on the descending central sequence of absolute galois groups let p be an odd prime number and f a field containing a primitive p th root of unity we prove a new restriction on the group theoretic structure of the absolute galois group g f of f namely the third subgroup g f 3 in the descending p central sequence of g f is the intersection of all open normal subgroups n such that g f n is 1 bbb z p 2 or the extra special group m p 3 of order p 3 and exponent p 2

robust beamforming via worst case sinr maximization minimum variance beamforming which uses a weight vector that maximizes the signal to interference plus noise ratio sinr is often sensitive to estimation error and uncertainty in the parameters steering vector and covariance matrix robust beamforming attempts to systematically alleviate this sensitivity by explicitly incorporating a data uncertainty model in the optimization problem in this paper we consider robust beamforming via worst case sinr maximization that is the problem of finding a weight vector that maximizes the worst case sinr over the uncertainty model we show that with a general convex uncertainty model the worst case sinr maximization problem can be solved by using convex optimization in particular when the uncertainty model can be represented by linear matrix inequalities the worst case sinr maximization problem can be solved via semidefinite programming the convex formulation result allows us to handle more general uncertainty models than prior work using a special form of uncertainty model we illustrate the method with a numerical example

some rules on resistance distance with applications in this work some rules for resistance distances of a graph g are established let s be a set of vertices of g such that all vertices in s have the same neighborhood n in g s if s 2 3 4 simple formulae are derived to compute resistance distances between vertices in s in terms of the cardinality of n these show that resistance distances between vertices in s depend only on the cardinality of n and the induced subgraph g s one question arises naturally does this property hold for s with arbitrarily many vertices we answer this question by the following reduction principle resistance distances between vertices in s can be computed as in the subgraph obtained from g s n by deleting all the edges between vertices in n

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

quotients of absolute galois groups which determine the entire galois cohomology for a prime power q pd and a field f containing a root of unity of order q we show that the galois cohomology ring h g f mathbb z q is determined by a quotient g f 3 of the absolute galois group gf related to its descending q central sequence conversely we show that g f 3 is determined by the lower cohomology of gf this is used to give new examples of pro p groups which do not occur as absolute galois groups of fields

theoretical and computational methods to minimize kirchhoff index of graphs with a given edge k partiteness abstract let g be a connected graph the edge k partiteness of g is the minimum number of edges whose deletion from g yields a k partite graph the kirchhoff index kf g of g is the sum of the resistance distance between all unordered pairs of vertices in this paper we study the problem to determine the minimum kirchhoff index of graphs with a given edge k partiteness first we theoretically characterize the graphs with minimum kirchhoff index in this graph family when the edge k partiteness is not big compared to the number of vertices of g then we propose an exhaustive search algorithm to find the optimal graphs at last three strategies are used to reduce the computation complexity of our algorithm and several performance comparisons of these strategies are given

the zassenhaus filtration massey products and representations of profinite groups abstract we consider the p zassenhaus filtration g n of a profinite group g suppose that g s n for a free profinite group s and a normal subgroup n of s contained in s n under a cohomological assumption on the n fold massey products which holds e g if g has p cohomological dimension 1 we prove that g n 1 is the intersection of all kernels of upper triangular unipotent n 1 dimensional representations of g over f p this extends earlier results by minac spira and the author on the structure of absolute galois groups of fields

on using a priori knowledge in space time adaptive processing in space time adaptive processing stap the clutter covariance matrix is routinely estimated from secondary ldquotarget freerdquo data because this type of data is more often than not rather scarce the so obtained estimates of the clutter covariance matrix are typically rather poor in knowledge aided ka stap an a priori guess of the clutter covariance matrix e g derived from knowledge of the terrain probed by the radar is available in this note we describe a computationally simple and fully automatic method for combining this prior guess with secondary data to obtain a theoretically optimal in the mean squared error sense estimate of the clutter covariance matrix the authors apply the proposed method to the kassper data set to illustrate the type of achievable performance

