Towards an analytical theory of the third-body problem for highly elliptical orbits

When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon as the altitude of the satellite becomes high, which is the case around the apocentre of this type of orbit. For several reasons, the traditional tools of celestial mechanics are not well adapted to the particular dynamic of highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and therefore limited to quasi-circular orbits [17, 25]. On the other hand, the time-dependency due to the motion of the third-body is often neglected. We propose several tools to overcome these limitations. Firstly, we have expanded the disturbing function into a finite polynomial using Fourier expansions of elliptic motion functions in multiple of the satellite's eccentric anomaly (instead of the mean anomaly) and involving Hansen-like coefficients. Next, we show how to perform a normalization of the expanded Hamiltonian by means of a time-dependent Lie transformation which aims to eliminate periodic terms. The difficulty lies in the fact that the generator of the transformation must be computed by solving a partial differential equation involving variables which are linear with time and the eccentric anomaly which is not time linear. We propose to solve this equation by means of an iterative process.Comment: Proceedings of the International Symposium on Orbit Propagation and Determination - Challenges for Orbit Determination and the Dynamics of Artificial Celestial Bodies and Space Debris, Lille, France, 201

Systolic geometry and simplicial complexity for groups

Twenty years ago Gromov asked about how large is the set of isomorphism classes of groups whose systolic area is bounded from above. This article introduces a new combinatorial invariant for finitely presentable groups called {\it simplicial complexity} that allows to obtain a quite satisfactory answer to his question. Using this new complexity, we also derive new results on systolic area for groups that specify its topological behaviour.Comment: 35 pages, 9 figure

Certifying floating-point implementations using Gappa

High confidence in floating-point programs requires proving numerical properties of final and intermediate values. One may need to guarantee that a value stays within some range, or that the error relative to some ideal value is well bounded. Such work may require several lines of proof for each line of code, and will usually be broken by the smallest change to the code (e.g. for maintenance or optimization purpose). Certifying these programs by hand is therefore very tedious and error-prone. This article discusses the use of the Gappa proof assistant in this context. Gappa has two main advantages over previous approaches: Its input format is very close to the actual C code to validate, and it automates error evaluation and propagation using interval arithmetic. Besides, it can be used to incrementally prove complex mathematical properties pertaining to the C code. Yet it does not require any specific knowledge about automatic theorem proving, and thus is accessible to a wide community. Moreover, Gappa may generate a formal proof of the results that can be checked independently by a lower-level proof assistant like Coq, hence providing an even higher confidence in the certification of the numerical code. The article demonstrates the use of this tool on a real-size example, an elementary function with correctly rounded output

Conditions socio-environnementales pour la réhabilitation de la biodiversité ordinaire

International audienceOur paper presents the state of our research on the socio-environmental conditions for the rehabilitation of common biodiversity-CLEVERT Program. The participation of local populations, on a district scale, in the public debates about the maintenance or the restoration of functional ecosystems is now an imperative of public policies. The originality of the program is based on a long term presence on the field, an easy implementation of the protocols and sessions of participative cartography. Our purpose /objective is to understand on what social configurations are based the conservation projects and to assess if the awareness of ecological issues is better taken into account in a context of local empowerment. Our paper has four sections: summarized account of ethno ecological data of the three fields, correlation of social and environmental data, analysis of the favorable factors regarding the co-construction of knowledge, mutual relations amongst the disciplines involved (anthropology, ecology and geography). MOTS CLES Sciences participatives, biodiversité ordinaire, échelle communale, populations locales.Notre exposé est un état des recherches portant sur le programme « conditions socio-environnementales pour la réhabilitation de la biodiversité ordinaire » – CLEVERT. La participation des populations locales, à l'échelle communale, aux débats publics portant sur le maintien ou la restauration d'écosystèmes fonctionnels, est désormais incontournable. L'originalité du programme repose sur le fort investissement des équipes scientifiques, la clarté des protocoles, la cartographie participative. L'objectif est de comprendre de quelles configurations sociales dépendent les projets de conservation et de vérifier si l'empowerment des populations locales favorise la prise en compte des enjeux écologiques. La communication comporte 4 sections : présentation des données ethnoécologiques des trois terrains ; corrélation des données sociales et environnementales ; analyse des facteurs favorables à la co-construction des savoirs ; rapports mutuels des disciplines impliquées (anthropologie, écologie et géographie)

Image Processing in Java Running on GPU

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Altimesh Hybridizer™ Enabling Accelerators in .Net and more

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Adaptive coarse-to-fine quantization for optimizing rate-distortion of progressive mesh compression

International audienceWe propose a new connectivity-based progressivecompression approach for triangle meshes. The keyidea is to adapt the quantization precision to the resolutionof each intermediate mesh so as to optimizethe rate-distortion trade-off. This adaptation is automaticallydetermined during the encoding processand the overhead is efficiently encoded using geometricalprediction techniques. We also introducean optimization of the geometry coding by usinga bijective discrete rotation. Results show that ourapproach delivers a better rate-distortion behaviorthan both connectivity-based and geometry-basedcompression state of the art method

Spike-based computation using classical recurrent neural networks

Spiking neural networks are a type of artificial neural networks in which communication between neurons is only made of events, also called spikes. This property allows neural networks to make asynchronous and sparse computations and therefore to drastically decrease energy consumption when run on specialized hardware. However, training such networks is known to be difficult, mainly due to the non-differentiability of the spike activation, which prevents the use of classical backpropagation. This is because state-of-the-art spiking neural networks are usually derived from biologically-inspired neuron models, to which are applied machine learning methods for training. Nowadays, research about spiking neural networks focuses on the design of training algorithms whose goal is to obtain networks that compete with their non-spiking version on specific tasks. In this paper, we attempt the symmetrical approach: we modify the dynamics of a well-known, easily trainable type of recurrent neural network to make it event-based. This new RNN cell, called the Spiking Recurrent Cell, therefore communicates using events, i.e. spikes, while being completely differentiable. Vanilla backpropagation can thus be used to train any network made of such RNN cell. We show that this new network can achieve performance comparable to other types of spiking networks in the MNIST benchmark and its variants, the Fashion-MNIST and the Neuromorphic-MNIST. Moreover, we show that this new cell makes the training of deep spiking networks achievable.Comment: 12 pages, 3 figure