the novikov conjecture for algebraic k theory of the group algebra over the ring of schatten class operators abstract in this paper we prove the algebraic k theory novikov conjecture for group algebras over the ring of schatten class operators the main technical tool in the proof is an explicit construction of the connes chern character

algebraic k theory of group rings and the cyclotomic trace map we prove that the farrell jones assembly map for connective alge braic k theory is rationally injective under mild homological niteness condi tions on the group and assuming that a weak version of the leopoldt schneider conjecture holds for cyclotomic elds this generalizes a result of bokstedt hsiang and madsen and leads to a concrete description of a large direct summand of kn z g z q in terms of group homology in many cases the number theoretic conjectures are true so we obtain rational injectivity results about assembly maps in particular for whitehead groups under niteness assumptions on the group only the proof uses the cyclotomic trace map to topological cyclic homology bokstedt hsiang madsen s functor c and new general injectivity results about the assembly maps for topological hochschild homology and c

continuous phase modulation part i full response signaling the continuous phase modulation cpm signaling scheme has gained interest in recent years because of its attractive spectral properties data symbol pulse shaping has previously been studied with regard to spectra for binary data and modulation index 0 5 in this paper these results have been extended to the m ary case where the pulse shaping is over a one symbol interval the so called full response systems results are given for modulation indexes of practical interest concerning both performance and spectrum comparisons are made with minimum shift keying msk and systems have been found which are significantly better in e b n 0 for a large signal to noise ratio snr without expanded bandwidth schemes with the same bit error probability as msk but with considerably smaller bandwidth have also been found significant improvement in both power and bandwidth are obtained by increasing the number of levels m from 2 to 4

low distortion embeddings of graphs with large girth the main purpose of the paper is to construct a sequence of graphs of constant degree with indefinitely growing girths admitting embeddings into l1 with uniformly bounded distortions this result solves the problem posed by n linial a magen and a naor 2002

the borel conjecture for hyperbolic and cat 0 groups we prove the borel conjecture for a class of groups containing word hyperbolic groups and groups acting properly isometrically and cocompactly on a finite dimensional cat 0 space

operator norm localization for linear groups and its application to k theory abstract we prove the operator norm localization property for linear groups as an application we prove the coarse novikov conjecture for box spaces of a linear group

the integral k theoretic novikov conjecture for groups with finite asymptotic dimension the integral assembly map in algebraic k theory is split injective for any geometrically finite discrete group with finite asymptotic dimension

a general method of minimum cross entropy spectral estimation a new general approach to estimating power spectra is presented based on minimizing a cross entropy functional involving spectral densities examples are worked out using this approach as well as shore s 5 minimum cross entropy spectral analysis mcesa and burg s 7 maximum entropy spectral analysis mesa the results show that aside from its wider applicability ease of implementation and pedagogical advantage the method performs better than mesa and equally well or better than mcesa

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

on the dimension growth of groups we prove that the thompson group f has exponential dimension growth we also prove that every solvable finitely generated subgroup of f has polynomial dimension growth while some elementary amenable subgroups of f and some solvable groups of class 3 have dimension growth at least exp n

on banach spaces with kasparov and yu s property h abstract a new geometric property of banach spaces recently introduced by g kasparov and g yu called property h has important applications to the strong novikov conjecture and the coarse novikov conjecture yet is far from being well understood in this paper we investigate various uniformly continuous maps on unit spheres of banach spaces and prove that all separable banach lattices with nontrivial cotype have property h

a cross linguistic study of speech modulation spectra languages show systematic variation in their sound patterns and grammars accordingly they have been classified into typological categories such as stress timed vs syllable timed or head complement hc vs complement head ch to date it has remained incompletely understood how these linguistic properties are reflected in the acoustic characteristics of speech in different languages in the present study the amplitude modulation am and frequency modulation fm spectra of 1797 utterances in ten languages were analyzed overall the spectra were found to be similar in shape across languages however significant effects of linguistic factors were observed on the am spectra these differences were magnified with a perceptually plausible representation based on the modulation index a measure of the signal to noise ratio at the output of a logarithmic modulation filterbank the maximum value distinguished between hc and ch languages with the exception of turkish while the exact frequency of this ma

