Dear Colleagues,
Many of you have enquired about our new book MATHEMATICAL NEUROSCIENCE.
I am pleased to accept pre-orders, just send me an email with your particulars
and number of copies required.
Yours Sincerely,
R. Poznanski
S. Brzychczy
ABOUT THE BOOK:
In collaboration with Stanislaw Brzychczy (AGH University of Science and Technology)- an upcoming book on the development of a nonlinear analysis to better understand the intricate fallacies of computationalism and methodological reductionism in neuroscience.
In computational neuroscience, reductionist approaches span multiple-levels of neural organization, however in integrative neuroscience, relational biology seamlessly sculptures the neural organization. Reductionism assumes a direct causal relationship between a molecular/cellular mechanism and a behavioral phenomenon, ignoring the constraints that higher-level properties exert on the possible functions of that mechanism. One of these constraints is dynamic continuity which is intrinsically difficult to harness computationally because compartmentalization and/or discretization is subject to dynamical misalignment, producing a false sense of biological reality.
Examples of this research include the application of functional analysis to nonlinear cable theory. The functional analysis proved that 'compartmental models of spiking neurons', and all software packages like NEURON and GENESIS, are dynamically implausible representations of real neurons. This also includes 'multi-scale' computational approaches that claim to 'integrate' through the use of computational methodologies.
In simple layman's terms, the approach of multi-scale computational modeling is a constructionist attempt at modeling the brain. The constructionist brain model postulates that as long as the algorithms work it suffices for the purpose of reverse engineering or building a brain model. However, there are severe problems with this approach. One such limitation is that multi-scale models are incapable of harnessing dynamical continuity across scale by means of discretization via computational approximation, unless the increment of discretization is infinitesimal. Multi-scale modeling has been developed largely through the theory of applied dynamical systems and global bifurcations. These low-dimensional dynamical systems have engendered highly successful tools for estimating the correlation dimensions and Lyapunov exponents. To be useful for neuroscience, however, dynamical system theory requires continuity in spatio-temporal dynamics. This dynamic continuity is manifested th!
rough an electric field inside neurons and across synapses, resulting in a field of influence for augmenting cognitive processes in assemblies of networks. In such a continuum, the brain is modeled as an infinite-dimensional dynamical system. Infinite systems represent hierarchical levels in a way that will not delude the continuous dynamics of the neuronal systems across spatio-temporal scales. Neural organization across various multi-hierarchical levels yield emergent complexities of different dynamical systems, but they are not disjoint sets (as in algebraic topology or category theory), therefore 'multi-scale computational modeling' remains a constructionist attempt at modeling the nervous system similar to the IBM Blue Brain Project.
Mathematical Neuroscience goes beyond unrealistic dynamics of physical abstractions into the realm of integrative modeling and dynamic continuity. It's the first book in mathematical neuroscience that can claim to include nonlinear analysis of infinite systems that is different from computational neuroscience.
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Roman R. Poznanski
Professor
Office: D218(Block D)2nd Floor
Universiti Tunku Abdul Rahman (UTAR)
Department of Physical & Mathematical Science
Faculty of Science
31900 Kampar, Perak
Malaysia
Office: (+605)468-8888 Ext. 2289
E-mail: roman@utar.edu.my
http://romanpoznanski.blogspot.com
and
Chief-Editor,
Journal of Integrative Neuroscience
http://www.worldscinet.com/jin/mkt/editorial.shtml
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