Quasi-local energy for cosmological models

First we briefly review our covariant Hamiltonian approach to quasi-local energy, noting that the Hamiltonian-boundary-term quasi-local energy expressions depend on the chosen boundary conditions and reference configuration. Then we present the quasi-local energy values resulting from the formalism applied to homogeneous Bianchi cosmologies. Finally we consider the quasi-local energies of the FRW cosmologies. Our results do not agree with certain widely accepted quasi-local criteria.Comment: Contributed to International Symposium on Cosmology and Particle Astrophysics (CosPA 2006), Taipei, Taiwan, 15-17 Nov 200

Quasi-local energy and the choice of reference

A quasi-local energy for Einstein's general relativity is defined by the value of the preferred boundary term in the covariant Hamiltonian formalism. The boundary term depends upon a choice of reference and a time-like displacement vector field (which can be associated with an observer) on the boundary of the region. Here we analyze the spherical symmetric cases. For the obvious analytic choice of reference based on the metric components, we find that this technique gives the same quasi-local energy values using several standard coordinate systems and yet can give different values in some other coordinate systems. For the homogeneous-isotropic cosmologies, the energy can be non-positive, and one case which is actually flat space has a negative energy. As an alternative, we introduce a way to determine the choice of both the reference and displacement by extremizing the energy. This procedure gives the same value for the energy in different coordinate systems for the Schwarzschild space, and a non-negative value for the cosmological models, with zero energy for the dynamic cosmology which is actually Minkowski space. The timelike displacement vector comes out to be the dual mean curvature vector of the two-boundary.Comment: 21 pages; revised version to appear in CQ

Multiple-Level Power Allocation Strategy for Secondary Users in Cognitive Radio Networks

In this paper, we propose a multiple-level power allocation strategy for the secondary user (SU) in cognitive radio (CR) networks. Different from the conventional strategies, where SU either stays silent or transmit with a constant/binary power depending on the busy/idle status of the primary user (PU), the proposed strategy allows SU to choose different power levels according to a carefully designed function of the receiving energy. The way of the power level selection is optimized to maximize the achievable rate of SU under the constraints of average transmit power at SU and average interference power at PU. Simulation results demonstrate that the proposed strategy can significantly improve the performance of SU compared to the conventional strategies.Comment: 12 page

Computational Inferences of Mutations Driving Mesenchymal Differentiation in Glioblastoma

This dissertation reviews the development and implementation of integrative, systems biology methods designed to parse driver mutations from high- throughput array data derived from human patients. The analysis of vast amounts of genomic and genetic data in the context of complex human genetic diseases such as Glioblastoma is a daunting task. Mutations exist by the hundreds, if not thousands, and only an unknown handful will contribute to the disease in a significant way. The goal of this project was to develop novel computational methods to identify candidate mutations from these data that drive the molecular differentiation of glioblastoma into the mesenchymal subtype, the most aggressive, poorest-prognosis tumors associated with glioblastoma

Image segmentation using fuzzy LVQ clustering networks

In this note we formulate image segmentation as a clustering problem. Feature vectors extracted from a raw image are clustered into subregions, thereby segmenting the image. A fuzzy generalization of a Kohonen learning vector quantization (LVQ) which integrates the Fuzzy c-Means (FCM) model with the learning rate and updating strategies of the LVQ is used for this task. This network, which segments images in an unsupervised manner, is thus related to the FCM optimization problem. Numerical examples on photographic and magnetic resonance images are given to illustrate this approach to image segmentation

Leptons from Dark Matter Annihilation in Milky Way Subhalos

Numerical simulations of dark matter collapse and structure formation show that in addition to a large halo surrounding the baryonic component of our galaxy, there also exists a significant number of subhalos that extend hundreds of kiloparsecs beyond the edge of the observable Milky Way. We find that for dark matter (DM) annihilation models, galactic subhalos can significantly modify the spectrum of electrons and positrons as measured at our galactic position. Using data from the recent Via Lactea II simulation we include the subhalo contribution of electrons and positrons as boundary source terms for simulations of high energy cosmic ray propagation with a modified version of the publicly available GALPROP code. Focusing on the DM DM -> 4e annihilation channel, we show that including subhalos leads to a better fit to both the Fermi and PAMELA data. The best fit gives a dark matter particle mass of 1.2 TeV, for boost factors of 90 in the main halo and 1950-3800 in the subhalos (depending on assumptions about the background), in contrast to the 0.85 TeV mass that gives the best fit in the main halo-only scenario. These fits suggest that at least a third of the observed electron cosmic rays from DM annihilation could come from subhalos, opening up the possibility of a relaxation of recent stringent constraints from inverse Compton gamma rays originating from the high-energy leptons.Comment: 8 pages, 13 figures; added referenc