the nuclear dimension of c algebras associated to homeomorphisms abstract we show that if x is a finite dimensional locally compact hausdorff space then the crossed product of c 0 x by any automorphism has finite nuclear dimension this generalizes previous results in which the automorphism was required to be free as an application we show that group c algebras of certain non nilpotent groups have finite nuclear dimension

classification of a class of crossed product c algebras associated with residually finite groups a residually finite group acts on a profinite completion by left translation we consider the corresponding crossed product c algebra for discrete countable groups that are central extensions of finitely generated abelian groups by finitely generated abelian groups these are automatically residually finite we prove that all such crossed products are classifiable by k theoretic invariants using techniques from the classification theory for nuclear c algebras

node capacitated ring routing we consider the node capacitated routing problem in an undirected ring network along with its fractional relaxation the node capacitated multicommodity flow problem for the feasibility problem farkas lemma provides a characterization for general undirected graphs asserting roughly that there exists such a flow if and only if the so called distance inequality holds for every choice of distance functions arising from nonnegative node weights for rings this straightforward result will be improved in two ways we prove that independent of the integrality of node capacities it suffices to require the distance inequality only for distances arising from 0 1 2 valued node weights a requirement that will be called the double cut condition moreover for integer valued node capacities the double cut condition implies the existence of a half integral multicommodity flow in this case there is even an integer valued multicommodity flow that violates each node capacity by at most one our approach gives rise to a combinatorial strongly polynomial algorithm to compute either a violating double cut or a node capacitated multicommodity flow a relation of the problem to its edge capacitated counterpart will also be explained

quasidiagonal representations of nilpotent groups we show that every unitary representation of a discrete solvable virtually nilpotent group g is quasidiagonal roughly speaking this says that every unitary representation of g approximately decomposes as a direct sum of finite dimensional approximate representations in operator algebraic terms we show that c g is strongly quasidiagonal

feedback vertex sets and cyclically reducible graphs the problem of finding a minimum cardinality feedback vertex set of a directed graph is considered of the classic np complete problems this is one of the least understood although karp showed the general problem to be np complete a linear algorithm for its solution on reducible flow graphs was given by shamir the class of reducible flow graphs is the only nontrivial class of graphs for which a polynomial time algorithm to solve this problem is known the main result of this paper is to present a new class of graphs the cyclically reducible graphs for which minimum feedback vertex sets can be found in polynomial time this class is not restricted to flow graphs and most small graphs 10 or fewer nodes fall into this class the identification of this class is particularly important since there do not exist approximation algorithms for this problem having a provably good worst case performance along with the class and a simple polynomial time algorithm for finding minimum feedback vertex sets of graphs in the class several related results are presented it is shown that there is no forbidden subgraph characterization of the class and that there is no particular inclusion relationship between this class and the reducible flow graphs in addition it is shown that a class of general graphs which are related to the reducible flow graphs are contained in the cyclically reducible class

z stability of crossed products by strongly outer actions ii we consider a crossed product of a unital simple separable nuclear stably finite z stable c algebra a by a strongly outer cocycle action of a discrete countable amenable group under the assumption that a has finitely many extremal tracial states and is elementary amenable we show that the twisted crossed product c algebra is z stable as an application we also prove that all strongly outer cocycle actions of the klein bottle group on z are cocycle conjugate to each other this is the first classification result for actions of non abelian infinite groups on stably finite c algebras

finitely generated nilpotent group c algebras have finite nuclear dimension we show that group c algebras of finitely generated nilpotent groups have finite nuclear dimension it then follows from a string of deep results that the c algebra a generated by an irreducible representation of such a group has decomposition rank at most 3 if in addition a satisfies the universal coefficient theorem another string of deep results shows it is classifiable by its ordered ktheory and is approximately subhomogeneous we observe that all c algebras generated by faithful irreducible representations of finitely generated torsion free nilpotent groups satisfy the universal coefficient theorem

