Let G be an infinite countable group and A be a finite set.IfΣ?A~G is a strongly irreducible subshift of finite type,we endow a locally compact and Hausdorff topology on the homoclinic equivalence relation■onΣand show that the reduced C^(*)-algebra C_(r)^(*)(■)of■is a unital simple approximately finite(AF)-dimensional C^(*)-algebra.The shift action G of onΣinduces a canonical automorphism action of G on the C^(*)-algebra C_(r)^(*)(■).We give the notion of noncommutative dynamical entropy invariants for amenable group actions on C^(*)-algebras,and show that,if G is an amenable group,then the noncommutative topological entropy of the canonical automorphism action of G on C_(r)^(*)(■)is equal to the topology entropy of the shift action of G onΣ.We also establish the variational principle with respect to the noncommutative measure entropy and the topological entropy for the C^(*)-dynamical system(C_(r)^(*)(■),G).
Existing solutions against wiretapping attacks for network coding either bring significant bandwidth overhead or incur a high computational complexity.In order to reduce the security overhead of the existing solutions for securing network coding,a novel securing network coding paradigm is presented relying on two coding models:intra-generation coding and inter-generation coding.The basic idea to secure network coding using intra-generation coding is to limit the encryption operations for each generation,and then subject the scrambled and the remaining original source vectors to a linear transformation.This method is then generalized seamlessly using inter-generation coding by further exploiting the algebraic structure of network coding.We show that the proposed schemes have properties of low-complexity security,little bandwidth consumption,and high efficiency in integrating with the existing security techniques effectively.
LIU GuangjunLIU BinyueLIU XimengLI FangGUO Wangmei
We show that many Kadison–Singer algebras are maximal triangular in all algebras containing them although their definition requires the maximality taken in the class of reflexive algebras. Diagonal-trivial maximal non self-adjoint subalgebras of matrix algebras with lower dimensions are classified.
We introduce the notion of property(RD) for a locally compact, Hausdorff and r-discrete groupoid G, and show that the set S_2~l(G) of rapidly decreasing functions on G with respect to a continuous length function l is a dense spectral invariant and Fréchet *-subalgebra of the reduced groupoid C~*-algebra C_r~*(G) of G when G has property(RD) with respect to l, so the K-theories of both algebras are isomorphic under inclusion. Each normalized cocycle c on G, together with an invariant probability measure on the unit space G^0 of G, gives rise to a canonical map τ_c on the algebra C_c(G) of complex continuous functions with compact support on G. We show that the map τ_c can be extended continuously to S_2~l(G) and plays the same role as an n-trace on C_r~*(G) when G has property(RD) and c is of polynomial growth with respect to l, so the Connes' fundament paring between the K-theory and the cyclic cohomology gives us the K-theory invariants on C_r~*(G).
Existing works for securing network coding against wiretapping either incur high coding complexity or bring large bandwidth overhead.For exploiting the lightweight security mechanism for resource-constrained networks,an efficient secure coding scheme is proposed in conjunction with the inherent mixing characteristic of network coding.The key idea is to minimize the randomizing operations to the entire plaintext data.The proposed scheme is shown to have properties of lightweight security complexity and lower communication overhead compared with the existing traditional solutions,and can be easy in implementation and combination with classical cryptography techniques.
