P_4-Decomposability in Regular Graphs and Multigraphs

The main objective of this thesis is to review and expand the study of graph decomposability. An H-decomposition of a graph G=(V,E) is a partitioning of the edge set, $E$, into edge-disjoint isomorphic copies of a subgraph H. In particular we focus on the decompositions of graphs into paths. We prove that a 2,4 mutligraph with maximum multiplicity 2 admits a C_2,C_3-free Euler tour (and thus, a decomposition into paths of length 3 if it has size a multiple of 3) if and only if it avoids a set of 15 forbidden structures. We also prove that a 4-regular multigraph with maximum multiplicity 2 admits a decomposition into paths of length three if and only if it has size a multiple of 3 and no three vertices induce more than 4 edges. We go on to outline drafted work reflecting further research into path decomposition problems

Relativistic models for Superconducting-Superfluid Mixtures

The material below the crust of a neutron star is understood to be describable in terms of three principal independently moving constituents, identifiable as neutrons, protons, and electrons, of which the first two are believed to form mutually coupled bosonic condensates. The large scale comportment of such a system will be that of a positively charged superconducting superfluid in a negatively charged ``normal'' fluid background. As a contribution to the development of the theory of such a system, the present work shows how, subject to neglect of dissipative effects, it is possible to set up an elegant category of simplified but fully relativistic three-constituent superconducting superfluid models whose purpose is to provide realistic approximations for cases in which a strictly conservative treatment is sufficient. A "mesoscopic" model, describing the fluid between the vortices, is constructed, as well as a "macroscopic" model taking into account the average effect of quantised vortices.Comment: 28 pages, LaTeX, no figure; to appear in Nuclear Physics

Bogomol'nyi Limit For Magnetic Vortices In Rotating Superconductor

This work is the sequel of a previous investigation of stationary and cylindrically symmetric vortex configurations for simple models representing an incompressible non-relativistic superconductor in a rigidly rotating background. In the present paper, we carry out our analysis with a generalized Ginzburg-Landau description of the superconductor, which provides a prescription for the radial profile of the normal density within the vortex. Within this framework, it is shown that the Bogomol'nyi limit condition marking the boundary between type I and type II behavior is unaffected by the rotation of the background.Comment: 7 pages, uses RevTeX, submitted to Phys.Rev.

Little genetic differentiation as assessed by uniparental markers in the presence of substantial language variation in peoples of the Cross River region of Nigeria

<p>Abstract</p> <p>Background</p> <p>The Cross River region in Nigeria is an extremely diverse area linguistically with over 60 distinct languages still spoken today. It is also a region of great historical importance, being a) adjacent to the likely homeland from which Bantu-speaking people migrated across most of sub-Saharan Africa 3000-5000 years ago and b) the location of Calabar, one of the largest centres during the Atlantic slave trade. Over 1000 DNA samples from 24 clans representing speakers of the six most prominent languages in the region were collected and typed for Y-chromosome (SNPs and microsatellites) and mtDNA markers (Hypervariable Segment 1) in order to examine whether there has been substantial gene flow between groups speaking different languages in the region. In addition the Cross River region was analysed in the context of a larger geographical scale by comparison to bordering Igbo speaking groups as well as neighbouring Cameroon populations and more distant Ghanaian communities.</p> <p>Results</p> <p>The Cross River region was shown to be extremely homogenous for both Y-chromosome and mtDNA markers with language spoken having no noticeable effect on the genetic structure of the region, consistent with estimates of inter-language gene flow of 10% per generation based on sociological data. However the groups in the region could clearly be differentiated from others in Cameroon and Ghana (and to a lesser extent Igbo populations). Significant correlations between genetic distance and both geographic and linguistic distance were observed at this larger scale.</p> <p>Conclusions</p> <p>Previous studies have found significant correlations between genetic variation and language in Africa over large geographic distances, often across language families. However the broad sampling strategies of these datasets have limited their utility for understanding the relationship within language families. This is the first study to show that at very fine geographic/linguistic scales language differences can be maintained in the presence of substantial gene flow over an extended period of time and demonstrates the value of dense sampling strategies and having DNA of known and detailed provenance, a practice that is generally rare when investigating sub-Saharan African demographic processes using genetic data.</p

Phosphoinositide-dependent kinase 1 controls migration and malignant transformation but not cell growth and proliferation in PTEN-null lymphocytes

In normal T cell progenitors, phosphoinositide-dependent kinase l (PDK1)–mediated phosphorylation and activation of protein kinase B (PKB) is essential for the phosphorylation and inactivation of Foxo family transcription factors, and also controls T cell growth and proliferation. The current study has characterized the role of PDK1 in the pathology caused by deletion of the tumor suppressor phosphatase and tensin homologue deleted on chromosome 10 (PTEN). PDK1 is shown to be essential for lymphomagenesis caused by deletion of PTEN in T cell progenitors. However, PTEN deletion bypasses the normal PDK1-controlled signaling pathways that determine thymocyte growth and proliferation. PDK1 does have important functions in PTEN-null thymocytes, notably to control the PKB–Foxo signaling axis and to direct the repertoire of adhesion and chemokine receptors expressed by PTEN-null T cells. The results thus provide two novel insights concerning pathological signaling caused by PTEN loss in lymphocytes. First, PTEN deletion bypasses the normal PDK1-controlled metabolic checkpoints that determine cell growth and proliferation. Second, PDK1 determines the cohort of chemokine and adhesion receptors expressed by PTEN-null cells, thereby controlling their migratory capacity

Prospects for observing and localizing gravitational-wave transients with advanced LIGO and advanced virgo

We present a possible observing scenario for the Advanced LIGO and Advanced Virgo gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We determine the expected sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron-star systems, which are considered the most promising for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and 90% credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5 deg^2 to 20 deg^2 will require at least three detectors of sensitivity within a factor of ~2 of each other and with a broad frequency bandwidth. Should the third LIGO detector be relocated to India as expected, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone

Search for gravitational wave bursts in LIGO's third science run

We report on a search for gravitational wave bursts in data from the three LIGO interferometric detectors during their third science run. The search targets subsecond bursts in the frequency range 100-1100 Hz for which no waveform model is assumed, and has a sensitivity in terms of the root-sum-square (rss) strain amplitude of hrss ~ 10^{-20} / sqrt(Hz). No gravitational wave signals were detected in the 8 days of analyzed data.Comment: 12 pages, 6 figures. Amaldi-6 conference proceedings to be published in Classical and Quantum Gravit

Quantum state preparation and macroscopic entanglement in gravitational-wave detectors

Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the new possibility of experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical behavior of objects in the realm of everyday experience - using gravitational-wave detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometer's classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the classical noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum state preparation, and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses, and the performance of the planned Advanced LIGO interferometers in quantum-state preparation

Searching for a Stochastic Background of Gravitational Waves with LIGO

The Laser Interferometer Gravitational-wave Observatory (LIGO) has performed the fourth science run, S4, with significantly improved interferometer sensitivities with respect to previous runs. Using data acquired during this science run, we place a limit on the amplitude of a stochastic background of gravitational waves. For a frequency independent spectrum, the new limit is $\Omega_{\rm GW} < 6.5 \times 10^{-5}$. This is currently the most sensitive result in the frequency range 51-150 Hz, with a factor of 13 improvement over the previous LIGO result. We discuss complementarity of the new result with other constraints on a stochastic background of gravitational waves, and we investigate implications of the new result for different models of this background.Comment: 37 pages, 16 figure