computing the table of marks of a cyclic extension the subgroup pattern of a finite groups g is the table of marks of g together with a list of representatives of the conjugacy classes of subgroups of g in this article we present an algorithm for the computation of the subgroup pattern of a cyclic extension of g from the subgroup pattern of g repeated application of this algorithm yields an algorithm for the computation of the table of marks of a solvable group g along a composition series of g

fast approximate 2d inversion of airborne tem data born approximation and empirical approach abstractairborne transient electromagnetic surveying provides data sections with a sufficient coverage to perform 2d imaging of electrical conductivity within the ground full 2d inversion using numerical modeling with finite differences or finite elements is still a time consuming method to process the large amount of data acquired during an airborne survey two dimensional structures increase the complexity of eddy current patterns within the ground consequently fast approximate imaging using 2d sensitivities of equivalent homogeneous media is not sufficient and causes strong artifacts in the resulting model to overcome this problem one prefers to use 1d inversion or 3d inversion using local sensitivity to process this kind of data however we consider a fast 2d inversion to be reachable by estimating numerically the 2d sensitivity caused by 2d perturbations and showing that it differs considerably from the ones derived from homogeneous media we propose an empirical model for in loop configurati

bayesian regression with network prior optimal bayesian filtering perspective the recently introduced intrinsically bayesian robust filter ibrf provides fully optimal filtering relative to a prior distribution over an uncertainty class of joint random process models whereas formerly the theory was limited to model constrained bayesian robust filters for which optimization was limited to the filters that are optimal for models in the uncertainty class this paper extends the ibrf theory to the situation where there are both a prior on the uncertainty class and sample data the result is optimal bayesian filtering obf where optimality is relative to the posterior distribution derived from the prior and the data the ibrf theories for effective characteristics and canonical expansions extend to the obf setting a salient focus of the present study is to demonstrate the advantages of bayesian regression within the obf setting over the classical bayesian approach in the context of linear gaussian models

bayesian minimum mean square error estimation for classification error part i definition and the bayesian mmse error estimator for discrete classification with the advent of high throughput genomic and proteomic technologies in conjunction with the difficulty in obtaining even moderately sized samples small sample classifier design has become a major issue in the biological and medical communities with small samples training data error estimation becomes mandatory yet none of the popular error estimation techniques have been rigorously designed based on statistical inference and optimization in this investigation we place classifier error estimation into the framework of optimal mean square error mse signal estimation in the presence of uncertainty which results in a bayesian approach to error estimation based on a parameterized family of feature label distributions with the prior distribution of the parameters governing the choice of feature label distribution these bayesian error estimators are optimal when averaged over a given family of distributions unbiased when averaged over a given family and all samples and analytically address a trade off between robustness modeling assumptions and accuracy minimum mean square error in this paper part i of a two part study we define the minimum mean square error mmse error estimator discuss its basic properties provide closed form analytic estimator representation for discrete classifiers with both non informative and informative prior distributions and examine the performance and robustness of the mmse error estimator via simulations in part ii of this paper in this same issue of ieee transactions on signal processing we address all of these issues in particular closed form representation for linear classification in the gaussian model with known and unknown covariance matrices for both the discrete and gaussian cases the mmse error estimator has especially good performance for distributions having moderate true errors

the cramer rao bound and robust m estimates for autoregressions summary a cramer rao lower bound is computed for estimates of the location innovations scale and autoregressive parameters for a finite variance pth order autoregression the implication of the bound is that the usual least squares estimates of all of these parameters have asymptotically the same lack of efficiency robustness toward heavytailed innovations distributions as does the sample mean for estimating location on the other hand autoregression analogues of huber s regression m estimates with the location estimate obtained from the intercept and autoregressive parameter estimates are shown to be efficiency robust the location estimate is also shown to be minimax robust

