Eigenfunctions of the Laplacian and associated Ruelle operator

Let $\Gamma$ be a co-compact Fuchsian group of isometries on the Poincar\'e disk \DD and $\Delta$ the corresponding hyperbolic Laplace operator. Any smooth eigenfunction $f$ of $\Delta$, equivariant by $\Gamma$ with real eigenvalue $\lambda=-s(1-s)$, where $s={1/2}+ it$, admits an integral representation by a distribution \dd_{f,s} (the Helgason distribution) which is equivariant by $\Gamma$ and supported at infinity \partial\DD=\SS^1. The geodesic flow on the compact surface \DD/\Gamma is conjugate to a suspension over a natural extension of a piecewise analytic map T:\SS^1\to\SS^1, the so-called Bowen-Series transformation. Let $\ll_s$ be the complex Ruelle transfer operator associated to the jacobian $-s\ln |T'|$. M. Pollicott showed that \dd_{f,s} is an eigenfunction of the dual operator $\ll_s^*$ for the eigenvalue 1. Here we show the existence of a (nonzero) piecewise real analytic eigenfunction $\psi_{f,s}$ of $\ll_s$ for the eigenvalue 1, given by an integral formula \psi_{f,s} (\xi)=\int \frac{J(\xi,\eta)}{|\xi-\eta|^{2s}} \dd_{f,s} (d\eta), \noindent where $J(\xi,\eta)$ is a $\{0,1\}$-valued piecewise constant function whose definition depends upon the geometry of the Dirichlet fundamental domain representing the surface \DD/\Gamma

Principled Versus Statistical Thinking in Diagnosis and Treatment of Stroke

Medical science is now synonymous with probability-based statistics. Statistics deals with a group; it does not need probability theory. Probability theory is consistent with the worldview that the universe is infinite, bounded, random, and governed by chance. Its logic is binary, its geometry is Cartesian, its rules offer a scientific method by which hypotheses may be tested. Clinical trials and even hypothesis testing at the bedside have nestled into the probability foundation. As a result, scientific “evidence” now appears only through the lens of probability theory. Because there is no definitive truth in the worldview of probability theory, the truth of evidence lies in probabilities only. The probabilistic view of science has a firm impact on the practice of medicine and implications for medical–legal decisions

Measurable Prediction for the Single Patient and the Results of Large Double Blind Controlled Randomized Trials

Background: It has been shown that the clinical state of one patient can be represented by known measured variables of interest, each of which then form the element of a fuzzy set as point in the unit hypercube. We hypothesized that precise comparison of a single patient with the average patient of a large double blind controlled randomized study is possible using fuzzy theory. Methods/Principle Findings: The sets as points unit hypercube geometry allows fuzzy subsethood to define in measures of fuzzy cardinality different conditions, similarity and comparison between fuzzy sets. A fuzzy measure of prediction is defined from fuzzy measures of similarity and comparison. It is a measure of the degree to which fuzzy set A is similar to fuzzy set B when different conditions are taken into account and removed from the comparison. When represented as a fuzzy set as point in the unit hypercube, a clinical patient can be compared to an average patient of a large group study in a precise manner. This comparison is expressed by the fuzzy prediction measure. This measure in itself is not a probability. Once thus precisely matched to the average patient of a large group study, risk reduction is calculated by multiplying the measured similarity of the clinical patient to the risk of the average trial patient. Conclusion/Significance: Otherwise not precisely translatable to the single case, the result of group statistics can be applied to the single case through the use of fuzzy subsethood and measured in fuzzy cardinality. This measure is an alternative to

Extremal Black Attractors in 8D Maximal Supergravity

Motivated by the new higher D-supergravity solutions on intersecting attractors obtained by Ferrara et al. in [Phys.Rev.D79:065031-2009], we focus in this paper on 8D maximal supergravity with moduli space [SL(3,R)/SO(3)]x[SL(2,R)/SO(2)] and study explicitly the attractor mechanism for various configurations of extremal black p- branes (anti-branes) with the typical near horizon geometries AdS_{p+2}xS^{m}xT^{6-p-m} and p=0,1,2,3,4; 2<=m<=6. Interpretations in terms of wrapped M2 and M5 branes of the 11D M-theory on 3-torus are also given. Keywords: 8D supergravity, black p-branes, attractor mechanism, M-theory.Comment: 37 page

Reconstructing emission from pre-reionization sources with cosmic infrared background fluctuation measurements by the JWST