lp lq boundedness of bergman type operators over the siegel upper half space abstract we characterize the l p l q boundedness of bergman type operators over the siegel upper half space this extends a recent result of cheng et al 2017 5 to higher dimensions

on a simple unital projectionless c algebra we construct a unital separable c algebra z as an analog of the hyperfinite type ii 1 factor besides being nuclear simple projectionless and infinite dimensional z has a unique tracial state and is kk equivalent to inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i the algebra of complex numbers it is shown that unital endomorphisms on z are approximately inner and that z is isomorphic to the infinite tensor product of its replicas it is also shown that a z a for certain interesting classes of unital simple nuclear c algebras a of real rank zero

index coding an interference alignment perspective author s maleki h cadambe vr jafar sa abstract the index coding problem is studied from an interference alignment perspective providing new results as well as new insights into and generalizations of previously known results an equivalence is established between the capacity of multiple unicast index coding where each message is desired by exactly one receiver and groupcast index coding where a message can be desired by multiple receivers which settles the heretofore open question of insufficiency of linear codes for the multiple unicast index coding problem by equivalence with groupcast settings where this question has previously been answered necessary and sufficient conditions for the achievability of rate half per message in the index coding problem are shown to be a natural consequence of interference alignment constraints and generalizations to feasibility of rate 1 l 1 per message when each destination desires at least l messages are similarly obtained finally capacity optimal solutions are presented to a series of symmetric index coding problems inspired by the local connectivity and local interference characteristics of wireless networks the solutions are based on vector linear coding 1963 2012 ieee

classification of c algebras generated by representations of the unitriangular group ut 4 z abstract it was recently shown that each c algebra generated by a faithful irreducible representation of a finitely generated torsion free nilpotent group is classified by its ordered k theory for the three step nilpotent group u t 4 z we calculate the ordered k theory of each c algebra generated by a faithful irreducible representation of u t 4 z and see that they are all simple a t algebras we also point out that there are many simple non a t algebras generated by irreducible representations of nilpotent groups

on capacity of line networks we consider communication through a cascade of discrete memoryless channels dmcs the source and destination node of this cascade are allowed to use coding schemes of arbitrary complexity but the intermediate relay nodes are restricted to process only blocks of a fixed length we investigate how the processing at the relays must be chosen in order to maximize the capacity of the cascade that is the maximum achievable end to end rate between the source and the destination for infinite cascades with fixed intermediate processing length at the relays we prove that this intermediate processing can be chosen to be identical without loss of optimality and that the capacity of the cascade coincides with the rate of the best zero error code of length equal to the block length of the intermediate processing we further show that for fixed and identical intermediate processing at all relays convergence of capacity as the length of the cascade goes to infinity is exponentially fast finally we characterize how the block length of the intermediate processing must scale with the length of the cascade to guarantee a constant end to end rate we prove that it is sufficient that the block length scales logarithmically with the network length in order to achieve any rate above the zero error capacity we show that in many cases of interest logarithmic growth is also necessary

sharp constants related to the triangle inequality in lorentz spaces we study the lorentz spaces lp s r in the range 1 p s for which the standard functional f p s 0 t1 pf t s dt t 1 s is only a quasi norm we find the optimal constant in the triangle inequality for this quasi norm which leads us to consider the following decomposition norm f p s inf

