It is well known that the identity is an operator with the following property: if the operator, initially defined on an n-dimensional Banach space V , can be extended to any Banach space with norm 1, then V is isometric to (n) ∞ . We show that the set of all such operators consists precisely of those with spectrum lying in the unit circle. This result answers a question raised in [5] for comple...

We give some characterizations of self-adjointness and symmetricity of operator monotone functions by using the Barbour transform f → t+f 1+f and show that there are many non-symmetric operator means between the harmonic mean ! and the arithmetic mean ∇. Indeed, we show that there exists a non-symmetric operator mean between any two symmetric operator means.

The development of reusable requirements and design artifacts often requires one to characterize families of problem and solution models. This paper presents a metamodeling approach to characterizing a family of models. A characterization is expressed as a Role Model that consists of roles that can be played by UML model elemets. In this paper we describe how a family of UML static structural d...

Then why are researchers and doctors striving to cure Alzheimer’s and other typical diseases of old age? Let us return to the good old days and the picturesque habits we have heard about in distant populations: the Eskimo people who left their old people alone on the ice to die; or those tribes in some wild place in the Amazon or Africa who ate their elderly people to absorb their experience an...

Recent work on modeling the Web graph has dwelt on capturing the degree distributions observed on the Web. Pointing out that this represents a heavy reliance on “local” properties of the Web graph, we study the distribution of PageRank values (used in the Google search engine) on the Web. This distribution is of independent interest in optimizing search indices and storage. We show that PageRan...

Let M be a bicomplete, closed symmetric monoidal category. Let P be an operad in M, i.e., a monoid in the category of symmetric sequences of objects in M, with its composition monoidal structure. Let R be a P-co-ring, i.e., a comonoid in the category of P-bimodules. The co-ring R induces a natural “fattening” of the category of P-(co)algebras, expanding the morphism sets while leaving the objec...

Motifs are repeating patterns that determine the local properties of networks. In this work, we characterized all 3-node motifs using enzyme commission numbers of the International Union of Biochemistry and Molecular Biology to show that motif abundance is related to biochemical function. Further, we present a comparative analysis of motif distributions in the metabolic networks of 21 species a...

The Tukey depth is an innovative concept in multivariate data analysis. It can be utilized to extend the univariate order concept and advantages to a multivariate setting. While it is still an open question as towhether the depth contours uniquely determine the underlying distribution, some positive answers have been provided. We extend these results to distributions with smooth depth contours,...