The equivalence problem under local unitary transformation for $n$--partite pure states is reduced to the one for $(n-1)$--partite mixed states. In particular, a tripartite system $\mathcal{H}_A\otimes\mathcal{H}_B\otimes\mathcal{H}_C$, where $\mathcal{H}_j$ is a finite dimensional complex Hilbert space for $j=A,B,C$, is considered and a set of invariants under local transformations is introduced, which is complete for the set of states whose partial trace with respect to $\mathcal{H}_A$ belongs to the class of generic mixed states.

Sergio Albeverio Laura Cattaneo Shao-Ming Fei Xiao-Hong Wang

Context. Known TeV sources detected by major Cerenkov telescopes are investigated to identify possible MeV-GeV gamma-ray counterparts. Aims. A systematic study of the known sources in the web-based TeVCat Catalog has been performed to search for possible gamma-ray counterpart on the AGILE data collected during the first period of operations in observing pointing mode. Methods. For each TeV source, a search for a possible gamma-ray counterpart based on a multi-source Maximum Likelihood algorithm is performed on the AGILE data taken with the GRID instrument from July 2007 to October 2009. Results. In case of high-significance detection, the average gamma-ray flux is estimated. For the cases of low-significance detection the 95 % Confidence Level (C.L.) flux upper limit is given. 52 TeV sources out of 152 (corresponding to ~34 % of the analysed sample) show a significant excess in the AGILE data covering the pointing observation period. Conclusions. This analysis found 26 new AGILE sources with respect to the AGILE reference catalogs, 15 of which are Galactic, 7 are extragalactic and 4 are unidentified. Detailed tables with all available information on the analysed sources are presented.

A. Rappoldi F. Lucarelli C. Pittori F. Longo P. W. Cattaneo F. Verrecchia M. Tavani A. Bulgarelli A. W. Chen S. Colafrancesco I. Donnarumma A. Giuliani A. Morselli S. Sabatini S. Vercellone

Radiation hardness is an important requirement for solid state readout devices operating in high radiation environments common in particle physics experiments. The MEGII experiment, at PSI, Switzerland, investigates the forbidden decay $\mu^+ \to \mathrm{e}^+ \gamma$. Exploiting the most intense muon beam of the world. A significant flux of non-thermal neutrons (kinetic energy $E_k\geq 0.5 ~MeV$) is present in the experimental hall produced along the beamline and in the hall itself. We present the effects of neutron fluxes comparable to the MEGII expected doses on several Silicon PhotoMulitpliers (SiPMs). The tested models are: AdvanSiD ASD-NUV3S-P50 (used in MEGII experiment), AdvanSiD ASD-NUV3S-P40, AdvanSiD ASD-RGB3S-P40, Hamamatsu and Excelitas C30742-33-050-X. The neutron source is the thermal Sub-critical Multiplication complex (SM1) moderated with water, located at the University of Pavia (Italy). We report the change of SiPMs most important electric parameters: dark current, dark pulse frequency, gain, direct bias resistance, as a function of the integrated neutron fluency.

P. W. Cattaneo T. Cervi A. Menegolli M. Oddone M. Prata M. C. Prata M. Rossella

GalICS 2.0 is a new semianalytic code to model the formation and evolution of galaxies in a cosmological context. N-body simulations based on a Planck cosmology are used to construct halo merger trees, track subhaloes, compute spins and measure concentrations. The accretion of gas onto galaxies and the morphological evolution of galaxies are modelled with prescriptions derived from hydrodynamic simulations. Star formation and stellar feedback are described with phenomenological models (as in other semianalytic codes). GalICS 2.0 computes rotation speeds from the gravitational potential of the dark matter, the disc and the central bulge. As the rotation speed depends not only on the virial velocity but also on the ratio of baryons to dark matter within a galaxy, our calculation predicts a different Tully-Fisher relation from models in which the rotation speed is proportional to the virial velocity. This is why GalICS 2.0 is able to reproduce the galaxy stellar mass function and the Tully-Fisher relation simultaneously. Our results are also in agreement with halo masses from weak lensing and satellite kinematics, gas fractions, the relation between star formation rate (SFR) and stellar mass, the evolution of the cosmic SFR density, bulge-to-disc ratios, disc sizes and the Faber-Jackson relation.

A. Cattaneo J. Blaizot J. E. G. Devriendt G. A. Mamon E. Tollet A. Dekel B. Guiderdoni M. Kucukbas A. C. R. Thob

We show that introducing a periodic time coordinate in the models of Penner-Kontsevich type generalizes the corresponding constructions to the case of the moduli space ${\cal S}_{gn}^k$ of curves $C$ with homology chains $\gamma\in H_1(C,\zet_k)$. We make a minimal extension of the resulting models by adding a kinetic term, and we get a new matrix model which realizes a simple dynamics of $\zet_k$-chains on surfaces. This gives a representation of $c=1$ matter coupled to two-dimensional quantum gravity with the target space being a circle of finite radius, as studied by Gross and Klebanov.