efficiency of a kernel density estimator under an autoregressive dependence model abstract the problem of estimating the probability density function of a strictly stationary process is considered to study the effect of a dependence structure on the efficiency of a kernel density estimator the mean integrated squared error mise of the fourier integral estimator fie is derived on the assumption that the observed data are generated by a first order autoregressive process numerical results for the normal and cauchy densities show that even moderate departures from independence can lead to a considerable loss in efficiency of the fie in addition to efficiency considerations the issue of determining an optimal smoothing parameter for the fie under the autoregressive model is addressed

discrete optimal bayesian classification with error conditioned sequential sampling when in possession of prior knowledge concerning the feature label distribution in particular when it is known that the feature label distribution belongs to an uncertainty class of distributions governed by a prior distribution this prior knowledge can be used in conjunction with the training data to construct the optimal bayesian classifier obc whose performance is on average optimal among all classifiers relative to the posterior distribution derived from the prior distribution and the data typically in classification theory it is assumed that sampling is performed randomly in accordance with the prior probabilities on the classes and this has heretofore been true in the case of obc in the present paper we propose to forego random sampling and utilize the prior knowledge and previously collected data to determine which class to sample from at each step of the sampling specifically we choose to sample from the class that leads to the smallest expected classification error with the addition of the new sample point we demonstrate the superiority of the resulting nonrandom sampling procedure to random sampling on both synthetic data and data generated from known biological pathways highlightsa sampling algorithm for training the optimal bayesian classifier is introduced the algorithm works based on minimization of the expected error on the uncertainty class of prior knowledge using a zipf model we show that our sampling algorithm leads to a less true error on average than random sampling our algorithm shows robustness even in case when prior knowledge drifts away from true distributions an example on data from p53 network shows that our method works well on from real pathway data as well

a simple sensitivity analysis of time domain and frequency domain electromagnetic measurements electromagnetic responses in both time and frequency domains can be looked upon as weighted spatial averages of the nearby conductivity distribution using this concept i analyze the simplest possible situation a uniform half space in the presence of uniform current sources both transient and harmonic measurements are equally effective in providing conductivity values for the half space while the conductivity values are the same the averaging processes are not to different types of measurements even within the same domain there correspond different types of sensitivity or weighting functions some of these functions emphasize the near surface conductivity while others emphasize the conductivity at depth these and other features of the weighting functions explain the behavior of magnetotelluric sounding curves

comparison of four least squares inversion schemes for studying equivalence in one dimensional resistivity interpretation the problem of equivalence in dc resistivity inversion is well known the ability to invert resistivity data successfully depends on the uniqueness of the model as well as the robustness of the inversion algorithm to study the problems of model uniqueness and resolution theoretical data are inverted using variations of a nonlinear least squares inversion it is only through model studies such as this one where the true solutions are known that realistic and meaningful comparisons of inversion methods can be undertaken the data are inverted using three schemes of fixed layer thickness where only the resistivity varies and the results are compared to the variable parameter inversion where both the layer resistivities and thicknesses are allowed to vary the purpose of fixing the layer thicknesses is to reduce the number of parameters solved for during the inversion process by doing this nonuniqueness may be reduced the fixed layer thickness schemes are uniform thickness geometrical progression of

wythoff polytopes and low dimensional homology of mathieu groups abstract we describe two methods for computing the low dimensional integral homology of the mathieu simple groups and use them to make computations such as h 5 m 23 z z 7 and h 3 m 24 z z 12 one method works via sylow subgroups the other method uses a wythoff polytope and perturbation techniques to produce an explicit free z m n resolution both methods apply in principle to arbitrary finite groups

on the robustness of the equal mean discrimination rule with uniform covariance structure against serially correlated training data abstract the effect of correlated training data on the error rates for the sample linear discriminant function has been studied by basu and odell 1 mclachlan 2 tubbs 3 and lawoko and mclachlan 4 6 this paper investigates the effect of serially correlated data on the expected error rate of the equal mean classifier with uniform covariance structure

