on the general linear group and hochschild homology our main result here is a rational computation of the homology of the adjoint action of the infinite general linear group of an arbitrary ring before stating the result we establish some notation and conventions rings are associative and with unit if a is a ring then gl a uk 0glk a is its infinite general linear group an a bimodule is an abelian group b which is both a left a module and a right a module and satisfies alb a2 al ba2 for ai ea be b for example b a if b is an a bimodule then m b uk omk b is the infinite additive group of matrices with entries in b conjugation defines an action the adjoint action of gl a on m b note that an a q bimodule is just an a bimodule which is also a rational vector space if b is an a q bimodule then hj a c q b denotes the hochschild homology of a q with coefficients in b our main result it appears in slightly more detailed form as theorem v 3 is

blind parameter estimation in multiple access systems a blind algorithm for the estimation of amplitude phase and relative time delay of each user in multiple access communication systems is proposed this algorithm is based on the cyclostationarity features of the received signals and provides estimates of the unknown parameters that are intrinsically immune to the effects of noise and interference provided that a cycle frequency of the user signals exists which is not shared with the disturbance terms the proposed estimators are under mild assumptions asymptotically unbiased and consistent moreover the proposed algorithm is asymptotically near far resistant and is not based on the usual assumption of white and or gaussian noise

on the negative k theory of schemes in finite characteristic abstract we show that if x is a d dimensional scheme of finite type over an infinite perfect field k of characteristic p 0 then k i x 0 and x is k i regular for i d 2 whenever the resolution of singularities holds over k this proves the k dimension conjecture of weibel c weibel k theory and analytic isomorphisms invent math 61 1980 177 197 2 9 except for d 1 i d 2 in all characteristics assuming the resolution of singularities

growing scale free networks with tunable clustering we extend the standard scale free network model to include a triad formation step we analyze the geometric properties of networks generated by this algorithm both analytically and by numerical c

robust detection in digital communications this paper deals with the problem of communicating through unspecified noise detectors robust against variations in the probability density function of the noise are developed and discussed the paper covers three issues first the relation between a distance measuring receiver and a correlating receiver in a general case is shown second a theoretical method for the computation of an upper limit for the probability of symbol error is presented this computation fits into the ordinary framework for computation of the error probability by changing the inverted noise density 2 n sub 0 to efficacy spl epsiv efficacy is defined in the paper third detectors based on m i e maximum likelihood type and r i e rank statistics are tested and compared for gmsk and spl pi 4 shifted dqpsk from numerical comparisons of the upper bounds and their simulated estimates for robust detectors it is concluded that the loss in gaussian noise is very small compared to the optimum quadratic detector the gain compared to a nonrobust receiver optimized to gaussian noise is around 0 5 to 2 db for large snr and around 2 to 4 db for low snr in impulsive noise this offers new methods of significantly improving communication when the noise is unknown

an analysis of nonlinear direct sequence correlators an analysis of the performance of nonlinear correlation reception of direct sequence signals in single and multiuser channels is presented the communications channel is modeled as containing non gaussian background noise and in some cases multiple access interference as well the error probability behavior is studied asymptotically as the lengths of the spreading codes increase without bound and conditions on the spreading sequences are obtained that assure asymptotic achievement of single user performance in a multiuser system a long spreading sequence approximation to the average error probability is also derived and this result is applied to the analysis of smooth limiting correlation receivers in impulsive channels simulation results are also provided to verify the analysis average bit error probabilities are computed by monte carlo simulations for linear hard limiting and smooth limiting correlation receivers in both single and two user impulsive channels the simulation results are compared to the error rates by asymptotic approximations for the smooth limiter and also to those from previous studies on linear and hard limiting correlators

convolutionally coded transmission over markov gaussian channels analysis and decoding metrics it has been widely acknowledged that the aggregate interference at the receiver for various practical communication channels can often deviate markedly from the classical additive white gaussian noise awgn assumption due to various ambient phenomena moreover the physical nature of the underlying interference generating process in such cases can lead to a bursty behaviour of the interfering signal implying that it is highly likely that consecutive symbols are affected by similar noise levels in this paper we devise and analyze detection techniques in conjunction with a convolution code for such interference channels that possess non negligible memory by considering optimum and sub optimum decoding metrics in particular the inherent memory in the noise process is modeled as a first order markov chain whose state selects the variance of the instantaneous gaussian noise leading to a markov gaussian channel model analytical expressions are obtained for the cut off rate which is an ensemble code parameter and the bit error rate for a convolutionally coded system that are subsequently employed for an extensive evaluation of the various metrics considered furthermore the interleaving depth is considered as a design parameter and its effect on performance is analyzed over a range of noise scenarios

