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Register a new userThe bistable brain: a neuronal model with symbiotic interactions
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In general, the behavior of large and complex aggregates of elementary components can not be understood nor extrapolated from the properties of a few components. The brain is a good example of this type of networked systems where some patterns of behavior are observed independently of the topology and of the number of coupled units. Following this insight, we have studied the dynamics of different aggregates of logistic maps according to a particular {it symbiotic} coupling scheme that imitates the neuronal excitation coupling. All these aggregates show some common dynamical properties, concretely a bistable behavior that is reported here with a certain detail. Thus, the qualitative relationship with neural systems is suggested through a naive model of many of such networked logistic maps whose behavior mimics the waking-sleeping bistability displayed by brain systems. Due to its relevance, some regions of multistability are determined and sketched for all these logistic models.
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We consider a Kuramoto model of coupled oscillators that includes quenched random interactions of the type used by van Hemmen in his model of spin glasses. The phase diagram is obtained analytically for the case of zero noise and a Lorentzian distribution of the oscillators natural frequencies. Depending on the size of the attractive and random coupling terms, the system displays four states: complete incoherence, partial synchronization, partial antiphase synchronization, and a mix of antiphase and ordinary synchronization.
The texture of phase space and bifurcation diagrams of two-dimensional discrete maps describing a lattice of interacting oscillators, confined in on-site potentials with deformable double-well shapes, are examined. The two double-well potentials considered belong to a family proposed by Dikande and Kofane (A. M. Dikande and T. C. Kofane, Solid State Commun. vol. 89, p. 559, 1994), whose shapes can be tuned distinctively: one has a variable barrier height and the other has variable minima positions. However the two parametrized double-well potentials reduce to the $phi^4$ substrate, familiar in the studies of structural phase transitions in centro-symmetric crystals or bistable processes in biophysics. It is shown that although the parametric maps are area preserving their routes to chaos display different characteristic features: the first map exhibits a cascade of period-doubling bifurcations with respect to the potential amplitude, but period-halving bifurcations with respect to the shape deformability parameter. On the other hand the first bifurcation of the second map always coincides with the first pitchfork bifurcation of the $phi^4$ map. However, an increase of the deformability parameter shrinks the region between successive period-doubling bifurcations. The two opposite bifurcation cascades characterizing the first map, and the shrinkage of regions between successive bifurcation cascades which is characteristic of the second map, suggest a non-universal character of the Feigenbaum-number sequences associate with the two discrete parametric double-well maps.
Reconstructing multiple molecularly defined neurons from individual brains and across multiple brain regions can reveal organizational principles of the nervous system. However, high resolution imaging of the whole brain is a technically challenging and slow process. Recently, oblique light sheet microscopy has emerged as a rapid imaging method that can provide whole brain fluorescence microscopy at a voxel size of 0.4 by 0.4 by 2.5 cubic microns. On the other hand, complex image artifacts due to whole-brain coverage produce apparent discontinuities in neuronal arbors. Here, we present connectivity-preserving methods and data augmentation strategies for supervised learning of neuroanatomy from light microscopy using neural networks. We quantify the merit of our approach by implementing an end-to-end automated tracing pipeline. Lastly, we demonstrate a scalable, distributed implementation that can reconstruct the large datasets that sub-micron whole-brain images produce.
In this paper we have considered the problem of parametric sound generation in an acoustic resonator flled with a fluid, taking explicitely into account the influence of the nonlinearly generated second harmonic. A simple model is presented, and its stationary solutions obtained. The main feature of these solutions is the appearance of bistable states of the fundamental field resulting from the coupling to the second harmonic. An experimental setup was designed to check the predictions of the theory. The results are consistent with the predicted values for the mode amplitudes and parametric thresholds. At higher driving values a self-modulation of the amplitudes is observed. We identify this phenomenon with a secondary instability previously reported in the frame of the theoretical model.
Understanding the basic operational logics of the nervous system is essential to advancing neuroscientific research. However, theoretical efforts to tackle this fundamental problem are lacking, despite the abundant empirical data about the brain that has been collected in the past few decades. To address this shortcoming, this document introduces a hypothetical framework for the functional nature of primitive neural networks. It analyzes the idea that the activity of neurons and synapses can symbolically reenact the dynamic changes in the world and thus enable an adaptive system of behavior. More significantly, the network achieves this without participating in an algorithmic structure. When a neurons activation represents some symbolic element in the environment, each of its synapses can indicate a potential change to the element and its future state. The efficacy of a synaptic connection further specifies the elements particular probability for, or contribution to, such a change. As it fires, a neurons activation is transformed to its postsynaptic targets, resulting in a chronological shift of the represented elements. As the inherent function of summation in a neuron integrates the various presynaptic contributions, the neural network mimics the collective causal relationship of events in the observed environment.
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