using wavelet packet denoising and anfis networks based on cosfla optimization for electrical resistivity imaging inversion abstract electrical resistivity imaging eri inversion is a complicated non linear inversion problem which is high dimensional and non convex using traditional neural networks to solve the eri inversion problem has an over fitting phenomenon and easily falls into local minima moreover the artificial neural network ann model is a black box its relationships between the inputs and outputs are not easy to interpret in order to solve these problems a wavelet packet denoising wpd procedure and an improved adaptive neuro fuzzy inference system anfis based on cauchy oscillation shuffled frog leaping algorithm cosfla are proposed in this paper the wavelet packet denoising methodology is based on soft thresholding and shannon entropy using a db10 wavelet which is applied to remove the noise component from the measured apparent resistivity data meanwhile cosfla is introduced for updating the premise parameters of the anfis to improve the learning ability and prediction accuracy of the algorithm the development of the proposed method and the total inversion process are also presented the inversion of the synthetic and field examples are provided to demonstrate the feasibility and validity of the proposed method additionally the introduced method is transparent and its if then rules are easy to understand and interpret

regularized discriminant analysis abstract linear and quadratic discriminant analysis are considered in the small sample high dimensional setting alternatives to the usual maximum likelihood plug in estimates for the covariance matrices are proposed these alternatives are characterized by two parameters the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassification risk computationally fast implementations are presented and the efficacy of the approach is examined through simulation studies and application to data these studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved

analytical study of performance of linear discriminant analysis in stochastic settings this paper provides exact analytical expressions for the first and second moments of the true error for linear discriminant analysis lda when the data are univariate and taken from two stochastic gaussian processes the key point is that we assume a general setting in which the sample data from each class do not need to be identically distributed or independent within or between classes we compare the true errors of designed classifiers under the typical i i d model and when the data are correlated providing exact expressions and demonstrating that depending on the covariance structure correlated data can result in classifiers with either greater error or less error than when training with uncorrelated data the general theory is applied to autoregressive and moving average models of the first order and it is demonstrated using real genomic data

on the table of marks of a direct product of finite groups abstract we present a method for computing the table of marks of a direct product of finite groups in contrast to the character table of a direct product of two finite groups its table of marks is not simply the kronecker product of the tables of marks of the two groups based on a decomposition of the inclusion order on the subgroup lattice of a direct product as a relation product of three smaller partial orders we describe the table of marks of the direct product essentially as a matrix product of three class incidence matrices each of these matrices is in turn described as a sparse block diagonal matrix as an application we use a variant of this matrix product to construct a ghost ring and a mark homomorphism for the rational double burnside algebra of the symmetric group s 3

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

some asymptotic results on the effect of autocorrelation on the error rates of the sample linear discriminant function abstract the effect of serial correlation of the training samples on the error rates associated with the sample linear disciminant function has been studied recently by tubbs 1 this paper investigates the effect of serial correlation under more general conditions also it is noted that the asymptotic expansion of the change in the expected error rate differs from that given by tubbs 1

inversion of ground constant offset loop loop electromagnetic data for a large range of induction numbers abstractground loop loop electromagnetic surveys are often conducted to fulfill the low induction number condition to image the distribution of electric conductivity inside the ground it is then necessary to collect a multioffset data set we considered that less time consuming constant offset measurements can also reach this objective this can be achieved by performing multifrequency soundings which are commonly performed for the airborne electromagnetic method ground multifrequency soundings have to be interpreted carefully because they contain high induction number data these data are interpreted in two steps first the in phase and out of phase data are converted into robust apparent conductivities valid for all the induction numbers second the apparent conductivity data are inverted in 1d and 2d to obtain the true distribution of the ground conductivity for the inversion we used a general half space jacobian for the apparent conductivity valid for all the induction numbers this method was