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

multiuser detection in flat fading non gaussian channels this paper deals with the problem of multiuser detection in direct sequence code division multiple access cdma fading channels with impulsive noise this issue arises in practical situations because in many realistic wireless channels the ambient channel noise is impulsive resulting from various natural and man made impulsive sources an m estimator based structure for noncoherent demodulation of differentially phase shift keyed dpsk signals transmitted simultaneously via a cdma flat fading channel and embedded in impulsive noise is proposed and analyzed analytical and numerical results show that in highly impulsive noise the performance gain afforded by the proposed multiuser detector can be substantial when compared to the linear decorrelating detector for dpsk with little attendant increase in algorithmic complexity

nonparametric multiuser detection in non gaussian channels existing multiuser detection techniques in wireless systems are based on the assumption that some information on the parameters of the probability density function pdf of ambient noise is available such information may not be available in all cases particularly for non gaussian and impulsive noises or may change depending on circumstances in this paper we present a technique for multiuser detection that does not require any a priori knowledge about the noise parameters this method is based on using pseudo norms for linear nonparametric regression analytical and simulation results show that the proposed method offers an improved or at least comparable performance over existing robust techniques in the absence of any information on the nature of noise in the environment the increased computational complexity is marginal compared to existing parametric detectors in addition the proposed nonparametric detector is portable in the sense that it does not need to be tuned for different noise models without any considerable degradation of performance we also show that in non gaussian noise the performance of blind adaptive nonparametric multiuser detectors is better than that of robust multiuser detectors

clustering in complex networks i general formalism we develop a full theoretical approach to clustering in complex networks a key concept is introduced the edge multiplicity that measures the number of triangles passing through an edge this quantity extends the clustering coefficient in that it involves the properties of two and not just one vertices the formalism is completed with the definition of a three vertex correlation function which is the fundamental quantity describing the properties of clustered networks the formalism suggests different metrics that are able to thoroughly characterize transitive relations a rigorous analysis of several real networks which makes use of this formalism and the metrics is also provided it is also found that clustered networks can be classified into two main groups the weak and the strong transitivity classes in the first class edge multiplicity is small with triangles being disjoint in the second class edge multiplicity is high and so triangles share many edges as we shall see in the following paper the class a network belongs to has strong implications in its percolation properties

subgraphs and network motifs in geometric networks many real world networks describe systems in which interactions decay with the distance between nodes examples include systems constrained in real space such as transportation and communication networks as well as systems constrained in abstract spaces such as multivariate biological or economic data sets and models of social networks these networks often display network motifs subgraphs that recur in the network much more often than in randomized networks to understand the origin of the network motifs in these networks it is important to study the subgraphs and network motifs that arise solely from geometric constraints to address this we analyze geometric network models in which nodes are arranged on a lattice and edges are formed with a probability that decays with the distance between nodes we present analytical solutions for the numbers of all three and four node subgraphs in both directed and nondirected geometric networks we also analyze geometric networks with arbitrary degree sequences and models with a bias for directed edges in one direction scaling rules for scaling of subgraph numbers with system size lattice dimension and interaction range are given several invariant measures are found such as the ratio of feedback and feed forward loops which do not depend on system size dimension or connectivity function we find that network motifs in many real world networks including social networks and neuronal networks are not captured solely by these geometric models this is in line with recent evidence that biological network motifs were selected as basic circuit elements with defined information processing functions

the obstruction to excision in k theory and in cyclic homology let f a b be a ring homomorphism of not necessarily unital rings and i triangleleft a an ideal which is mapped by f isomorphically to an ideal of b the obstruction to excision in k theory is the failure of the map between relative k groups k a i k b f i to be an isomorphism it is measured by the birelative groups k a b i similarly the groups hn a b i measure the obstruction to excision in negative cyclic homology we show that the rational jones goodwillie chern character induces an isomorphism ch k a b i otimes mathbb q overset sim to hn a otimes mathbb q b otimes mathbb q i otimes mathbb q

