Instanton Floer homology and the Alexander polynomial

The instanton Floer homology of a knot in the three-sphere is a vector space with a canonical mod 2 grading. It carries a distinguished endomorphism of even degree,arising from the 2-dimensional homology class represented by a Seifert surface. The Floer homology decomposes as a direct sum of the generalized eigenspaces of this endomorphism. We show that the Euler characteristics of these generalized eigenspaces are the coefficients of the Alexander polynomial of the knot. Among other applications, we deduce that instanton homology detects fibered knots.Comment: 25 pages, 6 figures. Revised version, correcting errors concerning mod 2 gradings in the skein sequenc

Magnetic permeability of near-critical 3d abelian Higgs model and duality

The three-dimensional abelian Higgs model has been argued to be dual to a scalar field theory with a global U(1) symmetry. We show that this duality, together with the scaling and universality hypotheses, implies a scaling law for the magnetic permeablity chi_m near the line of second order phase transition: chi_m ~ t^nu, where t is the deviation from the critical line and nu ~ 0.67 is a critical exponent of the O(2) universality class. We also show that exactly on the critical lines, the dependence of magnetic induction on external magnetic field is quadratic, with a proportionality coefficient depending only on the gauge coupling. These predictions provide a way for testing the duality conjecture on the lattice in the Coulomb phase and at the phase transion.Comment: 11 pages; updated references and small changes, published versio

Industry Career Guide: Manufacturing

Manufacturing sector in the Philippines has one of the largest contributions to the growth of the economy. Throughout the years, starting from the 1970s, the manufacturing sector has been one of the driving forces behind the country’s growth. It has proven its importance in the economy because of benefits such as employment generation and technological innovation

Cosmic censorship and spherical gravitational collapse with tangential pressure

We study the spherical gravitational collapse of a compact object under the approximation that the radial pressure is identically zero, and the tangential pressure is related to the density by a linear equation of state. It turns out that the Einstein equations can be reduced to the solution of an integral for the evolution of the area radius. We show that for positive pressure there is a finite region near the center which necessarily expands outwards, if collapse begins from rest. This region could be surrounded by an inward moving one which could collapse to a singularity - any such singularity will necessarily be covered by a horizon. For negative pressure the entire object collapses inwards, but any singularities that could arise are not naked. Thus the nature of the evolution is very different from that of dust, even when the ratio of pressure to density is infinitesimally small.Comment: 16 pages, Latex file, two figures, uses epsf.st

On the gravitational field of static and stationary axial symmetric bodies with multi-polar structure

We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo solution of the Einstein Equations in terms of bars. We find that each multi-pole correspond to the Newtonian potential of a bar with linear density proportional to a Legendre Polynomial. We use this fact to find an integral representation of the $\gamma$ function. These integral representations are used in the context of the inverse scattering method to find solutions associated to one or more rotating bodies each one with their own multi-polar structure.Comment: To be published in Classical and Quantum Gravit

Critical Exponents of the Three Dimensional Random Field Ising Model

The phase transition of the three--dimensional random field Ising model with a discrete ($\pm h$) field distribution is investigated by extensive Monte Carlo simulations. Values of the critical exponents for the correlation length, specific heat, susceptibility, disconnected susceptibility and magnetization are determined simultaneously via finite size scaling. While the exponents for the magnetization and disconnected susceptibility are consistent with a first order transition, the specific heat appears to saturate indicating no latent heat. Sample to sample fluctuations of the susceptibilty are consistent with the droplet picture for the transition.Comment: Revtex, 10 pages + 4 figures included as Latex files and 1 in Postscrip

Dynamical generalization of a solvable family of two-electron model atoms with general interparticle repulsion

Holas, Howard and March [Phys. Lett. A {\bf 310}, 451 (2003)] have obtained analytic solutions for ground-state properties of a whole family of two-electron spin-compensated harmonically confined model atoms whose different members are characterized by a specific interparticle potential energy u($r_{12}$). Here, we make a start on the dynamic generalization of the harmonic external potential, the motivation being the serious criticism levelled recently against the foundations of time-dependent density-functional theory (e.g. [J. Schirmer and A. Dreuw, Phys. Rev. A {\bf 75}, 022513 (2007)]). In this context, we derive a simplified expression for the time-dependent electron density for arbitrary interparticle interaction, which is fully determined by an one-dimensional non-interacting Hamiltonian. Moreover, a closed solution for the momentum space density in the Moshinsky model is obtained.Comment: 5 pages, submitted to J. Phys.

Acute toxicity of second generation HIV protease-inhibitors in combination with radiotherapy: a retrospective case series

<p>Abstract</p> <p>Background</p> <p>There is little data on the safety of combining radiation therapy and human immunodeficiency virus (HIV) protease inhibitors to treat cancers in HIV-positive patients. We describe acute toxicities observed in a series of HIV-positive patients receiving modern radiation treatments, and compare patients receiving HIV protease inhibitors (PI) with patients not receiving HIV PIs.</p> <p>Methods</p> <p>By reviewing the clinical records beginning January 1, 2009 from the radiation oncology department, we identified 29 HIV-positive patients who received radiation therapy to 34 body sites. Baseline information, treatment regimen, and toxicities were documented by review of medical records: patient age, histology and source of the primary tumor, HIV medication regimen, pre-radiation CD4 count, systemic chemotherapy, radiation therapy dose and fractionation, irradiated body region, toxicities, and duration of follow-up. Patients were grouped according to whether they received concurrent HIV PIs and compared using Pearson's chi-square test.</p> <p>Results</p> <p>At baseline, the patients in the two groups were similar with the exception of HIV medication regimens, CD4 count and presence of AIDS-defining malignancy. Patients taking concurrent PIs were more likely to be taking other HIV medications (p = 0.001) and have CD4 count >500 (p = 0.006). Patients taking PIs were borderline less likely to have an AIDS-defining malignancy (p = 0.06). After radiation treatment, 100 acute toxicities were observed and were equally common in both groups (64 [median 3 per patient, IQR 1-7] with PIs; 36 [median 3 per patient, IQR 2-3] without PIs). The observed toxicities were also equally severe in the two groups (Grades I, II, III respectively: 30, 30, 4 with PIs; 23, 13, 0 without PIs: p = 0.38). There were two cases that were stopped early, one in each group; these were not attributable to toxicity.</p> <p>Conclusions</p> <p>In this study of recent radiotherapy in HIV-positive patients taking second generation PIs, no difference in toxicities was observed in patients taking PIs compared to patients not taking PIs during radiation therapy. This suggests that it is safe to use unmodified doses of PIs and radiation therapy in HIV cancer patients, and that it is feasible to use PIs as a radiosensitizer in cancer therapy, as has been suggested by pre-clinical results.</p