Ground-based gamma-ray astronomy has had a major breakthrough with the impressive results obtained using systems of imaging atmospheric Cherenkov telescopes. Ground-based gamma-ray astronomy has a huge potential in astrophysics, particle physics and cosmology. CTA is an international initiative to build the next generation instrument, with a factor of 5-10 improvement in sensitivity in the 100 GeV-10 TeV range and the extension to energies well below 100 GeV and above 100 TeV. CTA will consist of two arrays (one in the north, one in the south) for full sky coverage and will be operated as open observatory. The design of CTA is based on currently available technology. This document reports on the status and presents the major design concepts of CTA.

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Design concepts for the Cherenkov Telescope Array CTA: An advanced facility for ground-based high-energy gamma-ray astronomy

Structural investigation of supply networks: A social network analysis approach

The Lovasz Local Lemma discovered by Erdos and Lovasz in 1975 is a powerful tool to non-constructively prove the existence of combinatorial objects meeting a prescribed collection of criteria. In 1991, Jozsef Beck was the first to demonstrate that a constructive variant can be given under certain more restrictive conditions, starting a whole line of research aimed at improving his algorithm's performance and relaxing its restrictions. In the present article, we improve upon recent findings so as to provide a method for making almost all known applications of the general Local Lemma algorithmic.

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A constructive proof of the general lovász local lemma

: Significant progress has been made with solution of location problems and in preprocessing and decomposition for discrete optimization. There has also been research on the application of techniques from combinational optimization to nonlinear problems.

http://www.dtic.mil/dtic/tr/fulltext/u2/a273552.pdf

Discrete Applied Mathematics

Precision measurements of the positron component in the cosmic radiation provide important information about the propagation of cosmic rays and the nature of particle sources in our Galaxy. The satellite-borne experiment PAMELA has been used to make a new measurement of the cosmic-ray positron flux and fraction that extends previously published measurements up to 300 GeV in kinetic energy. The combined measurements of the cosmic-ray positron energy spectrum and fraction provide a unique tool to constrain interpretation models. During the recent solar minimum activity period from July 2006 to December 2009, approximately 24 500 positrons were observed. The results cannot be easily reconciled with purely secondary production, and additional sources of either astrophysical or exotic origin may be required.

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Cosmic-Ray Positron Energy Spectrum Measured by PAMELA

We present results from a case study comparing different multivariate classification methods. The input is a set of Monte Carlo data, generated and approximately triggered and pre-processed for an imaging gamma-ray Cherenkov telescope. Such data belong to two classes, originating either from incident gamma rays or caused by hadronic showers. There is only a weak discrimination between signal (gamma) and background (hadrons), making the data an excellent proving ground for classification techniques. The data and methods are described, and a comparison of the results is made. Several methods give results comparable in quality within small fluctuations, suggesting that they perform at or close to the Bayesian limit of achievable separation. Other methods give clearly inferior or inconclusive results. Some problems that this study can not address are also discussed.

Methods for multidimensional event classification: A case study using images from a Cherenkov gamma-ray telescope

A Boolean formula in a conjunctive normal form is called a $(k,s)$ – formula if every clause contains exactly k variables and every variable occurs in at most s clauses. The $(k,s)$–${\text{SAT}}$ problem is the SATISFIABILITY problem restricted to $(k,s)$–formulas. It is proved that for every $k \geqslant 3$ there is an integer $f(k)$ such that $(k,s)$–${\text{SAT}}$ is trivial for $s \leqslant f(k)$ (because every $(k,s)$–formula is satisfiable) and is NP-complete for $s \geqslant f(k) + 1$. Moreover, $f(k)$ grows exponentially with k, namely, $\lfloor {{{2^k } / {ek}}} \rfloor \leqslant f(k) \leqslant 2^{k - 1} - 2^{k - 4} - 1$ for $k \geqslant 4$.

One more occurrence of variables makes satisfiability jump from trivial to NP-complete

Representations and rates of approximation of real-valued Boolean functions by neural networks

The main goal of this paper is to investigate methods of how to rank words in a way that corresponds to an intuitive notion of ‘commonness’. Since there is no formal definition of such a notion, our techniques may be considered as a suggestion for such a definition. The commonness of words is sometimes roughly substituted with their frequency in a language corpus. In order to suggest a better measure, we define a quantity, which we call corrected frequency. It depends not only on the frequency of a word in a corpus, but also on its distribution within the corpus. Unlike previous solutions of the same problem, we take the corpus as an uninterrupted sequence of words with no regard to borders between files, texts, genres, or any others. We introduce three different corrected frequencies. Their definitions are based on notions of information theory and analysis of random processes. Their values for individual words depend on the corpus. Hence, it is important to what extent they are stable with respect to th...

Measures of Word Commonness

Product Logic Π is an axiomatic extension of Hajek's Basic Fuzzy Logic BL coping with the 1-tautologies when the strong conjunction & and implication → are interpreted by the product of reals in [0, 1] and its residuum respectively. In this paper we investigate expansions of Product Logic by adding into the language a countable set of truth-constants (one truth-constant for each r in a countable Π-subalgebra of [0, 1]) and by adding the corresponding book-keeping axioms for the truthconstants. We first show that the corresponding logics Π( ) are algebraizable, and hence complete with respect to the variety of Π( )-algebras. The main result of the paper is the canonical standard completeness of these logics, that is, theorems of Π( ) are exactly the 1-tautologies of the algebra defined over the real unit interval where the truth-constants are interpreted as their own values. It is also shown that they do not enjoy the canonical strong standard completeness, but they enjoy it for finite theories when restricted to evaluated Π-formulas of the kind → ψ, where is a truth-constant and ψ a formula not containing truth-constants. Finally we consider the logics ΠΔ( ), the expansion of Π( ) with the well-known Baaz's projection connective Δ, and we show canonical finite strong standard completeness for them.

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Petr Savický

Papers

Methods for multidimensional event classification: A case study using images from a Cherenkov gamma-ray telescope

One more occurrence of variables makes satisfiability jump from trivial to NP-complete

Representations and rates of approximation of real-valued Boolean functions by neural networks

Measures of Word Commonness

On Product Logic with Truth-constants