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

asymptotic dimension and small cancellation for hierarchically hyperbolic spaces and groups we prove that all hierarchically hyperbolic groups have finite asymptotic dimension one application of this result is to obtain the sharpest known bound on the asymptotic dimension of the mapping class group of a finite type surface improving the bound from exponential to at most quadratic in the complexity of the surface we also apply the main result to various other hierarchically hyperbolic groups and spaces we also prove a small cancellation result namely if g is a hierarchically hyperbolic group h g is a suitable hyperbolically embedded subgroup and n h is sufficiently deep in h then g n is a relatively hierarchically hyperbolic group this new class provides many new examples to which our asymptotic dimension bounds apply along the way we prove new results about the structure of hhss for example the associated hyperbolic spaces are always obtained up to quasi isometry by coning off canonical coarse product regions in the original space generalizing a relation established by masur and minsky between the complex of curves of a surface and teichmuller space

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

cyclic cohomology and higher indexes for noncompact complete manifolds abstract the indices of generalized dirac operators on noncompact complete riemannian manifolds live in the k theory of uniform roe algebras in this paper we shall compute the cyclic cohomology of uniform roe algebras associated to noncompact manifolds the cyclic cohomology of the uniform roe algebras is identified with uniform simplical cohomology with infinite support of the rips polyhedrons associated to a net of the riemannian manifold we also compute the chern character of the k theoretic indices of generalized dirac operators we apply such a computation to the analysis and geometry of noncompact complete riemannian manifolds in particular we show that a uniformly contractible riemnannian manifold with bounded geometry cannot have uniform positive scalar curvature outside a compact set if the volume and contractibility radius have certain subexponential growth

asymmetric slepian wolf coding of nonstationarily correlated m ary sources with sliding window belief propagation asymmetric slepian wolf coding aswc of m ary sources with nonstationary correlation is a very useful model for many practical problems an effective implementation of this coding scheme is to binarize each m ary source into multiple bitplanes which are then compressed by a single binary low density parity check ldpc code though the inter bitplane correlation of m ary sources can be exploited at the decoder by the joint bitplane belief propagation jbbp algorithm accurate online estimation of varying local source correlation still remains a major challenge to tackle this problem this paper proposes an m ary counterpart of the sliding window belief propagation swbp algorithm to realize simultaneous source recovery and correlation estimation to search for the optimal sliding window size the expected rate is raised as a new criterion moreover an adaptive method is proposed to decide whether correlation reestimation is necessary the m ary swbp mswbp algorithm is then generalized to obtain its 2d form which can be used to tackle the aswc of 2d m ary sources with nonstationary correlation the developed 1d 2d mswbp algorithm inherits all merits of the original binary swbp algorithm e g near optimal coding efficiency low complexity insensitivity to initial settings etc making it a very attractive technique in practice

assouad nagata dimension of connected lie groups we prove that the asymptotic assouad nagata dimension of a connected lie group g equipped with a left invariant riemannian metric coincides with its topological dimension of g c where c is a maximal compact subgroup to prove it we will compute the assouad nagata dimension of connected solvable lie groups and semisimple lie groups as a consequence we show that the asymptotic assouad nagata dimension of a polycyclic group equipped with a word metric is equal to its hirsch length and that some wreath type finitely generated groups can not be quasi isometrically embedded into any cocompact lattice on a connected lie group

ldpc based lossless compression of nonstationary binary sources using sliding window belief propagation low density parity check ldpc codes have been used to implement lossless distributed or conventional source coding however block wise ldpc codes are difficult to adapt to varying source statistics as traditional symbol wise entropy coding techniques in this paper we propose the sliding window belief propagation swbp algorithm which is able to simultaneously recover the source and refine the estimate of varying source statistics the swbp is easy to implement and performs well in simulations

