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- Jürgen Jost
- 2008

- Nils Bertschinger, Johannes Rauh, Eckehard Olbrich, Jürgen Jost, Nihat Ay
- Entropy
- 2014

We propose new measures of shared information, unique information and synergistic information that can be used to decompose the mutual information of a pair of random variables (Y, Z) with a third random variable X . Our measures are motivated by an operational idea of unique information, which suggests that shared information and unique information should… (More)

- Nils Bertschinger, Johannes Rauh, Eckehard Olbrich, Jürgen Jost
- ArXiv
- 2012

How can the information that a set {X1, . . . , Xn} of random variables contains about another random variable S be decomposed? To what extent do different subgroups provide the same, i.e. shared or redundant, information, carry unique information or interact for the emergence of synergistic information? Recently Williams and Beer proposed such a… (More)

Spectral properties of coupled map lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The analytical results are supplemented with numerical examples. The quadratic map is used for the site dynamics with different… (More)

The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this spectrum under local and global operations like motif doubling, graph joining or splitting. The eigenvalue 1 plays a… (More)

- Weiyue Ding, Jürgen Jost, Jiayu Li, Guofang Wang
- 1997

Let M be a compact Riemann surface, h(x) a positive smooth function on M . In this paper, we consider the functional J(u) = 1 2 ∫

- Fatihcan M Atay, Jürgen Jost, Andreas Wende
- Physical review letters
- 2004

We consider networks of coupled maps where the connections between units involve time delays. We show that, similar to the undelayed case, the synchronization of the network depends on the connection topology, characterized by the spectrum of the graph Laplacian. Consequently, scale-free and random networks are capable of synchronizing despite the delayed… (More)

- Nils Bertschinger, Eckehard Olbrich, Nihat Ay, Jürgen Jost
- Biosystems
- 2008

We present a tentative proposal for a quantitative measure of autonomy. This is something that, surprisingly, is rarely found in the literature, even though autonomy is considered to be a basic concept in many disciplines, including artificial life. We work in an information theoretic setting for which the distinction between system and environment is the… (More)

- Weiyue Ding, Jürgen Jost, Jiayu Li, Guofang Wang, WEIYUE DING, GUOFANG WANG
- 1997

Let Ω be an annulus. We prove that the mean field equation −∆ψ = e ∫ Ω e−βψ in Ω

We evaluate information-theoretic quantities that quantify complexity in terms of kth-order statistical dependences that cannot be reduced to interactions among k-1 random variables. Using symbolic dynamics of coupled maps and cellular automata as model systems, we demonstrate that these measures are able to identify complex dynamical regimes.