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

Spacetime Defects: von K\'arm\'an vortex street like configurations

A special arrangement of spinning strings with dislocations similar to a von K\'arm\'an vortex street is studied. We numerically solve the geodesic equations for the special case of a test particle moving along twoinfinite rows of pure dislocations and also discuss the case of pure spinning defects.Comment: 9 pages, 2figures, CQG in pres

Network synchronization: Optimal and Pessimal Scale-Free Topologies

By employing a recently introduced optimization algorithm we explicitely design optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree correlations and observe a generic tendency towards disassortativity. Still, we show that there is not a one-to-one correspondence between synchronizability and disassortativity. On the other hand, we study the nature of optimally un-synchronizable networks, that is, networks whose topology minimizes the range of stability of the synchronous state. The resulting ``pessimal networks'' turn out to have a highly assortative string-like structure. We also derive a rigorous lower bound for the Laplacian eigenvalue ratio controlling synchronizability, which helps understanding the impact of degree correlations on network synchronizability.Comment: 11 pages, 4 figs, submitted to J. Phys. A (proceedings of Complex Networks 2007

Neutrino masses in the Lepton Number Violating MSSM

We consider the most general supersymmetric model with minimal particle content and an additional discrete Z_3 symmetry (instead of R-parity), which allows lepton number violating terms and results in non-zero Majorana neutrino masses. We investigate whether the currently measured values for lepton masses and mixing can be reproduced. We set up a framework in which Lagrangian parameters can be initialised without recourse to assumptions concerning trilinear or bilinear superpotential terms, CP-conservation or intergenerational mixing and analyse in detail the one loop corrections to the neutrino masses. We present scenarios in which the experimental data are reproduced and show the effect varying lepton number violating couplings has on the predicted atmospheric and solar mass^2 differences. We find that with bilinear lepton number violating couplings in the superpotential of the order 1 MeV the atmospheric mass scale can be reproduced. Certain trilinear superpotential couplings, usually, of the order of the electron Yukawa coupling can give rise to either atmospheric or solar mass scales and bilinear supersymmetry breaking terms of the order 0.1 GeV^2 can set the solar mass scale. Further details of our calculation, Lagrangian, Feynman rules and relevant generic loop diagrams, are presented in three Appendices.Comment: 48 pages, 7 figures, v2 references added, typos corrected, published versio

Literacy for Life: Evaluating the National Literacy Trust’s bespoke programme for schools

This paper presents an evaluation of ‘Literacy for Life’ (LfL) – a whole-school literacy programme, implemented in five secondary schools in England. The aims of LfL were to improve literacy attainment and to promote positive attitudes to reading and writing. However, when compared to other schools, there is little or no evidence that being in a LfL school, had any differential benefit for pupils’ attainment. In LfL schools, the gap for disadvantaged pupils and those with SEN grew in the early years of the intervention. There is also no evidence from repeated surveys that pupils’ attitudes to and enjoyment of reading showed any improvement. As such, LfL did not achieve its intended objectives. This matters because, despite limited evidence in its favour, schools continue to use it and programmes similar to it. We argue that programmes such as LfL, which are implemented on a whole-school level, need to be based upon evidence-informed approaches

When Statutory Regimes Collide:Will Wisconsin Right to Life and Citizens United Invalidate Federal Tax Regulation of Campaign Activity?

In Federal Election Commission v. Wisconsin Right to Life (2007) and Citizens United v. Federal Elections Commission (2010), the United States Supreme Court dramatically reduced the ability of Congress to regulate campaign finance activities of corporations and others active in elections. Many of the same activities are still subject to restrictions by the Internal Revenue Code, which regulates the type and amount of political campaign activities that certain nonprofits exempt under federal tax law can engage in. In the wake of the campaign finance decisions, the constitutionality of the tax law’s restrictions on campaign activity is now being challenged in the lower courts. This Article analyzes the two recent campaign finance decisions and campaign finance precedents more broadly to determine how, if at all, the Roberts’ Court’s campaign finance jurisprudence is likely to alter existing tax law jurisprudence in the area of campaign activity. It finds that, for the most part, tax law constitutional doctrines have developed independently of other areas of First Amendment free speech law. Based upon an analysis of the distinctive tax law doctrines, the Article concludes that the tax law provision prohibiting section 501(c)(3) charities from engaging in campaigns is likely to withstand challenges arguing that the provision prevents these nonprofits from engaging in protected political speech. However, there is some likelihood that the tax law prohibition is vulnerable to constitutional attack under traditional doctrines of vagueness or overbreadth due to the lack of precision of the terms of the political prohibition, as these have been elaborated by the IRS and the courts to date

Tests of Basic Quantum Mechanics in Oscillation Experiments

According to standard quantum theory, the time evolution operator of a quantum system is independent of the state of the system. One can, however, consider systems in which this is not the case: the evolution operator may depend on the density operator itself. The presence of such modifications of quantum theory can be tested in long baseline oscillation experiments.Comment: 8 pages, LaTeX; no macros neede

Microscopic Black Hole Pairs in Highly-Excited States

We consider the quantum mechanics of a system consisting of two identical, Planck-size Schwarzschild black holes revolving around their common center of mass. We find that even in a very highly-excited state such a system has very sharp, discrete energy eigenstates, and the system performs very rapid transitions from a one stationary state to another. For instance, when the system is in the 100th excited state, the life times of the energy eigenstates are of the order of $10^{-30}$ s, and the energies of gravitons released in transitions between nearby states are of the order of $10^{22}$ eV.Comment: 22 pages, 3 figures, uses RevTe

Contributing to WUDAPT: A Local Climate Zone Classification of Two Cities in Ukraine

Local climate zones (LCZs) divide the urban landscape into homogeneous types based on urban structure (i.e.,morphology of streets and buildings), urban cover (i.e., permeability of surfaces), construction materials, and human activities (i.e., anthropogenic heat). This classification scheme represents a standardized way of capturing the basic urban form of cities and is currently being applied globally as part of the world urban database and portal tools (WUDAPT) initiative. This paper assesses the transferability of the LCZ concept to two Ukrainian cities, i.e., Kyiv and Lviv, which differ in urban form and topography, and considers three ways to validate and verify this classification scheme. An accuracy of 64% was achieved for Kyiv using an independent validation dataset while a comparison of the LCZ maps with the GlobeLand30 land cover map resulted in a match that was greater than 75% for both cities. There was also good correspondence between the urban classes in the LCZ maps and the urban points of interest in OpenStreetMap (OSM). However, further research is still required to produce a standardized validation protocol that could be used on a regular basis by contributors to WUDAPT to help produce more accurate LCZ maps in the future