large riemannian manifolds which are flexible for each k z we construct a uniformly contractible metric on euclidean space which is not mod k hypereuclidean we also construct a pair of uniformly contractible riemannian metrics on r n n 11 so that the resulting manifolds z and z are bounded homotopy equivalent by a homotopy equivalence which is not boundedly close to a homeomorphism we show that for these spaces the c algebra assembly map k lf z k c z from locally finite k homology to the k theory of the bounded propagation algebra is not a monomorphism this shows that an integral version of the coarse novikov conjecture fails for real operator algebras if we allow a single cone like singularity a similar construction yields a counterexample for complex c algebras

random modulation a review a unified treatment of various aspects of random modulation is presented with emphasis on the spectral properties of fm signals the study includes reexamination of rice s representation woodward s theorem fsk and processes with normal markov and cyclostationary frequencies

a quasi local characterisation of lp roe algebras abstract very recently spakula and tikuisis provide a new characterisation of uniform roe algebras via quasi locality when the underlying metric spaces have straight finite decomposition complexity in this paper we improve their method to deal with the l p version of uniform roe algebras for any p 1 due to the lack of reflexivity on l 1 spaces some extra work is required for the case of p 1

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

large scale properties for bounded automata groups abstract in this paper we study some large scale properties of the mother groups of bounded automata groups first we give two methods to prove every mother group has infinite asymptotic dimension then we study the decomposition complexity of certain subgroup in the mother group we prove the subgroup belongs to d

embeddings of uniform roe algebras in this paper we study embeddings of uniform roe algebras generally speaking given metric spaces x and y we are interested in which large scale geometric properties are stable under embedding of the uniform roe algebra of x into the uniform roe algebra of y

time frequency coherent modulation filtering of nonstationary signals modulation filtering is a class of techniques for filtering slowly varying modulation envelopes of frequency subbands of a signal ideally without affecting the subband signal s temporal fine structure coherent modulation filtering is a potentially more effective type of such techniques where via an explicit product model subband envelopes are determined from demodulation of the subband signal with a coherently detected subband carrier in this paper we propose a coherent modulation filtering technique based on detecting the instantaneous frequency of a subband from its time frequency representation we devise theory to show that coherent modulation filtering imposes a new bandlimiting constraint on the product of the modulator and carrier as well as the ability to recover arbitrarily chosen envelopes and carriers from their modulation product we then formally show that a carrier estimate based on the time varying spectral center of gravity satisfies the bandlimiting condition this bandwidth constraint leads to effective and artifact free modulation filters offering new approaches for potential signal modification however the spectral center of gravity does not in general satisfy the condition of arbitrary carrier recovery finally the results from modulation filtering a speech signal are then used to validate the theory

on homological coherence of discrete groups abstract we explore a weakening of the coherence property of discrete groups studied by f waldhausen the new notion is defined in terms of the coarse geometry of groups and should be as useful for computing their k theory we prove that a group of finite asymptotic dimension is weakly coherent in particular there is a large collection of r modules of finite homological dimension when r is a finite dimensional regular ring this class contains word hyperbolic groups coxeter groups and as we show the cocompact discrete subgroups of connected lie groups

constructions preserving hilbert space uniform embeddability of discrete groups uniform embeddability in a hilbert space introduced by gromov is a geometric property of metric spaces as applied to countable discrete groups it has important consequences for the novikov conjecture exactness introduced and studied extensively by kirchberg and wassermann is a functional analytic property of locally compact groups recently it has become apparent that as properties of countable discrete groups uniform embeddability and exactness are closely related we further develop the parallel between these classes by proving that the class of uniformly embeddable groups shares a number of permanence properties with the class of exact groups in particular we prove that it is closed under direct and free products with and without amalgam inductive limits and certain extensions

spectral correlation of modulated signals part i analog modulation the importance of the concept of cyclostationarity in design and analysis of signal detectors synchronizers and extractors in communication systems is briefly discussed and the central role of spectral correlation in the characterization of random processes that are cyclostationary in the wide sense is explained a spectral correlation function that is a generalization of the power spectral density function is described and a corresponding generalization of the wiener khinchine relation and several other fundamental spectral correlation relations also are described explicit formulas for the spectral correlation function for various types of analog modulated signals are derived this includes pulse and carrier amplitude modulation quadrature amplitude carrier modulation and phase and frequency carrier modulation to illustrate the differing spectral correlation characteristics of different modulation types the magnitudes of the spectral correlation functions are graphed or described in graphical terms as the heights of surfaces above a bifrequency plane

