Why are probabilistic laws governing quantum mechanics and neurobiology?

We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.Comment: 40 pages, 8 fig

Quantum processes, space-time representation and brain dynamics

The recent controversy of applicability of quantum formalism to brain dynamics has been critically analysed. The prerequisites for any type of quantum formalism or quantum field theory is to investigate whether the anatomical structure of brain permits any kind of smooth geometric notion like Hilbert structure or four dimensional Minkowskian structure for quantum field theory. The present understanding of brain function clearly denies any kind of space-time representation in Minkowskian sense. However, three dimensional space and one time can be assigned to the neuromanifold and the concept of probabilistic geometry is shown to be appropriate framework to understand the brain dynamics. The possibility of quantum structure is also discussed in this framework.Comment: Latex, 28 page

Unnatural Selection: A new formal approach to punctuated equilibrium in economic systems

Generalized Darwinian evolutionary theory has emerged as central to the description of economic process (e.g., Aldrich et. al., 2008). Here we demonstrate that, just as Darwinian principles provide necessary, but not sufficient, conditions for understanding the dynamics of social entities, in a similar manner the asymptotic limit theorems of information theory provide another set of necessary conditions that constrain the evolution of socioeconomic process. These latter constraints can, however, easily be formulated as a statistics-like analytic toolbox for the study of empirical data that is consistent with a generalized Darwinism, and this is no small thing

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research