an iterative scheme to compute size probabilities in random graphs and branching processes

We deal with a functional equation that plays an important role in random graphs and in branching processes. In branching processes, the functional equation relates offspring probabilities to population size probabilities, while in random graph it relates degree probabilities to small component size probabilities. We present an iterative scheme that allows computing the size probabilities numerically. It is also theoretically possible to invert the iteration, although this inverse iteration is numerically unstable

Dynamic programming and minimum risk paths

This paper addresses the problem of computing minimum risk paths by taking as objective the expected accident cost. The computation is based on a dynamic programming formulation which can be considered an extension of usual dynamic programming models: path costs are recursively computed via functions which are assumed to be monotonic. A large part of the paper is devoted to analyze in detail this formulation and provide some new results. Based on the dynamic programming model a linear programming model is also presented to compute minimum risk paths. This formulation turns out to be useful in solving a biobjective version of the problem, in which also expected travel length is taken into consideration. This leads to define nondominated mixed strategies. Finally it is shown how to extend the basic updating device of dynamic programming in order to enumerate all nondominated paths

A Facility Location Model for Air Pollution Detection

We describe mathematical models and practical algorithms for a problem concerned with monitoring the air pollution in a large city. We have worked on this problem within a project for assessing the air quality in the city of Rome by placing a certain number of sensors on some of the city buses. We cast the problem as a facility location model. By reducing the large number of data variables and constraints, we were able to solve to optimality the resulting MILP model within minutes. Furthermore, we designed a genetic algorithm whose solutions were on average very close to the optimal ones. In our computational experiments we studied the placement of sensors on 187 candidate bus routes. We considered the coverage provided by 10 up to 60 sensors

De Finetti and Markowitz mean variance approach to reinsurance and portfolio selection problems: a comparison

Based on a critical analysis of de Finetti's paper, where the mean variance approach in finance was early introduced to deal with a reinsurance problem, we offer an alternative interpretative key of such an approach to the standard portfolio selection one. We discuss analogies and differences between de Finetti's and Markowitz's geometrical approaches

Gene variants with suicidal risk in a sample of subjects with chronic migraine and affective temperamental dysregulation

BACKGROUND: Risk factors for suicide are at least partially heritable and functional polymorphisms of targeted genes have been suggested to be implicated in the pathogenesis of this phenomenon. However, other studies examining the association between specific gene variants and suicide revealed inconsistent findings. We aims to evaluate the possible association between MAO-A3, CYP1A2*1F and GNB3 gene variants, hopelessness and suicidal risk in a sample of subjects with chronic migraine and affective temperamental dysregulation. METHODS: 56 women were genotyped for MAO-A3, CYP1A2*1F and GNB3 gene variants. Participants were also assessed using Beck Hopelessness Scale (BHS), the Temperament Evaluation of the Memphis, Pisa, Paris and San Diego-Autoquestionnaire (TEMPS-A), and the Suicidal History Self-Rating Screening Scale (SHSS). RESULTS: Patients with higher total scores on affective dysregulated temperaments are more likely to have higher BHS (11.27 +/- 5.54 vs. 5.73 +/- 3.81; t19.20 = -3.57; p = 9 indicating high levels of hopelessness. No association was found between MAO-A3, CYP1A2*1F and GNB3 gene variants and suicidal risk as assessed by BHS and SHSS. CONCLUSIONS: This study did not sustain the association between MAO-A3, CYP1A2*1F and GNB3 gene variants and increased suicidal risk in patients with chronic migraine and affective temperamental dysregulation. Further studies investigating the gene-environment interaction or focusing on other genetic risk factors involved in suicidal behaviour are needed

Deepening inside the pictorial layers of Etruscan sarcophagus of Hasti Afunei: An innovative micro-sampling technique for Raman/SERS analyses

The Hasti Afunei sarcophagus is a large Etruscan urn, made up of two chalky alabaster monoliths. Dated from the last quarter of the third century BC, it was found in 1826 in the small town of Chiusi (Tuscany- Il Colle place) by a landowner, Pietro Bonci Casuccini, who made it part of his private collection. The noble owner’s collection was sold in 1865 to the Royal Museum of Palermo (today under the name of Antonino Salinas Regional Archaeological Museum), where it is still displayed. The sarcophagus is characterized by a complex iconography that is meticulously illustrated through an excellent sculptural technique, despite having subjected to anthropic degradation and numerous restorative actions during the last century. During the restoration campaign carried out between 2016 and 2017, a targeted diagnostic campaign was carried out to identify the constituent materials of the artefact, the pigments employed and the executive technique, in order to get an overall picture of conservation status and conservative criticalities. In particular, this last intervention has allowed the use of the innovative micro-sampling technique, patented by the Cultural Heritage research group of Sapienza, in order to identify the employee of lake pigments through SERS analyses. Together with this analysis, Raman and NMR technique have completed the information requested by restorers, for what concerns the wax employed as protective layers, and allowed to rebuild the conservation history of the sarcophagus. In fact, together with the identification of red ocher and yellow ocher, carbon black, Egyptian blue and madder lake, pigments compatible with the historical period of the work, modern pigments (probably green Paris, chrome orange, barium yellow, blue phtalocyanine) have been recognized, attributable with not documented intervention during the eighteenth and twentieth centuries. © 2019 by the authors