Jeffreys's law for general games of prediction: in search of a theory

We are interested in the following version of Jeffreys's law: if two predictors are predicting the same sequence of events and either is doing a satisfactory job, they will make similar predictions in the long run. We give a classification of instances of Jeffreys's law, illustrated with examples.Comment: 12 page

Measuring the correlation length of intergalactic magnetic fields from observations of gamma-ray induced cascades

Context. The imaging and timing properties of {\gamma}-ray emission from electromagnetic cascades initiated by very-high-energy (VHE) {\gamma}-rays in the intergalactic medium depend on the strength B and correlation length {\lambda}B of intergalactic magnetic fields (IGMF). Aims. We study the possibility of measuring both B and {\lambda}B via observations of the cascade emission with {\gamma}-ray telescopes. Methods. For each measurement method, we find two characteristics of the cascade signal, which are sensitive to the IGMF B and {\lambda}B values in different combinations. For the case of IGMF measurement using the observation of extended emission around extragalactic VHE {\gamma}-ray sources, the two characteristics are the slope of the surface brightness profile and the overall size of the cascade source. For the case of IGMF measurement from the time delayed emission, these two characteristics are the initial slope of the cascade emission light curve and the overall duration of the cascade signal. Results. We show that measurement of the slope of the cascade induced extended emission and/or light curve can both potentially provide measure of the IGMF correlation length, provided it lies within the range 10 kpc< {\lambda}B <1 Mpc. For correlation lengths outside this range, gamma-ray observations can provide upper or lower bound on {\lambda}B. The latter of the two methods holds great promise in the near future for providing a measurement/constraint using measurements from present/next-generation {\gamma}-ray-telescopes. Conclusions. Measurement of the IGMF correlation length will provide an important constraint on its origin. In particular, it will enable to distinguish between an IGMF of galactic wind origin from an IGMF of cosmological origin.Comment: 5 pages, 3 figure

Prediction with Expert Advice under Discounted Loss

We study prediction with expert advice in the setting where the losses are accumulated with some discounting---the impact of old losses may gradually vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm for Regression to this case, propose a suitable new variant of exponential weights algorithm, and prove respective loss bounds.Comment: 26 pages; expanded (2 remarks -> theorems), some misprints correcte

Evidence for strong extragalactic magnetic fields from Fermi observations of TeV blazars

Magnetic fields in galaxies are produced via the amplification of seed magnetic fields of unknown nature. The seed fields, which might exist in their initial form in the intergalactic medium, were never detected. We report a lower bound $B\ge 3\times 10^{-16}$~gauss on the strength of intergalactic magnetic fields, which stems from the nonobservation of GeV gamma-ray emission from electromagnetic cascade initiated by tera-electron volt gamma-ray in intergalactic medium. The bound improves as $\lambda_B^{-1/2}$ if magnetic field correlation length, $\lambda_B$, is much smaller than a megaparsec. This lower bound constrains models for the origin of cosmic magnetic fields.Comment: 14 pages, 3 figure

Fast variability of γ-ray emission from supermassive black hole binary OJ 287

We report the discovery of fast variability of γ-ray flares from blazar OJ 287. This blazar is known to be powered by a binary system of supermassive black holes. The observed variability time-scale Tvar≲ 3-10 h is much shorter than the light-crossing time of the more massive (1.8 × 1010 M⊙) black hole and is comparable to the light-crossing time of the less massive (1.3 × 108 M⊙) black hole. This indicates that γ-ray emission is produced by the relativistic jet ejected by the black hole of smaller mass. Detection of γ-rays with energies in excess of 10 GeV during the fast variable flares constrains the Doppler factor of the jet to be larger than 4. The possibility of studying the orbital modulation of emission from the relativistic jet makes OJ 287 a unique laboratory for the study of the mechanism(s) of formation of jets by black holes, and in particular the response of the jet parameters to changes in the parameters of the medium from which the black hole accretes and into which the jet expand