We show that fluid stationary models are able to reproduce the observed, negative vertical gradient of the rotation velocity of the extra-planar gas in spiral galaxies. We have constructed models based on the simple condition that the pressure of the medium does not depend on density alone (baroclinic instead of barotropic solutions: isodensity and isothermal surfaces do not coincide). As an illustration, we have successfully applied our method to reproduce the observed velocity gradient of the lagging gaseous halo of NGC 891. The fluid stationary models discussed here can describe a hot homogeneous medium as well as a "gas" made of discrete, cold HI clouds with an isotropic velocity dispersion distribution. Although the method presented here generates a density and velocity field consistent with observational constraints, the stability of these configurations remains an open question.

M. Barnabè L. Ciotti F. Fraternali R. Sancisi

Routing games are amongst the most well studied domains of game theory. How relevant are these pen-and-paper calculations to understanding the reality of everyday traffic routing? We focus on a semantically rich dataset that captures detailed information about the daily behavior of thousands of Singaporean commuters and examine the following basic questions: (i) Does the traffic equilibrate? (ii) Is the system behavior consistent with latency minimizing agents? (iii) Is the resulting system efficient? In order to capture the efficiency of the traffic network in a way that agrees with our everyday intuition we introduce a new metric, the stress of catastrophe, which reflects the combined inefficiencies of both tragedy of the commons as well as price of anarchy effects.

Barnabé Monnot Francisco Benita Georgios Piliouras

The main goal of this paper is to study the structure of the graded algebra associated to a valuation. More specifically, we prove that the associated graded algebra ${\rm gr}_v(R)$ of a subring $(R,\mathfrak{m})$ of a valuation ring $\mathcal{O}_v$, for which $Kv:=\mathcal{O}_v / \mathfrak{m}_v=R / \mathfrak{m}$, is isomorphic to $Kv[t^{v(R)}]$, where the multiplication is given by a twisting. We show that this twisted multiplication can be chosen to be the usual one in the cases where the value group is free or the residue field is closed by radicals. We also present an example that shows that the isomorphism (with the trivial twisting) does not have to exist.

M. S. Barnabé J. Novacoski M. Spivakovsky

The combination of strong gravitational lensing and stellar kinematics provides a powerful and robust method to investigate the mass and dynamical structure of early-type galaxies. We demonstrate this approach by analysing two massive ellipticals from the XLENS Survey for which both high-resolution HST imaging and X-Shooter spectroscopic observations are available. We adopt a flexible axisymmetric two-component mass model for the lens galaxies, consisting of a generalised NFW dark halo and a realistic self-gravitating stellar mass distribution. For both systems, we put constraints on the dark halo inner structure and flattening, and we find that they are dominated by the luminous component within one effective radius. By comparing the tight inferences on the stellar mass from the combined lensing and dynamics analysis with the values obtained from stellar population studies, we conclude that both galaxies are characterised by a Salpeter-like stellar initial mass function.

Matteo Barnabè Chiara Spiniello Léon V. E. Koopmans

Routing games are one of the most successful domains of application of game theory. It is well understood that simple dynamics converge to equilibria, whose performance is nearly optimal regardless of the size of the network or the number of agents. These strong theoretical assertions prompt a natural question: How well do these pen-and-paper calculations agree with the reality of everyday traffic routing? We focus on a semantically rich dataset from Singapore's National Science Experiment that captures detailed information about the daily behavior of thousands of Singaporean students. Using this dataset, we can identify the routes as well as the modes of transportation used by the students, e.g. car (driving or being driven to school) versus bus or metro, estimate source and sink destinations (home-school) and trip duration, as well as their mode-dependent available routes. We quantify both the system and individual optimality. Our estimate of the Empirical Price of Anarchy lies between 1.11 and 1.22. Individually, the typical behavior is consistent from day to day and nearly optimal, with low regret for not deviating to alternative paths.

Barnabé Monnot Francisco Benita Georgios Piliouras

Growth in bacterial populations generally depends on the environment (availability and quality of nutrients, presence of a toxic inhibitor, product inhibition..). Here, we build a model to describe the action of a bacteriostatic antibiotic, assuming that this drug inhibits an essential autocatalytic cycle involved in the cell metabolism. The model recovers known growth laws, can describe various types of antibiotics and confirms the existence of two distinct regimes of growth-dependent susceptibility, previously identified only for ribosome targeting antibiotics. Interestingly, below a certain threshold in terms of antibiotic concentration, a coexistence between two values of the growth rate is possible, which has also been observed experimentally. Interesting extensions of the model include the antagonistic effect of two drugs targeting different autocatalytic cycles or the production of an inhibiting waste.

Barnabe Ledoux David Lacoste

We show how to construct families of stationary hydrodynamical configurations that reproduce the observed vertical gradient of the rotation velocity of the extra-planar gas in spiral galaxies. We then present a simple model for the lagging halo of the spiral galaxy NGC 891, which is in agreement with the HI observations. Our method is based on well known properties of baroclinic solutions, and it is an elementary application of a much more general and flexible method.

M. Barnabe' L. Ciotti F. Fraternali R. Sancisi

The combination of two-dimensional kinematics and gravitational lens modelling permits detailed reconstruction of the phase-space structure of early-type galaxies and sets constraints on the dark-matter distribution in their inner regions. We describe a project which combines integral-field spectroscopy from an ESO Large Programme using VIMOS on the VLT with deep HST ACS and NICMOS images to study a sample of 17 early-type lens galaxies at redshifts between 0.1 and 0.3, drawn from the Sloan Lens ACS survey (SLACS).

Oliver Czoske Matteo Barnabe Leon Koopmans

A pair $(\mathcal{A},\mathcal{B})$ of families of subsets of an $n$-element set is called cancellative if whenever $A,A'\in\mathcal{A}$ and $B\in\mathcal{B}$ satisfy $A\cup B=A'\cup B$, then $A=A'$, and whenever $A\in\mathcal{A}$ and $B,B'\in\mathcal{B}$ satisfy $A\cup B=A\cup B'$, then $B=B'$. It is known that there exist cancellative pairs with $|\mathcal{A}||\mathcal{B}|$ about $2.25^n$, whereas the best known upper bound on this quantity is $2.3264^n$. In this paper we improve this upper bound to $2.2682^n$. Our result also improves the best known upper bound for Simonyi's sandglass conjecture for set systems.

Barnabás Janzer

Jorge-Koutrofiotis and Pigola-Rigoli-Setti proved sharp sectional curvature estimates for extrinsically bounded submanifolds. Alias, Bessa and Montenegro showed that these estimates hold on properly immersed cylindrically bounded submanifolds. On the other hand, Alias, Bessa and Dajczer proved sharp mean curvature estimates for properly immersed cylindrically bounded submanifolds. In this paper we prove these sectional and mean curvature estimates for a larger class of submanifolds, the properly immersed $\phi$-bounded submanifolds.

G. Pacelli Bessa Barnabe P. Lima Leandro F. Pessoa