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

regularity properties in the classification program for separable amenable c algebras we report on recent progress in the program to classify separable amenable c algebras our emphasis is on the newly apparent role of regularity properties such as finite decomposition rank strict comparison of positive elements and z stability and on the importance of the cuntz semigroup we include a brief history of the program s successes since 1989 a more detailed look at the villadsen type algebras which have so dramatically changed the landscape and a collection of announcements on the structure and properties of the cuntz semigroup

quasidiagonality of nuclear c algebras we prove that faithful traces on separable and nuclear c algebras in the uct class are quasidiagonal this has a number of consequences firstly by results of many hands the classification of unital separable simple and nuclear c algebras of finite nuclear dimension which satisfy the uct is now complete secondly our result links the finite to the general version of the toms winter conjecture in the expected way and hence clarifies the relation between decomposition rank and nuclear dimension finally we confirm the rosenberg conjecture discrete amenable groups have quasidiagonal c algebras

subshifts and perforation we demonstrate that the perforative phenomena shown to occur among simple amenable c algebras by villadsen and toms can be realized within a dynamical framework more specically we construct a minimal homeomorphism for which the k0 group of the crossed product fails to be weakly unperforated and a minimal homeomor phism for which the crossed product has the same elliott invariant as an at algebra but has cuntz semigroup which fails to be almost unperforated

analytic besov spaces and hardy type inequalities in tube domains over symmetric cones we give various equivalent formulations to the partially open problem about l p boundedness of bergman projections in tubes over cones namely we show that such boundedness is equivalent to the duality identity between bergman spaces a p 0 a p and also to a hardy type inequality related to the wave operator we introduce analytic besov spaces in tubes over cones for which such hardy inequalities play an important role for p 2 we identify as a besov space the range of the bergman projection acting on l p and also the dual of a p 0 for the bloch space b 1 we give in addition new necessary conditions on the number of derivatives required in its deflnition

on the structure of twisted group c algebras we first give general structural results for the twisted group algebras c g of a locally compact group g with large abelian subgroups in particular we use a theorem of williams to realise c g as the sections of a c bundle whose fibres are twisted group algebras of smaller groups and then give criteria for the simplicity of these algebras next we use a device of rosenberg to show that when is a discrete subgroup of a solvable lie group g the k groups k c are isomorphic to certain twisted k groups k g of the homogeneous space g and we discuss how the twisting class h 3 g z depends on the cocycle

nuclear dimension and mathcal z stability of pure c algebras in this article i study a number of topological and algebraic dimension type properties of simple c algebras and their interplay in particular a simple c algebra is defined to be tracially m bar m pure if it has strong tracial m comparison and is tracially bar m almost divisible these notions are related to each other and to nuclear dimension

network coding in node constrained line and star networks line and star networks with both node and edge constraints are studied in the network coding framework for line networks the capacity region of the general multiple multicast problem is established the coding theorem is based on a binary linear coding scheme while the converse requires new upper bounds that improve on standard cut based bounds for star networks the multiple unicast problem is examined capacity upper bounds are derived and a simple linear coding scheme is proposed which is based on the combinatorial optimization problem of cycle packing in directed graphs the optimality of this scheme is established for a broad class of demands the connection of node constrained network coding in star networks and index coding with side information is discussed and used to partially characterize the optimal linear code for general rates

nonlinear index coding outperforming the linear optimum the following source coding problem was introduced by birk and kol a sender holds a word x isin 0 1 n and wishes to broadcast a codeword to n receivers rn rn the receiver ri is interested in xi and has prior side information comprising some subset of the n bits this corresponds to a directed graph g on n vertices where i j is an edge ri ri knows the bit xj an index code for g is an encoding scheme which enables each ri to always reconstruct xi given his side information the minimal word length of an index code was studied by bar yossef birk jayram and kol focs 06 they introduced a graph parameter minrk2 g which completely characterizes the length of an optimal linear index code for g they showed that in various cases linear codes attain the optimal word length and conjectured that linear index coding is in fact always optimal in this work we disprove the main conjecture of bar yossef birk jayram and kol in the following strong sense for any epsiv 0 and sufficiently large n there is an n vertex graph g so that every linear index code for g requires codewords of length at least nepsiv and yet a nonlinear index code for g has a word length of ne this is achieved by an explicit construction which extends alon s variant of the celebrated ramsey construction of frankl and wilson in addition we study optimal index codes in various less restricted natural models and prove several related properties of the graph parameter minrk g