on hypersphericity of manifolds with finite asymptotic dimension we prove the following embedding theorems in the coarse geometry theorem a every metric space x with bounded geometry whose asymptotic dimension does not exceed n admits a large scale uniform embedding into the product of n 1 locally finite trees corollary every metric space x with bounded geometry whose asymptotic dimension does not exceed n admits a large scale uniform embedding into a non positively curved manifold of dimension 2n 2 the corollary is used in the proof of the following theorem b for every uniformly contractible manifold x whose asymptotic dimension is finite the product x x r is integrally hyperspherical for some n theorem b together with a theorem of gromov lawson implies the result previously proven by g yu 1998 which states that an aspherical manifold whose fundamental group has a finite asymptotic dimension cannot carry a metric of positive scalar curvature we also prove that if a uniformly contractible manifold x of bounded geometry is large scale uniformly embeddable into a hilbert space then x is stably integrally hyperspherical

maximal and reduced roe algebras of coarsely embeddable spaces in 7 gong wang and yu introduced a maximal or universal version of the roe c algebra associated to a metric space we study the relationship between this maximal roe algebra and the usual version in both the uniform and non uniform cases the main result is that if a uniformly discrete bounded geometry metric space x coarsely embeds into a hilbert space then the canonical map between the maximal and usual uniform roe algebras induces an isomorphism on k theory we also give a simple proof that if x has property a then the maximal and usual uniform roe algebras are the same these two results are natural coarse geometric analogues of certain well known implications of a t menability and amenability for group c algebras the techniques used are e theoretic building on work of higson kasparov and trout 11 12 and yu 28

phase modulated resonances modeled as self similar processes with application to turbulent sounds in this paper we propose a nonlinear stochastic model for time varying resonances where the instantaneous phase and frequency of a sinusoidal oscillation is allowed to vary proportionally to an spl alpha stable self similar stochastic processes the main motivation of our work stems from previous experimental and theoretical evidence that speech resonances in fricative sounds can be modeled phenomenologically as am fm signals with randomly varying instantaneous frequencies and that several signal classes related to turbulent phenomena are self similar 1 f processes our general approach is to model the instantaneous phase of an am fm resonance as a self similar spl alpha stable process as a special case this random phase model includes the class of random fractal signals known as fractional brownian motion we theoretically explore this random modulation model and analytically derive its autocorrelation and power spectrum we also propose an algorithm to fit this model to arbitrary resonances with random phase modulation further we apply the above ideas to real speech data and demonstrate that this model is suitable for resonances of fricative sounds

groups generated by reflections and aspherical manifolds not covered by euclidean space a coxeter system r v is a group r a coxeter group together with a set of generators v such that each element of v has order two and such that all relations in r are consequences of relations of the form vw m v w 1 where v w e v and m v w denotes the order of vw the m v w s which are positive integers or oo obviously determine the coxeter system up to isomorphism the list of finite coxeter groups is short and well known however general coxeter groups are much more flexible in fact the set v and the m v w s can be specified arbitrarily at least if v is finite subject only to the conditions m v v 1 and m v w m w v 2 if v w suppose that r v is a coxeter system that x is a hausdorff space and that xv v v is a locally finite family of closed subspaces indexed by v the xv are called the panels of x 2 there is a classical method for constructing a transformation group from these data for each x e x let v x denote the set of v in v such that x e xv for each subset s of v let rs be the subgroup generated by s and let xs be the face of x defined by

finite decomposition complexity and the integral novikov conjecture for higher algebraic k theory decomposition complexity for metric spaces was recently introduced by guentner tessera and yu as a natural generalization of asymptotic dimension we prove a vanishing result for the continuously controlled algebraic k theory of bounded geometry metric spaces with finite decomposition complexity this leads to a proof of the integral k theoretic novikov conjecture regarding split injectivity of the k theoretic assembly map for groups with finite decomposition complexity and finite cw models for their classifying spaces by work of guentner tessera and yu this includes all geometrically finite linear groups

fibred coarse embeddings a t menability and the coarse analogue of the novikov conjecture abstract the connection between the coarse geometry of metric spaces and analytic properties of topological groupoids is well known one of the main results of skandalis tu and yu is that a space admits a coarse embedding into hilbert space if and only if a certain associated topological groupoid is a t menable this groupoid characterisation then reduces the proof that the coarse baum connes conjecture holds for a coarsely embeddable space to known results for a t menable groupoids the property of admitting a fibred coarse embedding into hilbert space was introduced by chen wang and yu to provide a property that is sufficient for the maximal analogue to the coarse baum connes conjecture and in this paper we connect this property to the traditional coarse baum connes conjecture using a restriction of the coarse groupoid and homological algebra additionally we use this results to give a characterisation of the a t menability for residually finite discrete groups

