High Energy Gamma-Ray Emission From Blazars: EGRET Observations

We will present a summary of the observations of blazars by the Energetic Gamma Ray Experiment Telescope (EGRET) on the Compton Gamma Ray Observatory (CGRO). EGRET has detected high energy gamma-ray emission at energies greater than 100 MeV from more that 50 blazars. These sources show inferred isotropic luminosities as large as $3\times 10^{49}$ ergs s$^{-1}$. One of the most remarkable characteristics of the EGRET observations is that the gamma-ray luminosity often dominates the bolometric power of the blazar. A few of the blazars are seen to exhibit variability on very short time-scales of one day or less. The combination of high luminosities and time variations seen in the gamma-ray data indicate that gamma-rays are an important component of the relativistic jet thought to characterize blazars. Currently most models for blazars involve a beaming scenario. In leptonic models, where electrons are the primary accelerated particles, gamma-ray emission is believed to be due to inverse Compton scattering of low energy photons, although opinions differ as to the source of the soft photons. Hardronic models involve secondary production or photomeson production followed by pair cascades, and predict associated neutrino production.Comment: 16 pages, 7 figures, style files included. Invited review paper in "Observational Evidence for Black Holes in the Universe," 1999, ed. S. K. Chakrabarti (Dordrecht: Kluwer), 215-23

Limit theorems for von Mises statistics of a measure preserving transformation

For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n} f(T^{i_1}x,...,T^{i_d}x),\, n=1,2,...,$$ where $f$ (called the \emph{kernel}) is a function from $X^d$ to $\R$ and $C_1, C_2,...$ are appropriate normalizing constants. We observe that the above random variables are well defined and belong to $L_r(\mu)$ provided that the kernel is chosen from the projective tensor product $$L_p(X_1,\mathcal F_1, \mu_1) \otimes_{\pi}...\otimes_{\pi} L_p(X_d,\mathcal F_d, \mu_d)\subset L_p(\mu^d)$$ with $p=d\,r,\, r\ \in [1, \infty).$ We establish a form of the individual ergodic theorem for such sequences. Next, we give a martingale approximation argument to derive a central limit theorem in the non-degenerate case (in the sense of the classical Hoeffding's decomposition). Furthermore, for $d=2$ and a wide class of canonical kernels $f$ we also show that the convergence holds in distribution towards a quadratic form $\sum_{m=1}^{\infty} \lambda_m\eta^2_m$ in independent standard Gaussian variables $\eta_1, \eta_2,...$. Our results on the distributional convergence use a $T$--\,invariant filtration as a prerequisite and are derived from uni- and multivariate martingale approximations

Human Public-Key Encryption

This paper proposes a public-key cryptosystem and a short password encryption mode, where traditional hardness assumptions are replaced by specific refinements of the CAPTCHA concept called Decisional and Existential CAPTCHAs. The public-key encryption method, achieving 128-bit security, typically requires from the sender to solve one CAPTCHA. The receiver does not need to resort to any human aid. A second symmetric encryption method allows to encrypt messages using very short passwords shared between the sender and the receiver. Here, a simple 5-character alphanumeric password provides sufficient security for all practical purposes. We conjecture that the automatic construction of Decisional and Existential CAPTCHAs is possible and provide candidate ideas for their implementation

Restrictions and extensions of semibounded operators

We study restriction and extension theory for semibounded Hermitian operators in the Hardy space of analytic functions on the disk D. Starting with the operator zd/dz, we show that, for every choice of a closed subset F in T=bd(D) of measure zero, there is a densely defined Hermitian restriction of zd/dz corresponding to boundary functions vanishing on F. For every such restriction operator, we classify all its selfadjoint extension, and for each we present a complete spectral picture. We prove that different sets F with the same cardinality can lead to quite different boundary-value problems, inequivalent selfadjoint extension operators, and quite different spectral configurations. As a tool in our analysis, we prove that the von Neumann deficiency spaces, for a fixed set F, have a natural presentation as reproducing kernel Hilbert spaces, with a Hurwitz zeta-function, restricted to FxF, as reproducing kernel.Comment: 63 pages, 11 figure

