The dynamics of social interaction with agents’ heterogeneity

We analyze a class of binary dynamic models inspired by [4] on agents’ choices and social interaction. The main feature of our analysis is that agents are heterogeneous, in particular their attitude to interact with the choices of the other agents changes over time endogenously. Although dynamic approaches to the study of models with heterogeneous agents have been already applied in different fields, to our knowledge a complete study of an endogenously varying population of agents has not yet been pursued. As observed in [3], the main problem is given by the fact that with heterogeneous agents the system may be non reversible. We address these problems, we describe the (possible multiple) steady states of the processes involved, we analyze local and global stability and we discuss the similarities and the differences with respect to the literature. Applications are also provided.heterogeneous agent models, intensity-based models, mean field interactions, random utilities, social interactions.

Identity, reputation and social interaction with an application to sequential voting

We analyze binary choices in a random utility model assuming that the agent's preferences are affected by conformism (with respect to the behavior of the society) and coherence (with respect to his identity). We apply the analysis to sequential voting when voters like to win.identity; reputation; social interaction; random utility models; voting system.

A family of quotients of the Rees algebra

A family of quotient rings of the Rees algebra associated to a commutative ring is studied. This family generalizes both the classical concept of idealization by Nagata and a more recent concept, the amalgamated duplication of a ring. It is shown that several properties of the rings of this family do not depend on the particular member.Comment: 17 pages. To appear on "Communications in Algebra

Arf characters of an algebroid curve

Two algebroid branches are said to be equivalent if they have the same multiplicity sequence. It is known that two algebroid branches $R$ and $T$ are equivalent if and only if their Arf closures, $R'$ and $T'$ have the same value semigroup, which is an Arf numerical semigroup and can be expressed in terms of a finite set of information, a set of characters of the branch. We extend the above equivalence to algebroid curves with $d>1$ branches. An equivalence class is described, in this more general context, by an Arf semigroup, that is not a numerical semigroup, but is a subsemigroup of $\mathbb N^d$. We express this semigroup in terms of a finite set of information, a set of characters of the curve, and apply this result to determine other curves equivalent to a given one.Comment: 17 page

Efficacy of MRI data harmonization in the age of machine learning. A multicenter study across 36 datasets

Pooling publicly-available MRI data from multiple sites allows to assemble extensive groups of subjects, increase statistical power, and promote data reuse with machine learning techniques. The harmonization of multicenter data is necessary to reduce the confounding effect associated with non-biological sources of variability in the data. However, when applied to the entire dataset before machine learning, the harmonization leads to data leakage, because information outside the training set may affect model building, and potentially falsely overestimate performance. We propose a 1) measurement of the efficacy of data harmonization; 2) harmonizer transformer, i.e., an implementation of the ComBat harmonization allowing its encapsulation among the preprocessing steps of a machine learning pipeline, avoiding data leakage. We tested these tools using brain T1-weighted MRI data from 1740 healthy subjects acquired at 36 sites. After harmonization, the site effect was removed or reduced, and we measured the data leakage effect in predicting individual age from MRI data, highlighting that introducing the harmonizer transformer into a machine learning pipeline allows for avoiding data leakage

Spectral imaging and archival data in analyzing the Madonna of the Rabbit painting by Manet and Titian

A concise insight into the outputs provided by the latest prototype of visible-near infrared (VIS-NIR) multispectral scanner (National Research Council-National Institute of Optics, CNR-INO, Italy) is presented. The analytical data acquired on an oil painting Madonna of the Rabbit by É. Manet are described. In this work, the VIS-NIR was complemented with X-ray fluorescence (XRF) mapping for the chemical and spatial characterization of several pigments. The spatially registered VIS-NIR data facilitated their processing by spectral correlation mapping (SCM) and artificial neural network (ANN) algorithm respectively for pigment mapping and improved visibility of pentimenti and of underdrawing style. The data provided several key elements for the comparison with a homonymous original work by Titian studied within the ARCHive LABoratory (ARCHLAB) transnational access project

Betti numbers for numerical semigroup rings

We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra and Applications (V. Ene, E. Miller Eds.

Marco Polo: A near Earth object sample return mission

From Introduction: MARCO POLO is a joint European-Japanese sample return mission to a Near-Earth Object. In late 2007 this mission was selected by ESA, in the framework of COSMIC VISION 2015-2025, for an assessment scheduled to last until mid 2009. This Euro-Asian mission will go to a primitive Near-Earth Object (NEO), such as a C or D type asteroid. The spacecraft will rendezvous with the object, and over an extended period scientifically characterize it at multiple scales and bring samples back to Earth for detailed scientific investigation