Introduction (with F. Bailly) With this text, we will first of all discuss a distinction, internal to mathematics, between "construction principles" and "proof principles" (see [Longo, 1999], [Longo, 2002]). In short, it will be a question of grasping the difference between the construction of mathematical concepts and structures and the role of proof, more or less formalised. The objective is ...

This paper explores the semiotic status of algebraic variables. To do that we build on a structuralist and post-structuralist train of thought going from Mauss and Lévi-Strauss to Baudrillard and Derrida. We import these authors’ semiotic thinking from the register of indigenous concepts (such as mana), and apply it to the register of algebra via a concrete case study of generating functions. T...

In this paper I investigate two notions of concepts that have played a dominant role in 20th century philosophy of mathematics. According to the first, concepts are definite and fixed; in contrast, according to the second notion concepts are open and subject to modifications. The motivations behind these two incompatible notions and how they can be used to account for conceptual change are pres...

The starting point for this paper is the well known equivalence between convolution filtering with a rescaled Gaussian and the solution of the heat equation. In the first chapters we analyze the equivalence between multiscale convolution filtering, linear smoothing methods based on continuous wavelet transforms and the solutions of linear diffusion equations. I.e. we determine a wavelet ψ, resp...

urvival analysis is seldom used in studies of the S of musculoskeletal therapy. Most clinical studies of musculoskeletal therapy use parametric statistical methods such as analysis of variance (ANOVA) to illustrate the effects of treatment on outcomes. Nonparametric techniques of analysis such as survival analysis are less frequently used. Survival analysis has a number of advantages that make ...

In elementary physics, in order to describe the motion of a physical system, a few quantities need to be specified. In 1833, Irish mathematician Hamilton proposed a new formalism of physics. Given a physical system, two sets of first order differential equations can capture all the information. With the aid of the mathematical concept of manifolds, which was developed later, Hamiltonian formali...

Since the turn of the 19 th and 20 th centuries when systematic research on antique Greek mathematics began, the general tone of historiographical work in the field has been dominated by the so-called internalist attitude. H.G. Zeuthen, P. Tannery and others initiated a research tradition whose goal is to reconstruct the mathematical development of the minus 5 th and 4 th century Greece by prov...

In this paper I will give a summary of the description of State Vector reduction using Topos Theory put forward by Isham in [1]. I will first briefly explain some mathematical concepts regarding Categories and Topoi. For a more detailed and complete explanation of the subjects of Topos and Category Theory the readers should refer to Topos-Physics and reference therein. I would like to point out...