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- Jürgen Jost
- 2008

We propose new measures of shared information, unique information and synergistic information that can be used to decompose the multi-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)

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

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)

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)

BACKGROUND
The giant synapses of Held play an important role in high-fidelity auditory processing and provide a model system for synaptic transmission at central synapses. Whether transmission of action potentials can fail at these synapses has been investigated in recent studies. At the endbulbs of Held in the anteroventral cochlear nucleus (AVCN) a… (More)

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)

We prove the following estimate for the spectrum of the normalized Laplace operator ∆ on a finite graph G, 1 − (1 − k[t]) 1 t ≤ λ 1 ≤ · · · ≤ λ N −1 ≤ 1 + (1 − k[t]) 1 t , ∀ integers t ≥ 1. Here k[t] is a lower bound for the Ollivier-Ricci curvature on the neighborhood graph G[t] (here we use the convention G[1] = G), which was introduced by Bauer-Jost. In… (More)

In Riemannian geometry, Ricci curvature controls how fast geodesics emanating from a common source are diverging on average, or equivalently, how fast the volume of distance balls grows as a function of the radius. Recently, such ideas have been extended to Markov processes and metric spaces. Employing a definition of generalized Ricci curvature proposed by… (More)