 3054 jun 2014 experiments show evidence that better nonlinear approximation and denoising results may be obtained by a better selection of these base matrices

bloch theorem with revised boundary conditions applied to glide screw and rotational symmetric structures abstract wave propagation in complex periodic systems is often addressed with the bloch theorem and consists in applying periodic boundary conditions to a discretized unit cell while this method has been developed for structures periodic by translation in a recent work for quasi one dimensional wave propagation it has been shown that screw translation plus rotation and glide translation plus reflection periodicities can be accounted for as well keeping the cartesian coordinate system but revisiting the periodic boundary conditions the goal of the present paper is to generalize this concept to quasi two dimensional wave propagation two dimensional waves propagating in three dimensional structures dispersion relations for a set of reduced problems are then compared to results from the classical method when available by considering a smaller periodicity the computational cost is decreased and the number of folding curves and non interacting intersecting curves is reduced improving their interpretability while the size of a unit cell is divided by a factor two when glide symmetries are considered this ratio is significantly increased for screw or rotational symmetries moreover the proposed revisited bloch method is applicable to screw symmetric structures that do not possess purely translational symmetries and for which the classical method cannot be used e g chiral nanotubes longitudinally wrinkled helicoids

cohomology of sheaves on the building and r representations this article contains four parts the subject of the first one is to compare open compact subgroups of a reductive connected group g over a local non archimedean field associated to certain natural concave functions by the theory of bruhat tits bt1 we compare the groups which appear in the theory of unrefined minimal types by moy and prasad mp1 mp2 with those which appear in the theory of complex sheaves on the building x by schneider and stuhler ss schneider and stuhler give to special vertices a predominant role hiding in this way some symetry that we restaure we need all vertices in particular we describe how the groups vary along a geodesic starting from any point in a discussion with kutzko and with schneider it appeared that there are in the literature two different definitions for an iwahori subgroup the connected and the non connected as i was not aware of this and as there are may be other definitions i include here the unique decomposition property for the possible iwahori subgroups this part is entirely geometric and is certainly trivial for someone who is familiar with the theory of bruhat and tits

bipartite approximation for graph wavelet signal decomposition to compactly represent a graph signal in the frequency domain critically sampled biorthogonal wavelet filterbanks have been proposed to decompose signals on bipartite graphs however in practice graph signals often reside on general graph structures that are not bipartite thus an original nonbipartite graph must be decomposed into a sequence of bipartite graph approximations so that the filterbanks can be applied successively for signal decomposition in this paper unlike previous proposals that are heuristic in nature we design new bipartite approximation strategies for model based and empirically derived probability distributions in the first case a signal prior assumes a gaussian markov random field gmrf model parametrized by the original graph in the second case beyond the gmrf signal prior empirical signal observations are available to compute a posterior probability distribution in both cases we optimize for energy compaction in the bipartite subgraphs with two criteria the kullback leibler divergence metric which encourages preserving the spectral characteristics of the original graph and multiplicity of eigenvalue at frequency 1 for graph laplacian which is the frequency with minimal energy discrimination the relative importance between the two criteria is determined by a proposed measure that evaluates the degree of mismatch between the signal prior and posterior given these criteria we first design a global numerical optimization and then propose a local heuristic approach for fast implementation with simplifications leading to local metric computation experimental results show that our proposed bipartite subgraph decomposition outperforms competing proposals in terms of energy compaction

a multiscale pyramid transform for graph signals multiscale transforms designed to process analog and discrete time signals and images cannot be directly applied to analyze high dimensional data residing on the vertices of a weighted graph as they do not capture the intrinsic topology of the graph data domain in this paper we adapt the laplacian pyramid transform for signals on euclidean domains so that it can be used to analyze high dimensional data residing on the vertices of a weighted graph our approach is to study existing methods and develop new methods for the four fundamental operations of graph downsampling graph reduction and filtering and interpolation of signals on graphs equipped with appropriate notions of these operations we leverage the basic multiscale constructs and intuitions from classical signal processing to generate a transform that yields both a multiresolution of graphs and an associated multiresolution of a graph signal on the underlying sequence of graphs

