On the Fueling of Massive Black Holes and the Properties of their Host Spheroids

We study the relation between nuclear massive black holes and their host spheroid gravitational potential. Using simple models, we analyze how gas is expected to be transported in the nuclear regions of galaxies. When we couple it with the expected gas lifetime given by the Kennicutt-Schmidt Law, this naturally leads to the `M_BH - M_virial' and `M_BH - sigma' relations. We also numerically test, using AMR simulations, our simple models for the mass transport with satisfactory results.Comment: Reduced version that fit the 4-page limit. In press ApJ Letter

Comments on "State equation for the three-dimensional system of 'collapsing' hard spheres"

A recent paper [I. Klebanov et al. \emph{Mod. Phys. Lett. B} \textbf{22} (2008) 3153; arXiv:0712.0433] claims that the exact solution of the Percus-Yevick (PY) integral equation for a system of hard spheres plus a step potential is obtained. The aim of this paper is to show that Klebanov et al.'s result is incompatible with the PY equation since it violates two known cases: the low-density limit and the hard-sphere limit.Comment: 4 pages; v2: title chang

On the equivalence between the energy and virial routes to the equation of state of hard-sphere fluids

The energy route to the equation of state of hard-sphere fluids is ill-defined since the internal energy is just that of an ideal gas and thus it is independent of density. It is shown that this ambiguity can be avoided by considering a square-shoulder interaction and taking the limit of vanishing shoulder width. The resulting hard-sphere equation of state coincides exactly with the one obtained through the virial route. Therefore, the energy and virial routes to the equation of state of hard-sphere fluids can be considered as equivalent.Comment: 2 page

Bayesian Analysis of ODE's: solver optimal accuracy and Bayes factors

In most relevant cases in the Bayesian analysis of ODE inverse problems, a numerical solver needs to be used. Therefore, we cannot work with the exact theoretical posterior distribution but only with an approximate posterior deriving from the error in the numerical solver. To compare a numerical and the theoretical posterior distributions we propose to use Bayes Factors (BF), considering both of them as models for the data at hand. We prove that the theoretical vs a numerical posterior BF tends to 1, in the same order (of the step size used) as the numerical forward map solver does. For higher order solvers (eg. Runge-Kutta) the Bayes Factor is already nearly 1 for step sizes that would take far less computational effort. Considerable CPU time may be saved by using coarser solvers that nevertheless produce practically error free posteriors. Two examples are presented where nearly 90% CPU time is saved while all inference results are identical to using a solver with a much finer time step.Comment: 28 pages, 6 figure

Explicit Soliton for the Laplacian Co-Flow on a Solvmanifold

We apply the general Ansatz in geometric flows on homogeneous spaces proposed by Jorge Lauret for the Laplacian co-flow of invariant $G_2$-structures on a Lie group, finding an explicit soliton on a particular almost Abelian $7$-manifold.Comment: Minor corrections, proof's Lemma 4.1 modified. To appear in the S\~ao Paulo Journal of mathematical scienc

Full-vector analysis of a realistic photonic crystal fiber

We analyze the guiding problem in a realistic photonic crystal fiber using a novel full-vector modal technique, a biorthogonal modal method based on the nonselfadjoint character of the electromagnetic propagation in a fiber. Dispersion curves of guided modes for different fiber structural parameters are calculated along with the 2D transverse intensity distribution of the fundamental mode. Our results match those achieved in recent experiments, where the feasibility of this type of fiber was shown.Comment: 3 figures, submitted to Optics Letter

Biomechanical analysis of a cranial Patient Specific Implant on the interface with the bone using the Finite Element Method

- New advance technologies based on reverse engineering , design and additive manufacturing, have expanded design capabilities for biomedical applications to include Patient Specific Implants (PSI). This change in design paradigms needs advanced tools to assess the mechanical performance of the product, and simulate the impact on the patient. In this work, we perform a structural analysis on the interface of a cranial PSI under static loading conditions. Based on those simulations, we have identified the regions with high stress and strain and checked the failure criteria both in the implant and the skull. We evaluate the quality of the design of the implant and determine their response given different materials, in order to ensure optimality of the final product to be manufactured

Can Network Analysis Techniques help to Predict Design Dependencies? An Initial Study

The degree of dependencies among the modules of a software system is a key attribute to characterize its design structure and its ability to evolve over time. Several design problems are often correlated with undesired dependencies among modules. Being able to anticipate those problems is important for developers, so they can plan early for maintenance and refactoring efforts. However, existing tools are limited to detecting undesired dependencies once they appeared in the system. In this work, we investigate whether module dependencies can be predicted (before they actually appear). Since the module structure can be regarded as a network, i.e, a dependency graph, we leverage on network features to analyze the dynamics of such a structure. In particular, we apply link prediction techniques for this task. We conducted an evaluation on two Java projects across several versions, using link prediction and machine learning techniques, and assessed their performance for identifying new dependencies from a project version to the next one. The results, although preliminary, show that the link prediction approach is feasible for package dependencies. Also, this work opens opportunities for further development of software-specific strategies for dependency prediction.Comment: Accepted at ICSA 201