eeg extended source localization tensor based vs conventional methods the localization of brain sources based on eeg measurements is a topic that has attracted a lot of attention in the last decades and many different source localization algorithms have been proposed however their performance is limited in the case of several simultaneously active brain regions and low signal to noise ratios to overcome these problems tensor based preprocessing can be applied which consists in constructing a space time frequency stf or space time wave vector stwv tensor and decomposing it using the canonical polyadic cp decomposition in this paper we present a new algorithm for the accurate localization of extended sources based on the results of the tensor decomposition furthermore we conduct a detailed study of the tensor based preprocessing methods including an analysis of their theoretical foundation their computational complexity and their performance for realistic simulated data in comparison to conventional source localization algorithms such as sloreta cortical loreta cloreta and 4 exso music our objective consists on the one hand in demonstrating the gain in performance that can be achieved by tensor based preprocessing and on the other hand in pointing out the limits and drawbacks of this method finally we validate the stf and stwv techniques on real measurements to demonstrate their usefulness for practical applications

symmetric galerkin boundary integral formulation for interface and multi zone problems domains containing an internal boundary such as a bi material interface arise in many applications e g composite materials and geophysical simulations this paper presents a symmetric galerkin boundary integral method for this important class of problems in this situation the physical quantities are known to satisfy continuity conditions across the interface but no boundary conditions are specied the algorithm described herein achieves a symmetric matrix of reduced size moreover the symmetry can also be invoked to lessen the numerical work involved in constructing the system of equations and thus the method is computationally very ecient a prototype numerical example with several variations in the boundary conditions and material properties is employed to validate the formulation and corresponding numerical procedure the boundary element results are compared with analytical solutions and with numerical results obtained with the nite element method 1997 by john wiley sons ltd

deflated decomposition of solutions of nearly singular systems when solving the linear system ax b where a may be nearly singular and b is not consistent with a one is often interested in computing a deflated solution i e a unique solution to a nearby singular but consistent system a s x d tilde b kelley 14 15 has considered deflated solutions with a s corresponding to setting a small pivot of the lu factorization of a to zero stewart 22 proposed an iterative algorithm for computing a deflated solution with a s corresponding to setting the smallest singular value of a to zero kelley s approach explicitly uses submatrices of the lu factors whereas stewart s approach is implicit in that it only involves solving systems with a in this paper we generalize the concept of a deflated solution to that of a deflated decomposition which expresses the solution x in terms of x d and the null vectors of a s we treat such decompositions in a uniform framework that includes the approaches of kelley and stewart and introduce some new deflated

hierarchical bayesian inference for the eeg inverse problem using realistic fe head models depth localization and source separation for focal primary currents the estimation of the activity related ion currents by measuring the induced electromagnetic fields at the head surface is a challenging and severely ill posed inverse problem this is especially true in the recovery of brain networks involving deep lying sources by means of eeg meg recordings which is still a challenging task for any inverse method recently hierarchical bayesian modeling hbm emerged as a unifying framework for current density reconstruction cdr approaches comprising most established methods as well as offering promising new methods our work examines the performance of fully bayesian inference methods for hbm for source configurations consisting of few focal sources when used with realistic high resolution finite element fe head models the main foci of interest are the correct depth localization a well known source of systematic error of many cdr methods and the separation of single sources in multiple source scenarios both aspects are very important in the analysis of neurophysiological data and in clinical applications for these tasks hbm provides a promising framework and is able to improve upon established cdr methods such as minimum norm estimation mne or sloreta in many aspects for challenging multiple source scenarios where the established methods show crucial errors promising results are attained additionally we introduce wasserstein distances as performance measures for the validation of inverse methods in complex source scenarios

mid p confidence intervals for the poisson expectation conventionally a confidence interval ci for the standardized mortality ratio is set using the conservative ci for a poisson expectation mu employing the mid p argument we present alternative cis that are shorter than the conventional ones the mid p intervals do not guarantee the nominal confidence level but the true coverage probability is only lower than the nominal level for a few short ranges of mu the implications for mid p confidence intervals of various proposed definitions of two sided tests for discrete data are discussed