robust adaptive beamforming based on conjugate gradient algorithms the mismatches of signal and array geometry will seriously degrade the performance of adaptive beamformer in this paper we propose two methods for robust adaptive beamforming based on the conjugate gradient cg algorithm the proposed beamformers offer a significant improvement in the computational complexity while providing the same performance of the best robust beamformers at present the first method belongs to the diagonal loading technique we derive a diagonal loading cgls algorithm cg applied to normal equations and propose a simple method to choose the loading level based on a coarse estimation of the desired signal power this parameter free method can effectively reduce the signal self cancellation at high signal to noise ratio the second method belongs to the regularization technique since the cg algorithm has a regularizing effect with iteration number being the regularization parameter the stopping criterion plays an important role on the robustness we develop three fast stopping criteria for cg iteration which reduce the stopping complexity from o n or o n 2 to o 1 the former two are the fast versions of existing methods and the later one is new moreover the new criterion based on fast ritz value estimation has better performance than others

on the cohomology of galois groups determined by witt rings let f denote a field of characteristic different from two in this paper we describe the mod 2 cohomology of a galois group gf called the w group of f which is known to essentially characterize the witt ring wf of anisotropic quadratic modules over f we show that h gf f2 contains the mod 2 galois cohomology of f and that its structure will reflect important properties of the field we construct a space xf endowed with an action of an elementary abelian group e such that the computation of the cohomology of gf reduces to calculating the equivariant cohomology h e xf f2 for the case of a field which is not formally real this amounts to computing the cohomology of an explicit euclidean space form an object which is interesting in its own right we provide a number of examples and a substantial combinatorial computation for the cohomology of the universal w groups

on the minimum kirchhoff index of graphs with a given vertex k partiteness and edge k partiteness abstract the kirchhoff index of a connected graph is the sum of the resistance distance between all unordered pairs of vertices and may also be expressed by its laplacian eigenvalues the vertex resp edge k partiteness of a graph g with n vertices is the minimum number of vertices resp edges whose deletion from g yields a k partite graph in this paper we determine the minimum kirchhoff index of graphs with a given vertex k partiteness and the minimum kirchhoff index of graphs with a given edge bipartiteness when the given edge bipartiteness is no more than n 4

an analysis of the projection method for robust adaptive beamforming two causes of performance degradation in adaptive beamforming are perturbation error and sample covariance error these causes were discussed by feldman and griffihs see ieee trans signal processing vol 42 p 867 april 1994 which proposed an approach termed the projection method to reduce the sensitivity of the beamformer performance to both types of error this paper contains an analysis of the expected performance of the beamformer when it is implemented either with or without using the projection method based on a second order taylor series expansion of an approximate expression for the signal to interference plus noise ratio sinr at the beamformer output the analysis provides accurate results when either perturbation error or sample covariance error occurs a less accurate analysis based on a zeroth order taylor series expansion includes results presented by jablon 1986 and chang and yeh see ibid vol 40 no 11 p 1336 1992 as special cases

on the witt equivalence of fields of characteristic 2 let e f be two fields of characteristic 2 and let w e w f be the witt rings of non singular symmetric bilinear forms over e and f in this note it is proved that if dime2 e dimf2 f 2 then e f is equivalent with w e w f

widely linear versus linear blind multiuser detection with subspace based channel estimation finite sample size effects in a recent paper a s cacciapuoti et al ldquofinite sample performance analysis of widely linear multiuser receivers in ds cdma systems ieee transactions on signal processing vol 56 no 4 pp 1572 1588 apr 2008 we presented the finite sample theoretical performance comparison between linear l and widely linear wl minimum output energy moe receivers for direct sequence code division multiple access ds cdma systems worked out under the assumption that the channel impulse response of the desired user is exactly known the main scope of this paper is to extend such an analysis taking into account not only autocorrelation matrix acm estimation effects but also the accuracy of subspace based blind channel estimation ce we aim to answer the two following questions which of the two estimation processes acm or ce is the main source of degradation when implementing the receivers on the basis of a finite sample size compared with the l moe one is the finite sample wl moe receiver with blind ce capable of achieving the performance gains predicted by the theory to this goal simple and easily interpretable formulas are developed for the signal to interference plus noise ratio sinr at the output of the l and wl moe receivers with blind ce when they are implemented using either the sample acm or its eigendecomposition in addition the derived formulas which are validated by simulations allow one to recognize and discuss interesting tradeoffs between the main parameters of the ds cdma system

