Cosmic Ray Small Scale Anisotropies and Local Turbulent Magnetic Fields

Cosmic ray anisotropy has been observed in a wide energy range and at different angular scales by a variety of experiments over the past decade. However, no comprehensive or satisfactory explanation has been put forth to date. The arrival distribution of cosmic rays at Earth is the convolution of the distribution of their sources and of the effects of geometry and properties of the magnetic field through which particles propagate. It is generally believed that the anisotropy topology at the largest angular scale is adiabatically shaped by diffusion in the structured interstellar magnetic field. On the contrary, the medium- and small-scale angular structure could be an effect of non-diffusive propagation of cosmic rays in perturbed magnetic fields. In particular, a possible explanation of the observed small-scale anisotropy observed at TeV energy scale, may come from the effect of particle scattering in turbulent magnetized plasmas. We perform numerical integration of test particle trajectories in low-$\beta$ compressible magnetohydrodynamic turbulence to study how the cosmic rays arrival direction distribution is perturbed when they stream along the local turbulent magnetic field. We utilize Liouville's theorem for obtaining the anisotropy at Earth and provide the theoretical framework for the application of the theorem in the specific case of cosmic ray arrival distribution. In this work, we discuss the effects on the anisotropy arising from propagation in this inhomogeneous and turbulent interstellar magnetic field.Comment: 14 pages, 7 figures. Accepted for publication in Ap

L^2 torsion without the determinant class condition and extended L^2 cohomology

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L^2 torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of the determinant line of the extended L^2 cohomology. Under the determinant class assumption the L^2 torsions of this paper specialize to the invariants studied in our previous work. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler we obtain a Cheeger - Muller type theorem stating the equality between the combinatorial and the analytic L^2 torsions.Comment: 39 page

Beyond the Formalism Debate: Expert Reasoning, Fuzzy Logic, and Complex Statutes

Formalists and antiformalists continue to debate the utility of using legislative history and current social values to interpret statutes. Lost in the debate, however, is a clear model of how judges actually make decisions. Rather than focusing on complex problems presented by actual judicial decisions, formalists and antiformalists concentrate on stylized examples of simple statutes. In this Article, Professors Adams and Farber construct a more functional model of judicial decisionmaking by focusing on complex problems. They use cognitive psychological research on expert reasoning and techniques from an emerging area in the field of artificial intelligence, fuzzy logic, to construct their model. To probe the complex interactions between judicial interpretation, the business and legal communities, and the legislature, the authors apply their model to two important bankruptcy cases written by prominent formalist judges. Professors Adams and Farber demonstrate how cognitive psychology and fuzzy logic can reveal the reasoning processes that both formalist and antiformalist judges use to interpret \u27complex statutes. To apply formalist rules, judges need to recognize the aspects of a case that trigger relevant rules. Cognitive psychologists have researched expert reasoning using this type of diagnostic process. Once the judge identifies the appropriate rules, she will often find they point in conflicting directions. Fuzzy logic provides a model of how to analyze such conflicts. Next, Professors Adams and Farber consider how these models of judicial decisionmaking inform efforts to improve statutory interpretation of complex statutes. They reason that expert decisionmaking builds on pattern recognition skills and fuzzy maps, both the result of intensive repeated experience. The authors explain that cases involving complex statutory interpretation frequently involve competing considerations, and that the implicit understandings of field insiders tend to be entrenched and difficult to displace. Consequently, Professors Adams and Farber argue that judges in specialty courts, such as the Bankruptcy Courts, are probably in a better position than generalist appellate judges to interpret complex statutes. Generalist judges should approach complex statutory issues with a strong degree of deference to the local culture of the field. Professors Adams and Farber conclude the Article with speculation on how fuzzy logic could be used in a more quantitative way to model legal problems. They note that computer modeling may ultimately provide insight into the subtle process of judicial practical reasoning, moving away from the false dichotomy often drawn between formalist and antiformalist approaches to practical judicial decision- making

Geometric and homological finiteness in free abelian covers

We describe some of the connections between the Bieri-Neumann-Strebel-Renz invariants, the Dwyer-Fried invariants, and the cohomology support loci of a space X. Under suitable hypotheses, the geometric and homological finiteness properties of regular, free abelian covers of X can be expressed in terms of the resonance varieties, extracted from the cohomology ring of X. In general, though, translated components in the characteristic varieties affect the answer. We illustrate this theory in the setting of toric complexes, as well as smooth, complex projective and quasi-projective varieties, with special emphasis on configuration spaces of Riemann surfaces and complements of hyperplane arrangements.Comment: 30 pages; to appear in Configuration Spaces: Geometry, Combinatorics and Topology (Centro De Giorgi, 2010), Edizioni della Normale, Pisa, 201

