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

convergence analysis of an online approach to parameter estimation problems based on binary observations in this paper we present an online identification method to the problem of parameter estimation from binary observations a recursive identification algorithm with low storage requirements and computational complexity is derived we prove the convergence of this method provided that the input signal satisfies a strong mixing property some simulation results are then given in order to illustrate the properties of this method under various scenarios this method is appealing in the context of micro electronic devices since it only requires a 1 bit analog to digital converter with low power consumption and minimal silicon area

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

minlip for the identification of monotone wiener systems this paper studies the minlip estimator for the identification of wiener systems consisting of a sequence of a linear fir dynamical model and a monotonically increasing or decreasing static function given t observations this algorithm boils down to solving a convex quadratic program with o t variables and inequality constraints implementing an inference technique which is based entirely on model complexity control a technique which is dubbed as einstein s razor this technique is proven to yield here almost consistent estimates in case the given data is suitably rich local persistently exciting of sufficient order and if the samples obey a true monotone wiener system satisfying some regularity conditions it is then indicated how to extend the method in order to cope with noisy data and empirical evidence is given in order to support the claim of efficiency

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

strong consistence of recursive identification for wiener systems the paper concerns identification of the wiener system consisting of a linear subsystem followed by a static nonlinearity f with no invertibility and structure assumption recursive estimates are given for coefficients of the linear subsystem and for the value f v at any fixed v the main contribution of the paper consists in establishing convergence with probability one of the proposed algorithms to the true values this probably is the first strong consistency result for this kind of wiener systems a numerical example is given which justifies the theoretical analysis

a partial ordering semantics for ccs a new operational semantics for pure ccs is proposed that considers the parallel operator as a first class one and permits a description of the calculus in terms of partial orderings the new semantics also for unguarded agents is given in the sos style via the partial ordering derivation relation ccs agents are decomposed into sets of sequential subagents the new derivations relate sets of subagents and describe their actions and the casual dependencies among them the computations obtained by composing partial ordering derivations are observed either as interleaving or partial orderings of events interleavings coincide with milner s many step derivations and linearizations of partial orderings are all and only interleavings abstract semantics are obtained by introducing two relations of observational equivalence and congruence that preserve concurrency these relations are finer than milner s in that they distinguish interleaving of sequential nondeterministic agents from their concurrent execution

adaptive filtering using quantized output measurements a normalized stochastic gradient adaptive filtering algorithm based on a finite impulse response fir model is discussed the algorithm identifies the system exactly given only coarsely quantized output measurements a description of the quantizer is included in the overall input output model and the scheme exploits an approximation of the derivative of the quantizer using an associated differential equation global convergence is established to a zero output error except for possible colored measurement disturbances parameter setting or to the boundary of the model set

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

parameter identification of wiener systems with discontinuous nonlinearities abstract the paper deals with modeling and parameter identification of wiener type nonlinear dynamic systems having discontinuous asymmetric piecewise linear characteristics with preloads and dead zones multiple application of a decomposition technique provides a special form of static nonlinearity description its incorporation into the wiener model leads to an input output equation where all the model parameters are separated and can be estimated iteratively using input output data and internal variable estimates more illustrative examples are included to demonstrate the feasibility of the proposed approach

identifiability and convergence analysis of the minlip estimator this paper studies the problem of identifying a monotone wiener system from observed noiseless input output signals specifically we study identifiability of such systems as well as the convergence properties of the recently introduced minimal lipschitz minlip estimator this estimator finds a system with minimal complexity by exploiting ordering of the output samples this makes the approach conceptual quite different from traditional identification schemes based on least squares prediction errors maximum likelihood or numerical projections sufficient conditions from which the result follows are given in terms of rotational complete inputs rci a generalization of the notion of persistency of excitation pe as used for the study of linear identification methods finally it is derived that a gaussian i i d sequence satisfies this rci property while any binary sequence does not