construction of unipotent galois extensions and massey products abstract for all primes p and for all fields we find a sufficient and necessary condition of the existence of a unipotent galois extension of degree p 6 the main goal of this paper is to describe an explicit construction of such a galois extension over fields admitting such a galois extension this construction is surprising in its simplicity and generality the problem of finding such a construction has been left open since 2003 recently a possible solution of this problem gained urgency because of an effort to extend new advances in galois theory and its relations with massey products in galois cohomology

robust adaptive beamforming with a novel interference plus noise covariance matrix reconstruction method recently a new robust adaptive beamforming rab technique was proposed to remove the signal of interest soi component from the sample covariance matrix based on interference plus noise covariance matrix reconstruction which utilizes the capon spectrum estimator integrated over a region separated from the direction of the soi however the extreme condition of the reconstruction based technique that the precise information about the array structure is known in advance is almost impossible in practice in this paper a novel method to reconstruct the interference plus noise covariance matrix is proposed considering the imprecise prior information about the array structure which means that the array may be uncalibrated we use an annulus uncertainty set to constrain the steering vectors of the interferences then we integrate the capon spectrum over the surface of the annulus by which we can obtain the reconstructed interference matrix without containing the soi since the integral interval is a high dimensional domain which is very difficult to solve we use a discrete sum method to calculate the integral approximately with the reconstructed interference plus noise matrix the nominal steering vector can be corrected via maximizing the beamformer output power by solving a quadratically constrained quadratic programming qcqp problem the previous reconstruction method can be seen as a special case of the proposed one the main advantage is that the proposed algorithm is robust against unknown arbitrary type mismatches theoretical analysis and simulation results demonstrate the effectiveness and robustness of the proposed algorithm

robust adaptive beamforming based on interference covariance matrix reconstruction and steering vector estimation adaptive beamformers are sensitive to model mismatch especially when the desired signal is present in training snapshots or when the training is done using data samples in contrast to previous works this correspondence attempts to reconstruct the interference plus noise covariance matrix instead of searching for the optimal diagonal loading factor for the sample covariance matrix the estimator is based on the capon spectral estimator integrated over a region separated from the desired signal direction this is shown to be more robust than using the sample covariance matrix subsequently the mismatch in the steering vector of the desired signal is estimated by maximizing the beamformer output power under a constraint that prevents the corrected steering vector from getting close to the interference steering vectors the proposed adaptive beamforming algorithm does not impose a norm constraint therefore it can be used even in applications where gain perturbations affect the steering vector simulation results demonstrate that the performance of the proposed adaptive beamformer is almost always close to the optimal value across a wide range of signal to noise and signal to interference ratios

line star sets for laplacian eigenvalues abstract let g be a mixed graph with a nonzero laplacian eigenvalue of multiplicity k a line star set for in g is a set y of k edges of g such that is not a laplacian eigenvalue of g y it is shown that line star set exists for any nonzero laplacian eigenvalue of any mixed graph some basic properties for line star sets are given we also obtain some results on line star sets in undirected graphs

description of galois unipotent extensions abstract given an arbitrary field f we describe all galois extensions l f whose galois groups are isomorphic to the group of upper triangular unipotent 4 by 4 matrices with entries in the field of two elements

robust minimum variance beamforming this paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold in our method uncertainty in the array manifold is explicitly modeled via an ellipsoid that gives the possible values of the array for a particular look direction we choose weights that minimize the total weighted power output of the array subject to the constraint that the gain should exceed unity for all array responses in this ellipsoid the robust weight selection process can be cast as a second order cone program that can be solved efficiently using lagrange multiplier techniques if the ellipsoid reduces to a single point the method coincides with capon s method we describe in detail several methods that can be used to derive an appropriate uncertainty ellipsoid for the array response we form separate uncertainty ellipsoids for each component in the signal path e g antenna electronics and then determine an aggregate uncertainty ellipsoid from these we give new results for modeling the element wise products of ellipsoids we demonstrate the robust beamforming and the ellipsoidal modeling methods with several numerical examples

