Transformation of context-dependent sensory dynamics into motor behavior

Latorre R, Levi R, Varona P (2013) Transformation of Context-dependent Sensory Dynamics into Motor Behavior. PLoS Comput Biol 9(2): e1002908. doi:10.1371/journal.pcbi.1002908The intrinsic dynamics of sensory networks play an important role in the sensory-motor transformation. In this paper we use conductance based models and electrophysiological recordings to address the study of the dual role of a sensory network to organize two behavioral context-dependent motor programs in the mollusk Clione limacina. We show that: (i) a winner take-all dynamics in the gravimetric sensory network model drives the typical repetitive rhythm in the wing central pattern generator (CPG) during routine swimming; (ii) the winnerless competition dynamics of the same sensory network organizes the irregular pattern observed in the wing CPG during hunting behavior. Our model also shows that although the timing of the activity is irregular, the sequence of the switching among the sensory cells is preserved whenever the same set of neurons are activated in a given time window. These activation phase locks in the sensory signals are transformed into specific events in the motor activity. The activation phase locks can play an important role in motor coordination driven by the intrinsic dynamics of a multifunctional sensory organThis work was supported by MINECO TIN2012-30883 and IPT-2011-0727-020000

Synchronization and coordination of sequences in two neural ensembles

There are many types of neural networks involved in the sequential motor behavior of animals. For high species, the control and coordination of the network dynamics is a function of the higher levels of the central nervous system, in particular the cerebellum. However, in many cases, especially for invertebrates, such coordination is the result of direct synaptic connections between small circuits. We show here that even the chaotic sequential activity of small model networks can be coordinated by electrotonic synapses connecting one or several pairs of neurons that belong to two different networks. As an example, we analyzed the coordination and synchronization of the sequential activity of two statocyst model networks of the marine mollusk Clione. The statocysts are gravity sensory organs that play a key role in postural control of the animal and the generation of a complex hunting motor program. Each statocyst network was modeled by a small ensemble of neurons with Lotka-Volterra type dynamics and nonsymmetric inhibitory interactions. We studied how two such networks were synchronized by electrical coupling in the presence of an external signal which lead to winnerless competition among the neurons. We found that as a function of the number and the strength of connections between the two networks, it is possible to coordinate and synchronize the sequences that each network generates with its own chaotic dynamics. In spite of the chaoticity, the coordination of the signals is established through an activation sequence lock for those neurons that are active at a particular instant of time.This work was supported by National Institute of Neurological Disorders and Stroke Grant No. 7R01-NS-38022, National Science Foundation Grant No. EIA-0130708, Fundación BBVA and Spanish MCyT Grant No. BFI2003-07276

Heteroclinic synchronization: Ultrasubharmonic locking

According to the traditional view of synchronization, a weak periodic input is able to lock a nonlinear oscillator at a frequency close to that of the input (1∶1 zone). If the forcing increases, it is possible to achieve synchronization at subharmonic bands also. Using a competitive dynamical system we show the inverse phenomenon: with a weak signal the 1∶1 zone is narrow, but the synchronization of ultrasubharmonics is dominant. In the system’s phase space, there exists a heteroclinic contour in the autonomous regime, which is the image of sequential dynamics. Under the action of a weak periodic forcing, in the vicinity of the contour a stable limit cycle with long period appears. This results in the locking of very low-frequency oscillations with the finite frequency of the forcing. We hypothesize that this phenomenon can be the origin for the synchronization of slow and fast brain rhythms.This work was supported by National Institute of Neurological Disorders and Stroke Grant No. 7R01-NS-38022, National Science Foundation Grant No. EIA-0130708, Spanish MEC BFI2003-07276, and Fundación BBVA

A qq-linear analogue of the plane wave expansion

We obtain a $q$-linear analogue of Gegenbauer's expansion of the plane wave. It is expanded in terms of the little $q$-Gegenbauer polynomials and the \textit{third} Jackson $q$-Bessel function. The result is obtained by using a method based on bilinear biorthogonal expansions.Comment: 12 pages, to appear in Adv. in Appl. Math. arXiv admin note: text overlap with arXiv:0909.006

An optimal three-point eighth-order iterative method without memory for solving nonlinear equations with its dynamics

We present a three-point iterative method without memory for solving nonlinear equations in one variable. The proposed method provides convergence order eight with four function evaluations per iteration. Hence, it possesses a very high computational efficiency and supports Kung and Traub's conjecture. The construction, the convergence analysis, and the numerical implementation of the method will be presented. Using several test problems, the proposed method will be compared with existing methods of convergence order eight concerning accuracy and basin of attraction. Furthermore, some measures are used to judge methods with respect to their performance in finding the basin of attraction.Comment: arXiv admin note: substantial text overlap with arXiv:1508.0174