We present new methodology to use cosmic infrared background (CIB) fluctuations to probe sources at 10<z<30 from a JWST/NIRCam configuration that will isolate known galaxies to 28 AB mag at 0.5--5 micron. At present significant mutually consistent source-subtracted CIB fluctuations have been identified in the Spitzer and Akari data at 2--5 micron, but we demonstrate internal inconsistencies at shorter wavelengths in the recent CIBER data. We evaluate CIB contributions from remaining galaxies and show that the bulk of the high-z sources will be in the confusion noise of the NIRCam beam, requiring CIB studies. The accurate measurement of the angular spectrum of the fluctuations and probing the dependence of its clustering component on the remaining shot noise power would discriminate between the various currently proposed models for their origin and probe the flux distribution of its sources. We show that the contribution to CIB fluctuations from remaining galaxies is large at visible wavelengths for the current instruments precluding probing the putative Lyman-break of the CIB fluctuations. We demonstrate that with the proposed JWST configuration such measurements will enable probing the Lyman break. We develop a Lyman-break tomography method to use the NIRCam wavelength coverage to identify or constrain, via the adjacent two-band subtraction, the history of emissions over 10<z<30 as the Universe comes out of the 'Dark Ages'. We apply the proposed tomography to the current Spitzer/IRAC measurements at 3.6 and 4.5 micron, to find that it already leads to interestingly low upper limit on emissions at z>30.Comment: ApJ, in press. Minor revisions/additions to match the version in proof

Pre-irrigation of a severely-saline soil with in-situ water to establish dryland forages

Non-Peer ReviewedAlfalfa serves as one of the most important forage plants in North America. It is also the recommended remedial crop for dryland salinity control. But, because of its limited salt tolerance, it does not establish satisfactorily in severely or moderately saline soils. A series of irrigations with the in-situ ground water located beneath a severely-saline site were delivered across seedbeds prepared within the same site prior to seeding ‘Beaver’ alfalfa (Medicago sativa) and ‘ AC Saltlander’ green wheatgrass (Elymus Hoffmannii). In this field study conducted in semiarid Saskatchewan, fall irrigations with 4.6 dS/m-water from a shallow, on-site, backhoe-dug well fitted with a solar-powered pump preceded spring seeding. Irrigation treatments ranged from zero to 2530 mm in total applied water. Plant emergence, spacing, height, cover, and forage yield of the alfalfa were significantly improved following pre-irrigation. Mean plant emergence increased from 20 to 79% for the alfalfa. The wheatgrass height and forage yield also improved significantly, but showed only an upward trend in emergence, spacing, height, and cover. The mean plant height in July increased from 90 to 159 mm for the wheatgrass and from 35 to 140 mm for the alfalfa. Based on linear regression of irrigated volume, every 119.3 mm of irrigated, in-situ water up to 2530 mm increased alfalfa forage yield by 10 g/m2

Localization in disordered superconducting wires with broken spin-rotation symmetry

Localization and delocalization of non-interacting quasiparticle states in a superconducting wire are reconsidered, for the cases in which spin-rotation symmetry is absent, and time-reversal symmetry is either broken or unbroken; these are referred to as symmetry classes BD and DIII, respectively. We show that, if a continuum limit is taken to obtain a Fokker-Planck (FP) equation for the transfer matrix, as in some previous work, then when there are more than two scattering channels, all terms that break a certain symmetry are lost. It was already known that the resulting FP equation exhibits critical behavior. The additional symmetry is not required by the definition of the symmetry classes; terms that break it arise from non-Gaussian probability distributions, and may be kept in a generalized FP equation. We show that they lead to localization in a long wire. When the wire has more than two scattering channels, these terms are irrelevant at the short distance (diffusive or ballistic) fixed point, but as they are relevant at the long-distance critical fixed point, they are termed dangerously irrelevant. We confirm the results in a supersymmetry approach for class BD, where the additional terms correspond to jumps between the two components of the sigma model target space. We consider the effect of random $\pi$ fluxes, which prevent the system localizing. We show that in one dimension the transitions in these two symmetry classes, and also those in the three chiral symmetry classes, all lie in the same universality class

Effective QCD Partition Function in Sectors with Non-Zero Topological Charge and Itzykson-Zuber Type Integral

It was conjectured by Jackson et.al. that the finite volume effective partition function of QCD with the topological charge $M-N$ coincides with the Itzyskon-Zuber type integral for $M\times N$ rectangular matrices. In the present article we give a proof of this conjecture, in which the original Itzykson-Zuber integral is utilized.Comment: 7pages, LaTeX2

The Central Correlations of Hypercharge, Isospin, Colour and Chirality in the Standard Model

The correlation of the fractionally represented hypercharge group with the isospin and colour group in the standard model determines as faithfully represented internal group the quotient group {\U(1)\x\SU(2)\x\SU(3)\over\Z_2\x\Z_3}. The discrete cyclic central abelian-nonabelian internal correlation involved is considered with respect to its consequences for the representations by the standard model fields, the electroweak mixing angle and the symmetry breakdown. There exists a further discrete $\Z_2$-correlation between chirality and Lorentz properties and also a continuous \U(1)-external-internal one between hyperisospin and chirality.Comment: 18 pages, latex, macros include