circle criteria in recursive identification positive real conditions and differential sector conditions have recently been shown to imply global convergence w p 1 for recursive identification schemes based on a class of single input single output linear wiener models the models consist of linear dynamics followed by a static output nonlinearity the model structure is hence closely related to that of the lure problem in the stability theory of feedback systems this paper proves that the conditions for convergence can be transformed to graphical circle criteria depending on the sector conditions and on the nyquist plot of a transfer function related to the prior knowledge of the poles of the identified system

recursive identification of fir systems with binary valued outputs and communication channels this paper investigates the recursive identification of the finite impulse response systems whose outputs are subject to both the binary valued quantization and the communication unreliability the discrete memoryless channel with packet losses and the additive white gaussian noise channel with time delay are considered a stochastic gradient type algorithm and a stochastic approximation type algorithm are respectively proposed to estimate the unknown system parameters under some mild conditions the algorithms can be proved to be convergent in the almost sure and mean square senses also the convergence rates are given numerical examples are included to illustrate the performance of the algorithms

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

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

fixed order fir approximation of linear systems from quantized input and output data the problem of identifying a fixed order fir approximation of linear systems with unknown structure assuming that both input and output measurements are subjected to quantization is dealt with in this paper a fixed order fir model providing the best approximation of the input output relationship is sought by minimizing the worst case distance between the output of the true system and the modeled output for all possible values of the input and output data consistent with their quantized measurements the considered problem is firstly formulated in terms of robust optimization then two different algorithms to compute the optimum of the formulated problem by means of linear programming techniques are presented the effectiveness of the proposed approach is illustrated by means of a simulation example

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

towards identification of wiener systems with the least amount of a priori information on the nonlinearity in this paper we investigate what constitutes the least amount of a priori information on the nonlinearity so that the fir linear part is identifiable in the non gaussian input case three types of a priori information are considered including quadrant information point information and locally monotonous information in all three cases identifiability has been established and corresponding identification algorithms are developed with their convergence proofs

towards identification of wiener systems with the least amount of a priori information iir cases in this paper we investigate what constitutes the least amount of a priori information on the nonlinearity so that the linear part is identifiable in the non gaussian input case under the white noise input three types of a priori information are considered quadrant information point information and monotonic information in all three cases identifiability has been established and the corresponding nonparametric identification algorithms are developed along with their convergence proofs

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

nonparametric identification of wiener systems a wiener system i e a system in which a linear dynamic part is followed by a nonlinear and memoryless one is identified no parametric restriction is imposed on the functional form of the nonlinear characteristic of the memoryless subsystem and a nonparametric algorithm recovering the characteristic from input output observations of the whole system is proposed its consistency is shown and the rate of convergence is given an idea for identification of the impulse response of the linear subsystem is proposed results of numerical simulation are also presented

a weighted least squares approach to parameter estimation problems based on binary measurements we present a new approach to parameter estimation problems based on binary measurements motivated by the need to add integrated low cost self test features to microfabricated devices this approach is based on the use of original weighted least squares criteria as opposed to other existing methods it requires no dithering signal and it does not rely on an approximation of the quantizer in this technical note we focus on a simple choice for the weights and establish some asymptotical properties of the corresponding criterion to achieve this the assumption that the quantizer s input is gaussian and centered is made in this context we prove that the proposed criterion is locally convex and that it is possible to use a simple gradient descent to find a consistent estimate of the unknown system parameters regardless of the presence of measurement noise at the quantizer s input

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

how nonlinear parametric wiener system identification is under gaussian inputs a number of methods exist for identifying nonlinear wiener systems however there is no attempt to address the fundamental question of how nonlinear these identification problems really are in this technical note we try to address this question by investigating the average squared error cost function used in identification by a proper normalization and a clever characterization of the cost function in terms of the angle between the true but unknown parameter vector and its estimate it is shown in the technical note that under iid gaussian inputs for parametric wiener systems with polynomial nonlinear parts and fir linear parts the cost function is globally monotonic and has one and only one local and global minimum the implication is that identification of such systems is nonlinear but very close to linear further any local search based identification algorithms would converge globally for such systems

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