relative property a and relative amenability for countable groups abstract we define a relative property a for a countable group with respect to a finite family of subgroups many characterizations for relative property a are given in particular a relative bounded cohomological characterization shows that if g has property a relative to a family of subgroups h and if each h h has property a then g has property a this result leads to new classes of groups that have property a in particular groups are of property a if they act cocompactly on locally finite property a spaces of bounded geometry with any stabilizer of property a specializing the definition of relative property a an analogue definition of relative amenability for discrete groups is introduced and similar results are obtained

brief paper stability analysis of adaptively controlled systems subject to bounded disturbances an approach for studying stability of adaptively controlled systems subject to bounded disturbances with unknown statistics is given a shorter proof of some results established for minimum phase systems is also given new results are established for nonminimum phase systems in each case the uniform boundedness of all signals is proven under a condition that is discussed examples of adaptive schemes that can be treated with this approach are given

on rigidity of roe algebras roe algebras are c algebras built using large scale or coarse aspects of a metric space x d in the special case that x is a finitely generated group and d is a word metric the simplest roe algebra associated to d is isomorphic to the crossed product c algebra l 1 r roe algebras are coarse invariants in the sense that if x and y are coarsely equivalent metric spaces then their roe algebras are isomorphic motivated in part by the coarse baum connes conjecture we ask if there is a converse to the above statement that is if x and y are metric spaces with isomorphic roe algebras must x and y be coarsely equivalent we show that for very large classes of spaces the answer to this question and some related questions is yes this can be thought of as a c rigidity result it shows that the roe algebra construction preserves a large amount of information about the space and is thus surprisingly rigid as an example of our results in the group case we have that if and are finitely generated elementary amenable hyperbolic or linear groups

a bott periodicity theorem for infinite dimensional euclidean space abstract we formulate and prove an equivariant bott periodicity theorem for infinite dimensional euclidean vector spaces the main features of our argument are i the construction of a non commutative c algebra to play the role of the algebra of functions on infinite dimensional euclidean space and ii the construction of a certain index one elliptic partial differential operator which provides the basis for an inverse to the bott periodicity map these tools have applications to index theory and the novikov conjecture notably a proof of the novikov conjecture for amenable groups the applications will be considered elsewhere

an etale approach to the novikov conjecture we show that the rational novikov conjecture for a group of finite homological type follows from the mod 2 acyclicity of the higson compactification of an e we then show that for groups of finite asymptotic dimension the higson compactification is mod p acyclic for all p and deduce the integral novikov conjecture for these groups 2007 wiley periodicals inc

on the k theory of groups with finite asymptotic dimension it is proved that the assembly maps in algebraic kand l theory with respect to the family of finite subgroups is injective for groups with finite asymptotic dimension that admit a finite model for e the result also applies to certain groups that admit only a finite dimensional model for e in particular it applies to discrete subgroups of virtually connected lie groups

isomorphism conjectures in algebraic k theory duff in this paper we are concerned with the four functors y y3 if and which map from the category of topological spaces x to the category diff of q spectra the functor 3 or if maps the space x to the qspectrum of stable topological or smooth pseudoisotopies of x the spaces diff dif 3i x id9 x i 0 are hatcher s deloopings of 970 x yd x cf 29 the functor j maps a path connected space x to the algebraic ktheoretic s2 spectrum for the integral group ring z7r1x the spaces x x i 0 are the gersten wagoner deloopings of z o x cf 27 52 5 x is also defined on a nonpath connected space x to be x1 where xi i e i are the path components of x and ii xi indicates the direct limit of all finite products of the i xi i e i if x is path connected then the functor maps x to the l surgery classifying spaces for oriented surgery problems with fundamental group r i1x identified by their fourfold periodicity k 90 x k 4j x cf 35 39 44 47 in addition if x is not path connected then we set y77 x tiei5 fj xi where xi i e i are the path components of x results obtained by the authors over the past five years cf 15 25 and in particular 19 16 a 1 a 18 together with many earlier results and conjectures which are reviewed in 1 6 1 1 6 6 suggest that for any connected cwcomplex x and for 5 denoting any of the above functors the q spectrum x should be computable in a simple way from the values taken by 9 on covering spaces of x which have very simple fundamental groups in more detail we let 9 x denote the collection of all subgroups h c ir ix which are either finite or virtually infinite cyclic a group h is virtually infinite cyclic if there is a short exact sequence of groups 1 z h f 1 with f equal to a finite group and z equal to the infinite cyclic group for each such group we let xh x denote the covering space projection corresponding to h then the q spectrum 5 x should be computable in a simple way from the q spectra 5 xh h e 9 x the purpose of this paper is to formulate precisely a conjecture along these lines and to verify the conjecture for any x

