Results 1 - 10
of
282
Fractals in the nervous system: conceptual implications for theoretical neuroscience
- Front Physiol
, 2010
"... This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relations ..."
Abstract
-
Cited by 24 (1 self)
- Add to MetaCart
(Show Context)
This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review.
Nonextensive statistical mechanics: A brief introduction
- Continuum Mechanics and Thermodynamics
"... iv ..."
(Show Context)
Maximum entropy change and least action principle for nonequilibrium systems, Invited talk at the Twelfth United
- Nations/European Space Agency Workshop on Basic Space Science
, 2004
"... A path information is defined in connection with different possible paths of irregular dynamic systems moving in its phase space between two points. On the basis of the assumption that the paths are physically differentiated by their actions, we show that the maximum path information leads to a path ..."
Abstract
-
Cited by 14 (7 self)
- Add to MetaCart
(Show Context)
A path information is defined in connection with different possible paths of irregular dynamic systems moving in its phase space between two points. On the basis of the assumption that the paths are physically differentiated by their actions, we show that the maximum path information leads to a path probability distribution in exponentials of action. This means that the most probable paths are just the paths of least action. This distribution naturally leads to important laws of normal diffusion. A conclusion of this work is that, for probabilistic mechanics or irregular dynamics, the principle of maximization of path information is equivalent to the least action principle for regular dynamics. We also show that an average path information between the initial phase volume and the final phase volume can be related to the entropy change defined with natural invariant measure of dynamic system. Hence the principles of least action and maximum path information suggest the maximum entropy change. This result is used for some chaotic systems evolving in fractal phase space in order to derive their invariant measures. 1 1
Source coding with escort distributions and Rényi entropy bounds
- Physics Letters A
, 2009
"... ..."
(Show Context)
Article Geometry of q-Exponential Family of Probability Distributions
, 2011
"... entropy ..."
(Show Context)
On generalized Cramér-Rao inequalities, generalized Fisher information and characterizations of generalized q-Gaussian distributions
- Journal of Physics A: Mathematical and Theoretical
, 2012
"... informations and characterizations of generalized q-Gaussian distributions‡ ..."
Abstract
-
Cited by 8 (8 self)
- Add to MetaCart
(Show Context)
informations and characterizations of generalized q-Gaussian distributions‡
