Primary Particle Type of the Most Energetic Fly's Eye Air Shower

The longitudinal profile of the most energetic cosmic-ray air shower measured so far, the event recorded by the Fly's Eye detector with a reconstructed primary energy of about 320 EeV, is compared to simulated shower profiles. The calculations are performed with the CORSIKA code and include primary photons and different hadron primaries. For primary photons, preshower formation in the geomagnetic field is additionally treated in detail. For primary hadrons, the hadronic interaction models QGSJET01 and SIBYLL2.1 have been employed. The predicted longitudinal profiles are compared to the observation. A method for testing the hypothesis of a specific primary particle type against the measured profile is described which naturally takes shower fluctuations into account. The Fly's Eye event is compatible with any assumption of a hadron primary between proton and iron nuclei in both interaction models, although differences between QGSJET01 and SIBYLL2.1 in the predicted profiles of lighter nuclei exist. The primary photon profiles differ from the data on a level of ~1.5 sigma. Although not favoured by the observation, the primary photon hypothesis can not be rejected for this particular event.Comment: 20 pages, 8 figures; v2 matches version accepted by Astroparticle Physic

Symmetries of modules of differential operators

Let ${\cal F}\_\lambda(S^1)$ be the space of tensor densities of degree (or weight) $\lambda$ on the circle $S^1$. The space ${\cal D}^k\_{\lambda,\mu}(S^1)$ of $k$-th order linear differential operators from ${\cal F}\_\lambda(S^1)$ to ${\cal F}\_\mu(S^1)$ is a natural module over $\mathrm{Diff}(S^1)$, the diffeomorphism group of $S^1$. We determine the algebra of symmetries of the modules ${\cal D}^k\_{\lambda,\mu}(S^1)$, i.e., the linear maps on ${\cal D}^k\_{\lambda,\mu}(S^1)$ commuting with the $\mathrm{Diff}(S^1)$-action. We also solve the same problem in the case of straight line $\mathbb{R}$ (instead of $S^1$) and compare the results in the compact and non-compact cases.Comment: 29 pages, LaTeX, 4 figure

BNFinder: exact and efficient method for learning Bayesian networks

Motivation: Bayesian methods are widely used in many different areas of research. Recently, it has become a very popular tool for biological network reconstruction, due to its ability to handle noisy data. Even though there are many software packages allowing for Bayesian network reconstruction, only few of them are freely available to researchers. Moreover, they usually require at least basic programming abilities, which restricts their potential user base. Our goal was to provide software which would be freely available, efficient and usable to non-programmers

Biopython: freely available Python tools for computational molecular biology and bioinformatics

Summary: The Biopython project is a mature open source international collaboration of volunteer developers, providing Python libraries for a wide range of bioinformatics problems. Biopython includes modules for reading and writing different sequence file formats and multiple sequence alignments, dealing with 3D macro molecular structures, interacting with common tools such as BLAST, ClustalW and EMBOSS, accessing key online databases, as well as providing numerical methods for statistical learning. Availability: Biopython is freely available, with documentation and source code at www.biopython.org under the Biopython license. Contact: All queries should be directed to the Biopython mailing lists, see www.biopython.org/wiki/[email protected]

Invariants of pseudogroup actions: Homological methods and Finiteness theorem

We study the equivalence problem of submanifolds with respect to a transitive pseudogroup action. The corresponding differential invariants are determined via formal theory and lead to the notions of k-variants and k-covariants, even in the case of non-integrable pseudogroup. Their calculation is based on the cohomological machinery: We introduce a complex for covariants, define their cohomology and prove the finiteness theorem. This implies the well-known Lie-Tresse theorem about differential invariants. We also generalize this theorem to the case of pseudogroup action on differential equations.Comment: v2: some remarks and references addee

Hamiltonian evolutions of twisted gons in \RP^n

In this paper we describe a well-chosen discrete moving frame and their associated invariants along projective polygons in \RP^n, and we use them to write explicit general expressions for invariant evolutions of projective $N$-gons. We then use a reduction process inspired by a discrete Drinfeld-Sokolov reduction to obtain a natural Hamiltonian structure on the space of projective invariants, and we establish a close relationship between the projective $N$-gon evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that {any} Hamiltonian evolution is induced on invariants by an evolution of $N$-gons - what we call a projective realization - and we give the direct connection. Finally, in the planar case we provide completely integrable evolutions (the Boussinesq lattice related to the lattice $W_3$-algebra), their projective realizations and their Hamiltonian pencil. We generalize both structures to $n$-dimensions and we prove that they are Poisson. We define explicitly the $n$-dimensional generalization of the planar evolution (the discretization of the $W_n$-algebra) and prove that it is completely integrable, providing also its projective realization