Are randomly grown graphs really random?

We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time steps. In the limit of large t, the resulting graph displays surprisingly rich characteristics. In particular, a giant component emerges in an infinite-order phase transition at delta = 1/8. At the transition, the average component size jumps discontinuously but remains finite. In contrast, a static random graph with the same degree distribution exhibits a second-order phase transition at delta = 1/4, and the average component size diverges there. These dramatic differences between grown and static random graphs stem from a positive correlation between the degrees of connected vertices in the grown graph--older vertices tend to have higher degree, and to link with other high-degree vertices, merely by virtue of their age. We conclude that grown graphs, however randomly they are constructed, are fundamentally different from their static random graph counterparts.Comment: 8 pages, 5 figure

Random Geometric Graphs

We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size of the largest cluster. We derive an analytical expression for the cluster coefficient which shows that the graphs are distinctly different from standard random graphs, even for infinite dimensionality. Insights relevant for graph bi-partitioning are included.Comment: 16 pages, 10 figures. Minor changes. Added reference

Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions

A microscopic heterogeneous system under random influence is considered. The randomness enters the system at physical boundary of small scale obstacles as well as at the interior of the physical medium. This system is modeled by a stochastic partial differential equation defined on a domain perforated with small holes (obstacles or heterogeneities), together with random dynamical boundary conditions on the boundaries of these small holes. A homogenized macroscopic model for this microscopic heterogeneous stochastic system is derived. This homogenized effective model is a new stochastic partial differential equation defined on a unified domain without small holes, with static boundary condition only. In fact, the random dynamical boundary conditions are homogenized out, but the impact of random forces on the small holes' boundaries is quantified as an extra stochastic term in the homogenized stochastic partial differential equation. Moreover, the validity of the homogenized model is justified by showing that the solutions of the microscopic model converge to those of the effective macroscopic model in probability distribution, as the size of small holes diminishes to zero.Comment: Communications in Mathematical Physics, to appear, 200

Physics Opportunities with the 12 GeV Upgrade at Jefferson Lab

This white paper summarizes the scientific opportunities for utilization of the upgraded 12 GeV Continuous Electron Beam Accelerator Facility (CEBAF) and associated experimental equipment at Jefferson Lab. It is based on the 52 proposals recommended for approval by the Jefferson Lab Program Advisory Committee.The upgraded facility will enable a new experimental program with substantial discovery potential to address important topics in nuclear, hadronic, and electroweak physics.Comment: 64 page

From Spectroscopy to the Strong Coupling Constant with Heavy Wilson Quarks

In this work we present lattice calculations of the masses of P-wave mesons using Monte Carlo simulations. Our valence fermions are defined by the Wilson action. Our gauge fields are generated with both dynamical staggered fermions at a lattice coupling $\beta\equiv 6/g^2=5.6$ for sea quark masses of $am_q=0.010$ and 0.025, and in the quenched approximation at $\beta=6.0$. We present results for charm and charmonium spectroscopy and use them to compute the strong coupling constant $\alpha_s$. We compare our results to those of other recent lattice calculations and experiments.Comment: 45 pages, uuencoded compressed PostScript fil

Upstream Solutions: Does the Supplemental Security Income Program Reduce Disability in the Elderly?

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72843/1/j.1468-0009.2007.00512.x.pd

Supersymmetry beyond minimal flavour violation

We review the sources and phenomenology of non-minimal flavour violation in the MSSM. We discuss in some detail the most important theoretical and experimental constraints, as well as promising observables to look for supersymmetric effects at the LHC and in the future. We emphasize the sensitivity of flavour physics to the mechanism of supersymmetry breaking and to new degrees of freedom present at fundamental scales, such as the grand unification scale. We include a discussion of present data that may hint at departures from the Standard Model.Comment: 23pp. Version to appear in the EPJC special volume "Supersymmetry on the Eve of the LHC", dedicated to the memory of Julius Wess. References and brief discussion on collider signatures adde

Collider aspects of flavour physics at high Q

This review presents flavour related issues in the production and decays of heavy states at LHC, both from the experimental side and from the theoretical side. We review top quark physics and discuss flavour aspects of several extensions of the Standard Model, such as supersymmetry, little Higgs model or models with extra dimensions. This includes discovery aspects as well as measurement of several properties of these heavy states. We also present public available computational tools related to this topic.Comment: Report of Working Group 1 of the CERN Workshop ``Flavour in the era of the LHC'', Geneva, Switzerland, November 2005 -- March 200

Zoledronate in the prevention of Paget's (ZiPP) : protocol for a randomised trial of genetic testing and targeted zoledronic acid therapy to prevent SQSTM1-mediated Paget's disease of bone.

Introduction Paget’s disease of bone (PDB) is characterised by increased and disorganised bone remodelling affecting one or more skeletal sites. Complications include bone pain, deformity, deafness and pathological fractures. Mutations in sequestosome-1 (SQSTM1) are strongly associated with the development of PDB. Bisphosphonate therapy can improve bone pain in PDB, but there is no evidence that treatment alters the natural history of PDB or prevents complications. The Zoledronate in the Prevention of Paget’s disease trial (ZiPP) will determine if prophylactic therapy with the bisphosphonate zoledronic acid (ZA) can delay or prevent the development of PDB in people who carry SQSTM1 mutations. Methods and analysis People with a family history of PDB aged >30 years who test positive for SQSTM1 mutations are eligible to take part. At the baseline visit, participants will be screened for the presence of bone lesions by radionuclide bone scan. Biochemical markers of bone turnover will be measured and questionnaires completed to assess pain, health-related quality of life (HRQoL), anxiety and depression. Participants will be randomised to receive a single intravenous infusion of 5 mg ZA or placebo and followed up annually for between 4 and 8 years at which point baseline assessments will be repeated. The primary endpoint will be new bone lesions assessed by radionuclide bone scan. Secondary endpoints will include changes in biochemical markers of bone turnover, pain, HRQoL, anxiety, depression and PDB-related skeletal events