eeg fmri fusion of paradigm free activity using kalman filtering we address here the use of eeg and fmri and their combination in order to estimate the full spatiotemporal patterns of activity on the cortical surface in the absence of any particular assumptions on this activity such as stimulation times for handling such a high dimension inverse problem we propose the use of 1 a global forward model of how these measures are functions of the neural activity of a large number of sources distributed on the cortical surface formalized as a dynamical system and 2 adaptive filters as a natural solution to solve this inverse problem iteratively along the temporal dimension this estimation framework relies on realistic physiological models uses eeg and fmri in a symmetric manner and takes into account both their temporal and spatial information we use the kalman filter and smoother to perform such an estimation on realistic artificial data and demonstrate that the algorithm can handle the high dimensionality of these data and that it succeeds in solving this inverse problem combining efficiently the information provided by the two modalities this information being naturally predominantly temporal for eeg and spatial for fmri it performs particularly well in reconstructing a random temporally and spatially smooth activity spread over the cortex the kalman filter and smoother show some limitations however which call for the development of more specific adaptive filters first they do not cope well with the strong nonlinearity in the model that is necessary for an adequate description of the relation between cortical electric activities and the metabolic demand responsible for fmri signals second they fail to estimate a sparse activity i e presenting sharp peaks at specific locations and times finally their computational cost remains high we use schematic examples to explain these limitations and propose further developments of our method to overcome them

on torsion in the cohomology of locally symmetric varieties the main result of this paper is the existence of galois representations associated with the mod p or mod p m cohomology of the locally symmetric spaces for gln over a totally real or cm eld proving conjectures of ash and others following an old suggestion of clozel recently realized by harris lan taylor thorne for characteristic 0 cohomology classes one realizes the cohomology of the locally symmetric spaces for gln as a boundary contribution of the cohomology of symplectic or unitary shimura varieties so that the key problem is to understand torsion in the cohomology of shimura varieties thus we prove new results on the p adic geometry of shimura varieties of hodge type namely the shimura varieties become perfectoid when passing to the inverse limit over all levels at p and a new period map towards the ag variety exists on them called the hodge tate period map it is roughly analogous to the embedding of the hermitian symmetric domain which is roughly the inverse limit over all levels of the complex points of the shimura variety into its compact dual the hodge tate period map has several favorable properties the most important being that it commutes with the hecke operators away from p for the trivial action of these hecke operators on the ag variety and that automorphic vector bundles come via pullback from the ag variety

a quasi exact test for comparing two binomial proportions the use of the fisher exact test for comparing two independent binomial proportions has spawned an extensive controversy in the statistical literature many critics have faulted this test for being highly conservative partly in response to such criticism some statisticians have suggested the use of a modified non randomized version of this test namely the mid p value test this paper examines the actual type i error rates of this test for both one sided and two sided tests and for a wide range of sample sizes we show that the actual levels of significance of the mid p test tend to be closer to the nominal level as compared with various classical tests the computational effort required for the mid p test is no more than that needed for the fisher exact test further the basis for its modification is a natural adjustment for discreteness thus the test easily generalizes to r c contingency tables and other discrete data problems

exact inference for categorical data recent advances and continuing controversies methods for exact small sample analyses with categorical data have been increasingly well developed in recent years a variety of exact methods exist primarily using the approach that eliminates unknown parameters by conditioning on their sufficient statistics in addition a variety of algorithms now exist for implementing the methods this paper briefly summarizes the exact approaches and describes recent developments controversy continues about the appropriateness of some exact methods primarily relating to their conservative nature because of discreteness this issue is examined for two simple problems in which discreteness can be severe interval estimation of a proportion and the odds ratio in general adjusted exact methods based on the mid p value seem a reasonable way of reducing the severity of this problem