multiscale local polynomial smoothing in a lifted pyramid for non equispaced data this paper integrates burt adelson s laplacian pyramids with lifting schemes for the construction of slightly redundant decompositions these decompositions implement multiscale smoothing on possibly non equidistant point sets thanks to the slight redundancy and to the smoothing operations in the lifting scheme the proposed construction unifies sparsity of the analysis smoothness of the reconstruction and stability of the transforms the decomposition is of linear computational complexity with just a slightly larger constant than the fast lifted wavelet transform this paper also discusses several alternatives in the design of non stationary finite impulse response filters for a stable multiresolution smoothing system these filters are adapted to each other and to the locations of the observations

extending classical multirate signal processing theory to graphs part ii m channel filter banks this paper builds upon the basic theory of multirate systems for graph signals developed in the companion paper part i and studies m channel polynomial filter banks on graphs the behavior of such graph filter banks differs from that of classical filter banks in many ways the precise details depending on the eigenstructure of the adjacency matrix boldsymbol a it is shown that graph filter banks represent linear and periodically shift variant systems only when boldsymbol a satisfies the noble identity conditions developed in part i it is then shown that perfect reconstruction graph filter banks can always be developed when boldsymbol a satisfies the eigenvector structure satisfied by m block cyclic graphs and has distinct eigenvalues further restrictions on eigenvalues being unnecessary for this if boldsymbol a is actually m block cyclic then these pr filter banks indeed become practical i e arbitrary filter polynomial orders are possible and there are robustness advantages in this case the pr condition is identical to pr in classical filter banks any classical pr example can be converted to a graph pr filter bank on an m block cyclic graph it is shown that for m block cyclic graphs with all eigenvalues on the unit circle the frequency responses of filters have meaningful correspondence with classical filter banks polyphase representations are then developed for graph filter banks and utilized to develop alternate conditions for alias cancellation and perfect reconstruction again for graphs with specific eigenstructures it is then shown that the eigenvector condition on the graph can be relaxed by using similarity transforms

subgraph based filterbanks for graph signals we design a critically sampled compact support biorthogonal transform for graph signals via graph filterbanks instead of partitioning the nodes in two sets so as to remove one every two nodes in the filterbank downsampling operations the design is based on a partition of the graph in connected subgraphs coarsening is achieved by defining one supernode for each subgraph and the edges for this coarsened graph derives from the connectivity between the subgraphs unlike the one every two nodes downsampling on bipartite graphs this coarsening operation does not have an exact formulation in the graph fourier domain instead we rely on the local fourier bases of each subgraph to define filtering operations we apply successfully this method to decompose graph signals and show promising performance on compression and denoising

learning parametric dictionaries for signals on graphs in sparse signal representation the choice of a dictionary often involves a tradeoff between two desirable properties the ability to adapt to specific signal data and a fast implementation of the dictionary to sparsely represent signals residing on weighted graphs an additional design challenge is to incorporate the intrinsic geometric structure of the irregular data domain into the atoms of the dictionary in this work we propose a parametric dictionary learning algorithm to design data adapted structured dictionaries that sparsely represent graph signals in particular we model graph signals as combinations of overlapping local patterns we impose the constraint that each dictionary is a concatenation of subdictionaries with each subdictionary being a polynomial of the graph laplacian matrix representing a single pattern translated to different areas of the graph the learning algorithm adapts the patterns to a training set of graph signals experimental results on both synthetic and real datasets demonstrate that the dictionaries learned by the proposed algorithm are competitive with and often better than unstructured dictionaries learned by state of the art numerical learning algorithms in terms of sparse approximation of graph signals in contrast to the unstructured dictionaries however the dictionaries learned by the proposed algorithm feature localized atoms and can be implemented in a computationally efficient manner in signal processing tasks such as compression denoising and classification

m channel oversampled graph filter banks this paper proposes m channel oversampled filter banks for graph signals the filter set satisfies the perfect reconstruction condition a method of designing oversampled graph filter banks is presented that allows us to design filters with arbitrary parameters unlike the conventional critically sampled graph filter banks the oversampled graph laplacian matrix is also introduced with a discussion of the entire redundancy of the oversampled graph signal processing system the practical performance of the proposed filter banks is validated through graph signal denoising experiments

the usage of standard finite element codes for computation of dispersion relations in materials with periodic microstructure a method with which standard finite element programs can be used to compute dispersion relations in periodic composites is proposed the method is applied to two composite microstructures a two phase laminate and a fiber composite the dispersion relations computed for the laminate are compared with a known analytical solution and the agreement is very good the dispersion relations computed for the fibrous composite are compared with an existing approximate model and experimental results from the literature the agreement between the approximate model the experiments and the computations is very good in the wave guide case and satisfactory for the wave reflect case