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

limit operators compactness and essential spectra on bounded symmetric domains abstract this paper is a follow up to a recent article about the essential spectrum of toeplitz operators acting on the bergman space over the unit ball as mentioned in the said article some of the arguments can be carried over to the case of bounded symmetric domains and some cannot the aim of this paper is to close the gaps to obtain comparable results for general bounded symmetric domains in particular we show that a toeplitz operator on the bergman space a p is fredholm if and only if all of its limit operators are invertible even more generally we show that this is in fact true for all band dominated operators an algebra that contains the toeplitz algebra moreover we characterize compactness and explain how the berezin transform comes into play in particular we show that a bounded linear operator is compact if and only if it is band dominated and its berezin transform vanishes at the boundary for p 2 band dominated can be replaced by contained in the toeplitz algebra

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

c algebra extension theory and duality we develop a duality theory introduced by paschke to give a simplified account of the main results of the brown douglas fillmore extension theory and the relative k homology theory of baum and douglas

distributed coding using punctured quasi arithmetic codes for memory and memoryless sources this correspondence considers the use of punctured quasi arithmetic qa codes for the slepian wolf problem these entropy codes are defined by finite state machines for memoryless and first order memory sources puncturing an entropy coded bit stream leads to an ambiguity at the decoder side the decoder makes use of a correlated version of the original message in order to remove this ambiguity a complete distributed source coding dsc scheme based on qa encoding with side information at the decoder is presented together with iterative structures based on qa codes the proposed schemes are adapted to memoryless and first order memory sources simulation results reveal that the proposed schemes are efficient in terms of decoding performance for short sequences compared to well known dsc solutions using channel codes

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

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

farkas type results with conjugate functions we present some new farkas type results for inequality systems involving a finite as well as an infinite number of convex constraints for this we use two kinds of conjugate dual problems namely an extended fenchel type dual problem and the recently introduced fenchel lagrange dual problem for the latter which is a combination of the classical fenchel and lagrange duals the strong duality is established

hamming distance spectrum of dac codes for equiprobable binary sources distributed arithmetic coding dac is an effective technique for implementing slepian wolf coding swc it has been shown that a dac code partitions source space into unequal size codebooks so that the overall performance of dac codes depends on the cardinality and structure of these codebooks the problem of dac codebook cardinality has been solved by the so called codebook cardinality spectrum ccs this paper extends the previous work on ccs by studying the problem of dac codebook structure we define hamming distance spectrum hds to describe dac codebook structure and propose a mathematical method to calculate the hds of dac codes the theoretical analyses are verified by experimental results

improved binary dac codec with spectrum for equiprobable sources slepian wolf coding swc can be effectively implemented by distributed arithmetic coding dac codes a theoretical tool named spectrum has been developed to analyze the complexity of the full search binary dac bdac decoder for equiprobable sources following this work this paper aims at improving the coding efficiency of bdac codes to achieve this goal this paper analyzes how bdac codes partition source space into codebooks and links codebook cardinalities with the initial spectrum further by exploiting the final spectrum this paper proves that the decoding error probability of bdac codes will not tend to zero as code length goes to infinity even at rates greater than the slepian wolf limit on the basis of theoretical analyses two techniques are proposed to reduce the decoding error probability of bdac codes i e the permutation technique which removes near in the sense of hamming distance codewords in each codebook and the weighted branching technique which reduces the mis pruning risk of proper paths during the decoding the effectiveness of both techniques is well verified by experimental results

quantitative k theory for banach algebras abstract quantitative or controlled k theory for c algebras was used by guoliang yu in his work on the novikov conjecture and later developed more formally by yu together with herve oyono oyono in this paper we extend their work by developing a framework of quantitative k theory for the class of algebras of bounded linear operators on subquotients i e subspaces of quotients of l p spaces we also prove the existence of a controlled mayer vietoris sequence in this framework