galois representations attached to tensor products of arithmetic cohomology abstract we compute the action of hecke operators on tensor products of cohomology classes of lower congruence subgroups of sl n z in trivial weight we use this computation to prove that if each representation in a collection of galois representations is attached to a cohomology class of a lower congruence subgroup in trivial weight then a sum of certain twists of the representations consistent with the main conjectures of 5 10 is also attached to such a cohomology class

confidence intervals for a binomial proportion thirteen methods for computing binomial confidence intervals are compared based on their coverage properties widths and errors relative to exact limits the use of the standard textbook method x n 1 96 square root of x n 1 x n n or its continuity corrected version is strongly discouraged a commonly cited rule of thumb stating that alternatives to exact methods may be used when the estimated proportion p is such that np and n 1 p both exceed 5 does not ensure adequate accuracy score limits are easily calculated from closed form solutions to quadratic equations and can be used at all times based on coverage functions the continuity corrected score method is recommended over exact methods its conservative nature should be kept in mind as should the wider fluctuation of actual coverage that accompanies omission of the continuity correction

a common formalism for the integral formulations of the forward eeg problem the forward electroencephalography eeg problem involves finding a potential v from the poisson equation spl nabla spl middot spl sigma spl nabla v f in which f represents electrical sources in the brain and spl sigma the conductivity of the head tissues in the piecewise constant conductivity head model this can be accomplished by the boundary element method bem using a suitable integral formulation most previous work uses the same integral formulation corresponding to a double layer potential we present a conceptual framework based on a well known theorem theorem 1 that characterizes harmonic functions defined on the complement of a bounded smooth surface this theorem says that such harmonic functions are completely defined by their values and those of their normal derivatives on this surface it allows us to cast the previous bem approaches in a unified setting and to develop two new approaches corresponding to different ways of exploiting the same theorem specifically we first present a dual approach which involves a single layer potential then we propose a symmetric formulation which combines single and double layer potentials and which is new to the field of eeg although it has been applied to other problems in electromagnetism the three methods have been evaluated numerically using a spherical geometry with known analytical solution and the symmetric formulation achieves a significantly higher accuracy than the alternative methods additionally we present results with realistically shaped meshes beside providing a better understanding of the foundations of bem methods our approach appears to lead also to more efficient algorithms

an analogue of serre s conjecture for galois representations and hecke eigenclasses in the mod p cohomology of gl n ℤ

galois representations with conjectural connections to arithmetic cohomology in this paper we extend a conjecture of a ash and w sinnott relating niveau 1 galois representations to the mod p cohomology of congruence subgroups ofsln z to include galois representations of higher niveau we then present computational evidence for our conjecture in the case n 3 in the form of three dimensional galois representations which appear to correspond to cohomology eigenclasses as predicted by the conjecture our examples include galois representations with nontrivial weight and level as well as irreducible three dimensional representations that are in no obvious way related to lower dimensional representations in addition we prove that certain symmetric square representations are actually attached to cohomology eigenclasses predicted by the conjecture

on alleged gains in power from lower p values the various suggestions that have been made to increase the power of fisher s test for 2 2 tables are shown to give no real increases one sided tests are examined in detail but two sided test problems are also considered the need for flexibility in use of p values is stressed

resolutions of the steinberg module for gl n abstract we give several resolutions of the steinberg representation st n for the general linear group over a principal ideal domain in particular over z we compare them and use these results to prove that the computations in avner ash et al 2011 agm11 are definitive in particular in avner ash et al 2011 agm11 we use two complexes to compute certain cohomology groups of congruence subgroups of sl 4 z one complex is based on voronoi s polyhedral decomposition of the symmetric space for sl n r whereas the other is a larger complex that has an action of the hecke operators we prove that both complexes allow us to compute the relevant cohomology groups and that the use of the voronoi complex does not introduce any spurious hecke eigenclasses

cohomology of congruence subgroups of sl4 z iii in two previous papers we computed cohomology groups h 5 0 n c for a range of levels n where 0 n is the congruence subgroup of sl 4 consisting of all matrices with bottom row congruent to 0 0 0 mod n in this note we update this earlier work by carrying it out for prime levels up to n 211 this requires new methods in sparse matrix reduction which are the main focus of the paper our computations involve matrices with up to 20 million nonzero entries we also make two conjectures concerning the contributions to h 5 0 n for n prime coming from eisenstein series and siegel modular forms