polylogarithms regulators and arakelov motivic complexes we construct an explicit regulator map from bloch s higher chow group complex to the deligne complex of a complex algebraic variety x we define the arakelov motivic complex as the cone of this map shifted by one its last cohomology group is a version of the arakelov chow group defined by h gillet and c soule we relate the grassmannian n logarithms defined as in g5 to the geometry of symmetric space sln c su n for n 2 we recover lobachevsky s formula expressing the volume of an ideal geodesic simplex in the hyperbolic space via the dilogarithm using the relationship with symmetric spaces we construct the borel regulator on k2n 1 c via the grassmannian n logarithms we study the chow dilogarithm and prove a reciprocity law which strengthens suslin s reciprocity law for milnor s group k 3 on curves our note g5 can serve as an introduction to this paper

detection of unknown signals under complex elliptically symmetric distributions detection of unknown signals is considered under complex elliptically symmetric ces distributions a wide family that includes several well known distributions as special cases we study the detection problem for unknown deterministic signals and random ces signals both corrupted by ces noise for detection of unknown deterministic signals we form the generalized likelihood ratio test and reduce it to a sufficient test statistic which is either the norm of the received vector or a function of it performance analysis is provided under both known and estimated noise scatter matrix for detection of random ces signals we form the likelihood ratio test provide performance analysis and establish conditions under which the sufficient test statistic is given by the norm of the received vector interestingly this norm test statistic is proven to be the uniformly most powerful test for the detection of all ces distributed signals

organization of complex networks without multiple connections we find a new structural feature of equilibrium complex random networks without multiple and self connections we show that if the number of connections is sufficiently high these networks contain a core of highly interconnected vertices the number of vertices in this core varies in the range between const x n1 2 and const x n2 3 where is the number of vertices in a network at the birth point of the core we obtain the size dependent cutoff of the distribution of the number of connections and find that its position differs from earlier estimates

multiuser detection in single path fading channels the performance analysis of maximum likelihood sequence and decorrelating multiuser detectors is developed for the single path rayleigh fading channel the received signal in this multipoint to point channel is additively composed of white gaussian noise and independently faded waveforms from a finite number of asynchronous users the optimum sequence detector consists of a bank of single user matched filters followed by a dynamic programming algorithm has a demodulation complexity per symbol which is exponential in the number of users and requires the knowledge of the system as well of the fading parameters the decorrelating detector has a complexity which is polynomial in the number of users and does not require knowledge of the signal amplitudes which are assumed to vary slowly relative to the symbol rate the single user error rates are presented for both detectors and compared to conventional detection and isolated transmission and the notion of asymptotic multiuser efficiency is developed for this channel in contrast to conventional detection which suffers from near far effects due to rayleigh fading it is shown that the aforementioned multiuser detectors exhibit performance which rivals that of isolated transmission for sufficiently small thermal noise power the results of the analysis are illustrated with numerical examples and indicate that the near far problem may be alleviated by a more sophisticated receiver design

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

generation of arbitrarily two point correlated random networks random networks are intensively used as null models to investigate properties of complex networks we describe an efficient and accurate algorithm to generate arbitrarily two point degree degree correlated undirected random networks without self edges or multiple edges among vertices with the goal to systematically investigate the influence of two point correlations we furthermore develop a formalism to construct a joint degree distribution p j k which allows one to fix an arbitrary degree distribution p k and an arbitrary average nearest neighbor function k nn k simultaneously using the presented algorithm this formalism is demonstrated with scale free networks p k proportional variantk gamma and empirical complex networks p k taken from network as examples finally we generalize our algorithm to annealed networks which allows networks to be represented in a mean field like manner

generation of uncorrelated random scale free networks uncorrelated random scale free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks we propose and analyze a model capable of generating random uncorrelated scale free networks with no multiple and self connections the model is based on the classical configuration model with an additional restriction on the maximum possible degree of the vertices we check numerically that the proposed model indeed generates scale free networks with no two and three vertex correlations as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k respectively complex networks constitute a general framework for the topological characterization of many natural and technological systems whose complexity prevents a more detailed microscopic description f1 3g within this framework these systems are represented in terms of networks or graphs f4g in which vertices stand for the units composing the system while edges among vertices represent the interactions or relations between pairs of units the focus is thus shift to the topological characterization of the representative network a task which is largely more feasible and yields nevertheless a noticeable amount of information on the structure and properties of the original system the empirical analysis of many real complex networks has unveiled the presence of several typical properties widely found in systems belonging to a large variety of realms one of the most relevant is given by the scale free nature of the degree distribution pskd f1 3 5g defined as the probability that a randomly chosen vertex has degree k si e it is connected to other k verticesd in mathematical terms the scale free property translates into a power law function of the form psk d k g

