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origin of the primary dynamical effects which can be caused by electromechanical coupling and mechanoelec-trical feedback in a cardiac tissue.
On the basis of the reaction-diffusion-mechanics model with the self-consistent electromechanical coupling, we have numerically analyzed the emergence of structures and wave propagation in the excitable contractile fiber for various contraction types (isotonic, isometric, and auxotonic) and electromechanical coupling strengths. We have identified two main regimes of excitation spreading along the fiber: (i) the common quasi-steady-state propagation and (ii) the simultaneous ignition of the major fiber part and have obtained the analytical estimate for the boundary between the regimes in the parameter space. The uncommon oscillatory regimes have been found for the FiteHugh-Nagumo-like system: (i) the propagation of the soliton-like waves with the boundary reflections and (ii) the clusterized self-oscillations. The single space-time localized stimulus has been shown to be able to induce long-lasting transient activity as a result of the after-excitation effect when the just excited fiber parts are reexcited due to the electromechanical global coupling. The results obtained demonstrate the wide variety of possible dynamical regimes in the electromechanical activity of the cardiac tissue and the significant role of the mechanical fixation properties (particularly, the contraction type), which role should be taken into consideration in similar studies. In experiments with isolated cardiac fibers and cells, these parameters can be relatively easily controlled, which opens a way to assess electrical and mechanical parameters of the fibers and cells through analysis of dynamical regimes as dependent on fixation stiffness and external force. In real heart, high blood pressure and hindered blood flow play similar role to the applied external force and increased fixation stiffness. Our results provide a hint of how such global (i.e., associated with the large areas of the heart tissue) parameters can affect the heart electrical and contraction activity.
Chaos & Biological Information Processing: Coarse-Graining, Rough Set Approximations and Quantum Cognition in Decision Making
V. Basios*
Interdisciplinary Centre for Nonlinear Phenomena and Complex systems, & Dept. de Physique des Systèmes Complexes et Mécanique Statistique, University of Brussels, Brussels, Belgium. * Presenting e-mail: [email protected]
Aims
The role of chaos in biological information processing has been established as an important breakthrough of nonlinear dynamics, after the early pioneering work of J.S. Nicolis [1] (and notably in neuroscience by the work of Walter J. Freeman and co-workers spanning more than three decades, see Chapter 13 by Walter J. Freeman in [1]). Yet the models describing apprehension, judgment and decision making in various populations of biological systems, be it a large collective of neural networks, a colony of ants, a hive of bees or other communities of "agents', do not readily accommodate such an insight. With this work we aim at bridging this gap by considering recent advances in apprehension and judgment (see Chapter 15, by T. Arrechi in [1]). We propose a scheme [2] that underlies the mechanism of classification in judgememt and decision making, under uncertainty and conflict, by utilizing coarse-graining techniques from chaotic dynamics [5] based in "rough-sef theory with self-referential, non-linear, feed-back loops.
Methods
Our methods derive from an interdisciplinary framework combining tools from statistical mechanics, dynamical system theory and in particular coarse-graining (via 'rough-sef approximation) computational techniques. We use data coming from experiments targeted on recording populations of neurons under controlled decision-making processes. We have identified the basis of this scheme as compatible with the principles of quantum cognition [4] and investigated the properties of it's logical structure as an orthomodular lattice known from Quantum Logic. Bayesian inference based on the upper/lower approximation selects the modification and/or replacement of the algorithms for decision-making by a composition of two different equivalence relations.
Results
At this stage we have identified a minimal model for apprehension and judgment and interpreted data from human subjects [2]. The proposed 'non-algorithmic jumps' reveal the associated quantum-like effects reported in the literature. The composition of the two kinds of equivalence relations, leads to a logic structure expressed as an orthomodular lattice. Conversely it
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Section DYNAMICS IN LIFE SCIENCES, NEUROSCIENCE APPLICATIONS WORKSHOP
reveals that the modification or replacement of algorithms (i.e. replacement of equivalence relations) is affected by the reported quantum-like effects. Crowds of cortical neurons 'the workspace' provide the substratum, in terms of complexity flexibility, adaptability and plasticity, for collective agreement and synchronization in both instances of apprehension and judgment. A fascinating question that results from this line of investigations is whether or not this is the only such substratum in existence. Research in collective decision-making and event-anticipation in collectives, other than groups of neurons, i.e. super-organisms of social animals such as bee-hives, ant-colonies and other model systems [3,4,6] reveal certain analogies in recruiting, reinforcement and consensus building. Our approach instigates research toward this kind of investigations.
Conclusions
Given the successful synergy of mathematical, agent-based simulations and biological experiments in a common research platform a useful extension is to augment the setting in [3] with feedback mechanisms which can control the experimental constrains and launch trials according to the outcome of an in-situ monitoring. Results based on other biological models and neural networks enrich this research program [3,6]. In view of recent developments in data collecting & processing technology and the important advances in coarse-graining methods (especially in relation to autonomous agents and neural populations [6]) emphasis is to be placed in the complexity of the underlying dynamics. For example the role of the group's size, the complexity of the units or their propensities and their differentiation, the trends for forming sub-groups, clustering & cliques, environmental and dynamical constrains etc. By its nature such a "research platform' can only be truly interdisciplinary and fully integrated as a complex-system lab or network of such [3,6].
Acknowledgements
Special thanks to Professors Andrey Shilnikov (Georgia State), Dmitri Turaev (Imperial College), Y. Kevrekidis (Princeton), Yukio-Pegio Gunji (Waseda) and S. Nicolis, Jean-Louis Deneubourg (ULB) for fascinating & inspiring discussions.
References
1. 'Chaos, information processing and paradoxical games: the legacy of John S Nicolis', G. Nicolis, V. Basios, eds. World Scientific (2015).
2. "Quantum cognition based on an ambiguous representation derived from a rough set approximation', Y-P. Gunji, K. Sonoda & V. Basios. BioSystems 141, 55-66 (2016).
3. 'Coordinated Aggregation in Complex Systems: an interdisciplinary approach', V. Basios, S. Nicolis & J-L. Deneubourg, The European Physical Journal, Special Topics: Mathematical Modeling of Complex Systems, in press (2016).
4. 'Quantum probability and the mathematical modelling of decision making7, E. Haven and A. Khrennikov, eds. Phil. Trans. R. Soc. A (Theme issue), 374, 2058 (2016).
5. 'Symbolic dynamics, coarse graining and the monitoring of complex systems'. V Basios, D Mac Kernan, International Journal of Bifurcation and Chaos 21 (12), 3465-3475 (2011).
6. 'Coarse-Grained Clustering Dynamics of Heterogeneously Coupled Neurons', S.J. Moon, K.A. Cook, K. Rajendran, I.G. Kevrekidis, J. Cisternas, C.R. Laing. Journal of Mathematical Neuroscience, 5,2 (2015).
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The work of the International Workshop Dynamics in Life Sciences, Neuroscience Applications was supported by the RSF fund (grant 14-4100044) and the RFBR fund (grant 16-02-20460\16).