potential integrals for uniform and linear source distributions on polygonal and polyhedral domains formulas for the potentials due to uniform and linearly varying source distributions defined on simply shaped domains are systematically developed and presented domains considered are infinite planar strips infinite cylinders of polygonal cross sections planar surfaces with polygonal boundaries and volumetric regions with polyhedral boundaries the expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated

estimators of the mantel haenszel variance consistent in both sparse data and large strata limiting models summary this paper proposes a new estimator of the variance of the mantel haenszel estimator of common odds ratio that is easily computed and consistent in both sparse data and large strata limiting models monte carlo experiments compare its performance to that of previously proposed variance estimators

a full subtraction approach for finite element method based source analysis using constrained delaunay tetrahedralisation a mathematical dipole is widely used as a model for the primary current source in electroencephalography eeg source analysis in the governing poisson type differential equation the dipole leads to a singularity on the right hand side which has to be treated specifically in this paper we will present a full subtraction approach where the total potential is divided into a singularity and a correction potential the singularity potential is due to a dipole in an infinite region of homogeneous conductivity the correction potential is computed using the finite element fe method special care is taken in order to evaluate the right hand side integral appropriately with the objective of achieving highest possible convergence order for linear basis functions our new approach allows the construction of transfer matrices for fast computation of the inverse problem for anisotropic volume conductors a constrained delaunay tetrahedralisation cdt approach is used for the generation of high quality fe meshes we validate the new approach in a four layer sphere model with a highly conductive cerebrospinal fluid csf and an anisotropic skull compartment for radial and tangential sources with eccentricities up to 1 mm below the csf compartment we achieve a maximal relative error of 0 71 in a cdt fe model with 360 k nodes which is not locally refined around the source singularity and therefore useful for arbitrary dipole locations the combination of the full subtraction approach with the high quality cdt meshes leads to accuracies that to the best of the author s knowledge have not yet been presented before

analytic sensing noniterative retrieval of point sources from boundary measurements we consider the problem of locating point sources in the planar domain from overdetermined boundary measurements of solutions of poisson s equation in this paper we propose a novel technique termed analytic sensing which combines the application of green s theorem to functions with vanishing laplacian known as the reciprocity gap principle with the careful selection of analytic functions that sense the manifestation of the sources in order to determine their positions and intensities using this formalism we express the problem at hand as a generalized sampling problem where the signal to be reconstructed is the source distribution to determine the positions of the sources which is a nonlinear problem we extend the annihilating filter method which reduces the problem to solving a linear system of equations for a polynomial whose roots are the positions of the point sources once these positions are found resolving the according intensities boils down to solving a linear system of equations we demonstrate the performance of our technique in the presence of noise by comparing the achieved accuracy with the theoretical lower bound provided by cramer rao theory

time frequency mixed norm estimates sparse m eeg imaging with non stationary source activations magnetoencephalography meg and electroencephalography eeg allow functional brain imaging with high temporal resolution while solving the inverse problem independently at every time point can give an image of the active brain at every millisecond such a procedure does not capitalize on the temporal dynamics of the signal linear inverse methods minimum norm dspm sloreta beamformers typically assume that the signal is stationary regularization parameter and data covariance are independent of time and the time varying signal to noise ratio snr other recently proposed non linear inverse solvers promoting focal activations estimate the sources in both space and time while also assuming stationary sources during a time interval however such an hypothesis only holds for short time intervals to overcome this limitation we propose time frequency mixed norm estimates tf mxne which use time frequency analysis to regularize the ill posed inverse problem this method makes use of structured sparse priors defined in the time frequency domain offering more accurate estimates by capturing the non stationary and transient nature of brain signals state of the art convex optimization procedures based on proximal operators are employed allowing the derivation of a fast estimation algorithm the accuracy of the tf mxne is compared to recently proposed inverse solvers with help of simulations and by analyzing publicly available meg datasets