p adic deformation of algebraic cycle classes we study the p adic deformation properties of algebraic cycle classes modulo rational equivalence we show that the crystalline chern character of a vector bundle on the closed fibre lies in a certain part of the hodge filtration if and only if rationally the class of the vector bundle lifts to a formal pro class in k theory on the p adic scheme

growing network with local rules preferential attachment clustering hierarchy and degree correlations the linear preferential attachment hypothesis has been shown to be quite successful in explaining the existence of networks with power law degree distributions it is then quite important to determine if this mechanism is the consequence of a general principle based on local rules in this work it is claimed that an effective linear preferential attachment is the natural outcome of growing network models based on local rules it is also shown that the local models offer an explanation for other properties like the clustering hierarchy and degree correlations recently observed in complex networks these conclusions are based on both analytical and numerical results for different local rules including some models already proposed in the literature

regulators on additive higher chow groups as an attempt to understand motives over k x x m we define the cubical additive higher chow groups with modulus for all dimensions extending the works of s bloch h esnault and k r ulling on 0 dimensional cycles we give an explicit construction of regulator maps on the groups of 1 cycles with an aid of the residue theory of a parshin and v lomadze

excision in algebraic k theory introduction 1 excision and the homology of affine groups 2 volodin s spaces 3 excision for rings with the triple factorization property 4 lie analogue of volodin s construction 5 the homology of nilpotent groups and nilpotent lie algebras 6 a proof of the main theorems 7 the tensor product of h unital algebras 8 the matrix ring of a small category 9 the acyclicity of triangular complexes 10 a proof of karoubi s conjecture

multiuser detectors with disjoint kalman channel estimators for synchronous cdma mobile radio channels we compare performance of several multiuser detectors for differentially encoded data combined with simple disjoint decision directed kalman channel estimators over flat rayleigh fading channels simpler detectors with noncoherent differential detection are also compared different performance trends relative to the case of perfect channel estimation are observed we find that in the presence of channel mismatch the linear decorrelator is the most robust detector in terms of the bit error rate and the near far resistance parameter adjustment for fading channel modeling and estimation in the decision directed mode are also discussed

torsion and divisibility for reciprocity sheaves and 0 cycles with modulus the notion of modulus is a striking feature of rosenlicht serre s theory of generalized jacobian varieties of curves it was carried over to algebraic cycles on general varieties by bloch esnault park rulling krishna levine recently kerz saito introduced a notion of chow group of 0 cycles with modulus in connection with geometric class field theory with wild ramification for varieties over finite fields we study the non homotopy invariant part of the chow group of 0 cycles with modulus and show their torsion and divisibility properties modulus is being brought to sheaf theory by kahn saito yamazaki in their attempt to construct a generalization of voevodsky suslin friedlander s theory of homotopy invariant presheaves with transfers we prove parallel results about torsion and divisibility properties for them

performance of ds ssma communications in impulsive channels part i linear correlation receivers the performance of digital linear correlation receivers is studied in a multiuser environment there are assumed to be two types of sources interfering with data transmission multiple access interference and additive channel noise which is attributed to impulsive noise sources in the environment the contribution of multiple access interference is examined by considering k asynchronous users transmitting simultaneously over a linear channel using the binary psk direct sequence spreadspectrum multiple access ds ssma technique alternatively the effects of the non gaussian impulsive channel in such a system are studied by modeling the samples of noise after front end filtering errorprobability performance under these conditions is compared to that for additive white gaussian noise awgn channels due to computational complexity exact analysis is limited here to systems utilizing short spreading sequences computationally simple methods are proposed for approximating the average error probability when the length of the signature sequences is large furthermore some asymptotic results are obtained for the case of infinitely long sequences in all cases performance variation is examined as the shape of the noise density varies with snr held constant the results of this analysis indicate that the presence of impulsive noise can cause significant performance degradation over that predicted from an awgn model even when the total noise power does not increase

higher chow groups with modulus and relative milnor theory let x be a smooth variety over a field k and d an effective divisor whose support has simple normal crossings we construct an explicit cycle map from z r x d nis the nisnevich motivic complex of the pair x d to km r x d nis r a shift of the relative milnor k sheaf of x d we show that this map induces an isomorphism h m nis x d z r h xnis k r x d nis for all i dimx this generalizes the well known isomorphism in the case d 0 we use this to prove a certain zariski descent property for the motivic cohomology of the pair ak m 1 0