A. S. Cattaneo A. Gamba M. Martellini

In this article, we express the Alexander polynomial of null-homologous long knots in punctured rational homology $3$-spheres in terms of integrals over configuration spaces. To get such an expression, we use a previously established formula, which gives generalized Bott-Cattaneo-Rossi invariants in terms of the Alexander polynomial and vice versa, and we relate these Bott-Cattaneo-Rossi invariants to the perturbative expansion of Chern-Simons theory.

David Leturcq

We consider the time-fractional Cattaneo equation involving the tempered Caputo space-fractional derivative. We find the characteristic function of the related process and we explain the main differences with previous stochastic treatments of the time-fractional Cattaneo equation.

Luisa Beghin Roberto Garra Francesco Mainardi Gianni Pagnini

The MEG experiment, designed to search for the mu+->e+ gamma decay at a 10^-13 sensitivity level, completed data taking in 2013. In order to increase the sensitivity reach of the experiment by an order of magnitude to the level of 6 x 10-14 for the branching ratio, a total upgrade, involving substantial changes to the experiment, has been undertaken, known as MEG II. We present both the motivation for the upgrade and a detailed overview of the design of the experiment and of the expected detector performance.

A. M. Baldini E. Baracchini C. Bemporad F. Berg M. Biasotti G. Boca P. W. Cattaneo G. Cavoto F. Cei M. Chiappini G. Chiarello C. Chiri G. Cocciolo A. Corvaglia A. de Bari M. De Gerone A. D'Onofrio M. Francesconi Y. Fujii L. Galli F. Gatti F. Grancagnolo M. Grassi D. N. Grigoriev M. Hildebrandt Z. Hodge F. Grancagnolo M. Grassi D. N. Grigoriev M. Hildebrandt Z. Hodge K. Ieki F. Ignatov R. Iwai T. Iwamoto D. Kaneko K. Kasami P. -R. Kettle B. I. Khazin N. Khomutov A. Korenchenko N. Kravchuk T. Libeiro M. Maki N. Matsuzawa S. Mihara M. Milgie W. Molzon Toshinori Mori F. Morsani A. Mtchedilishvili M. Nakao S. Nakaura D. Nicoló H. Nishiguchi M. Nishimura S. Ogawa W. Ootani M. Panareo A. Papa A. Pepino G. Piredda A. Popov F. Raffaelli F. Renga E. Ripiccini S. Ritt M. Rossella G. Rutar R. Sawada G. Signorelli M. Simonetta G. F. Tassielli Y. Uchiyama M. Usami M. Venturini C. Voena K. Yoshida Yu. V. Yudin Y. Zhang

We prove a relative version of Kontsevich's formality theorem. This theorem involves a manifold M and a submanifold C and reduces to Kontsevich's theorem if C=M. It states that the DGLA of multivector fields on an infinitesimal neighbourhood of C is L-infinity-quasiisomorphic to the DGLA of multidifferential operators acting on sections of the exterior algebra of the conormal bundle. Applications to the deformation quantisation of coisotropic submanifolds are given. The proof uses a duality transformation to reduce the theorem to a version of Kontsevich's theorem for supermanifolds, which we also discuss. In physical language, the result states that there is a duality between the Poisson sigma model on a manifold with a D-brane and the Poisson sigma model on a supermanifold without branes (or, more properly, with a brane which extends over the whole supermanifold).

Alberto S. Cattaneo Giovanni Felder

A network is a countable, connected graph X viewed as a one-complex, where each edge [x,y]=[y,x] (x,y in X^0, the vertex set) is a copy of the unit interval within the graph's one-skeleton X^1 and is assigned a positive conductance c(xy). A reference "Lebesgue" measure on X^1 is built up by using Lebesgue measure with total mass c(xy) on each edge [x,y]. There are three natural operators on X : the transition operator P acting on functions on X^0 (the reversible Markov chain associated with the conductances), the averaging operator A over spheres of radius 1 on X^1, and the Laplace operator on X^1 (with Kirchhoff conditions weighted by c(.) at the vertices). The relation between the l^2-spectrum of P and the H^2-spectrum of the Laplacian was described by Cattaneo (Mh. Math. 124, 1997). In this paper we describe the relation between the l^2-spectrum of P and the L^2-spectrum of A.

Donald I. Cartwright Wolfgang Woess