Convex Clustering via Optimal Mass Transport

We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we consider is that of approximating sample distributions by ones with sparse support. This provides a new viewpoint to clustering. We propose different relaxations of a cardinality function which penalizes the size of the support set. We establish that a certain relaxation provides the tightest convex lower approximation to the cardinality penalty. We compare the performance of alternative relaxations on a numerical study on clustering.Comment: 12 pages, 12 figure

Mars Encounters cause fresh surfaces on some near-Earth asteroids

All airless bodies are subject to the space environment, and spectral differences between asteroids and meteorites suggest many asteroids become weathered on very short (<1My) timescales. The spectra of some asteroids, particularly Q-types, indicate surfaces that appear young and fresh, implying they have been recently been exposed. Previous work found that Earth encounters were the dominant freshening mechanism and could be responsible for all near-Earth object (NEO) Q-types. In this work we increase the known NEO Q-type sample of by a factor of three. We present the orbital distributions of 64 Q-type near-Earth asteroids, and seek to determine the dominant mechanisms for refreshing their surfaces. Our sample reveals two important results: i) the relatively steady fraction of Q-types with increasing semi-major axis and ii) the existence of Q-type near-Earth asteroids with Minimum Orbit Intersection Distances (MOID) that do not have orbit solutions that cross Earth. Both of these are evidence that Earth-crossing is not the only scenario by which NEO Q-types are freshened. The high Earth-MOID asteroids represent 10% of the Q-type population and all are in Amor orbits. While surface refreshing could also be caused by Main Belt collisions or mass shedding from YORP spinup, all high Earth-MOID Q-types have the possibility of encounters with Mars indicating Mars could be responsible for a significant fraction of NEOs with fresh surfaces.Comment: Accepted for publication in Icarus -- 14 pages, 8 figures, 1 table, 2 appendice

Rotationally Resolved Spectroscopy of Asteroid Pairs: No Spectral Variation Suggests Fission is followed by Settling of Dust

We examine the spectral properties of asteroid pairs that were disrupted in the last 2 Myrs to examine whether the site of the fission can be revealed. We studied the possibility that the sub-surface material, perhaps on one hemisphere, has spectral characteristics differing from the original weathered surface, by performing rotationally-resolved spectroscopic observations to look for local variations as the asteroid rotates. We observed 11 asteroids in pairs in the near-IR and visible range. Photometry was also conducted to determine the rotational phases of a spectrum on the asteroid lightcurves. We do not detect any rotational spectral variations within the signal-to-noise, which allow us to constrain the extent of any existing surface heterogeneity. For each observed spectrum of a longitudinal segment of an asteroid, we estimate the maximal size of an un-detected "spot" with a spectral signature different than the average. For 5 asteroids the maximal diameter of such a spot is smaller by a factor of two than the diameter of the secondary member. Therefore, the site of the fission is larger than any area with a unique spectral parameters and the site of the fission does not have a unique spectrum. In the case of an S-complex asteroid, where the site of fission is expected to present non-weathered spectra, a lack of a fission spot can be explained if the rotational-fission process is followed by the spread of dust that re-accumulates on the primary asteroid and covers it homogeneously. This is demonstrated for the young asteroid 6070 that presents an Sq-type spectrum while its inner material, that is presumably revealed on the surface of its secondary member, 54827, has a fresher, Q-type spectrum. The spread of dust observed in the disruption event of asteroid P/2013 R3, might be an example of such a process and an indication that it was indeed formed in a rotational-fission event.Comment: 16 pages, 15 figures, 6 Tables. Accepted for publication in Icaru

Opinion dynamics with disagreement and modulated information

Opinion dynamics concerns social processes through which populations or groups of individuals agree or disagree on specific issues. As such, modelling opinion dynamics represents an important research area that has been progressively acquiring relevance in many different domains. Existing approaches have mostly represented opinions through discrete binary or continuous variables by exploring a whole panoply of cases: e.g. independence, noise, external effects, multiple issues. In most of these cases the crucial ingredient is an attractive dynamics through which similar or similar enough agents get closer. Only rarely the possibility of explicit disagreement has been taken into account (i.e., the possibility for a repulsive interaction among individuals' opinions), and mostly for discrete or 1-dimensional opinions, through the introduction of additional model parameters. Here we introduce a new model of opinion formation, which focuses on the interplay between the possibility of explicit disagreement, modulated in a self-consistent way by the existing opinions' overlaps between the interacting individuals, and the effect of external information on the system. Opinions are modelled as a vector of continuous variables related to multiple possible choices for an issue. Information can be modulated to account for promoting multiple possible choices. Numerical results show that extreme information results in segregation and has a limited effect on the population, while milder messages have better success and a cohesion effect. Additionally, the initial condition plays an important role, with the population forming one or multiple clusters based on the initial average similarity between individuals, with a transition point depending on the number of opinion choices

Seismic vulnerability assessment on a territorial scale based on a Bayesian approach

Italian historical centres are mostly characterized by aggregate buildings. As defined by the Italian codes (Norme Tecniche per le Costruzioni 2008 and Circolare n. 617), the analysis of the most representative local mechanisms of collapse must be performed in order to assess their vulnerability. In this article, the out-of-plane local mechanisms of collapse analysis is implemented by applying a new method of analysis based on a probabilistic approach. Usually information which are necessary for the implementation of the local mechanisms analyses are affected by uncertainty or are missing, therefore in lots of cases it is only possible to hypothesize them on the basis of the other buildings information collected during the on-site survey. In this context, the implementation of a Bayesian approach allows to deduce buildings lacking information (i.e. wall thickness and interstorey height) starting from certain collected data (i.e. facades height). The historical centre of Timisoara (Romania) is selected as the case study for the implementation of this new method of analysis, given the extension of the on-site survey already carried out in the area (information about more than 200 structural units have been collected) and the seismic vulnerability assessment on an urban scale already performed by applying a traditional method. Results obtained by adopting the two approaches are then compared and a validation and a calibration of the new one is carried out

Unexpected D-type Interlopers in the Inner Main Belt

Very red featureless asteroids (spectroscopic D-types) are expected to have formed in the outer solar system far from the sun. They comprise the majority of asteroids in the Jupiter Trojan population, and are also commonly found in the outer main belt and among Hildas. The first evidence for D-types in the inner and middle parts of the main belt was seen in the Sloan Digital Sky Survey (SDSS). Here we report follow-up observations of SDSS D-type candidates in the near-infrared. Based on follow up observations of 13 SDSS D-type candidates, we find a ~20% positive confirmation rate. Known inner belt D-types range in diameter from roughly 7 to 30 kilometers. Based on these detections we estimate there are ~100 inner belt D-types with diameters between 2.5 and 20km. The lower and upper limits for total mass of inner belt D-types is 2x$10^{16}$ kg to 2x$10^{17}$ kg which represents 0.01% to 0.1% of the mass of the inner belt. The inner belt D-types have albedos at or above the upper end typical for D-types which raises the question as to whether these inner belt bodies represent only a subset of D-types, they have been altered by external factors such as weathering processes, or if they are compositionally distinct from other D-types. All D-types and candidates have diameters less than 30km, yet there is no obvious parent body in the inner belt. Dynamical models have yet to show how D-types originating from the outer solar system could penetrate into the inner reaches of the Main Belt under current scenarios of planet formation and subsequent Yarkovsky drift.Comment: 16 pages, 3 figures, 4 tables -- accepted for publication in Icaru