Approximability of Connected Factors

Finding a d-regular spanning subgraph (or d-factor) of a graph is easy by Tutte's reduction to the matching problem. By the same reduction, it is easy to find a minimal or maximal d-factor of a graph. However, if we require that the d-factor is connected, these problems become NP-hard - finding a minimal connected 2-factor is just the traveling salesman problem (TSP). Given a complete graph with edge weights that satisfy the triangle inequality, we consider the problem of finding a minimal connected $d$-factor. We give a 3-approximation for all $d$ and improve this to an (r+1)-approximation for even d, where r is the approximation ratio of the TSP. This yields a 2.5-approximation for even d. The same algorithm yields an (r+1)-approximation for the directed version of the problem, where r is the approximation ratio of the asymmetric TSP. We also show that none of these minimization problems can be approximated better than the corresponding TSP. Finally, for the decision problem of deciding whether a given graph contains a connected d-factor, we extend known hardness results.Comment: To appear in the proceedings of WAOA 201

ARQ-197, a small-molecule inhibitor of c-Met, reduces tumour burden and prevents myeloma-induced bone disease in vivo

The receptor tyrosine kinase c-Met, its ligand HGF, and components of the downstream signalling pathway, have all been implicated in the pathogenesis of myeloma, both as modulators of plasma cell proliferation and as agents driving osteoclast differentiation and osteoblast inhibition thus, all these contribute substantially to the bone destruction typically caused by myeloma. Patients with elevated levels of HGF have a poor prognosis, therefore, targeting these entities in such patients may be of substantial benefit. We hypothesized that ARQ-197 (Tivantinib), a small molecule c-Met inhibitor, would reduce myeloma cell growth and prevent myeloma-associated bone disease in a murine model. In vitro we assessed the effects of ARQ-197 on myeloma cell proliferation, cytotoxicity and c-Met protein expression in human myeloma cell lines. In vivo we injected NOD/SCID-γ mice with PBS (non-tumour bearing) or JJN3 cells and treated them with either ARQ-197 or vehicle. In vitro exposure of JJN3, U266 or NCI-H929 cells to ARQ-197 resulted in a significant inhibition of cell proliferation and an induction of cell death by necrosis, probably caused by significantly reduced levels of phosphorylated c-Met. In vivo ARQ-197 treatment of JJN3 tumour-bearing mice resulted in a significant reduction in tumour burden, tumour cell proliferation, bone lesion number, trabecular bone loss and prevented significant decreases in the bone formation rate on the cortico-endosteal bone surface compared to the vehicle group. However, no significant differences on bone parameters were observed in non-tumour mice treated with ARQ-197 compared to vehicle, implying that in tumour-bearing mice the effects of ARQ-197 on bone cells was indirect. In summary, these res ults suggest that ARQ-197 could be a promising therapeutic in myeloma patients, leading to both a reduction in tumour burden and an inhibition of myeloma-induced bone disease

Monte Carlo Simulations with Indefinite and Complex-Valued Measures

A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using absolute values of the original measures. Exactly solvable, one-dimensional Ising models with complex temperature and complex activity illustrate the considerable improvements and the workability of the new method even when the crude one fails.Comment: 10 A4 pages, postscript (140K), UM-P-93-7

A 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem

We give a 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem.Comment: 6 figure

Entanglement of two-mode Bose-Einstein condensates

We investigate the entaglement characteristics of two general bimodal Bose-Einstein condensates - a pair of tunnel-coupled Bose-Einstein condensates and the atom-molecule Bose-Einstein condensate. We argue that the entanglement is only physically meaningful if the system is viewed as a bipartite system, where the subsystems are the two modes. The indistinguishibility of the particles in the condensate means that the atomic constituents are physically inaccessible and thus the degree of entanglement between individual particles, unlike the entanglement between the modes, is not experimentally relevant so long as the particles remain in the condensed state. We calculate the entanglement between the modes for the exact ground state of the two bimodal condensates and consider the dynamics of the entanglement in the tunnel-coupled case.Comment: 11 pages, 8 figures, submitted to Physical Review A, to be presented at the third UQ Mathematical Physics workshop, Oct. 4-6; changes made in response to referee comment

Exactly solvable model of quantum diffusion

We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of correlation functions which are delta-correlated in space and time. For weak coupling, the time evolution of the subsystem density matrix is ruled by a quantum master equation of Lindblad type. Thanks to the invariance under spatial translations, we can apply the Bloch theorem to the subsystem density matrix and exactly diagonalize the time evolution superoperator to obtain the complete spectrum of its eigenvalues, which fully describe the relaxation to equilibrium. Above a critical coupling which is inversely proportional to the size of the subsystem, the spectrum at given wavenumber contains an isolated eigenvalue describing diffusion. The other eigenvalues rule the decay of the populations and quantum coherences with decay rates which are proportional to the intensity of the environmental noise. On the other hand, an analytical expression is obtained for the dispersion relation of diffusion. The diffusion coefficient is proportional to the square of the width of the energy band and inversely proportional to the intensity of the environmental noise because diffusion results from the perturbation of quantum tunneling by the environmental fluctuations in this model. Diffusion disappears below the critical coupling.Comment: Submitted to J. Stat. Phy

