Pedersen ideals of tensor products of nonunital C*-algebras

We show that positive elements of a Pedersen ideal of a tensor product can be approximated in a particularly strong sense by sums of tensor products of positive elements. This has a range of applications to the structure of tracial cones and related topics, such as the Cuntz-Pedersen space or the Cuntz semigroup. For example, we determine the cone of lower semicontinuous traces of a tensor product in terms of the traces of the tensor factors, in an arbitrary C*-tensor norm. We show that the positive elements of a Pedersen ideal are sometimes stable under Cuntz equivalence. We generalize a result of Pedersen's by showing that certain classes of completely positive maps take a Pedersen ideal into a Pedersen ideal. We provide theorems that in many cases compute the Cuntz semigroup of a tensor product.Comment: circulated as preprint 2017

Energy-aware Load Balancing Policies for the Cloud Ecosystem

The energy consumption of computer and communication systems does not scale linearly with the workload. A system uses a significant amount of energy even when idle or lightly loaded. A widely reported solution to resource management in large data centers is to concentrate the load on a subset of servers and, whenever possible, switch the rest of the servers to one of the possible sleep states. We propose a reformulation of the traditional concept of load balancing aiming to optimize the energy consumption of a large-scale system: {\it distribute the workload evenly to the smallest set of servers operating at an optimal energy level, while observing QoS constraints, such as the response time.} Our model applies to clustered systems; the model also requires that the demand for system resources to increase at a bounded rate in each reallocation interval. In this paper we report the VM migration costs for application scaling.Comment: 10 Page

Clustering Algorithms for Scale-free Networks and Applications to Cloud Resource Management

In this paper we introduce algorithms for the construction of scale-free networks and for clustering around the nerve centers, nodes with a high connectivity in a scale-free networks. We argue that such overlay networks could support self-organization in a complex system like a cloud computing infrastructure and allow the implementation of optimal resource management policies.Comment: 14 pages, 8 Figurs, Journa

Spontaneous photon emission stimulated by two Bose condensates

We show that the phase difference of two overlapping ground state Bose-Einstein condensates can effect the optical spontaneous emission rate of excited atoms. Depending on the phase difference the atom stimulated spontaneous emission rate can vary between zero and the rate corresponding to all the ground state atoms in a single condensate. Besides giving control over spontaneous emission this provides an optical method for detecting the condensate phase difference. It differs from previous methods in that no light fields are applied. Instead the light is spontaneously emitted when excited atoms make a transition into either condensate.Comment: 14 pages, 2 postscript figures, Revtex. Corrections and significant additions in revisio