Physics in Riemann's mathematical papers

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann's mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann's philosophical points of view, we review some ideas on the same subjects emitted by Riemann's predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle. The final version of this paper will appear in the book: From Riemann to differential geometry and relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Argumentation in school science : Breaking the tradition of authoritative exposition through a pedagogy that promotes discussion and reasoning

The value of argumentation in science education has become internationally recognised and has been the subject of many research studies in recent years. Successful introduction of argumentation activities in learning contexts involves extending teaching goals beyond the understanding of facts and concepts, to include an emphasis on cognitive and metacognitive processes, epistemic criteria and reasoning. The authors focus on the difficulties inherent in shifting a tradition of teaching from one dominated by authoritative exposition to one that is more dialogic, involving small-group discussion based on tasks that stimulate argumentation. The paper builds on previous research on enhancing the quality of argument in school science, to focus on how argumentation activities have been designed, with appropriate strategies, resources and modelling, for pedagogical purposes. The paper analyses design frameworks, their contexts and lesson plans, to evaluate their potential for enhancing reasoning through foregrounding the processes of argumentation. Examples of classroom dialogue where teachers adopt the frameworks/plans are analysed to show how argumentation processes are scaffolded. The analysis shows that several layers of interpretation are needed and these layers need to be aligned for successful implementation. The analysis serves to highlight the potential and limitations of the design frameworks

Trade secrets law

The standardisation of trade secret protection was one of the goals of the TRIPs Agreement of 1998. Nevertheless, substantial differences in this protection remain across jurisdictions. When defining the optimal scope of trade secrets law, lawmakers should be aware that strong trade secret protection is likely to promote inventiveness, but it is also likely to hinder the diffusion of knowledge and prevent competition

Multifrequency Strategies for the Identification of Gamma-Ray Sources

More than half the sources in the Third EGRET (3EG) catalog have no firmly established counterparts at other wavelengths and are unidentified. Some of these unidentified sources have remained a mystery since the first surveys of the gamma-ray sky with the COS-B satellite. The unidentified sources generally have large error circles, and finding counterparts has often been a challenging job. A multiwavelength approach, using X-ray, optical, and radio data, is often needed to understand the nature of these sources. This chapter reviews the technique of identification of EGRET sources using multiwavelength studies of the gamma-ray fields.Comment: 35 pages, 22 figures. Chapter prepared for the book "Cosmic Gamma-ray Sources", edited by K.S. Cheng and G.E. Romero, to be published by Kluwer Academic Press, 2004. For complete article and higher resolution figures, go to: http://www.astro.columbia.edu/~muk/mukherjee_multiwave.pd

Microbial catabolic activities are naturally selected by metabolic energy harvest rate

The fundamental trade-off between yield and rate of energy harvest per unit of substrate has been largely discussed as a main characteristic for microbial established cooperation or competition. In this study, this point is addressed by developing a generalized model that simulates competition between existing and not experimentally reported microbial catabolic activities defined only based on well-known biochemical pathways. No specific microbial physiological adaptations are considered, growth yield is calculated coupled to catabolism energetics and a common maximum biomass-specific catabolism rate (expressed as electron transfer rate) is assumed for all microbial groups. Under this approach, successful microbial metabolisms are predicted in line with experimental observations under the hypothesis of maximum energy harvest rate. Two microbial ecosystems, typically found in wastewater treatment plants, are simulated, namely: (i) the anaerobic fermentation of glucose and (ii) the oxidation and reduction of nitrogen under aerobic autotrophic (nitrification) and anoxic heterotrophic and autotrophic (denitrification) conditions. The experimentally observed cross feeding in glucose fermentation, through multiple intermediate fermentation pathways, towards ultimately methane and carbon dioxide is predicted. Analogously, two-stage nitrification (by ammonium and nitrite oxidizers) is predicted as prevailing over nitrification in one stage. Conversely, denitrification is predicted in one stage (by denitrifiers) as well as anammox (anaerobic ammonium oxidation). The model results suggest that these observations are a direct consequence of the different energy yields per electron transferred at the different steps of the pathways. Overall, our results theoretically support the hypothesis that successful microbial catabolic activities are selected by an overall maximum energy harvest rate