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Section COMPUTATIONAL NEUROSCIENCE
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Fig. 2. Detuning of two frequency bands (nodes 15,16 and nodes 19,20,21) from y = -0.25 to y = -2.0: The initial s-1.5 power-law distribution changes into a strictly convex distribution shape (line L)
In the context of the theory of the thermodynamical formalism of dynamical systems, this change can be interpreted as the specification of a ground state of the network able to accommodate all potential stimulations, towards a more specific sound-targeting network.
In this way, the analysis of the hearing system contributes fundamental insight also for the brainWe hope that our approach will also lead us to a deeper understanding of the nature of otoacoustic emissions, the phenomenon of the sounds generated in many constructs of the mammalian ear.
Acknowledgements
We acknowledge the support by the Swiss National Science Foundation SNF and by the ETHZ Internal Grant system that made these investigations possible.
References
1. A. Kern and R. Stoop, Phys. Rev. Lett. 2003, 8(3), 555-566.
2. R. Stoop and A Kern., Phys. Rev. Lett. 2004, 8(3), 555-566.
3. R. Stoop and A. Kern, Proc.Nat. Ac. Sci U.S.A. 2004, 555-566.
4. R. Stoop, A. Kern and J.P. v.d. Vyver, US Patent 2012.
5. S. Martignoli and R. Stoop, Phys. Rev. Lett. 2010, 8(3), 555-566.
6. F. Gomez and R. Stoop, Phys. Rev. Lett. 2016, 8(3), 555-566.
7. F. Gomez and R. Stoop, Nat. Phys. 2014, 8(3), 555-566.
8. F. Gomez, R. Saase, N. Buchheim, and R. Stoop, Phys. Rev. Appl. 2014, 555-566.
9. Martignoli, F. Gomez, and R. Stoop, Sci. Rep. 2013, 555-566.
Analysis of the Brain Activity in Rodents Being Under Influence of General Anesthesia
M. O. Zhuravlev1,2,3*, O. I. Moskalenko1,2, A. A. Koronovskii1,2, A. E. Hramov21, S.A. Lobov3, V. A. Makarov3,4
1 Saratov State University, Saratov, 410012, Russia;
2 Saratov State Technical University, Saratov, 410054, Russia;
3 Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, 603950, Russia;
4 Instituto de Matemática Interdisciplinar, Applied Mathematics Dept., Universidad Complutense de Madrid, Avda Complutense s/n, 28040 Madrid, Spain.
* Presenting e-mail: zhuravlevmo@gmail.com
This time a great attention of researchers is devoted to the study of the brain activity [1; 2]. Such interest is connected, first of all, with the desire of the researchers to understand the fundamental principles of the brain activity as well as
Section COMPUTATIONAL NEUROSCIENCE
OM&P
with the possibility to apply the obtained knowledge for creation of the brain-computer interfaces. It should be noted that a number of research teams and private companies (for example, Google and Honda) are currently working on solution of this complex interdisciplinary problem. However, for realization of such ambitious problem it is necessary to understand the main fundamental processes occurring in the brain during the solution of different tasks. One of such tasks is the problem of cognitive behavior of living subject in the real world. Such function is known to be controlled by the neural activity in the hypothalamus in the brain of mammals. Thus, there is an interesting question related to the study of oscillatory activity of neural ensembles in the hypothalamus by means of the fundamental approaches of nonlinear dynamics.
In present Report we have studied the behavior of rodents being in the state of rest (under the influence of general anesthesia). We have considered the electrical activity observed in the left and right hippocampus of rats using the continuous wavelet transform with the complex basis [3 - 5]. Using continuous wavelet transform spectral analysis was carried activity of local field potentials generators in the left and right hippocampus of rats. The electrical activity observed in the left and right hippocampus of rats, we can distinguish two characteristic modes of behavior primarily is a mode with a slowly varying amplitude oscillations (4 - 12 Hz), the so-called hippocampal the theta rhythm. In addition, you can select the second mode for typical generators field potentials in the left and right hippocampus of rats, this behavior is rapidly changing the amplitude of the oscillations (30 - 60 Hz). Thus, these results confirm that the bond between the generator field potentials in right and left hippocampus of rats is performed in the frequency range (0 - 60 Hz). It should be noted that the degree of coherence (or, in turn, the relationship between the potentials of the field generators in the right and left side of the rat hippocampus) vary depending on the experiments.
We have found the characteristic features of the brain activity in the case when the animal does not solve any problem of cognitive navigation. The study intermitentnoy synchronization fluctuations in the ways Schaffer, in which has been developed and used a new technique based on a previously proposed methods of analysis on different time scales synchronization [6]. Thus it was obtained the dependence of duration synchronous behavior between field potentials generators right and left parts of the rodent hippocampus, which is close to exponential.
References
1. G. Buzsaki, A. Draguhn Neuronal Oscillations in Cortical Networks // Science. 2004. V. 304. P. 1926
2. M. I. Rabinovich et al. Dynamical principles in neuroscience // Rev. Mod. Phys. 78 1213 (2006)
3. B. Torresani, Continuous Wavelet Transform, Savoire, Paris, 1995
4. A. E. Hramov, A. A. Koronovskii, An approach to chaotic synchronization. // Chaos 14 (3), 603 (2004)
5. A. E. Hramov, A. A. Koronovskii, Time scale synchronization of chaotic oscillators. // Physica D 206 (3-4), 252 (2005)
6. Zhuravlev M.O., Koronovskii A.A., Moskaleriko O.I., Ovchinnikov A.A., Hramov A.E. Ring intermittency near the boundary of the synchronous time scales of chaotic oscillators. // Phys. Rev. E. 83, (2011) 027201
Learning in Coupled Neural Networks with Heteroclinic Circuits
A.O. Selskii1 *and V.A. Makarov1'2
1 N.I. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia;
2 Instituto de Matematica Interdisciplinar, Universidad Complutense de Madrid, Madrid, Spain.
Relatively recently it has been shown that regular but complex enough oscillatory activity in dynamical systems can emerge from the so-called stable heteroclinic channels [1,2]. In a neural network consisting of several coupled cells, one may observe a situation when all neurons are excited sequentially, i.e. each neuron becomes a winner for a limited time. Such a dynamic regime, called winner-less competition (WLC), can be implemented in a vicinity of heteroclinic trajectories connecting saddle equilibria in a loop [3,4]. From the one side, earlier it has been shown that a heteroclinic circuit may exist if certain relationships among synaptic coupling strength in the neural network are fulfilled [5,6]. From the other side, in neuronal systems synaptic plasticity may potentially change dynamic regimes. The latter may enable the emergence of WLC under special network training.
In this work we propose a model of learning, i.e., a learning rule, which allows one neural network, call a teacher, to impose its own dynamic to another neural network, call a learner. As a result, in the learner there appear WLC oscillations synchronized in phase with the oscillations of the teacher.
