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We consider a porous media type equation over all of R d with d = 1, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. One of the main… (More)

- Paolo Castorina, Philippe Blanchard
- SpringerPlus
- 2012

Complex systems, in many different scientific sectors, show coarse-grain properties with simple growth laws with respect to fundamental microscopic algorithms. We propose a classification scheme of growth laws which includes human aging, tumor (and/or tissue) growth, logistic and generalized logistic growth and the aging of technical devices. The proposed… (More)

The Schrödinger problem of deducing the microscopic dynamics from the input-output statistics data is known to admit a solution in terms of Markov diffusions.The uniqueness of solution is found linked to the natural boundaries respected by the underlying random motion.By choosing a reference Smoluchowski diffusion,we automatically fix the Feynman-Kac… (More)

The existing formulations of the Schrödinger interpolating dynamics, which is constrained by the prescribed input-output statistics data, utilize strictly positive Feynman-Kac kernels. This implies that the related Markov diffusion processes admit vanishing probability densities only at the boundaries of the spatial volume confining the process. We extend… (More)

- Philippe Blanchard, Santo Fortunato, Tyll Krüger
- Physical review. E, Statistical, nonlinear, and…
- 2005

The structure and the properties of complex networks essentially depend on the way nodes get connected to each other. We assume here that each node has a feature which attracts the others. We model the situation by assigning two numbers to each node, omega and alpha, where omega indicates some property of the node and alpha the affinity towards that… (More)

- Philippe Blanchard, Arkadiusz Jadczyk
- 1997

The new solution to the problem of time of arrival in quantum theory is presented herein. It allows for computer simulation of particle counters and it implies Born's interpretation. It also suggests new experiments that can answer the question: can a quantum particle detect a detector without being detected?

- Philippe Blanchard, Dimitri Volchenkov
- Towards an Information Theory of Complex Networks
- 2011

In the strong coupling limit the partition function of SU(2) gauge theory can be reduced to that of the continuous spin Ising model with nearest neighbour pair-interactions. The random cluster representation of the continuous spin Ising model in two dimensions is derived through a Fortuin-Kasteleyn transformation, and the properties of the corresponding… (More)

- Michael J. Barber, Philippe Blanchard, Eva Buchinger, Bruno Cessac, Ludwig Streit
- J. Artificial Societies and Social Simulation
- 2006

We introduce an agent-based model of interaction, drawing on the contingency approach from Luhmann's theory of social systems. The agent interactions are defined by the exchange of distinct messages. Message selection is based on the history of the interaction and developed within the confines of the problem of double contingency. We examine interaction… (More)

We introduce an agent-based model of interaction, drawing on the contingency approach from Luhmann's theory of social systems. The agent interactions are defined by the exchange of distinct messages. Message selection is based on the history of the interaction and developed within the confines of the problem of double contingency. We examine interaction… (More)