An example of a non-Borel locally-connected finite-dimensional topological group

Answering a question posed by S.Maillot in MathOverFlow, for every $n\in\mathbb N$ we construct a locally connected subgroup $G\subset\mathbb R^{n+1}$ of dimension $dim(G)=n$, which is not locally compact.Comment: 2 page

A spatial likelihood analysis for MAGIC telescope data

Context. The increase in sensitivity of Imaging Atmospheric Cherenkov Telescopes (IACTs) has lead to numerous detections of extended $\gamma$-ray sources at TeV energies, sometimes of sizes comparable to the instrument's field of view (FoV). This creates a demand for advanced and flexible data analysis methods, able to extract source information by utilising the photon counts in the entire FoV. Aims. We present a new software package, "SkyPrism", aimed at performing 2D (3D if energy is considered) fits of IACT data, possibly containing multiple and extended sources, based on sky images binned in energy. Though the development of this package was focused on the analysis of data collected with the MAGIC telescopes, it can further be adapted to other instruments, such as the future Cherenkov Telescope Array (CTA). Methods. We have developed a set of tools that, apart from sky images (count maps), compute the instrument response functions (IRFs) of MAGIC (effective exposure throughout the FoV, point spread function (PSF), energy resolution and background shape), based on the input data, Monte-Carlo simulations and the pointing track of the telescopes. With this information, the presented package can perform a simultaneous maximum likelihood fit of source models of arbitrary morphology to the sky images providing energy spectra, detection significances, and upper limits. Results. We demonstrate that the SkyPrism tool accurately reconstructs the MAGIC PSF, on and off-axis performance as well as the underlying background. We further show that for a point source analysis with MAGIC's default observational settings, SkyPrism gives results compatible with those of the standard tools while being more flexible and widely applicable.Comment: 13 pages, 10 figure

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

Leading strategies in competitive on-line prediction

We start from a simple asymptotic result for the problem of on-line regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a "leading prediction strategy", which not only asymptotically performs at least as well as any continuous limited-memory strategy but also satisfies the property that the excess loss of any continuous limited-memory strategy is determined by how closely it imitates the leading strategy. More specifically, for any class of prediction strategies constituting a reproducing kernel Hilbert space we construct a leading strategy, in the sense that the loss of any prediction strategy whose norm is not too large is determined by how closely it imitates the leading strategy. This result is extended to the loss functions given by Bregman divergences and by strictly proper scoring rules.Comment: 20 pages; a conference version is to appear in the ALT'2006 proceeding

Determination Of Toxicity Of Chopped Meat-based Semi-products In Vivo

At solving the problem of protein deficiency, the great role of the raw material for its production is played by leguminous cultures such as peas, haricot beans, lupine, forage beans, lentil, chick-peas, peavine and other. The chemical composition and food value of proteins of these cultures are most close to animal proteins – of meat, fish and also milk. Among the essential quantity of vegetable raw material that contains protein (33 - 50 %), the special place is occupied by lupine, characterized as an important reserve of high-quality protein substances at the World congress in 1991 in the USA [1].There were elaborated certain recipes of meat chopped semi-products, based on beef that contains 5 %, 10 %, 15 % of lupine flour and 0,5 % of elecampane root powder.There were carried out the studies on the determination of toxicity of functional raw material and cutlets with 10 % content of lupine flour and 0,5 % of elecampane on white mice organisms. There were used methods, based on toxic substances extraction from forages and peeled gains under condition of the intra-stomach administration and cutlets feed during 10 days. Blood was taken for hematological studies in mice, fed by functional cutlets.It was proved, that these products have no toxic influence on organisms. At the pathoanatomical dissection, any macroscopic changes in tissues were not revealed, blood hematological results are within norm.The best sample № 2 with 10 % content of lupine flour and 0,5 % of elecampane was determined by the gustatory method.It was determined, that functional meat chopped semi-product may be included in the ration for the sound, treating-prophylactic nutrition