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

farkas type results for inequality systems with composed convex functions via conjugate duality we present some farkas type results for inequality systems involving finitely many functions therefore we use a conjugate duality approach applied to an optimization problem with a composed convex objective function and convex inequality constraints some recently obtained results are rediscovered as special cases of our main result

distributed arithmetic coding for the slepian wolf problem distributed source coding schemes are typically based on the use of channels codes as source codes in this paper we propose a new paradigm named ldquodistributed arithmetic coding rdquo which extends arithmetic codes to the distributed case employing sequential decoding aided by the side information in particular we introduce a distributed binary arithmetic coder for the slepian wolf coding problem along with a joint decoder the proposed scheme can be applied to two sources in both the asymmetric mode wherein one source acts as side information and the symmetric mode wherein both sources are coded with ambiguity at any combination of achievable rates distributed arithmetic coding provides several advantages over existing slepian wolf coders especially good performance at small block lengths and the ability to incorporate arbitrary source models in the encoding process e g context based statistical models in much the same way as a classical arithmetic coder we have compared the performance of distributed arithmetic coding with turbo codes and low density parity check codes and found that the proposed approach is very competitive

composite nonsmooth programming with gâteaux differentiability this paper examines constrained nonsmooth optimization problems where the objective function and the constraints are compositions of locally lipschitz functions and g teaux differentiable functions but are not necessarily frechet differentiable or strict differentiable lagrangian necessary and sufficient optimality conditions are presented for various classes of composite programs these are obtained by constructing appropriate convex approximations for composite functions the lagrange multipliers are also characterized in terms of subgradients of the value function under appropriate conditions

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

the coarse geometric novikov conjecture for subspaces of non positively curved manifolds abstract in this paper we prove the coarse geometric novikov conjecture for metric spaces with bounded geometry which admit a coarse embedding into a simply connected complete riemannian manifold of non positive sectional curvature

dac spectrum of binary sources with equally likely symbols though distributed arithmetic coding dac is an effective implementation of slepian wolf coding its performance which is closely linked with its decoding complexity has not received a thorough analysis with binary sources with equally likely symbols as the research object this paper develops the dac spectrum and makes use of it as a tool to answer the complexity problem of the ideal dac decoder based on an in depth analysis on dac decoding process we define the dac spectrum and propose to find it by a recursive formulation firstly the initial dac spectrum is constrained by a functional equation and the fourier transform is utilized to obtain its general explicit form secondly an equation is given through which stage i 1 dac spectrum can be deduced from stage i dac spectrum a numerical method is also proposed for calculating dac spectrum whose convergency is proved to measure the complexity of the ideal dac decoder we define the expansion factor and relate it to dac spectrum it is proved that if binary symbols 0 and 1 are mapped onto partially overlapped intervals 0 q and 1 q 1 respectively the expansion factor will converge to 2q i e the complexity of the ideal rate dac decoder is approximately o 2 n 1

farkas type results for fractional programming problems abstract considering a constrained fractional programming problem within the present paper we present some necessary and sufficient conditions which ensure that the optimal objective value of the considered problem is greater than or equal to a given real constant the desired results are obtained using the fenchel lagrange duality approach applied to an optimization problem with convex or difference of convex dc objective functions and finitely many convex constraints these are obtained from the initial fractional programming problem using an idea due to dinkelbach we also show that our general results encompass as special cases some recently obtained farkas type results

on the zero in the spectrum conjecture we prove that the answer to the zero in the spectrum conjecture in the form suggested by j lott is negative namely we show that for any n ge 6 there exists a closed n dimensional smooth manifold m n so that zero does not belong to the spectrum of the laplace beltrami operator acting on the l 2 forms of all degrees on the universal covering tilde m

