Self-organized criticality refers to the spontaneous emergence of self-similar dynamics in complex systems poised between order and randomness. The presence of self-organized critical dynamics in biological neuronal networks is supported by recent neurophysiological studies; these studies additionally associate critical neuronal network dynamics with several appealing properties, including optimized information transfer. Here we systematically seek the structural determinants of self-organized critical neuronal dynamics and quantify directed information transfer at criticality, in neurobiologically realistic neuronal networks. We study dynamics in hierarchically modular networks of leaky integrate-and-fire neurons with spike-timing-dependent synaptic plasticity and axonal conduction delays. We characterize emergent dynamics in our networks by distributions of active neuronal ensemble modules (neuronal avalanches) and rigorously assess these distributions for power-law scaling. We define three novel transfer-entropy based measures of directed information transfer; these measures compute the amount of predictive information present in neuronal avalanche properties (avalanche size, avalanche duration and inter-avalanche period) of the source region about avalanche properties of the destination region. We find that synaptic plasticity enables a rapid phase transition from random subcritical dynamics to ordered supercritical dynamics. Importantly, modular connectivity and low wiring cost broaden this transition, and enable a regime indicative of self-organized criticality. The critical regime is associated with maximized directed information transfer on all three computed measures. We hence infer a novel association between self-organized critical neuronal dynamics and several neurobiologically realistic features of structural connectivity, and find quantitative evidence for maximized directed information transfer at criticality.
Some aspects of the characterization of the "complexity" problem are reviewed, in particular for the two ubiquitous dichotomies chaos-noise and discete-continuous.
A special attention is devoted to finite-resolution effects on predictability. The problems involved in systems with intrinsic randomness is discussed, with emphasis on the important problems of distinguishing chaos from noise and of modeling the system.
We show that the practical difficulties in the distinction chaos from noise and of modeling the system, has a positive role in the problem of generation of Pseudo Random Numbers and the approximation of continuous system as discrete states automata.
The Cahnam-Helfrich bending energy is a surface energy for closed biological membranes that can be represented by smooth boundaryless surfaces. Minimizers and critical points in the class of surfaces with a constraint on the area and the enclosed volume, are expected to describe (approximately) the shape of biological membranes such as monolayers or lipid bilayers. In my talk I will present a result concerning the approximability of the Cahnam-Helfrich bending energy via diffused interfaces under a constraint on the ratio between two elastic parameters, the so called bending-rigidity and Gauss-rigity.
What makes decision making troublesome is that the consequences often will depend on yet unknown factors. When asking experts or forecasters about their opinions concerning the future course of events, it seems reasonable to reward them by a scheme related to the extent to which their assessments become reality. At first sight, it might appear impossible to avoid expert's assessment which at least to a certain degree depend on the particular reward scheme. The concept of probabilistic scores though provides reward systems with an incentive towards giving forecasts in the form of probabilities. These probabilities turn out to be independent of the particular scoring system.
Scores can of course be applied as well in situations where the forecaster is not a human but a machine. In this talk, I will discuss the application of scores to (numerically generated) probability forecasts. Scores can be used either to assess the performance of existing forecasting systems, or to train new machines that issue probabilistic forecasts in a statistical learning context. I will present several examples involving weather forecasting. Finally I would like to discuss a few limitations and problems I encountered.
Synchronized timings of cellular processes such as metabolic activity, differentiation, division, or cell death result in observation of functional macroscopic tissue-patterns, frequently periodic in time and/or space. Primary regulation is intracellular, originates in adaptive control of gene expression, and can be reproduced by dynamics of simple, delay negative feedback model. We analyze impact of model parameters including nonlinearities or transport/processing delay on stability, bifurcation direction, periodic solutions, and global attractor structure and dimension. Discussed are dynamic classes of transcription regulators, generic 'cellular clock' systems, and their mutual (in)dependence.
Systems where something new suddenly appears have always fascinated mankind. A series of fundamental scientific questions are linked with these systems, such as, were does novelty come from? or, how to explain novelty and its potential dynamics? Obviously, innovation plays an important role in our world. However, most of our formal theories that describe parts of our world do not deal with innovations. In the flavor of a structural science (S. Artmann, Philosphia naturalis, 40:183-205, 2003) I present a transdisciplinary perspective of systems that change qualitatively. Inspired by Fontana and Buss (Bull. Math. Biol., 56:1-64, 1994) we call such systems "constructive". A constructive system is a system where new component types can appear and disappear, i.e., where the set of component types present in the system is not constant over time. From a general point of view there is a huge variety of constructive systems.
They appear in Chemistry, Biology, Computer Science, and Social Sciences, just to a name a few. Apparently, I do not intent to present a solution covering all problems. Rather the theory I present is meant to provide a pice that may eventually contribute to a general theory of constructive systems.
A fundamental problem of statistical mechanics is to understand transport processes such as diffusion on the basis of dynamical systems theory. In my talk I will outline an approach by which physical quantities like diffusion coefficients can be calculated exactly in terms of dynamical systems properties. Applying this theory to piecewise linear maps deterministically coupled on a one-dimensional lattice, the diffusion coefficient is found to be a fractal function of control parameters. This fractality is a consequence of memory effects that are topologically unstable under parameter variation. Another type of dynamical correlations occurs in intermittent variants of this model leading to anomalous diffusion. In a first approximation subdiffusion in such maps is well described by continuous time random walk theory and fractional diffusion equations. However, on fine scales the same fractal parameter dependencies show up as discussed for normal diffusion asking for more refined theories.
In this talk we shall demonstrate how the notion of automaticity can help to understand certain structures which occur either as orbits of cellular automata or as a fixed point of certain renormalization procedures.
Projection operator techniques known from nonequilibrium statistical mechanics are applied to eliminate fast chaotic degrees of freedom in a low-dimensional dynamical system. A perturbative approach shows that the slow degrees of freedom can be modeled by an effective stochastic differential equation.
In the Hamiltonian case a fluctuation-dissipation relation holds which is crucial for respecting the conservation of energy. A comparison of the effective dynamics with the exact one shows the accuracy of the stochastic approximation on all time scales.