On the Computational Complexity of Measuring Global Stability of Banking Networks

Threats on the stability of a financial system may severely affect the functioning of the entire economy, and thus considerable emphasis is placed on the analyzing the cause and effect of such threats. The financial crisis in the current and past decade has shown that one important cause of instability in global markets is the so-called financial contagion, namely the spreading of instabilities or failures of individual components of the network to other, perhaps healthier, components. This leads to a natural question of whether the regulatory authorities could have predicted and perhaps mitigated the current economic crisis by effective computations of some stability measure of the banking networks. Motivated by such observations, we consider the problem of defining and evaluating stabilities of both homogeneous and heterogeneous banking networks against propagation of synchronous idiosyncratic shocks given to a subset of banks. We formalize the homogeneous banking network model of Nier et al. and its corresponding heterogeneous version, formalize the synchronous shock propagation procedures, define two appropriate stability measures and investigate the computational complexities of evaluating these measures for various network topologies and parameters of interest. Our results and proofs also shed some light on the properties of topologies and parameters of the network that may lead to higher or lower stabilities.Comment: to appear in Algorithmic

Antiferromagnetic Domains and Superconductivity in UPt3

We explore the response of an unconventional superconductor to spatially inhomogeneous antiferromagnetism (SIAFM). Symmetry allows the superconducting order parameter in the E-representation models for UPt3 to couple directly to the AFM order parameter. The Ginzburg-Landau equations for coupled superconductivity and SIAFM are solved numerically for two possible SIAFM configurations: (I) abutting antiferromagnetic domains of uniform size, and (II) quenched random disorder of `nanodomains' in a uniform AFM background. We discuss the contributions to the free energy, specific heat, and order parameter for these models. Neither model provides a satisfactory account of experiment, but results from the two models differ significantly. Our results demonstrate that the response of an E_{2u} superconductor to SIAFM is strongly dependent on the spatial dependence of AFM order; no conclusion can be drawn regarding the compatibility of E_{2u} superconductivity with UPt3 that is independent of assumptions on the spatial dependence of AFMComment: 12 pages, 13 figures, to appear in Phys. Rev.

Development of a tight-binding potential for bcc-Zr. Application to the study of vibrational properties

We present a tight-binding potential based on the moment expansion of the density of states, which includes up to the fifth moment. The potential is fitted to bcc and hcp Zr and it is applied to the computation of vibrational properties of bcc-Zr. In particular, we compute the isothermal elastic constants in the temperature range 1200K < T < 2000K by means of standard Monte Carlo simulation techniques. The agreement with experimental results is satisfactory, especially in the case of the stability of the lattice with respect to the shear associated with C'. However, the temperature decrease of the Cauchy pressure is not reproduced. The T=0K phonon frequencies of bcc-Zr are also computed. The potential predicts several instabilities of the bcc structure, and a crossing of the longitudinal and transverse modes in the (001) direction. This is in agreement with recent ab initio calculations in Sc, Ti, Hf, and La.Comment: 14 pages, 6 tables, 4 figures, revtex; the kinetic term of the isothermal elastic constants has been corrected (Eq. (4.1), Table VI and Figure 4

Preliminary assessment of the environmental baseline in the Fylde, Lancashire

This report presents the collated preliminary results from the British Geological Survey (BGS) led project Science-based environmental baseline monitoring associated with shale gas development in the Fylde, Lancashire. The project has been funded by a combination of BGS National Capability funding, in-kind contributions from project partners and a grant awarded by the Department of Business Energy and Investment Strategy (BEIS). It complements an on-going project, in which similar activities are being carried out, in the Vale of Pickering, North Yorkshire. Further information on the projects can be found on the BGS website: www.bgs.ac.uk. The project has initiated a wide-ranging environmental baseline monitoring programme that includes water quality (groundwater and surface water), seismicity, ground motion, atmospheric composition (greenhouse gases and air quality), soil gas and radon in air (indoors and outdoors). The motivation behind the project(s) was to establish independent monitoring in the area around the proposed shale gas hydraulic fracturing sites in the Fylde, Lancashire (Cuadrilla Resources Ltd) before any shale gas operations take place. As part of the project, instrumentation has been deployed to measure, in real-time or near real-time, a range of environmental variables (water quality, seismicity, atmospheric composition). These data are being displayed on the project’s web site (www.bgs.ac.uk/lancashire). Additional survey, sampling and monitoring has also been carried out through a co-ordinated programme of fieldwork and laboratory analysis, which has included installation of new monitoring infrastructure, to allow compilation of one of the most comprehensive environmental datasets in the UK. The monitoring programme is continuing. However, there are already some very important findings emerging from the limited datasets which should be taken into account when developing future monitoring strategy, policy and regulation. The information is not only relevant to Lancashire but will be applicable more widely in the UK and internationally. Although shale gas operations in other parts of the world are well-established, there is a paucity of good baseline data and effective guidance on monitoring. The project will also allow the experience gained, and the scientifically-robust findings to be used, to develop and establish effective environmental monitoring strategies for shale gas and similar industrial activities