Waldschmidt constants for Stanley-Reisner ideals of a class of graphs

In the present note we study Waldschmidt constants of Stanley-Reisner ideals of a hypergraph and a graph with vertices forming a bipyramid over a planar n-gon. The case of the hypergraph has been studied by Bocci and Franci. We reprove their main result. The case of the graph is new. Interestingly, both cases provide series of ideals with Waldschmidt constants descending to 1. It would be interesting to known if there are bounded ascending sequences of Waldschmidt constants.Comment: 7 pages, 2 figure

Waldschmidt constants for Stanley-Reisner ideals of a class of Simplicial Complexes

We study the symbolic powers of the Stanley-Reisner ideal $I_{B_n}$ of a bipyramid $B_n$ over a $n-$gon $Q_n$. Using a combinatorial approach, based on analysis of subtrees in $Q_n$ we compute the Waldschmidt constant of $I_{B_n}$.Comment: 10 pages, 2 figure

Geometry of diagonal-effect models for contingency tables

In this work we study several types of diagonal-effect models for two-way contingency tables in the framework of Algebraic Statistics. We use both toric models and mixture models to encode the different behavior of the diagonal cells. We compute the invariants of these models and we explore their geometrical structure.Comment: 20 page

Osculating spaces to secant varieties

We generalize the classical Terracini's Lemma to higher order osculating spaces to secant varieties. As an application, we address with the so-called Horace method the case of the $d$-Veronese embedding of the projective 3-space

Special effect varieties in higher dimension

Here we introduce the concept of special effect varieties in higher dimension and we generalize to the n-dimensional projective space, n>=3, the two conjectures given in AG/0410527 for the planar case. Finally, we propose some examples on the product of projective spaces and we show how these results fit with the ones of Catalisano, Geramita and Gimigliano.Comment: 24 page

An educational distributed Cosmic Ray detector network based on ArduSiPM

The advent of microcontrollers with enough CPU power and with analog and digital peripherals makes possible to design a complete particle detector with relative acquisition system around one microcontroller chip. The existence of a world wide data infrastructure as internet allows for devising a distributed network of cheap detectors capable to elaborate and send data or respond to settings commands. The internet infrastructure enables to distribute the absolute time (with precision of few milliseconds), to the simple devices far apart, with few milliseconds precision, from a few meters to thousands of kilometres. So it is possible to create a crowdsourcing experiment of citizen science that use small scintillation-based particle detectors to monitor the high energetic cosmic ray and the radiation environment