Search results for "Geometric"

Stochastic Approximation for Multivariate and Functional Median

2010

We propose a very simple algorithm in order to estimate the geometric median, also called spatial median, of multivariate (Small (1990)) or functional data (Gervini (2008)) when the sample size is large. A simple and fast iterative approach based on the Robbins-Monro algorithm (Duflo (1997)) as well as its averaged version (Polyak and Juditsky (1992)) are shown to be effective for large samples of high dimension data. They are very fast and only require O(Nd) elementary operations, where N is the sample size and d is the dimension of data. The averaged approach is shown to be more effective and less sensitive to the tuning parameter. The ability of this new estimator to estimate accurately …

Knots, Music and DNA

2020

Musical gestures connect the symbolic layer of the score to the physical layer of sound. I focus here on the mathematical theory of musical gestures, and I propose its generalization to include braids and knots. In this way, it is possible to extend the formalism to cover more case studies, especially regarding conducting gestures. Moreover, recent developments involving comparisons and similarities between gestures of orchestral musicians can be contextualized in the frame of braided monoidal categories. Because knots and braids can be applied to both music and biology (they apply to knotted proteins, for example), I end the article with a new musical rendition of DNA.

L'ornementation des bracelets de l'âge du Bronze européen : analyse descriptive et perspectives

2013

This paper discusses the ornamental patterns of metal bracelets worn on the arms and legs of people during the European Bronze Age. A method has been specially created to study geometric patterns. Some sets of metal bands (bracelets métalliques) of Bronze Age reach a high level of complexity due to the use of combined patterns in an overall structure. This paper deals with an experimental criterion concerning this phenomenon. The methodology, developed for the purpose i.e. the experimental criterion developed for the purpose of this study, was to extract geometric patterns from the original media. The principle is to release the geometrical compositions of the deformations induced by the mo…

Single cigar-shaped nanopores functionalized with amphoteric amino acid chains: experimental and theoretical characterization.

2012

We present an experimental and theoretical characterization of single cigar-shaped nanopores with pH-responsive carboxylic acid and lysine chains functionalized on the pore surface. The nanopore characterization includes (i) optical images of the nanostructure obtained by FESEM; (ii) different chemical procedures for the nanopore preparation (etching time and functionalizations; pH and electrolyte concentration of the external solution) allowing externally tunable nanopore responses monitored by the current-voltage (I-V) curves; and (iii) transport simulations obtained with a multilayer nanopore model. We show that a single, approximately symmetric nanopore can be operated as a reconfigurab…

Global attractors from the explosion of singular cycles

1997

Abstract In this paper we announce recent results on the existence and bifurcations of hyperbolic systems leading to non-hyperbolic global attractors.

On the geometric structure of the class of planar quadratic differential systems

2002

In this work we are interested in the global theory of planar quadratic differential systems and more precisely in the geometry of this whole class. We want to clarify some results and methods such as the isocline method or the role of rotation parameters. To this end, we recall how to associate a pencil of isoclines to each quadratic differential equation. We discuss the parameterization of the space of regular pencils of isoclines by the space of its multiple base points and the equivariant action of the affine group on the fibration of the space of regular quadratic differential equations over the space of regular pencils of isoclines. This fibration is principal, with a projective group…

GEOMETRIC FUNCTION THEORY AND NON-LINEAR ANALYSIS (Oxford Mathematical Monographs)

2002

FINITE ELEMENT APPROXIMATION OF NONLOCAL HEAT RADIATION PROBLEMS

1998

This paper focuses on finite element error analysis for problems involving both conductive and radiative heat transfers. The radiative heat exchange is modeled with a nonlinear and nonlocal term that also makes the problem non-monotone. The continuous problem has a maximum principle which suggests the use of inverse monotone discretizations. We also estimate the error due to the approximation of the boundary by showing continuous dependence on the geometric data for the continuous problem. The final result of this paper is a rigorous justification and error analysis for methods that use the so-called view factors for numerical modeling of the heat radiation.

Chess Thinking and Configural Concepts

2012

The purpose of this work is to connect chess and mathematics education. First, we introduce the idea of configural concepts in chess thinking and then we outline a scheme to show the phases of chess reasoning and how to apply this idea to some conflictual situations. We conclude this work proposing two research problems in introducing chess in mathematical classroom activities.

COULD STUDY AND PLAY OF CHESS IMPROVE SOCIAL INTERACTIONS? RE PORT OF AN ITALIAN CASE STUDY.

2012

Aim of this work is to improve the social interactions within a math classrooms (6 th grade), introducing a chess activity during the curricula hours. The theoretical framework upon which this research is based consists of: Vygotsky’s Theory of child developmen t (Vygotsky, 1986), the knowledge objectification theory (Radford, 2006) and theory of configural concepts (a personal review of Fischbein’s theory of figural concepts). We will discuss the results of an experimentation that has the purpose to create an appropriate environment wher e the students develop the abilities to solve and pose problems.