A numerical method for Mean Field Games on networks

We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence of the scheme and we also propose a least squares method for the solution of the discrete system. Numerical experiments are carried out

Boulders on asteroid Toutatis as observed by Chang'e-2

Boulders are ubiquitously found on the surfaces of small rocky bodies in the inner solar system and their spatial and size distributions give insight into the geological evolution and collisional history of the parent bodies. Using images acquired by the Chang'e-2 spacecraft, more than 200 boulders have been identified over the imaged area of the near-Earth asteroid Toutatis. The cumulative boulder size frequency distribution (SFD) shows a steep slope of -4.4 $\pm$ 0.1, which is indicative of a high degree of fragmentation. Similar to Itokawa, Toutatis probably has a rubble-pile structure, as most boulders on its surface cannot solely be explained by impact cratering. The significantly steeper slope for Toutatis' boulder SFD compared to Itokawa may imply a different preservation state or diverse formation scenarios. In addition, the cumulative crater SFD has been used to estimate a surface crater retention age of approximately 1.6 $\pm$ 0.3 Gyr.Comment: 12 pages, 4 figure

Mercury's geochronology revised by applying Model Production Functions to Mariner 10 data: geological implications

Model Production Function chronology uses dynamic models of the Main Belt Asteroids (MBAs) and Near Earth Objects (NEOs) to derive the impactor flux to a target body. This is converted into the crater size-frequency-distribution for a specific planetary surface, and calibrated using the radiometric ages of different regions of the Moon's surface. This new approach has been applied to the crater counts on Mariner 10 images of the highlands and of several large impact basins on Mercury. MPF estimates for the plains show younger ages than those of previous chronologies. Assuming a variable uppermost layering of the Hermean crust, the age of the Caloris interior plains may be as young as 3.59 Ga, in agreement with MESSENGER results that imply that long-term volcanism overcame contractional tectonics. The MPF chronology also suggests a variable projectile flux through time, coherent with the MBAs for ancient periods and then gradually comparable also to the NEOs.Comment: Accepted by Journal Geophysical Research Letter

Constraining the Cratering Chronology of Vesta

Vesta has a complex cratering history, with ancient terrains as well as recent large impacts that have led to regional resurfacing. Crater counts can help constrain the relative ages of different units on Vesta's surface, but converting those crater counts to absolute ages requires a chronology function. We present a cratering chronology based on the best current models for the dynamical evolution of asteroid belt, and calibrate it to Vesta using the record of large craters on its surface. While uncertainties remain, our chronology function is broadly consistent with an ancient surface of Vesta as well as other constraints such as the bombardment history of the rest of the inner Solar System and the Ar-Ar age distribution of howardite, eucrite and diogenite (HED) meteorites from Vesta.Comment: Accepted to Planetary and Space Science on May 1, 201

Ontology Learning and Semantic Annotation: a Necessary Symbiosis

Semantic annotation of text requires the dynamic merging of linguistically structured information and a ?world model?, usually represented as a domain-specific ontology. On the other hand, the process of engineering a domain-ontology through semi-automatic ontology learning system requires the availability of a considerable amount of semantically annotated documents. Facing this bootstrapping paradox requires an incremental process of annotation-acquisition-annotation, whereby domain-specific knowledge is acquired from linguistically-annotated texts and then projected back onto texts for extra linguistic information to be annotated and further knowledge layers to be extracted. The presented methodology is a first step in the direction of a full ?virtuous? circle where the semantic annotation platform and the evolving ontology interact in symbiosis. As a case study we have chosen the semantic annotation of product catalogues. We propose a hybrid approach, combining pattern matching techniques to exploit the regular structure of product descriptions in catalogues, and Natural Language Processing techniques which are resorted to analyze natural language descriptions. The semantic annotation involves the access to the ontology, semi-automatically bootstrapped with an ontology learning tool from annotated collections of catalogues

A rescaled method for RBF approximation

In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allow us to consider its error and stability properties

A rescaled method for RBF approximation

A new method to compute stable kernel-based interpolants has been presented by the second and third authors. This rescaled interpolation method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allow us to consider its error and stability properties. First, we prove that the method is an instance of the Shepard\u2019s method, when certain weight functions are used. In particular, the method can reproduce constant functions. Second, it is possible to define a modified set of cardinal functions strictly related to the ones of the not-rescaled kernel. Through these functions, we define a Lebesgue function for the rescaled interpolation process, and study its maximum - the Lebesgue constant - in different settings. Also, a preliminary theoretical result on the estimation of the interpolation error is presented. As an application, we couple our method with a partition of unity algorithm. This setting seems to be the most promising, and we illustrate its behavior with some experiments

A new chronology for the Moon and Mercury

In this paper we present a new method for dating the surface of the Moon, obtained by modeling the incoming flux of impactors and converting it into a size distribution of resulting craters. We compare the results from this model with the standard chronology for the Moon showing their similarities and discrepancies. In particular, we find indications of a non-constant impactor flux in the last 500 Myr and also discuss the implications of our findings for the Late Heavy Bombardment hypothesis. We also show the potential of our model for accurate dating of other inner Solar System bodies, by applying it to Mercury.Comment: 27 pages, 13 figures, 1 table; accepted by A

NLP-based Metadata Extraction for Legal Text Consolidation

The paper describes a system for the automatic consolidation of Italian legislative texts to be used as a support of an editorial consolidating activity and dealing with the following typology of textual amendments: repeal, substitution and integration. The focus of the paper is on the semantic analysis of the textual amendment provisions and the formalized representation of the amendments in terms of metadata. The proposed approach to consolidation is metadata- oriented and based on Natural Language Processing (NLP) techniques: we use XML-based standards for metadata annotation of legislative acts and a flexible NLP architecture for extracting metadata from parsed texts. An evaluation of achieved results is also provided

Acquiring Legal Ontologies from Domain-specific Texts

The paper reports on methodology and preliminary results of a case study in automatically extracting ontological knowledge from Italian legislative texts in the environmental domain. We use a fully-implemented ontology learning system (T2K) that includes a battery of tools for Natural Language Processing (NLP), statistical text analysis and machine language learning. Tools are dynamically integrated to provide an incremental representation of the content of vast repositories of unstructured documents. Evaluated results, however preliminary, are very encouraging, showing the great potential of NLP-powered incremental systems like T2K for accurate large-scale semi?automatic extraction of legal ontologies