Bias Analysis in Entropy Estimation

We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction formulas of current entropy estimates recently discussed in literature. The trade-off between bias reduction and the increase of the corresponding statistical error is analyzed.Comment: 5 pages, 3 figure

Random perfect lattices and the sphere packing problem

Motivated by the search for best lattice sphere packings in Euclidean spaces of large dimensions we study randomly generated perfect lattices in moderately large dimensions (up to d=19 included). Perfect lattices are relevant in the solution of the problem of lattice sphere packing, because the best lattice packing is a perfect lattice and because they can be generated easily by an algorithm. Their number however grows super-exponentially with the dimension so to get an idea of their properties we propose to study a randomized version of the algorithm and to define a random ensemble with an effective temperature in a way reminiscent of a Monte-Carlo simulation. We therefore study the distribution of packing fractions and kissing numbers of these ensembles and show how as the temperature is decreased the best know packers are easily recovered. We find that, even at infinite temperature, the typical perfect lattices are considerably denser than known families (like A_d and D_d) and we propose two hypotheses between which we cannot distinguish in this paper: one in which they improve Minkowsky's bound phi\sim 2^{-(0.84+-0.06) d}, and a competitor, in which their packing fraction decreases super-exponentially, namely phi\sim d^{-a d} but with a very small coefficient a=0.06+-0.04. We also find properties of the random walk which are suggestive of a glassy system already for moderately small dimensions. We also analyze local structure of network of perfect lattices conjecturing that this is a scale-free network in all dimensions with constant scaling exponent 2.6+-0.1.Comment: 19 pages, 22 figure

Study of the 12C+12C fusion reactions near the Gamow energy

The fusion reactions 12C(12C,a)20Ne and 12C(12C,p)23Na have been studied from E = 2.10 to 4.75 MeV by gamma-ray spectroscopy using a C target with ultra-low hydrogen contamination. The deduced astrophysical S(E)* factor exhibits new resonances at E <= 3.0 MeV, in particular a strong resonance at E = 2.14 MeV, which lies at the high-energy tail of the Gamow peak. The resonance increases the present non-resonant reaction rate of the alpha channel by a factor of 5 near T = 8x10^8 K. Due to the resonance structure, extrapolation to the Gamow energy E_G = 1.5 MeV is quite uncertain. An experimental approach based on an underground accelerator placed in a salt mine in combination with a high efficiency detection setup could provide data over the full E_G energy range.Comment: 4 Pages, 4 figures, accepted for publication in Phys. Rev. Let

Improved treatment of the T2T_2 molecular final-states uncertainties for the KATRIN neutrino-mass measurement

The KArlsruhe TRItium Neutrino experiment (KATRIN) aims to determine the effective mass of the electron antineutrino via a high-precision measurement of the tritium beta-decay spectrum in its end-point region. The target neutrino-mass sensitivity of 0.2 eV / c^2 at 90% C.L. can only be achieved in the case of high statistics and a good control of the systematic uncertainties. One key systematic effect originates from the calculation of the molecular final states of T_2 beta decay. In the first neutrino-mass analyses of KATRIN the contribution of the uncertainty of the molecular final-states distribution (FSD) was estimated via a conservative phenomenological approach to be 0.02 eV^2 / c^4. In this paper a new procedure is presented for estimating the FSD-related uncertainties by considering the details of the final-states calculation, i.e. the uncertainties of constants, parameters, and functions used in the calculation as well as its convergence itself as a function of the basis-set size used in expanding the molecular wave functions. The calculated uncertainties are directly propagated into the experimental observable, the squared neutrino mass m_nu^2. With the new procedure the FSD-related uncertainty is constrained to 0.0013 eV^2 / c^4, for the experimental conditions of the first KATRIN measurement campaign

Logic, logical form and the disunity of truth

Monists say that the nature of truth is invariant, whichever sentence you consider; pluralists say that the nature of truth varies between different sets of sentences. The orthodoxy is that logic and logical form favour monism: there must be a single property that is preserved in any valid inference; and any truth-functional complex must be true in the same way as its components. The orthodoxy, I argue, is mistaken. Logic and logical form impose only structural constraints on a metaphysics of truth. Monistic theories are not guaranteed to satisfy these constraints, and there is a pluralistic theory that does so

Использование средств e-learning в высшей школе

Применение информационных технологий в образовательном процессе делает его более увлекательным и более эффективным, позволяет формировать творческое мышление, стимулирует студентов к саморазвитию и самостоятельности. В статье раскрывается потенциал средств электронного обучения в оптимизации учебного процесса в высшей школе

A New Elimination Rule for the Calculus of Inductive Constructions

Published in the post-proceedings of TYPES but actually not presented orally to the conferenceInternational audienceIn Type Theory, definition by dependently-typed case analysis can be expressed by means of a set of equations — the semantic approach — or by an explicit pattern-matching construction — the syntactic approach. We aim at putting together the best of both approaches by extending the pattern-matching construction found in the Coq proof assistant in order to obtain the expressivity and flexibility of equation-based case analysis while remaining in a syntax-based setting, thus making dependently-typed programming more tractable in the Coq system. We provide a new rule that permits the omission of impossible cases, handles the propagation of inversion constraints, and allows to derive Streicher's K axiom. We show that subject reduction holds, and sketch a proof of relative consistency

Algebraic totality, towards completeness

Finiteness spaces constitute a categorical model of Linear Logic (LL) whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and morphisms as continuous linear maps. First, we recall definitions of finiteness spaces and describe their basic properties deduced from the general theory of linearly topologised spaces. Then we give an interpretation of LL based on linear algebra. Second, thanks to separation properties, we can introduce an algebraic notion of totality candidate in the framework of linearly topologised spaces: a totality candidate is a closed affine subspace which does not contain 0. We show that finiteness spaces with totality candidates constitute a model of classical LL. Finally, we give a barycentric simply typed lambda-calculus, with booleans ${\mathcal{B}}$ and a conditional operator, which can be interpreted in this model. We prove completeness at type ${\mathcal{B}}^n\to{\mathcal{B}}$ for every n by an algebraic method