further study on robust adaptive beamforming with optimum diagonal loading significant effort has gone into designing robust adaptive beamforming algorithms to improve robustness against uncertainties in array manifold these uncertainties may be caused by uncertainty in direction of arrival doa imperfect array calibration near far effect mutual coupling and other mismatch and modeling errors a diagonal loading technique is obligatory to fulfil the uncertainty constraint where the diagonal loading level is amended to satisfy the constrained value the major drawback of diagonal loading techniques is that it is not clear how to get the optimum value of diagonal loading level based on the recognized level of uncertainty constraint in this paper an alternative realization of the robust adaptive linearly constrained minimum variance beamforming with ellipsoidal uncertainty constraint on the steering vector is developed the diagonal loading technique is integrated into the adaptive update schemes by means of optimum variable loading technique which provides loading on demand mechanism rather than fixed continuous or ad hoc loading we additionally enrich the proposed robust adaptive beamformers by imposing a cooperative quadratic constraint on the weight vector norm to overcome noise enhancement at low snr several numerical simulations with doa mismatch moving jamming and mutual coupling are carried out to explore the performance of the proposed schemes and compare their performance with other traditional and robust beamformers

a bayesian framework for blind adaptive beamforming in this work the problem of blind adaptive beamforming in the presence of steering vector uncertainty is addressed within a bayesian estimation framework we express the single input multiple output simo observation model in the short time fourier transform stft domain and employ a variational formulation to obtain iterative closed form learning rules for inferring approximate posteriors on the steering vector and the target signal by varying the a priori belief in the top level statistical model i e modeling a quantity as a random process or an unknown deterministic entity it is shown that the considered framework yields a variety of beamforming algorithms including the celebrated minimum variance distortionless response mvdr beamformer we highlight these interconnections and show by means of simulation results that the bayesian approach alleviates signal distortion in noisy and uncertain environments as compared to the conventional mvdr beamformer by adaptively learning and incorporating uncertainty pertaining to the steering vector

resistance distance in subdivision vertex join and subdivision edge join of graphs abstract the subdivision graph s g of a graph g is the graph obtained by inserting a new vertex into every edge of g let g 1 g 2 be the disjoint union of two graphs g 1 and g 2 the subdivision vertex join of g 1 and g 2 denoted by g 1 g 2 is the graph obtained from s g 1 g 2 by joining every vertex in v g 1 to every vertex in v g 2 the subdivision edge join of g 1 and g 2 denoted by g 1 g 2 is the graph obtained from s g 1 g 2 by joining every vertex in i g 1 to every vertex in v g 2 where i g 1 is the set of inserted vertices of s g 1 in this paper formulae for resistance distance in g 1 g 2 and g 1 g 2 are obtained

minimizing kirchhoff index among graphs with a given vertex bipartiteness the resistance distance between any two vertices of a graph g is defined as the effective resistance between them if each edge of g is replaced by a unit resistor the kirchhoff index kf g is the sum of the resistance distances between all the pairs of vertices in g the vertex bipartiteness vb of a graph g is the minimum number of vertices whose deletion from g results in a bipartite graph in this paper we characterize the graph having the minimum kf g values among graphs with a fixed number n of vertices and fixed vertex bipartiteness 1 v b n 3

field theory and the cohomology of some galois groups abstract we prove that two arithmetically significant extensions of a field f coincide if and only if the witt ring wf is a group ring z n g furthermore working modulo squares with galois groups which are 2 groups we establish a theorem analogous to hilbert s theorem 90 and show that an identity linking the cohomological dimension of the galois group of the quadratic closure of f the length of a filtration on a certain module over a galois group and the dimension over f 2 of the square class group of the field holds for a number of interesting families of fields finally we discuss the cohomology of a particular galois group in a topological context

