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Register a new userUn portrait kaleidoscopique du jeune Camille Jordan
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Frederic Brechenmacher
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This paper aims to provide an overview of recent researches studies on Camille Jordans early works (1860-1870). We especially shed new light on the relation between Galois and Jordan by discussing the collective dimensions of Jordans works and their receptions.
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During the whole of 1874, Camille Jordan and Leopold Kronecker quar- relled vigorously over the organisation of the theory of bilinear forms. That theory promised a general and homogeneous treatment of numerous questions arising in various 19th-century theoretical contexts, and it hinged on two theorems, stated independently by Jordan and Weierstrass, that would today be considered equivalent. It was, however, the perceived difference between those two theorems that sparked the 1874 controversy. Focusing on this quarrel allows us to explore the algebraic identity of the polynomial practices of the manipulations of forms in use before the advent of structural approaches to linear algebra. The latter approaches identified these practices with methods for the classification of similar matrices. We show that the prac- tices -- Jordans canonical reduction and Kroneckers invariant computation -- reflect identities inseparable from the social context of the time. Moreover, these practices reveal not only tacit knowledge, local ways of thinking, but also -- in light of a long history tracing back to the work of Lagrange, Laplace, Cau- chy, and Hermite -- two internal philosophies regarding the significance of generality which are inseparable from two disciplinary ideals opposing algebra and arithmetic. By interrogating the cultural identities of such practices, this study aims at a deeper understanding of the history of linear algebra without focusing on issues related to the origins of theories or structures.
The legacy of Jordans canonical form on Poincares algebraic practices. This paper proposes a transversal overview on Henri Poincares early works (1878-1885). Our investigations start with a case study of a short note published by Poincare on 1884 : Sur les nombres complexes. In the perspective of todays mathematical disciplines - especially linear algebra -, this note seems completely isolated in Poincares works. This short paper actually exemplifies that the categories used today for describing some collective organizations of knowledge fail to grasp both the collective dimensions and individual specificity of Poincares work. It also highlights the crucial and transversal role played in Poincares works by a specific algebraic practice of classification of linear groups by reducing the analytical representation of linear substitution to their Jordans canonical forms. We then analyze in detail this algebraic practice as well as the roles it plays in Poincares works. We first provide a micro-historical analysis of Poincares appropriation of Jordans approach to linear groups through the prism of the legacy of Hermites works on algebraic forms between 1879 and 1881. This mixed legacy illuminates the interrelations between all the papers published by Poincare between 1878 and 1885 ; especially between some researches on algebraic forms and the development of the theory of Fuchsian functions. Moreover, our investigation sheds new light on how the notion of group came to play a key role in Poincares approach. The present paper also offers a historical account of the statement by Jordan of his canonical form theorem. Further, we analyze how Poincare transformed this theorem by appealing to Hermites
Overland flow on agricultural fields may have some undesirable effects such as soil erosion, flood and pollutant transport. To better understand this phenomenon and limit its consequences, we developed a code using state-of-the-art numerical methods: FullSWOF (Full Shallow Water equations for Overland Flow), an object oriented code written in C++. It has been made open-source and can be downloaded from http://www.univ-orleans.fr/mapmo/soft/FullSWOF/. The model is based on the classical system of Shallow Water (SW) (or Saint-Venant system). Numerical difficulties come from the numerous dry/wet transitions and the highly-variable topography encountered inside a field. It includes runon and rainfall inputs, infiltration (modified Green-Ampt equation), friction (Darcy-Weisbach and Manning formulas). First we present the numerical method for the resolution of the Shallow Water equations integrated in FullSWOF_2D (the two-dimension version). This method is based on hydrostatic reconstruction scheme, coupled with a semi-implicit friction term treatment. FullSWOF_2D has been previously validated using analytical solutions from the SWASHES library (Shallow Water Analytic Solutions for Hydraulic and Environmental Studies). Finally, FullSWOF_2D is run on a real topography measured on a runoff plot located in Thies (Senegal). Simulation results are compared with measured data. This experimental benchmark demonstrate the capabilities of FullSWOF to simulate adequately overland flow. FullSWOF could also be used for other environmental issues, such as river floods and dam-breaks.
Casually-taken portrait photographs often suffer from unflattering lighting and shadowing because of suboptimal conditions in the environment. Aesthetic qualities such as the position and softness of shadows and the lighting ratio between the bright and dark parts of the face are frequently determined by the constraints of the environment rather than by the photographer. Professionals address this issue by adding light shaping tools such as scrims, bounce cards, and flashes. In this paper, we present a computational approach that gives casual photographers some of this control, thereby allowing poorly-lit portraits to be relit post-capture in a realistic and easily-controllable way. Our approach relies on a pair of neural networks---one to remove foreign shadows cast by external objects, and another to soften facial shadows cast by the features of the subject and to add a synthetic fill light to improve the lighting ratio. To train our first network we construct a dataset of real-world portraits wherein synthetic foreign shadows are rendered onto the face, and we show that our network learns to remove those unwanted shadows. To train our second network we use a dataset of Light Stage scans of human subjects to construct input/output pairs of input images harshly lit by a small light source, and variably softened and fill-lit output images of each face. We propose a way to explicitly encode facial symmetry and show that our dataset and training procedure enable the model to generalize to images taken in the wild. Together, these networks enable the realistic and aesthetically pleasing enhancement of shadows and lights in real-world portrait images
This work takes part of the development of far-infrared and millimeter astrophysics. We have worked on the data processing and analysis in the fields of the Galactic interstellar medium, through the dust thermal emission, and cosmology through the observation of the cosmic microwave background fluctuations. We have been particularly interested in optimal map-making by inverse linear methods. We have developed a new map-making method for the balloon-borne submillimeter experiment PRONAOS, based on a Wiener inversion matrix, which allows to globally reconstruct the map. The analysis of PRONAOS maps in massive star-forming complexes as Orion and M17 allowed us to discover the large variations of the physical conditions and the dust properties. We showed an anticorrelation between the temperature and the submillimeter spectral index. Our investigations concerning this effect favour causes related to the intrinsic physics of the grains. We have also developed optimal map-making methods for the experiments aiming at measuring the cosmic microwave background fluctuations. The iterative methods that we have developed allow to reconstruct the sky maps very accurately, in spite of the large amount of self-correlated noise present in the timelines. We have also worked on the data processing and analysis for the Archeops balloon-borne experiment.
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