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

the nuclear dimension of c algebras abstract we introduce the nuclear dimension of a c algebra this is a noncommutative version of topological covering dimension based on a modification of the earlier concept of decomposition rank our notion behaves well with respect to inductive limits tensor products hereditary subalgebras hence ideals quotients and even extensions it can be computed for many examples in particular it is finite for all uct kirchberg algebras in fact all classes of nuclear c algebras which have so far been successfully classified consist of examples with finite nuclear dimension and it turns out that finite nuclear dimension implies many properties relevant for the classification program surprisingly the concept is also linked to coarse geometry since for a discrete metric space of bounded geometry the nuclear dimension of the associated uniform roe algebra is dominated by the asymptotic dimension of the underlying space

quasi slater and farkas minkowski qualifications for semi infinite programming with applications the well known farkas minkowski fm type qualification plays an important role in linear semi infinite programming and has been extensively developed by many authors in establishing optimality conditions duality and stability for semi infinite programming in this paper we introduce the concept of the quasi slater condition for a semi infinite convex inequality system and present that the slater type conditions imply the fm qualification under some appropriate continuity assumption of the set valued mapping i mapsto f i x applying these relationships we establish dual characterizations both asymptotic and nonasymptotic for set containment problems and provide some sufficient conditions for ensuring the strong lagrangian duality and farkas lemma

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

embedding of hyperbolic groups into products of binary trees we show that every gromov hyperbolic group admits a quasi isometric embedding into the product of n 1 binary trees where n dim is the topological dimension of the boundary at infinity of

characterizations of e duality gap statements for composed optimization problems abstract in this paper we present different regularity conditions that equivalently characterize e duality gap statements for optimization problems consisting of minimizing the sum of a function with the precomposition of a cone increasing function to a vector function these regularity conditions are formulated by using epigraphs and e subdifferentials taking e 0 one can rediscover recent results on stable strong and total duality and zero duality gap from the literature moreover we deliver as byproducts e optimality conditions and e saddle point statements for the aforementioned kind of problems and e farkas statements involving the sum of a function with the precomposition of a cone increasing function to a vector function

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

characterizing set containments involving infinite convex constraints and reverse convex constraints dual characterizations of the containment of a closed convex set defined by infinite convex constraints in an arbitrary polyhedral set in a reverse convex set defined by convex constraints and in another convex set defined by finite convex constraints are given a special case of these dual characterizations has played a key role in generating knowledge based support vector machine classifiers which are powerful tools in data classification and mining the conditions in these dual characterizations reduce to simple nonasymptotic conditions under slater s constraint qualification

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

analysis on tailed distributed arithmetic codes for uniform binary sources distributed arithmetic coding dac is a variant of ac that can realize slepian wolf coding in a nonlinear way in our previous work we defined codebook cardinality spectrum ccs and hamming distance spectrum hds for dac in this paper we make use of ccs and hds to analyze tailed dac which is a form of dac that as traditional ac maps the last few symbols of each source block onto non overlapped intervals first we derive the exact hds formula for tailless dac a form of dac that maps all the symbols of each source block onto overlapped intervals and show that the hds formula previously given is in fact approximation then the hds formula is extended to tailed dac using ccs we also deduce the average codebook cardinality which is closely related to decoding complexity and rate loss of tailed dac the effects of tail length are extensively analyzed it is revealed that by increasing tail length to a value not close to the bitstream length closely spaced codewords within the same codebook can be removed at the cost of a higher decoding complexity and a larger rate loss finally theoretical analyses are verified by experiments

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

fibred coarse embedding into non positively curved manifolds and higher index problem abstract let x n 1 x n be the coarse disjoint union of a sequence of finite metric spaces with uniform bounded geometry in this paper we show that the coarse novikov conjecture holds for x if x admits a fibred coarse embedding into a simply connected complete riemannian manifold of non positive sectional curvature this includes a large class of expander graphs with geometric property t

new formulas for the legendre fenchel transform we present new formulas for the legendre fenchel transform of functions they concern the following three operations inverting a strictly monotone convex function post composing an arbitrary function with a strictly monotone concave function multiplying two positively valued strictly monotone convex functions

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