Evidence for a Bulk Complex Order-Parameter in Y0.9Ca0.1Ba2Cu3O7-delta Thin Films

We have measured the penetration depth of overdoped Y0.9Ca0.1Ba2Cu3O7-delta (Ca-YBCO) thin films using two different methods. The change of the penetration depth as a function of temperature has been measured using the parallel plate resonator (PPR), while its absolute value was obtained from a quasi-optical transmission measurements. Both sets of measurements are compatible with an order parameter of the form: Delta*dx2-y2+i*delta*dxy, with Delta=14.5 +- 1.5 meV and delta=1.8 meV, indicating a finite gap at low temperature. Below 15 K the drop of the scattering rate of uncondensed carriers becomes steeper in contrast to a flattening observed for optimally doped YBCO films. This decrease supports our results on the penetration depth temperature dependence. The findings are in agreement with tunneling measurements on similar Ca-YBCO thin films.Comment: 11 pages, 4 figure

Current state of forest mapping with Landsat data in Siberia

We review a current state of a forest type mapping with Landsat data in Siberia. Target algorithm should be based on dynamic vegetation approach to be applicable to the analysis of the forest type distribution for Siberia, aiming at capability of mapping Siberian forest landscapes for applications such as predicting response of forest composition to climate change. We present data for several areas in West Siberian middle taiga, Central Siberia and East Siberia near Yakutsk. Analysis of the field survey, forest inventory data was made to produce forest type classification accounting for several stages for forest succession and variations in habitats and landforms. Supervised classification was applied to the areas were the ground truth and inventory data are available, including several limited area maps and vegetation survey transects. In Laryegan basin in West Siberia the upland forest areas are dominated by mix of Scots pine on sandy soils and Siberian pine with presence of fir and spruce on the others. Abundance of Scots pine decreases to the west due to change in soils. Those types are separable using Landsat spectral data. In the permafrost area around Yakutsk the most widespread succession type is birch to larch. Three stages of the birch to larch succession are detectable from Landsat image. When Landsat data is used in both West and East Siberia, distinction between deciduous broad-leaved species (birch, aspen, and willow) is generally difficult. Similar problem exist for distinguishing between dark coniferous species (Siberian pine, fir and spruce). Image classification can be improved by applying landform type analysis, such as separation into floodplain, terrace, sloping hills. Additional layers of information can be a promising way to complement Landsat data

A comparison of arbitration procedures for risk averse disputants

We propose an arbitration model framework that generalizes many previous quantitative models of final offer arbitration, conventional arbitration, and some proposed alternatives to them. Our model allows the two disputants to be risk averse and assumes that the issue(s) in dispute can be summarized by a single quantifiable value. We compare the performance of the different arbitration procedures by analyzing the gap between the disputants' equilibrium offers and the width of the contract zone that these offers imply. Our results suggest that final offer arbitration should give results superior to those of conventional arbitration.Natural Sciences & Engineering Research Council (NSERC) Discovery Gran

Evidence of a subenergy gap in the overdoped regime of Y_{1-x}Ca_{x}Ba_{2}Cu_{3}O_{7-\delta} thin films from THz Spectroscopy

We measured the terahertz (THz) complex conductivity of Ca doped YBa_{2}Cu_{3}O_{7-\delta} thin films in the frequency range of 0.1 to 3 THz (3 to 100 cm^{-1}) and at a temperature range of 20 to 300 K. The films were measured using both time domain and frequency domain THz methods. We showed evidence for the existence of a sub-gap in overdoped Y_{1-x}Ca_{x}Ba_{2}Cu_{3}O_{7-\delta} samples doped with 5% and 10% Ca. Evidence for the opening of this sub-gap appears as a sharp decrease in the spectrum of the real part of conductivity at frequencies equivalent to a gap energy of 1 meV and is more prominent with increased doping. This decrease in conductivity can be explained by using d-wave pairing symmetry with an imaginary part of is or id_{xy} which suggests node removal.Comment: 7 pages, 7 figure