Concept

Benoit Mandelbrot

Related publications (20)

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Path properties of the solution to the stochastic heat equation with Levy noise

Robert Dalang, Carsten Hao Ye Chong, Thomas Marie Jean-Baptiste Humeau

We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...

SPRINGER2019

Predictive Hydrology: A Frequency Analysis Approach

Anne-Catherine Favre

The unusual frequency of hydro-meteorological events in recent decades, often with catastrophic consequences for society and the environment, require new methods for designing water management projects and the structures meant to protect us from natural ha ...

Science Publishers, CRC Press2012

Apollonian packings as physical fractals

Francesco Varrato, Giuseppe Foffi

The Apollonian packings (APs) of spheres are fractals that result from a space-filling procedure. We discuss the finite size effects for finite intervals s is an element of [s(min), s(max)] between the largest and the smallest sizes of the filling spheres. ...

2011

Apollonian packings as physical fractals

Francesco Varrato, Giuseppe Foffi

2011

Out of Sample Forecasts of Quadratic Variation

Loriano Mancini

We compare the forecasts of Quadratic Variation given by the Realized Volatility (RV) and the Two Scales Realized Volatility (TSRV) computed from high frequency data in the presence of market microstructure noise, under several different dynamics for the v ...

2008

Fibertract segmentation in position orientation space from high angular resolution diffusion MRI

Jean-Philippe Thiran, Reto Meuli, Patric Hagmann, Lisa Jonasson, Van Jay Wedeen, Thomas Deffieux

Abstract In diffusion MRI, standard approaches for fibertract identification are based on algorithms that generate lines of coherent diffusion, currently known as tractography. A tract is then identified as a set of such lines selected on some criteria. In ...

2006

Models of fractal river basins

Andrea Rinaldo, Amos Maritan

Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following nontrivial power laws in experimentally relevant distributions. Previous numerical estimates on the critical e ...

1998

Sculpting of a fractal river basin

Andrea Rinaldo, Amos Maritan

The principle of reparametrization invariance is used to derive a dynamical equation for the erosion of the landscape of the drainage basin of river networks. The stationary solutions of the equation are found to have scaling behavior that is consistent wi ...

1997

Self-Organized Fractal River Networks

Andrea Rinaldo

Optimal channel networks (OCN's) obtained by minimizing the local and global rates of energy expenditure evolve automatically from arbitrary initial conditions to network configurations exhibiting fractal and multifractal statistics indistinguishable from ...

1993

A Note on Fractal Channel Networks

Andrea Rinaldo

This paper studies the relation between the structure of river networks and the features of their geomorphologic hydrologic response. A mathematical formulation of connectivity of a drainage network is proposed to relate contributing areas and the network ...

1991