generating random networks with given degree degree correlations and degree dependent clustering random networks are widely used to model complex networks and research their properties in order to get a good approximation of complex networks encountered in various disciplines of science the ability to tune various statistical properties of random networks is very important in this brief report we present an algorithm which is able to construct arbitrarily degree degree correlated networks with adjustable degree dependent clustering we verify the algorithm by using empirical networks as input and describe additionally a simple way to fix a degree dependent clustering function if degree degree correlations are given

sequence detection and adaptive channel estimation for isi channels under class a impulsive noise in this paper sequence detection and channel estimation for frequency selective intersymbol interference isi producing channels under class a impulsive noise are considered we introduce a novel suboptimum sequence detection ssd scheme and show that although ssd employs a simplified metric it achieves practically the same performance as maximum likelihood sequence detection mlsd for both ssd and mlsd a lower bound on the achievable performance is derived which is similar to the classical matched filter bound for frequency selective fading channels under gaussian noise for channel estimation we adopt a minimum entropy criterion and derive efficient least mean entropy and recursive least entropy algorithms for both adaptive algorithms we analyze the steady state channel estimation error variance theoretical considerations and simulation results show that in class a impulsive noise the proposed sequence detection and adaptive channel estimation schemes yield significant performance gains over their respective conventional counterparts designed for gaussian noise although the novel algorithms require knowledge of the class a noise model parameters their computational complexity is comparable to that of the corresponding conventional algorithms

large scale topological and dynamical properties of the internet we study the large scale topological and dynamical properties of real internet maps at the autonomous system level collected in a 3 yr time interval we find that the connectivity structure of the internet presents statistical distributions settled in a well defined stationary state the large scale properties are characterized by a scale free topology consistent with previous observations correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the internet the study of the internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models we compare the properties of growing network models with the present real internet data analysis

additive polylogarithms and their functional equations let k varepsilon 2 k varepsilon varepsilon 2 the single valued real analytic n polylogarithm mathcal l n mathbb c to mathbb r is fundamental in the study of weight n motivic cohomology over a field k of characteristic 0 in this paper we extend the construction in unver algebra number theory 3 1 34 2009 to define additive n polylogarithms li n k varepsilon 2 to k and prove that they satisfy functional equations analogous to those of mathcal l n under a mild hypothesis we show that these functions descend to an analog of the nth bloch group b n k varepsilon 2 defined by goncharov adv math 114 197 318 1995 we hope that these functions will be useful in the study of weight n motivic cohomology over k e 2

excision in cyclic homology and in rational algebraic k theory for a precise definition see 1 below by replacing everywhere k by k q one obtains the corresponding notion in rational algebraic k theory the above definition has an obvious counterpart for cyclic homology and algebras over a fixed field in the case of a general commutative ground ring k some restrictions on the class of allowable extensions seem inevitable due to the well known limitations of cyclic homology considered as a homology functor for algebras not flat over a ground ring an extension of k algebras will be called pure if it is pure as an extension of k modules in the sense of p m cohn 6 cf also appendix a 3 below the class of pure extensions contains e g i extensions which admit a k module splitting ii extensions a e r s with s flat over k in fact one among the several possible characterizations of purity says that an extension is pure if and only if the underlying extension of k modules is an inductive limit of split extensions see theorem a 4 of appendix a below everywhere in this paper the word excision used in the context of cyclic homology will mean excision with respect to the class of pure extensions the second purpose of the present paper is to give a complete characterization of the class of algebras possessing the excision property in cyclic homology before stating the corresponding result we need the following definition let us

blind mimo channel identification from second order statistics using rank deficient channel convolution matrix for multiuser systems several direct blind identification algorithms require that the linear multiple input multiple output mimo system have a full rank convolution matrix this condition requires that the system transfer function be irreducible and column reduced we show that this restrictive identification condition can be relaxed for some direct blind identification methods to accommodate more practical scenarios algorithms such as the outer product decomposition algorithm only require minor length adjustment to its processing window without the column reduced condition this result allows direct blind identification methods to be applicable to mimo without requiring a full rank channel convolution matrix

properties of highly clustered networks we propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient among other things our results indicate that increased clustering leads to a decrease in the size of the giant component of the network we also study susceptible infective recovered type epidemic processes within the model and find that clustering decreases the size of epidemics but also decreases the epidemic threshold making it easier for diseases to spread in addition clustering causes epidemics to saturate sooner meaning that they infect a near maximal fraction of the network for quite low transmission rates

