Computational physics of the mind

In the XIX century and earlier such physicists as Newton, Mayer, Hooke, Helmholtz and Mach were actively engaged in the research on psychophysics, trying to relate psychological sensations to intensities of physical stimuli. Computational physics allows to simulate complex neural processes giving a chance to answer not only the original psychophysical questions but also to create models of mind. In this paper several approaches relevant to modeling of mind are outlined. Since direct modeling of the brain functions is rather limited due to the complexity of such models a number of approximations is introduced. The path from the brain, or computational neurosciences, to the mind, or cognitive sciences, is sketched, with emphasis on higher cognitive functions such as memory and consciousness. No fundamental problems in understanding of the mind seem to arise. From computational point of view realistic models require massively parallel architectures

Neural implementation of psychological spaces

Psychological spaces give natural framework for construction of mental representations. Neural model of psychological spaces provides a link between neuroscience and psychology. Categorization performed in high-dimensional spaces by dynamical associative memory models is approximated with low-dimensional feedforward neural models calculating probability density functions in psychological spaces. Applications to the human categorization experiments are discussed

Dispersion behavior of torsional guided waves in a small diameter steel gas pipe

Condition monitoring of gas pipes has been an important issue for gas companies. Failure to accurately identify condition of gas pipes result in numerous problems. Also, producing a condition monitoring system for buried pipelines is challenging. Small pipes (with diameters less than 50 mm) are considered here as most of the literature focuses on larger pipes. Guided wave theory will be introduced alongside a numerical simulation of the relevant dispersion curves of the system. This paper investigates the feasibility of using torsional guided waves for inspecting defects in buried pipes with small diameters. The pipes are assumed to be lossless and hence the effect of attenuation is ignored in the calculations. Upon finding the theoretical guided wave characteristics, experiments were conducted to see if the aim could be achieved in a realistic scenario. A steel pipe with a diameter of 34 mm and wall thickness of 5.5 mm is considered. High reverberation levels at high frequency propagations due to mode conversion are studied. Having only a limited number of transducers could be a reason for high reverberation at high frequencies

Full Wave Form Inversion for Seismic Data

In seismic wave inversion, seismic waves are sent into the ground and then observed at many receiving points with the aim of producing high-resolution images of the geological underground details. The challenge presented by Saudi Aramco is to solve the inverse problem for multiple point sources on the full elastic wave equation, taking into account all frequencies for the best resolution. The state-of-the-art methods use optimisation to find the seismic properties of the rocks, such that when used as the coefficients of the equations of a model, the measurements are reproduced as closely as possible. This process requires regularisation if one is to avoid instability. The approach can produce a realistic image but does not account for uncertainty arising, in general, from the existence of many different patterns of properties that also reproduce the measurements. In the Study Group a formulation of the problem was developed, based upon the principles of Bayesian statistics. First the state-of-the-art optimisation method was shown to be a special case of the Bayesian formulation. This result immediately provides insight into the most appropriate regularisation methods. Then a practical implementation of a sequential sampling algorithm, using forms of the Ensemble Kalman Filter, was devised and explored

Stochastic TDHF in an exactly solvable model

We apply in a schematic model a theory beyond mean-field, namely Stochastic Time-Dependent Hartree-Fock (STDHF), which includes dynamical electron-electron collisions on top of an incoherent ensemble of mean-field states by occasional 2-particle-2-hole ($2p2h$) jumps. The model considered here is inspired by a Lipkin-Meshkov-Glick model of $\Omega$ particles distributed into two bands of energy and coupled by a two-body interaction. Such a model can be exactly solved (numerically though) for small $\Omega$. It therefore allows a direct comparison of STDHF and the exact propagation. The systematic impact of the model parameters as the density of states, the excitation energy and the bandwidth is presented and discussed. The time evolution of the STDHF compares fairly well with the exact entropy, as soon as the excitation energy is sufficiently large to allow $2p2h$ transitions. Limitations concerning low energy excitations and memory effects are also discussed.Comment: 23 pages, 8 figures, accepted in Annals of Physic

Convergence under dynamical thresholds with delays

Necessary and sufficient conditions are obtained for the existence of a globally asymptotically stable equilibrium of a class of delay differential equations modeling the action of a neuron with dynamical threshold effects

Platonic model of mind as an approximation to neurodynamics

Hierarchy of approximations involved in simplification of microscopic theories, from sub-cellural to the whole brain level, is presented. A new approximation to neural dynamics is described, leading to a Platonic-like model of mind based on psychological spaces. Objects and events in these spaces correspond to quasi-stable states of brain dynamics and may be interpreted from psychological point of view. Platonic model bridges the gap between neurosciences and psychological sciences. Static and dynamic versions of this model are outlined and Feature Space Mapping, a neurofuzzy realization of the static version of Platonic model, described. Categorization experiments with human subjects are analyzed from the neurodynamical and Platonic model points of view

Propagation of Cascades in Complex Networks: From Supply Chains to Food Webs

A general theory of top-down cascades in complex networks is described which explains two similar types of perturbation amplifications in the complex networks of business supply chains (the `bullwhip effect') and ecological food webs (trophic cascades). The dependence of the strength of the effects on the interaction strength and covariance in the dynamics as well as the graph structure allows both explanation and prediction of widely recognized effects in each type of system.Comment: 16 pages, 3 figure