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Results n° 1 to 8 of 46 matches
| Title |
André Krop, La quadrature du cercle et le nombre π, Paris, Ellipses, 2005 |
| Author |
HUDRY Olivier |
| Keywords |
None |
| Topics |
Book review, Geometry, History of Mathematics, Number theory |
| Abstract |
Book review |
| Number |
178, Summer 2007, special issue: Art, mathematics, language and emotion |
| Language |
 French | Read the article
| Title |
Brigitte Le Roux, Henry Rouanet, "Geometric Data Analysis from Correspondence Analysis to Structured Data Analysis", Dordrecht-Boston-London, Kluwer Academic Publisher, 2004 |
| Author |
BRU Bernard |
| Keywords |
None |
| Topics |
Book review, Data Analysis, Geometry, Regression, Statistics |
| Abstract |
Book review |
| Number |
171, Fall 2005 |
| Language |
French | Read the article
| Title |
Social Choice Theory for Everyone: comments on four books by Donald Saari |
| Author |
MERLIN Vincent |
| Keywords |
None |
| Topics |
Book review, Decision Theory, Geometry, Voting |
| Abstract |
D. Saari, "Geometry of voting", Studies in economic theory, Berlin-Heidelberg-New-York, Springer, 1994.
D. Saari, "Basic geometry of voting", Berlin-Heidelberg-New-York, Springer, 1995.
D. Saari, "Chaotic elections! A mathematician looks at voting", American Mathematical Society, 2001.
D. Saari, "Decisions and elections, explaining the unexpected", Cambridge, Cambridge Universiy Press, 2001. |
| Number |
163, Fall 2003, special issue: Social choice theory: golden jubilee |
| Language |
French | Read the article
| Title |
Regression and geometric data analysis: reflections and suggestions |
| Author |
ROUANET Henry, LEBARON Frédéric, LE HAY Viviane, ACKERMANN Werner, LE ROUX Brigitte |
| Keywords |
Descriptive versus explanatory, Geometric data analysis, Regression, Structural effect |
| Topics |
Data Analysis, Geometry, Regression, Statistics |
| Abstract |
Multivariate data are often treated with regression methods on one hand, Geometric Data Analyse methods (PCA, AC.) on the other hand. We intend to show, thanks to the mathematical structures common to the two methods, illustrated by examples, how one can integrate regression methods in geometric analysis. Geometric analysis allows a visualization of structural effects. There is no ground to oppose «explanatory» and «descriptive» statistical methods. |
| Number |
160, Winter 2002 |
| Language |
French | Read the article
| Title |
M. Aigner, G. M Ziegler, "Raisonnements divins. Quelques démonstrations mathématiques particulièrement élégantes", Paris, Springer Verlag, 2002 |
| Author |
HUDRY Olivier |
| Keywords |
None |
| Topics |
Book review, Arithmetic - Number Theory, Combinatorics, Geometry, Graphs, History of Mathematics |
| Abstract |
Book review |
| Number |
158, Summer 2002 |
| Language |
French | Read the article
| Title |
Genesis of a theory |
| Author |
FREY Louis |
| Keywords |
Approximation, Architecture of Antiquity, Divisions of a line segment, Pell-Fermat equation, Various means |
| Topics |
Approximation, Archeology, Arithmetic - Number Theory, Geometry, History of sciences, Modelling |
| Abstract |
A mathematical (here, specifically arithmetical) theory is presented to explain many observed proportions in monuments of the ancient Greek and Roman civilizations. |
| Number |
156, Winter 2001 |
| Language |
French | Read the article
| Title |
Specific analysis of a euclidean cloud: application to the study of questionnaires |
| Author |
LE ROUX Brigitte |
| Keywords |
Biweighted principal component analysis, Euclidean cloud, Geometric data analysis, Specific multiple correspondence analysis, Stability |
| Topics |
Data Analysis, Geometry, Social Sciences, Statistics |
| Abstract |
In this paper, we propose a method of specific Correspondence Analysis which allows to treat questionnaires when some responses are missing, and thus to free oneself from the yoke of complete disjunctive encoding. The method of specific analysis is presented within the general framework of Geometric Data Analysis for a Euclidean cloud, then particularized to multinumerical protocols and to questionnaires. We show that, in this approach, beweighted Principal Component Analysis (PCA) is privileged and that Multiples Correspondence Analysis (MCA) is equivalent to a biweighted PCA on indicator variables. Finally, we compare the specific analysis to the conventional one by writing inequalities between eigenvalues and studying the rotation of principal subspaces when one goes from the global analysis to the specific one. |
| Number |
146, Summer 1999 |
| Language |
French | Read the article
| Title |
Towards a neurogeometry. Cortical fibrations, contact structure and subjective contours |
| Author |
PETITOT Jean, TONDUT Yannick |
| Keywords |
Association field, Contact structure, Elastica, Euler-Lagrange equation, Fibration, Geodesic, Integrability condition, Lie groups, Subjective contours, Variational models, Vielbein |
| Topics |
Cognitive Sciences, Dynamical Systems, Epistemology, Geometry, Modelling |
| Abstract |
This work presents some variational models for the cortical algorithms processing Kanizsa modal subjective contours . These models are based on the geometric concepts of fibration and contact structure.
The retinoptic structure of the orientation hypercolumns in the visual area V1 is a functionnal architecture which can be mathematically idealized by the fibration having the retinian plane M as base and the projective line P1 as fiber F. The total space E of Pi p is isomorphic to the direct product M x F. The cortico-cortical horizontal connections implement what is called the local triviality of this fibration, and also a Cartan connection defining a parallel transport between neighboring fibers.
Then the paper focuses on the geometrical interpretation of the results of Field, Hayes and Hess concerning the association field. It shows that the latter implements what is called the contact structure of the fibration. The association field expresses an integrability condition for the skew curves in E : they have to be a lifting of their projection on the retinian plane M.
This model of fibration endowed with a contact structure is then applied to the modal subjective contours and provides a variant of the elastica model developped by B.K.P. Horn and D. Mumford. The key idea is that the lifting of subjective contours satisfy a "geodesic" condition in the cortical fibration E : they have to be of minimal lenght (for an appropriate metrics) among the class of curves satisfying the integrability condition.
These "geodesic" models are then reformulated, according to R. Bryant and P. Griffiths, in the more fondamental geometric framework of Lie groups and Cartan's "repère mobile" (Vielbein).
Finally, some experimental possibilities are suggested. |
| Number |
145, Spring 1999, special issue: Geometry and vision |
| Language |
French | Read the article
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