the characteristic class and ramification of an l adic etale sheaf we introduce the characteristic class of an l adic etale sheaf using a cohomological pairing due to verdier sga5 as a consequence of the lefschetz verdier trace formula its trace computes the euler poincare characteristic of the sheaf we compare the characteristic class to two other invariants arising from ramification theory one is the swan class of kato saito 17 and the other is the 0 cycle class defined by kato for rank 1 sheaves in 16

extending classical multirate signal processing theory to graphs part i fundamentals signal processing on graphs finds applications in many areas in recent years renewed interest on this topic was kindled by two groups of researchers narang and ortega constructed two channel filter banks on bipartitie graphs described by laplacians sandryhaila and moura developed the theory of linear systems filtering and frequency responses for the case of graphs with arbitrary adjacency matrices and showed applications in signal compression prediction etc inspired by these contributions this paper extends classical multirate signal processing ideas to graphs the graphs are assumed to be general with a possibly nonsymmetric and complex adjacency matrix the paper revisits ideas such as noble identities aliasing and polyphase decompositions in graph multirate systems drawing such a parallel to classical systems allows one to design filter banks with polynomial filters with lower complexity than arbitrary graph filters it is shown that the extension of classical multirate theory to graphs is nontrivial and requires certain mathematical restrictions on the graph thus classical noble identities cannot be taken for granted similarly one cannot claim that the so called delay chain system is a perfect reconstruction system as in classical filter banks it will also be shown that m partite extensions of the bipartite filter bank results will not work for m channel filter banks but a more restrictive condition called m block cyclic property should be imposed such graphs are studied in detail a detailed theory for m channel filter banks is developed in a companion paper

resolutions for representations of reductive p adic groups via their buildings schneider stuhler and vigneras have used cosheaves on the affine bruhat tits building to construct natural projective resolutions of finite type for admissible representations of reductive p adic groups in characteristic not equal to p we use a system of idempotent endomorphisms of a representation with certain properties to construct a cosheaf and a sheaf on the building and to establish that these are acyclic and compute homology and cohomology with these coefficients this implies bernstein s result that certain subcategories of the category of representations are serre subcategories furthermore we also get results for convex subcomplexes of the building following work of korman this leads to trace formulas for admissible representations

the characteristic cycle and the singular support of a constructible sheaf we define the characteristic cycle of an etale sheaf as a cycle on the cotangent bundle of a smooth variety in positive characteristic using the singular support recently defined by beilinson we prove a formula a la milnor for the total dimension of the space of vanishing cycles and an index formula computing the euler poincare characteristic generalizing the grothendieck ogg shafarevich formula to higher dimension an essential ingredient of the construction and the proof is a partial generalization to higher dimension of the semi continuity of the swan conductor due to deligne laumon we prove the index formula by establishing certain functorial properties of characteristic cycles

arithmetic and differential swan conductors of rank one representations with finite local monodromy we consider a complete discrete valuation field of characteristic p with possibly nonperfect residue field let rm v be a rank one continuous representation of its absolute galois group with finite local monodromy we will prove that the it arithmetic swan conductor of rm v defined after k kato which fits in the more general theory of abbes saito coincides with the it differential swan conductor of the associated differential module rm d dag rm v defined by k kedlaya this construction is a generalization to the nonperfect residue case of the fontaine s formalism as presented in the work of n tsuzuki our method of proof will allow us to give a new interpretation of the refined swan conductor

theorie de lubin tate non abelienne et representations elliptiques non abelian lubin tate theory studies the cohomology of some moduli spaces for p divisible groups the broadest definition of which is due to rapoport zink aiming both at providing explicit realizations of local langlands functoriality and at studying bad reduction of shimura varieties in this paper we consider the most famous examples the so called drinfeld and lubin tate towers in the lubin tate case harris and taylor proved that the supercuspidal part of the cohomology realizes both the local langlands and jacquet langlands correspondences as conjectured by carayol recently boyer computed the remaining part of the cohomology and exhibited two defects first the representations of gl d which appear are of a very particular and restrictive form second the langlands correspondence is not realized anymore in this paper we study the cohomology complex in a suitable equivariant derived category and show how it encodes langlands correspondence for elliptic representations then we transfer this result to the drinfeld tower via an enhancement of a theorem of faltings due to fargues we deduce that deligne s weight monodromy conjecture is true for varieties uniformized by drinfeld s coverings of his symmetric spaces this completes the computation of local l factors of some unitary shimura varieties

