7 citations · 10 across the 8 of their papers we have counts for
10 papers
Emergent Loewner Dynamics in Slime Mold Growth
Claire David, Aurèle Boussard, Nizare Riane +2
Growth fronts of slime molds are characterized through a direct geometric analysis based on Loewner evolutions, using experimentally acquired time-resolved images. The associated L…
Generalized measure Black-Scholes equation: Towards option self-similar pricing
Nizar Riane, Claire David
In this work, we give a generalized formulation of the Black-Scholes model. The novelty resides in considering the Black-Scholes model to be valid on 'average', but such that the p…
The inverse Black-Scholes problem in Radon measures space revisited: towards a new measure of market uncertainty
Nizar Riane
In this paper, we revisit the inverse Black-Scholes model, the existence of the solution is proved in more rigorous way, and the empirical study is done using different approach ba…
Input-Output Analysis: New Results From Markov Chain Theory
Nizar Riane, Claire David
In this work, we propose a new lecture of input-output model reconciliation Markov chain and the dominance theory, in the field of interindustrial poles interactions. A deeper lect…
Optimization on fractal sets
Nizar Riane, Claire David
We outline necessary and sufficient condition to the existence of extrmas of a function on a self-similar set, and we describe discrete gradient algorithm to find the extrema.
The finite volume method on Sierpiński simplices
Nizare Riane, Claire David
In this work, we exploit Strichartz average approach \cite{Strichartz2001} to define the Laplacian on Sierpiński gasket, in the construction of the finite volume method. The approa…
The Finite Difference Method, for the heat equation on Sierpiński simplices
Nizare Riane, Claire David
In the sequel, we extend our previous work on the Minkowski Curve to Sierpiński simplices (Gasket and Tetrahedron), in the case of the heat equation. First, we build the finite dif…
A spectral study of the Minkowski Curve
Nizare Riane, Claire David
In the following, we give an explicit construction of a Laplacian on the Minkowski curve, with energy forms that bear the geometric characteristic of the structure. The spectrum of…
The Finite difference method for the Minkowski Curve
Nizare Riane, Claire David
In this work, we describe how to approximate solutions of some partial differential equations using the finite difference method defined on the Minkowski self-similar curve.
Laplacian, on the Sierpinski tetrahedron
Nizare Riane, Claire David
Numerous work revolve around the Sierpinski gasket. Its three-dimensional analogue, the Sierpinski tetrahedron, obtained by means of an iterative process which consists in repeated…