a new method for the automatic interpretation of schlumberger and wenner sounding curves a fast iterative method for the automatic interpretation of schlumberger and wenner sounding curves is based on obtaining interpreted depths and resistivities from shifted electrode spacings and adjusted apparent resistivities respectively the method is fully automatic it does not require an initial guess of the number of layers their thicknesses or their resistivities and it does not require extrapolation of incomplete sounding curves the number of layers in the interpreted model equals the number of digitized points on the sounding curve the resulting multilayer model is always well behaved with no thin layers of unusually high or unusually low resistivities for noisy data interpretation is done in two sets of iterations two passes anomalous layers created because of noise in the first pass are eliminated in the second pass such layers are eliminated by considering the best fitting curve from the first pass to be a smoothed version of the observed curve and automatically reinterpreting i

an approach for on line extraction of fuzzy rules using a self organising fuzzy neural network this paper presents a hybrid neural network called the self organising fuzzy neural network sofnn to extract fuzzy rules from the training data the first hidden layer of this network consists of ellipsoidal basis function ebf neurons every ebf neuron in the sofnn has both a centre vector and a width vector neurons are organised by the network itself the methods of the structure and parameter learning based on new adding and pruning techniques and a recursive learning algorithm are simple and effective with a high accuracy and a compact structure simulations show that the sofnn has the capability to encode fuzzy rules in the resulting network

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

intrinsically bayesian robust kalman filter an innovation process approach in many contemporary engineering problems model uncertainty is inherent because accurate system identification is virtually impossible owing to system complexity or lack of data on account of availability time or cost the situation can be treated by assuming that the true model belongs to an uncertainty class of models in this context an intrinsically bayesian robust ibr filter is one that is optimal relative to the cost function in the classical sense and the prior distribution over the uncertainty class in the bayesian sense ibr filters have previously been found for both wiener and granulometric morphological filtering in this paper we derive the ibr kalman filter that performs optimally relative to an uncertainty class of state space models introducing the notion of bayesian innovation process and the bayesian orthogonality principle we show how the problem of designing an ibr kalman filter can be reduced to a recursive system similar to the classical kalman recursive equations except with effective counterparts such as the effective kalman gain matrix after deriving the recursive ibr kalman equations for discrete time we use the limiting method to obtain the ibr kalman bucy equations for continuous time finally we demonstrate the utility of the proposed framework for two real world problems sensor networks and gene regulatory network inference

some homotopy equivalences for sporadic geometries a previous work rsy90 established the projectivity of the reduced lefschetz modules of certain sporadic group geometries and the present paper continues that work in a wider context recent developments in sporadic group cohomology include some applications of rsy90 which in turn suggested treatment of a broader class of geometries recurring similarities in the proofs also led to a more unified treatment establishing the stronger result of homotopy equivalence of thep local geometry with the usual elementary poset ap g one equivalence method proceeds by means of a new closed set in a standard technique of quillen it was further observed that the larger list of simple groups now treated essentially coincides with those of characteristicp type suggesting another equivalence method via the poset bp g of radical or stubborn p subgroups in particular one finds that these sporadic groups satisfy an analogue of the borel tits theorem that normalizers ofp groups lie in simplex stabilizers still further intriguing coincidences remain to be explained

nonlinear integral equations for electromagnetic inverse problems the scaling properties of maxwell s equations allow the existence of simple yet general nonlinear integral equations for electrical conductivity these equations were developed in an attempt to reduce the generality of linearization to the exclusive scope of electromagnetic problems the reduction is achieved when the principle of similitude for quasi static fields is imposed on linearized forms of the field equations the combination leads to exact integral relations which represent a unifying framework for the general electromagnetic inverse problem the equations are of the same form in both time and frequency domains and hold for all observations that scale as electric and magnetic fields do direct current resistivity and magnetometric resistivity methods are considered as special cases the kernel functions of the integral equations are closely related through a normalization factor to the frechet kernels of the conventional equations obtained by linearization accordingly the sensitivity functio

