Rate of decay for the mass ratio of pseudo-holomorphic integral 2-cycles

We consider any pseudo holomorphic integral 2-cycle in an arbitrary almost complex manifold and perform a blow up analysis at an arbitrary point. Building upon a pseudo algebraic blow up (previously introduced by the author) we prove a geometric rate of decay for the mass ratio towards the limiting density, with an explicit exponent of decay expressed in terms of the density of the current at the point.Comment: in Calc. Var. published online (2015

Tangent cones to positive-(1,1) De Rham currents

We consider positive-(1,1) De Rham currents in arbitrary almost complex manifolds and prove the uniqueness of the tangent cone at any point where the density does not have a jump with respect to all of its values in a neighbourhood. Without this assumption, counterexamples to the uniqueness of tangent cones can be produced already in C^n, hence our result is optimal. The key idea is an implementation, for currents in an almost complex setting, of the classical blow up of curves in algebraic or symplectic geometry. Unlike the classical approach in C^n, we cannot rely on plurisubharmonic potentials.Comment: 37 pages, 2 figure

Reachability Analysis of Time Basic Petri Nets: a Time Coverage Approach

We introduce a technique for reachability analysis of Time-Basic (TB) Petri nets, a powerful formalism for real- time systems where time constraints are expressed as intervals, representing possible transition firing times, whose bounds are functions of marking's time description. The technique consists of building a symbolic reachability graph relying on a sort of time coverage, and overcomes the limitations of the only available analyzer for TB nets, based in turn on a time-bounded inspection of a (possibly infinite) reachability-tree. The graph construction algorithm has been automated by a tool-set, briefly described in the paper together with its main functionality and analysis capability. A running example is used throughout the paper to sketch the symbolic graph construction. A use case describing a small real system - that the running example is an excerpt from - has been employed to benchmark the technique and the tool-set. The main outcome of this test are also presented in the paper. Ongoing work, in the perspective of integrating with a model-checking engine, is shortly discussed.Comment: 8 pages, submitted to conference for publicatio

Approximation of the Helfrich's functional via Diffuse Interfaces

We give a rigorous proof of the approximability of the so-called Helfrich's functional via diffuse interfaces, under a constraint on the ratio between the bending rigidity and the Gauss-rigidity

Why not in your Backyard? On the Location and Size of a Public Facility

In this paper, we tackle the issue of locating a public facility which provides a public good in a closed and populated territory. This facility generates differentiated benefits to neighborhoods depending on their distance from it. In the case of a Nimby facility, the smaller is the distance, the lower is the individual benefit. The opposite is true in the case of an anti-Nimby facility. We first characterize the optimal location which would be chosen by a social planner. Then we introduce a common-agency lobbying game, where agents attempt to influence the location and provision decisions by the government. Some interesting results arise in the case where only a subset of neighborhoods lobby. First, the solution of the lobbying game can replicate the optimal solution. Second, under-provision and over-provision of the public good may be obtained both in the Nimby and the anti-Nimby cases. The provision outcome depends on the presence of either a congestion effect or an agglomeration effect. Third, some non-lobbying neighborhoods may be better off than in the case where all neighborhoods lobby, which raises the possibility of free-riding at the lobbying stage.