some results on the asymptotic relative efficiency of a random threshold decision rule the random threshold decision rule which is an equalizer rule in terms of probability of error for symmetrically distributed bounded amplitude nonstationary noise is compared with the sign detector and linear detector for bounded amplitude noise via asymptotic relative efficiency are explicit are expressions are derived for these detectors the result shows that the random threshold decision rule can be as effective as or better than the sign detector and as effective as the linear detector in terms of are for some bounded amplitude noise cases

a notion of geometric complexity and its application to topological rigidity we introduce a geometric invariant called finite decomposition complexity fdc to study topological rigidity of manifolds we prove for instance that if the fundamental group of a compact aspherical manifold m has fdc and if n is homotopy equivalent to m then m n is homeomorphic to n n for n large enough this statement is known as the stable borel conjecture on the other hand we show that the class of fdc groups includes all countable subgroups of gl n k for any field k

dynamic asymptotic dimension relation to dynamics topology coarse geometry and c algebras we introduce dynamic asymptotic dimension a notion of dimension for actions of discrete groups on locally compact spaces and more generally for locally compact etale groupoids we study our notion for minimal actions of the integer group its relation with conditions used by bartels luck and reich in the context of controlled topology and its connections with gromov s theory of asymptotic dimension we also show that dynamic asymptotic dimension gives bounds on the nuclear dimension of winter and zacharias for c algebras associated to dynamical systems dynamic asymptotic dimension also has implications for k theory and manifold topology these will be drawn out in subsequent work

on single sample robust detection of known signals with additive unknown mean amplitude bounded random interference ii the randomized decision rule solution corresp a randomized decision rule is derived and proved to be the saddlepoint solution of the robust detection problem for known signals in independent unknown mean amplitude bounded noise the saddlepoint solution phi 0 uses an equauy likely mixed strategy to chose one of n bayesian single threshold decision rules phi i 0 i 1 cdots n having been obtained previously by the author these decision rules are also all optimal against the maximin least favorable nonrandomized noise probability density f 0 where f 0 is a picket fence function with n pickets on its domain thee pair phi 0 f 0 is shown to satisfy the saddlepoint condition for probability of error i e p e phi 0 f leq p e phi 0 f 0 leq p e phi f 0 holds for all f and phi the decision rule phi 0 is also shown to be an eqoaliir rule i e p e phi 0 f p e phi 0 f 0 for all f with 4 1 leq p e phi 0 f 0 2 1 1 n 1 leq2 1 n geq 2 thus nature can force the communicator to use an em optimal randomized decision rule that generates a large probability of error and does not improve when less pernicious conditions prevail

stable model reference adaptive control in the presence of bounded disturbances the adaptive control of a linear time invariant plant in the presence of bounded disturbances is considered in addition to the usual assumptions made regarding the plant transfer function it is also assumed that the high frequency gain k p of the plant and an upper bound on the magnitude of the controller parameters are known under these conditions the adaptive controller suggested assures the boundedness of all signals in the overall system

a hurewicz type theorem for asymptotic dimension and applications to geometric group theory we prove an asymptotic analog of the classical hurewicz theorem on mappings that lower dimension this theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite dimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension as applications we find upper bound estimates for the asymptotic dimension of nilpotent and polycyclic groups in terms of their hirsch length we are also able to improve the known upper bounds on the asymptotic dimension of fundamental groups of complexes of groups amalgamated free products and the hyperbolization of metric spaces possessing the higson property

geometrization of the strong novikov conjecture for residually finite groups in this paper we prove that the strong novikov conjecture for a residually finite group is essentially equivalent to the coarse geometric novikov conjecture for a certain metric space associated to the group as an application we obtain the coarse geometric novikov conjecture for a large class of sequences of expanders