the computation of dispersion relations for three dimensional elastic waveguides using the scaled boundary finite element method abstract in this paper a numerical approach for the computation of dispersion relations for three dimensional waveguides with arbitrary cross section is proposed the formulation is based on the scaled boundary finite element method sbfem it is an extension of the approach previously derived for plate structures it is shown that the wavenumbers of guided waves in a waveguide can be obtained as the eigenvalues of the z matrix which is well known in the sbfem the hamiltonian properties of this matrix are utilized to derive an efficient way to compute the group velocities of propagating waves as eigenvalue derivatives the cross section of the waveguide is discretized using higher order spectral elements it is discussed in detail how symmetry axes can be utilized to reduce computational costs in order to sort the solutions at different frequencies a mode tracking algorithm is proposed based on the pade expansion

local set based graph signal reconstruction signal processing on graph is attracting more and more attentions for a graph signal in the low frequency subspace the missing data associated with unsampled vertices can be reconstructed through the sampled data by exploiting the smoothness of the graph signal in this paper the concept of local set is introduced and two local set based iterative methods are proposed to reconstruct bandlimited graph signal from sampled data in each iteration one of the proposed methods reweights the sampled residuals for different vertices while the other propagates the sampled residuals in their respective local sets these algorithms are built on frame theory and the concept of local sets based on which several frames and contraction operators are proposed we then prove that the reconstruction methods converge to the original signal under certain conditions and demonstrate the new methods lead to a significantly faster convergence compared with the baseline method furthermore the correspondence between graph signal sampling and time domain irregular sampling is analyzed comprehensively which may be helpful to future works on graph signals computer simulations are conducted the experimental results demonstrate the effectiveness of the reconstruction methods in various sampling geometries imprecise priori knowledge of cutoff frequency and noisy scenarios

gft centrality a new node importance measure for complex networks abstract identifying central nodes is very crucial to design efficient communication networks or to recognize key individuals of a social network in this paper we introduce graph fourier transform centrality gft c a metric that incorporates local as well as global characteristics of a node to quantify the importance of a node in a complex network gft c of a reference node in a network is estimated from the gft coefficients derived from the importance signal of the reference node our study reveals the superiority of gft c over traditional centralities such as degree centrality betweenness centrality closeness centrality eigenvector centrality and google pagerank centrality in the context of various arbitrary and real world networks with different degree degree correlations

l espace symetrique de drinfeld et correspondance de langlands locale i we study the geometry and the cohomology of the tamely ramified cover of drinfeld s p adic symmetric space over a p adic field k for this tame level we prove in a purely local way most of a conjecture of harris on the form of the ell adic cohomologies as well as the torsion freeness of the integral cohomology in this paper we also compute the ell adic cohomology of coxeter deligne lusztig variety associated to mathrm gl d and some results of independent interest on the coefficient systems over the bruhat tits building associated to mathrm gl d k have been established

phase space tunneling in multistate scattering abstract we prove exponentially small estimates on the off diagonal terms of the scattering matrix associated to two state semiclassical schrodinger hamiltonians our method is based on phase space tunneling estimates and a splitting of the operator by means of toeplitz type phase space cutoff operators

perfect reconstruction two channel wavelet filter banks for graph structured data in this work we propose the construction of two channel wavelet filter banks for analyzing functions defined on the vertices of any arbitrary finite weighted undirected graph these graph based functions are referred to as graph signals as we build a framework in which many concepts from the classical signal processing domain such as fourier decomposition signal filtering and downsampling can be extended to graph domain especially we observe a spectral folding phenomenon in bipartite graphs which occurs during downsampling of these graphs and produces aliasing in graph signals this property of bipartite graphs allows us to design critically sampled two channel filter banks and we propose quadrature mirror filters referred to as graph qmf for bipartite graph which cancel aliasing and lead to perfect reconstruction for arbitrary graphs we present a bipartite subgraph decomposition which produces an edge disjoint collection of bipartite subgraphs graph qmfs are then constructed on each bipartite subgraph leading to multi dimensional separable wavelet filter banks on graphs our proposed filter banks are critically sampled and we state necessary and sufficient conditions for orthogonality aliasing cancellation and perfect reconstruction the filter banks are realized by chebychev polynomial approximations