sensitivity of fisher s exact test to minor perturbations in 2 2 contingency tables the two tailed fisher s exact p value is extremely sensitive to small perturbations in 2 x 2 contingency tables an example indicates that a 1 per cent increase in the denominator of one treatment group results in a 32 per cent drop in the exact p value but a mere 0 1 per cent decrease in the treatment success rate this is equivalent to the increase in significance obtained by a 20 per cent increase in the sample size of both treatments without changing the observed success rates this drop results from small changes in the probabilities of unobserved events a systematic evaluation of 920 pairs of similar contingency tables shows that these fluctuations occur frequently over a wide range of sample sizes and significance levels doubling the one tailed exact p value provides a more consistent measure of inferential strength we discuss various chi squared continuity corrections

doubling the one sided p value in testing independence in 2 2 tables against a two sided alternative dupont investigated the advantages of doubling the one sided p value in conducting a two sided test of independence in a 2 x 2 table and claimed that the main advantage was that unlike the exact p value small changes in the table resulted in small changes in the significance he admitted that this practice had no obvious theoretical justification in this paper i take the view that repeated sampling properties should form the basis of any such justification i develop an appropriate framework for studying p values and show that doubling the one sided p value produces a biased test whenever the table is asymmetric i show how one may derive a slightly more complicated p value from a uniformly most powerful test while there are difficulties in interpreting these p values i argue that in principle one should prefer the latter in practice the difference between the two is typically less than 10 per cent for the tables dupont considered the difference is of the order of 1 per cent but with highly skew tables the difference can be much larger

the method of fundamental solutions in solving coupled boundary value problems for m eeg the estimation of neuronal activity in the human brain from electroencephalography eeg and magnetoencephalography meg signals is a typical inverse problem whose solution process requires an accurate and fast forward solver in this paper the method of fundamental solutions is for the first time proposed as a meshfree boundary type and easy to implement alternative to the boundary element method bem for solving the m eeg forward problem the solution of the forward problem is obtained by numerically solving a set of coupled boundary value problems for the three dimensional laplace equation numerical accuracy convergence and computational load are investigated the proposed method is shown to be a competitive alternative to the state of the art bem for m eeg forward solving

confidence intervals for directly standardized rates a method based on the gamma distribution we offer an approximation to central confidence intervals for directly standardized rates where we assume that the rates are distributed as a weighted sum of independent poisson random variables like a recent method proposed by dobson kuulasmaa eberle and scherer our method gives exact intervals whenever the standard population is proportional to the study population in cases where the two populations differ non proportionally we show through simulation that our method is conservative while other methods the dobson et al method and the approximate bootstrap confidence method can be liberal

two sided confidence intervals for the single proportion comparison of seven methods simple interval estimate methods for proportions exhibit poor coverage and can produce evidently inappropriate intervals criteria appropriate to the evaluation of various proposed methods include closeness of the achieved coverage probability to its nominal value whether intervals are located too close to or too distant from the middle of the scale expected interval width avoidance of aberrations such as limits outside 0 1 or zero width intervals and ease of use whether by tables software or formulae seven methods for the single proportion are evaluated on 96 000 parameter space points intervals based on tail areas and the simpler score methods are recommended for use in each case methods are available that aim to align either the minimum or the mean coverage with the nominal 1 alpha

two volume integral equations for the inhomogeneous and anisotropic forward problem in electroencephalography abstract this work presents two new volume integral equations for the electroencephalography eeg forward problem which differently from the standard integral approaches in the domain can handle heterogeneities and anisotropies of the head brain conductivity profiles the new formulations translate to the quasi static regime some volume integral equation strategies that have been successfully applied to high frequency electromagnetic scattering problems this has been obtained by extending to the volume case the two classical surface integral formulations used in eeg imaging and by introducing an extra surface equation in addition to the volume ones to properly handle boundary conditions numerical results corroborate theoretical treatments showing the competitiveness of our new schemes over existing techniques and qualifying them as a valid alternative to differential equation based methods