Origin and physics of the highest energy cosmic rays: What can we learn from Radio Astronomy?

Here in this lecture we will touch on two aspects, one the new radio methods to observe the effects of high energy particles, and second the role that radio galaxies play in helping us understand high energy cosmic rays. We will focus here on the second topic, and just review the latest developments in the first. Radio measurements of the geosynchrotron radiation produced by high energy cosmic ray particles entering the atmosphere of the Earth as well as radio \v{C}erenkov radiation coming from interactions in the Moon are another path; radio observations of interactions in ice at the horizon in Antarctica is a related attempt. Radio galaxy hot spots are prime candidates to produce the highest energy cosmic rays, and the corresponding shock waves in relativistic jets emanating from nearly all black holes observed. We will review the arguments and the way to verify the ensuing predictions. This involves the definition of reliable samples of active sources, such as black holes, and galaxies active in star formation. The AUGER array will probably decide within the next few years, where the highest energy cosmic rays come from, and so frame the next quests, on very high energy neutrinos and perhaps other particles.Comment: 11 pages, To appear in Proceedings of International School of Astrophysics at Ultra-high Energies, 20-27 June, 2006, Erice, Sicily, Ital

Tridiagonal realization of the anti-symmetric Gaussian β\beta-ensemble

The Householder reduction of a member of the anti-symmetric Gaussian unitary ensemble gives an anti-symmetric tridiagonal matrix with all independent elements. The random variables permit the introduction of a positive parameter $\beta$, and the eigenvalue probability density function of the corresponding random matrices can be computed explicitly, as can the distribution of $\{q_i\}$, the first components of the eigenvectors. Three proofs are given. One involves an inductive construction based on bordering of a family of random matrices which are shown to have the same distributions as the anti-symmetric tridiagonal matrices. This proof uses the Dixon-Anderson integral from Selberg integral theory. A second proof involves the explicit computation of the Jacobian for the change of variables between real anti-symmetric tridiagonal matrices, its eigenvalues and $\{q_i\}$. The third proof maps matrices from the anti-symmetric Gaussian $\beta$-ensemble to those realizing particular examples of the Laguerre $\beta$-ensemble. In addition to these proofs, we note some simple properties of the shooting eigenvector and associated Pr\"ufer phases of the random matrices.Comment: 22 pages; replaced with a new version containing orthogonal transformation proof for both cases (Method III

Soliton Lattice and Single Soliton Solutions of the Associated Lam\'e and Lam\'e Potentials

We obtain the exact nontopological soliton lattice solutions of the Associated Lam\'e equation in different parameter regimes and compute the corresponding energy for each of these solutions. We show that in specific limits these solutions give rise to nontopological (pulse-like) single solitons, as well as to different types of topological (kink-like) single soliton solutions of the Associated Lam\'e equation. Following Manton, we also compute, as an illustration, the asymptotic interaction energy between these soliton solutions in one particular case. Finally, in specific limits, we deduce the soliton lattices, as well as the topological single soliton solutions of the Lam\'e equation, and also the sine-Gordon soliton solution.Comment: 23 pages, 5 figures. Submitted to J. Math. Phy

The postfinasteride syndrome; an overview

As a 5-α reductase inhibitor, Finasteride has proven effective in ameliorating two conditions documented to be androgen dependent, namely male androgenic alopecia and benign prostatic hyperplasia. Therapeutic results are maintained as long as the drug is administered, with treatment cessation generally leading to the return of symptomatology for each condition. In addition, during the therapeutic phase, several adverse effects have been reported, some of which persist long or indefinitely after treatment cessation, known as “post-finasteride syndrome.” Herein we present and discuss the most common finasteride side effects, along with a psycho-neuroendocrine rationale that could explain the persistence of many adverse effects after treatment cessation. Moreover, we argue that finasteride adverse effects occurring during finasteride administration should be delineated from postfinasteride side effects (encountered after treatment cessation), suggesting the need to be addressed separately within a therapeutic perspective. Until a tailored therapeutic approach of postfinasteride syndrome becomes available, we have noted that hand preference and sexual orientation seem to be useful as possible predicting factors for finasteride side effects and postfinasteride syndrome. Finally, even though finasteride administration is considered relatively safe, literature data urges prudence. Specifically, recent studies report that some subjects receiving finasteride develop severe depressive episodes including suicidal thoughts, in part due to persistent sexual side effects