construction de p extensions galoisiennes d un corps de caracteristique differente de p abstract let p be a prime number let k be a field with characteristic different from p containing the pth roots of unity and let e k be a galois extension of degree pd d n o with an abelian galois group gal e k g of exponent p the aim of this article is to state explicit formulas by which one can construct any field n of degree p over e such that n k is a galois extension soient p un nombre premier k un corps de caracteristique differente de p contenant les racines p iemes de l unite et e k une extension galoisienne de degre pd d n o de groupe de galois gal e k g abelien d exposant p le but de cet article est d etablir des formules explicites permettant de construire tous les corps n de degre p sur e tels que l extension n k soit galoisienne

a projection approach for robust adaptive beamforming it is well known that calibration errors can seriously degrade performance in adaptive arrays particularly when the input signal to noise ratio is large the effect is caused by the perturbation of the presumed steering vector from its optimal value although it is not as widely known similar degradation occurs in sampled matrix inversion processing when the covariance matrix is estimated while the desired signal is present in the snapshot data under these conditions performance loss is due to errors in the estimated covariance matrix and occurs even when the steering vector is known exactly in the paper a new method based of modification of the steering vector is proposed to overcome both the problems of perturbation and of sample covariance errors the method involves projection of the presumed steering vector onto the observed signal plus interference subspace an analysis is also presented illustrating that the sample covariance errors can be viewed as a particular type of perturbation error and a simple approximation is derived for the expected beamformer performance as a function of the number of data snapshots both analytical and experimental results are presented that illustrate the advantages of the proposed method

the kernel unipotent conjecture and the vanishing of massey products for odd rigid fields abstract a major difficult problem in galois theory is the characterization of profinite groups which are realizable as absolute galois groups of fields recently the kernel n unipotent conjecture and the vanishing n massey conjecture for n 3 were formulated these conjectures evolved in the last forty years as a byproduct of the application of topological methods to galois cohomology we show that both of these conjectures are true for odd rigid fields this is the first case of a significant family of fields where both of the conjectures are verified besides fields whose galois groups of p maximal extensions are free pro p groups we also prove the kernel unipotent conjecture for demushkin groups of rank 2 and establish various filtration results for free pro p groups provide examples of pro p groups which do not have the kernel n unipotent property compare various zassenhaus filtrations with the descending p central series and establish new type of automatic galois realization

primitives and central detection numbers in group cohomology abstract fix a prime p given a finite group g let h g denote its mod p cohomology in the early 1990s henn lannes and schwartz introduced two invariants d 0 g and d 1 g of h g viewed as a module over the mod p steenrod algebra they showed that in a precise sense h g is respectively detected and determined by h d c g v for d d 0 g and d d 1 g with v running through the elementary abelian p subgroups of g the main goal of this paper is to study how to calculate these invariants we find that a critical role is played by the image of the restriction of h g to h c where c is the maximal central elementary abelian p subgroup of g a measure of this is the top degree e g of the finite dimensional hopf algebra h c h g f p a number that tends to be quite easy to calculate our results are complete when g has a p sylow subgroup p in which every element of order p is central using the benson carlson duality we show that in this case d 0 g d 0 p e p and a similar exact formula holds for d 1 as a bonus we learn that h e g p contains nontrivial essential cohomology reproving and sharpening a theorem of adem and karagueuzian in general we are able to show that d 0 g max e c g v v g if certain cases of benson s regularity conjecture hold in particular this inequality holds for all groups such that the difference between the p rank of g and the depth of h g is at most 2 when we look at examples with p 2 we learn that d 0 g 14 for all groups with 2 sylow subgroup of order up to 64 with equality realized when g su 3 4 en route we study two objects of independent interest if c is any central elementary abelian p subgroup of g then h g is an h c comodule and we prove that the subalgebra of h c primitives is always noetherian of krull dimension equal to the p rank of g minus the p rank of c if the depth of h g equals the rank of z g we show that the depth essential cohomology of g is nonzero reproving and extending a theorem of green and cohen macauley in a certain sense and prove related structural results