quasi locality and property a abstract let x be a metric space with bounded geometry p 0 1 and let e be a banach space the main result of this paper is that either if x has yu s property a and p 1 or without any condition on x when p 0 1 then quasi local operators on l p x e belong to the appropriate variant of the roe algebra of x this generalises the existing results of this type by lange and rabinovich engel tikuisis and the first author and li wang and the second author as consequences we obtain that uniform l p roe algebras of spaces with property a are closed under taking inverses and another condition characterising property a akin to the operator norm localisation for quasi local operators

going down functors and the kunneth formula for crossed products by etale groupoids we study the connection between the baum connes conjecture for an ample groupoid g with coefficient a and the kunneth formula for the mathrm k theory of tensor products by the crossed product a rtimes r g to do so we develop the machinery of going down functors for ample groupoids as an application we prove that both the uniform roe algebra of a coarse space which uniformly embeds in a hilbert space and the maximal roe algebra of a space admitting a fibered coarse embedding in a hilbert space satisfy the kunneth formula additionally we give an example of a space that does not admit a coarse embedding in a hilbert space but whose uniform roe algebra satisfies the kunneth formula and provides a stability result for the kunneth formula using controlled mathrm k theory as a byproduct of our methods we also prove a permanence property for the baum connes conjecture with respect to equivariant inductive limits of the coefficient algebra

signal enhancement by time frequency peak filtering time frequency peak filtering tfpf allows the reconstruction of signals from observations corrupted by additive noise by encoding the noisy signal as the instantaneous frequency if of a frequency modulated fm analytic signal if estimation is then performed on the analytic signal using the peak of a time frequency distribution tfd to recover the filtered signal this method is biased when the peak of the wigner ville distribution wvd is used to estimate the encoded signal s instantaneous frequency we characterize a class of signals for which the method implemented using the pseudo wvd is approximately unbiased this class contains deterministic bandlimited nonstationary multicomponent signals in additive white gaussian noise wgn we then derive the pseudo wvd window length that gives a reduced bias when tfpf is used for signals from this class testing of the method on both synthetic and real life newborn electroencephalogram eeg signals shows clean recovery of the signals in noise level down to a signal to noise ratio snr of 9 db

asymptotically convergent modified recursive least squares with data dependent updating and forgetting factor for systems with bounded noise continual updating of estimates required by most recursive estimation schemes often involves redundant usage of information and may result in system instabilities in the presence of bounded output disturbances an algorithm which eliminates these difficulties is investigated based on a set theoretic assumption the algorithm yields modified least squares estimates with a forgetting factor it updates the estimates selectively depending on whether the observed data contain sufficient information the information evaluation required at each step involves very simple computations in addition the parameter estimates are shown to converge asymptotically at an exponential rate to a region around the true parameter

identifying assembly maps in k and l theory in this paper we prove the equivalence of various algebraically or geometrically defined assembly maps used in formulating the main conjectures in k and l theory and c theory

a random threshold decision rule for known signals with additive amplitude bounded nonstationary random interference the robust single sample randomized decision rule for known signals in independent unknown mean amplitude bounded additive noise is extended to a two stage suboptimal multisample decision rule for independent finite sample size m nonstationary measurement sequences x sub 1 x sub m the first stage is a robust single sample decision rule using n random thresholds the second stage is the m sample sign detector with n randomly chosen sample thresholds this random threshold detector for a given number of thresholds n is shown to be an equalizer decision rule for a class of nonstationary symmetrical noise moreover the equalizer rule p sub e performance is a lower bound on independent asymmetrical noise performance the set of random threshold detectors n 1 when combined with the modified sign detector n 1 forms a family of equalizer rule multisample detectors for known signals in nonstationary bounded amplitude noise where the choice of n and corresponding performance depend only on the ratio of bounded noise range to signal separation s sub 1 s sub 0

the novikov conjecture for groups with finite asymptotic dimension recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology page 28 14 more precisely the asymptotic dimension for a metric space is the smallest integer n such that for any r 0 there exists a uniformly bounded cover c ui iei of the metric space for which the r multiplicity of c is at most n 1 i e no ball of radius r in the metric space intersects more than n 1 members of c 14 the class of finitely generated discrete groups with finite asymptotic dimension is hereditary in the sense that if a finitely generated group has finite asymptotic dimension as metric space with a word length metric then its finitely generated subgroups also have finite asymptotic dimension as metric spaces with word length metrics cf section 6 this together with a result of gromov in 14 implies that finitely generated subgroups of gromov s hyperbolic groups have finite asymptotic dimension currently no example of a finitely generated group with infinite asymptotic dimension and finite classifying space is known it should also be noted that two different definitions of asymptotic dimension