Opening the Black Box of the Matching Function: The Power of Words

How do employers attract the right workers? How important are posted wages vs. other job characteristics? Using data from the leading job board CareerBuilder.com, we show that most vacancies do not post wages, and, for those that do, job titles explain more than 90% of the wage variance. Job titles also explain more than 80% of the across-vacancies variance in the education and experience of applicants. Finally, failing to control for job titles leads to a spurious negative elasticity of labor supply. Thus, our results uncover the previously undocumented power of words in the job matching process

Comparison of near-interface traps in Al2_2O3_3/4H-SiC and Al2_2O3_3/SiO2_2/4H-SiC structures

Aluminum oxide (Al2O3) has been grown by atomic layer deposition on n-type 4H-SiC with and without a thin silicon dioxide (SiO2) intermediate layer. By means of Capacitance Voltage and Thermal Dielectric Relaxation Current measurements, the interface properties have been investigated. Whereas for the samples with an interfacial SiO2 layer the highest near-interface trap density is found at 0.3 eV below the conduction band edge, Ec, the samples with only the Al2O3 dielectric exhibit a nearly trap free region close to Ec. For the Al2O3/SiC interface, the highest trap density appears between 0.4 to 0.6 eV below Ec. The results indicate the possibility for SiC-based MOSFETs with Al2O3 as the gate dielectric layer in future high performance devices.Comment: 3 figures. Applied Physics Letters, accepted for publicatio

Data sharing and reanalysis of randomized controlled trials in leading biomedical journals with a full data sharing policy: survey of studies published in the BMJ and PLOS Medicine

Objectives To explore the effectiveness of data sharing by randomized controlled trials (RCTs) in journals with a full data sharing policy and to describe potential difficulties encountered in the process of performing reanalyses of the primary outcomes. Design Survey of published RCTs. Setting PubMed/Medline. Eligibility criteria RCTs that had been submitted and published by The BMJ and PLOS Medicine subsequent to the adoption of data sharing policies by these journals. Main outcome measure The primary outcome was data availability, defined as the eventual receipt of complete data with clear labelling. Primary outcomes were reanalyzed to assess to what extent studies were reproduced. Difficulties encountered were described. Results 37 RCTs (21 from The BMJ and 16 from PLOS Medicine) published between 2013 and 2016 met the eligibility criteria. 17/37 (46%, 95% confidence interval 30% to 62%) satisfied the definition of data availability and 14 of the 17 (82%, 59% to 94%) were fully reproduced on all their primary outcomes. Of the remaining RCTs, errors were identified in two but reached similar conclusions and one paper did not provide enough information in the Methods section to reproduce the analyses. Difficulties identified included problems in contacting corresponding authors and lack of resources on their behalf in preparing the datasets. In addition, there was a range of different data sharing practices across study groups. Conclusions Data availability was not optimal in two journals with a strong policy for data sharing. When investigators shared data, most reanalyses largely reproduced the original results. Data sharing practices need to become more widespread and streamlined to allow meaningful reanalyses and reuse of data

Functional limit theorems for random regular graphs

Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as n grows to infinity, either when d is kept fixed or grows slowly with n. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein's method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn-Szemer\'edi argument for estimating the second largest eigenvalue for all values of d and n.Comment: Added Remark 27. 39 pages. To appear in Probability Theory and Related Field

Numerical Approximations Using Chebyshev Polynomial Expansions

We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the Chebyshev polynomial of order N (El-gendi's method). The solutions are exact at these points, apart from round-off computer errors and the convergence of other numerical methods used in connection to solving the linear system of equations. Applications to initial value problems in time-dependent quantum field theory, and second order boundary value problems in fluid dynamics are presented.Comment: minor wording changes, some typos have been eliminate