Michel Henon, a playfull and simplifying mind

Several chapters in this book present various aspects of Michel Henon's scientific acheivements that spread over a large range of subjects, and yet managed to make deep contributions to most of them. The authors of these chapters make a much better job at demonstrating the big advancements that Michel Henon allowed in these fields than I could ever do. Here I rather present some facets of his personnality that most appealed to me. Michel Henon was a reserved person, almost shy, so it was not obvious for a young student to grasp the profoundness of his insight and what a marvelous advisor he could be. The two most prominent aspects of his mind, in my view, were his ability to simplify any scientific question to its core complexity, and to find the fun and amusing part in his everyday work, even in the tiniest details of his scientific investigations.Comment: Invited talk at the "hommage a Michel Henon" conference held at the "Institut Henri Poincare" Paris, GRAVASCO trimestre, autumn 2013. Proceeding by Hermann Press, editors: Jean-Michel Alimi, Roya Mohayaee, Jerome Perez. Videos of all talks are available at: https://www.youtube.com/playlist?list=PL9kd4mpdvWcBLrN8u04IZW6-akNgLG7-

Polynomial approximation of Poincare maps for Hamiltonian system

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps

SQL Query Completion for Data Exploration

Within the big data tsunami, relational databases and SQL are still there and remain mandatory in most of cases for accessing data. On the one hand, SQL is easy-to-use by non specialists and allows to identify pertinent initial data at the very beginning of the data exploration process. On the other hand, it is not always so easy to formulate SQL queries: nowadays, it is more and more frequent to have several databases available for one application domain, some of them with hundreds of tables and/or attributes. Identifying the pertinent conditions to select the desired data, or even identifying relevant attributes is far from trivial. To make it easier to write SQL queries, we propose the notion of SQL query completion: given a query, it suggests additional conditions to be added to its WHERE clause. This completion is semantic, as it relies on the data from the database, unlike current completion tools that are mostly syntactic. Since the process can be repeated over and over again -- until the data analyst reaches her data of interest --, SQL query completion facilitates the exploration of databases. SQL query completion has been implemented in a SQL editor on top of a database management system. For the evaluation, two questions need to be studied: first, does the completion speed up the writing of SQL queries? Second , is the completion easily adopted by users? A thorough experiment has been conducted on a group of 70 computer science students divided in two groups (one with the completion and the other one without) to answer those questions. The results are positive and very promising

Extended Dualization: Application to Maximal Pattern Mining

International audienceThe dualization in arbitrary posets is a well-studied problem in combinatorial enumeration and is a crucial step in many applications in logics, databases, artificial intelligence and pattern mining.The objective of this paper is to study reductions of the dualization problem on arbitrary posets to the dualization problem on boolean lattices, for which output quasi-polynomial time algorithms exist. Quasi-polynomial time algorithms are algorithms which run in no(logn) where n is the size of the input and output. We introduce convex embedding and poset reflection as key notions to characterize such reductions. As a consequence, we identify posets, which are not boolean lattices, for which the dualization problem remains in quasi-polynomial time and propose a classification of posets with respect to dualization.From these results, we study how they can be applied to maximal pattern mining problems. We deduce a new classification of pattern mining problems and we point out how known problems involving sequences and conjunctive queries patterns, fit into this classification. Finally, we explain how to adapt the seminal Dualize & Advance algorithm to deal with such patterns.As far as we know, this is the first contribution to explicit non-trivial reductions for studying the hardness of maximal pattern mining problems and to extend the Dualize & Advance algorithm for complex patterns

Expectations for the Deep Impact collision from cometary nuclei modelling

Using the cometary nucleus model developed by Espinasse et al. (1991), we calculate the thermodynamical evolution of Comet 9P/Tempel 1 over a period of 360 years. Starting from an initially amorphous cometary nucleus which incorporates an icy mixture of H2O and CO, we show that, at the time of Deep Impact collision, the crater is expected to form at depths where ice is in its crystalline form. Hence, the subsurface exposed to space should not be primordial. We also attempt an order-of-magnitude estimate of the heating and material ablation effects on the crater activity caused by the 370 Kg projectile released by the DI spacecraft. We thus show that heating effects play no role in the evolution of crater activity. We calculate that the CO production rate from the impacted region should be about 300-400 times higher from the crater resulting from the impact with a 35 m ablation than over the unperturbed nucleus in the immediate post-impact period. We also show that the H2O production rate is decreased by several orders of magnitude at the crater base just after ablation

Dualization on Partially Ordered Sets: Preliminary Results

International audienceThe dualization problem on arbitrary posets is a crucial step in many applications in logics, databases, artificial intelligence and pattern mining. The objective of this paper is to study reductions of the dualization problem on arbitrary posets to the dualization problem on boolean lattices, for which output quasi-polynomial time algorithms exist. We introduce convex embedding and poset reflection as key notions to characterize such reductions. As a consequence, we identify posets, which are not boolean lattices, for which the dualization problem remains quasi-polynomial and propose a classification of posets with respect to dualization. As far as we know, this is the first contribution to explicit non-trivial reductions for studying the hardness of dualization problems on arbitrary posets

KBO binaries: are they really primordial ?

Given the large orbital separation and high satellite-to-primary mass ratio of all known Kuiper Belt Object (KBO) binaries, it is important to reassess their stability as bound pairs with respect to several disruptive mechanisms. Besides the classical shattering and dispersing of the secondary due to a high-velocity impact, we considered the possibility that the secondary is kicked off its orbit by a direct collision of a small impactor, or that it is gravitationally perturbed due to the close approach of a somewhat larger TNO. Depending on the values for the size/mass/separation of the binaries that we used, 2 or 3 of the 8 pairs can be dispersed in a timescale shorter than the age of the solar system in the current rarefied environment. A contemporary formation scenario could explain why we still observe these binaries, but no convincing mechanism has been proposed to date. The primordial formation scenarios, which seem to be the only viable ones, must be revised to increase the formation efficiency in order to account for this high dispersal rate. Objects like the large-separatioKBO binary n2001 QW$_{322}$ must have been initially an order of magnitude more numerous. If the KBO binaries are indeed primordial, then we show that the mass depletion of the Kuiper belt cannot result from collisional grinding, but must rather be due to dynamical ejection.Comment: Submitted to Icarus, Mai 9th, 200

Carbon-rich planet formation in a solar composition disk

The C--to--O ratio is a crucial determinant of the chemical properties of planets. The recent observation of WASP 12b, a giant planet with a C/O value larger than that estimated for its host star, poses a conundrum for understanding the origin of this elemental ratio in any given planetary system. In this paper, we propose a mechanism for enhancing the value of C/O in the disk through the transport and distribution of volatiles. We construct a model that computes the abundances of major C and O bearing volatiles under the influence of gas drag, sublimation, vapor diffusion, condensation and coagulation in a multi--iceline 1+1D protoplanetary disk. We find a gradual depletion in water and carbon monoxide vapors inside the water's iceline with carbon monoxide depleting slower than water. This effect increases the gaseous C/O and decreases the C/H ratio in this region to values similar to those found in WASP 12b's day side atmosphere. Giant planets whose envelopes were accreted inside the water's iceline should then display C/O values larger than those of their parent stars, making them members of the class of so-called ``carbon-rich planets''.Comment: 8 pages, 4 figures, accepted for publication Ap