the geometry and cohomology of the mathieu group m12 it is usually very complex to calculate the cohomology of a finite group g to date the most significant results have been on the symmetric and alternating groups n m m ma mu a m m the general linear groups over a finite field q1 and the extra special p groups q2 in the list above only the alternating groups and the gln f2 are simple indeed among the simple groups only a very few aside from those above have been understood it is probable that away from the characteristic p h psln fpn z q is available but even this is not obvious especially for q 2 and certainly we currently have no information on most of the families of groups of lie type for example g2 fq e6 fq e7 fq e8 fq or any of the sporadic groups but m11 and j1 about 15 years ago quillen introduced very powerful techniques that allowed for a much deeper understanding of group cohomology however it is also apparent that successful calculations over z p have only occurred when the group has a well behaved lattice of p elementary abelian subgroups formidable combinatorial problems arise in the general situation as well as necessarily complicated multiplicative relations for example the general calculation of h gln fp z p remains quite inaccessible and there has been only marginal progress since quillen s landmark results

straightforward inversion of vertical electrical sounding data a straightforward inversion scheme sis has been developed to interpret vertical electrical sounding data this scheme does not require quasi linearization of the inverse resistivity problem and thereby dispenses with the iterative process and the necessity of guessing the number of layers and their resistivities and thicknesses the entire solution domain is divided into uniform thickness layers whose scale must be judiciously selected for the desired resolution the apparent resistivity formula can now be posed as an underdetermined matrix equation whose minimum norm solution is downward continued to obtain the reflection coefficients which in turn yield the vertical resistivity distribution a recurrence relation has been developed especially for this purpose in general when data are expected to be noisy a regressed minimum norm solution is used exhaustive tests of the algorithm have established its numerical efficiency results of six typical synthetic models representing diverse geological conditions as well as results of two field examples are included to demonstrate this claim

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

symmetric invariants and cohomology of groups some time ago nakaoka in determined the additive structure of h z f2 around the same time the ring structure of h 274 f2 was calculated and it was assumed that the same type of simple multiplicative relations would appear for n 4 since then most work has concentrated on the embedding 2 o using the polynomial ring structure of h xo f2 in particular most of the recent work in hi was explicitly or implicitly described in m m more than a decade ago and provides no new information on the multiplicative structure of the mod 2 cohomology of finite symmetric groups in this paper we use invariant theory to detect unexpected multiplicative relations in h z f2 the complicated nature of the numerical evidence which we present explains the absence of complete calculations for n 16 the rings of invariants which we study are at the core of any computation of h 2 f2 they build up sucessively yielding relations rich in symmetry but of a highly convoluted type the following problem lies at the heart of all this let p be a polynomial ring k over f2 on n variables and let p k p then ek acts by permuting blocks of generators 1

least squares deconvolution of apparent resistivity pseudosections a fast technique for the inversion of data from resistivity tomography surveys has been developed this technique is based on the smoothness constrained least squares method and it produces a 2 d subsurface model that is free of distortions in the apparent resistivity pseudosection caused by the electrode array geometry used a homogeneous earth model is used as the starting model for which the apparent resistivity partial derivative values can be calculated analytically tests with a variety of models and data from field surveys show that this technique is insensitive to random noise provided a sufficiently large damping factor is used and that it can resolve structures that cause overlapping anomalies in the pseudosection on a 33 mhz 80486dx microcomputer it takes about 5 s to process a single data set

wavelet shrinkage asymptopia much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects curves densities spectral densities images from noisy data a now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems unfortunately the results have rarely moved into practice for a variety of reasons among them being similarity to known methods computational intractability and lack of spatial adaptivity we discuss a method for curve estimation based on n noisy data translate the empirical wavelet coefficients towards the origin by an amount 2 log n n the proposal differs from those in current use is computationally practical and is spatially adaptive it thus avoids several of the previous objections further the method is nearly minimax both for a wide variety of loss functions pointwise error global error measured in l p norms pointwise and global error in estimation of derivatives and for a wide range of smoothness classes including standard holder and sobolev classes and bounded variation this is a much broader near optimality than anything previously proposed we draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves finally the theory underlying the method is interesting as it exploits a correspondence between statistical questions and questions of optimal recovery and information based complexity