rate equation approach for correlations in growing network models we propose a rate equation approach to compute two vertex correlations in scale free growing network models based on the preferential attachment mechanism the formalism based on previous work of szabo et al fphys rev e 67 056102 s2002dg for the clustering spectrum measuring three vertex correlations is based on a rate equation in the continuous degree and time approximation for the average degree of the nearest neighbors of vertices of degree k with an appropriate boundary condition we study the properties of both two and three vertex correlations for linear preferential attachment models and also for a model yielding a large clustering coefficient the expressions obtained are checked by means of extensive numerical simulations the rate equation proposed can be generalized to more sophisticated growing network models and also extended to deal with related correlation measures as an example we consider the case of a recently proposed model of weighted networks for which we are able to compute a weighted two vertex correlation function taking into account the strength of the interactions between connected vertices

threshold detection in narrow band non gaussian noise the middleton class a narrow band non gaussian noise model 9 12 is examined it is shown that this noise model which is known to fit closely a variety of non gaussian noises can itself be closely approximated by a computationally much simpler noise model it is then shown by numerical examples that for the problem of locally optimum detection the simplest form of this approximation yields nearly optimal asymptotic performance the performance of other simple suboptimal threshold detectors in class a noise is also examined finally a useful relationship between the class a model and the e mixture model is developed

k theory of endomorphism rings and of rings of invariants abstract this paper gives the following description ofk0of the endomorphism ring of a finitely generated projective module t heorem let t be a ring and p a finitely generated projective t module let i be the trace ideal of p then k0 end pt is isomorphic to a subgroup of k0 t i if further the natural map k1 t k1 t i is surjective then k0 end pt is isomorphic to the subgroup of k0 t generated by the direct summands of pn for n n as a corollary we can determinek0of the ring of invariants for many free linear actions in particular the following result is proved t heorem let v be a fixed point free linear representation of a finite group g over a field k of characteristic zero and let s v be the symmetric algebra of v let k be any finite dimensional k vector space then k0 s v g ks k s v g ks k similar results are given for suitable noncommutative versions ofs v

cyclic homology and equivariant homology the purpose of this paper is to explore the relationship between the cyclic homology and cohomology theories of connes 9 11 see also loday and quillen 20 and if equivariant homology and cohomology theories here ii is the circle group the most general results involve the definitions of the cyclic homology of cyclic chain complexes and the notions of cyclic and cocyclic spaces so precise statements will be postponed until w 3 in this introduction we explain some of the formal similarities between the cyclic theory and the equivariant theory and give two examples where the general results apply let a be an associative algebra over a commutative ring k then one can form the cyclic homology hc a and cohomology hc a of a these groups have periodicity operators

tuning clustering in random networks with arbitrary degree distributions we present a generator of random networks where both the degree dependent clustering coefficient and the degree distribution are tunable following the same philosophy as in the configuration model the degree distribution and the clustering coefficient for each class of nodes of degree k are fixed ad hoc and a priori the algorithm generates corresponding topologies by applying first a closure of triangles and second the classical closure of remaining free stubs the procedure unveils an universal relation among clustering and degree degree correlations for all networks where the level of assortativity establishes an upper limit to the level of clustering maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior correlation measures in real networks are seen to observe this structural bound

infinitesimal cohomology and the chern character to negative cyclic homology there is a chern character from k theory to negative cyclic homology we show that it preserves the decomposition coming from adams operations at least in characteristic zero

performance of ds ssma communications in impulsive channels ii hard limiting correlation receivers for pt i see ibid vol com 35 no 11 p 1179 88 1987 in part i it was demonstrated that impulsive channel noise can be a serious detriment to the performance of direct sequence spread spectrum multiple access ds ssma communications when conventional linear correlation reception is used here a hard limiting correlator as an alternative for reception of multiple access transmission in impulsive channels is considered for k asynchronous binary psk ds ssma users sharing a linear channel corrupted by impulsive noise that is modeled at the output of the front end filter of the receiver techniques are developed for analyzing bit error probabilities of this hard limiting receiver by exact computation for short spreading sequences by approximation for longer spreading sequences and by asymptotic limits for infinitely long spreading sequences performance is compared to that of the linear correlator under a variety of conditions showing that hard limiting correlation reception can offer substantial improvement over conventional systems in impulsive channels however the linear receiver is more effective against multiple access noise only and so a tradeoff emerges between rejection of impulsive noise and rejection of multiple access interference