Fundamental Principles of Neural Organization of Cognition

The manuscript advances a hypothesis that there are few fundamental principles of neural organization of cognition, which explain several wide areas of the cognitive functioning. We summarize the fundamental principles, experimental, theoretical, and modeling evidence for these principles, relate them to hypothetical neural mechanisms, and made a number of predictions. We consider cognitive functioning including concepts, emotions, drives-instincts, learning, “higher” cognitive functions of language, interaction of language and cognition, role of emotions in this interaction, the beautiful, sublime, and music. Among mechanisms of behavior we concentrate on internal actions in the brain, learning and decision making. A number of predictions are made, some of which have been previously formulated and experimentally confirmed, and a number of new predictions are made that can be experimentally tested. Is it possible to explain a significant part of workings of the mind from a few basic principles, similar to how Newton explained motions of planets? This manuscript summarizes a part of contemporary knowledge toward this goal

Non-stationary resonance dynamics of weakly coupled pendula

In this paper we fill the gap in understanding the non-stationary resonance dynamics of the weakly coupled pendula model, having significant applications in numerous fields of physics such as super- conducting Josephson junctions, Bose-Einstein condensates, DNA, etc.. While common knowledge of the problem is based on two alternative limiting asymptotics, namely the quasi-linear approach and the approximation of independent pendula, we present a unified description in the framework of new concept of Limiting Phase Trajectories (LPT), without any restriction on the amplitudes of oscillation. As a result the conditions of intense energy exchange between the pendula and transition to energy localization are revealed in all possible diapason of initial conditions. By doing so, the roots and the domain of chaotic behavior are clarified as they are associated with this transition while simultaneously approaching the pendulum separatrix. The analytical findings are corrobo- rated by numerical simulations. By considering the simplest case of two weakly coupled pendula, we pave the ground for new opening possibilities of significant extensions in both fundamental and applied directions.Comment: 7 pages, 7 figure

Edge effects in the magnetic interference pattern of a ballistic SNS junction

We investigate the Josephson critical current $I_c(\Phi)$ of a wide superconductor-normal metal-superconductor (SNS) junction as a function of the magnetic flux $\Phi$ threading it. Electronic trajectories reflected from the side edges alter the function $I_c(\Phi)$ as compared to the conventional Fraunhofer-type dependence. At weak magnetic fields, $B\lesssim \Phi_0/d^2$, the edge effect lifts zeros in $I_c(\Phi)$ and gradually shifts the minima of that function toward half-integer multiples of the flux quantum. At $B>\Phi_0/d^2$, the edge effect leads to an accelerated decay of the critical current $I_c(\Phi)$ with increasing $\Phi$. At larger fields, eventually, the system is expected to cross into a regime of "classical" mesoscopic fluctuations that is specific for wide ballistic SNS junctions with rough edges.Comment: 14 pages, 8 figure