asymptotic error rates of the w and z statistics when the training observations are dependent in this paper consideration is given to the properties of the classification statistics w and z which were developed for use in discrimination problems with independent training observations the relative behaviour of these two statistics when the training observations are dependent is investigated for training observations following a stationary autoregressive process of order p the asymptotic expansion of the expected error rates associated with w and z are derived up to and including terms of the second order with respect to the reciprocals of the sample sizes it is shown that neither z nor w is absolutely superior to the other numerical results are given to show that their relative performance is dependent on the extent of correlation among the training observations and the size of the separation between the two populations as measured by the mahalanobis distance

the inverse problem of resistivity sounding the electric potential due to a single point electrode at the surface of a layered conducting medium is calculated by means of a linear combination of the potentials associated with a set of two layer systems this new representation is called the bilayer expansion for the green s function it enables the forward problem of resistivity sounding to be solved very efficiently even for complicated profiles also the bilayer expansion facilitates the solution of the resistivity inverse problem the coefficients in the expansion are linearly related to apparent resistivity as it is measured and they are readily mapped into parameters for a model specifically i consider models comprising uniformly conducting layers of equal thickness for a given finite data set a quadratic program can be used to find the best fitting model in this class for any specified thickness as the thickness is reduced models of this kind can approximate arbitrary profiles with unlimited accuracy if there is a model that satisfies

intrinsically optimal bayesian robust filtering when designing optimal filters it is often unrealistic to assume that the statistical model is known perfectly the issue is then to design a robust filter that is optimal relative to an uncertainty class of processes robust filter design has been treated from minimax best worst case performance and bayesian best average performance perspectives heretofore the bayesian approach has involved finding a model specific optimal filter one that is optimal for some model in the uncertainty class lifting this constraint we optimize over the full class from which the original optimal filters were obtained for instance over all linear filters by extending the original characteristics determining the filter such as the power spectral density to effective characteristics that apply across the uncertainty class we demonstrate for both linear and morphological filtering that an intrinsically optimal bayesian robust filter can be represented in the same form as the standard solution to the optimal filter except via the effective characteristics solutions for intrinsic bayesian robust filters are more transparent and intuitive than solutions for model specific filters and also less tedious because effective characteristics push through the spectral theory into the bayesian setting whereas solutions in the model specific case depend on grinding out the optimization

discrimination with autocorrelated observations abstract the effect of serial correlation on the multivariate sample linear discriminant function when the parameters are estimated under the assumption that the observations are independent has been studied by lawoko and mclachlan this paper investigates the performance of the univariate sample linear discriminant function when the parameters are estimated under a model which takes the correlation into consideration this is contrasted with the performance of the sample discriminant function when the parameters are estimated under the assumption that the observations are independent the intraclass correlation model assumed here is the univariate autoregressive process of order p

optimal bayesian classification with vector autoregressive data dependency in classification theory it is generally assumed that the data are independent and identically distributed however in many practical applications we face a set of observations that are collected sequentially with a dependence structure among samples the primary focus of this investigation is to construct the optimal bayesian classifier obc when the training observations are serially dependent to model the effect of dependency we assume the training observations are generated from text var p which is a multidimensional vector autoregressive process of order p at the same time we assume there exists uncertainty about parameters governing the text var p model to model this uncertainty we assume that model parameters coefficient matrices are random variables with a prior distribution and find the resulting obc under the assumption of known covariance matrices of white noise processes we employ simulations using both synthetic and real data to demonstrate the efficacy of the constructed obc

cohomology of the double cover of the mathieu group m12 abstract in this paper we calculate the mod two cohomology of the double cover of the mathieu group m 12 the starting point is the calculation by adem maginnis and milgram of the mod two cohomology of m 12 we use a hypercohomology spectral sequence to determine a differential in the lyndon hochschild serre spectral sequence of the central extension and this gets us as far as the e page ungrading requires restriction to the sylow 2 subgroup and here some computer calculations come to our rescue