One of the key ingredients of A. Connes’ noncommutative geometry is a generalized Dirac operator which induces a metric(Connes’ distance) on the state space. We generalize such a Dirac operator devised by A. Dimakis et al , whose Connes’ distance recovers the linear distance on a 1D lattice, into 2D lattice. This Dirac operator being “naturally” defined has the “local eigenvalue property” and i...

Abstract. We reformulate the Baum-Connes conjecture with coe cients by introducing a new crossed product functor for C⇤-algebras. All confirming examples for the original Baum-Connes conjecture remain confirming examples for the reformulated conjecture, and at present there are no known counterexamples to the reformulated conjecture. Moreover, some of the known expander-based counterexamples to...

let $a$ be an arbitrary banach algebra and $varphi$ a homomorphism from $a$ onto $bbb c$. our first purpose in this paper is to give some equivalent conditions under which guarantees a $varphi$-mean of norm one. then we find some conditions under which there exists a $varphi$-mean in the weak$^*$ cluster of ${ain a; |a|=varphi(a)=1}$ in $a^{**}$.

In this paper, we present an automated approach to discover patterns that can distinguish between sequences belonging to different labeled groups. Our method searches for approximately conserved motifs that occur with varying statistical properties in positive and negative training examples. We propose a two-step process to discover such patterns. Using locality sensitive hashing (LSH), we firs...

This paper defines the area measure of the quality of approximate convex hulls and proposes two new approximate convex hull algorithms. The first one is superior to known techniques under the area measure and comparable under the distance measure and time complexity. The second algorithm is superior to all known algorithms in both area and distance measures (including the first algorithm) while...

In this paper, we present an automated approach to discover patterns that can distinguish between sequences belonging to different labeled groups. Our method searches for approximately conserved motifs that occur with varying statistical properties in positive and negative training examples. We propose a two-step process to discover such patterns. Using locality sensitive hashing (LSH), we firs...

The paper presents a first level of coarse-grained parallelization in a sequential approximate optimization framework. A sequential approximate optimization framework builds local approximations of the system every iteration by evaluating a set of design points around the current design. In this research the database is generated by distributing the data sampling process among several processor...

In many practical problems, in particular in engineering design, the function form of criteria is not given explicitly in terms of design variables. Given the value of design variables, under this circumstance, the value of objective functions is obtained by real/computational experiments such as structural analysis, fluidmechanic analysis, thermodynamic analysis, and so on. Usually, these expe...