Soliton Model of Competitive Neural Dynamics during Binocular Rivalry
Binocular rivalry is investigated in a continuum model of the primary visual cortex that includes neural excitation and inhibition, stimulus orientation preference, and spike-rate adaptation. Visual stimuli consisting of bars or edges result in localized states of neural activity described by solitons. Stability analysis shows binocular fusion gives way to binocular rivalry when the orientation difference between left-eye and right-eye stimuli destabilizes one or more solitons. The model yields conditions for binocular rivalry, and two types of competitive dynamics are found: either one soliton oscillates between two stimulus regions or two solitons fixed in position at the stimulus regions oscillate out of phase with each other.
Spike-rate adaptation and neuronal bursting in a mean-field model of brain activity
Spike-rate adaptation is investigated within a mean-field model of brain activity. Two different mechanisms of negative feedback are considered; one involving modulation of the mean firing threshold, and the other, modulation of the mean synaptic strength. Adaptation to a constant stimulus is shown to take place for both mechanisms, and limit-cycle oscillations in the firing rate corresponding to bursts of neuronal activity are investigated. These oscillations are found to result from a Hopf bifurcation when the equilibrium lies between the local maximum and local minimum of a given nullcline. Oscillations with amplitudes significantly below the maximum firing rate are found over a narrow range of possible equilibriums.
The Two-Dimensional Gabor Function Adapted to Natural Image Statistics: A Model of Simple-Cell Receptive Fields and Sparse Structure in Images
The two-dimensional Gabor function is adapted to natural image statistics, leading to a tractable probabilistic generative model that can be used to model simple cell receptive field profiles, or generate basis functions for sparse coding applications. Learning is found to be most pronounced in three Gabor function parameters representing the size and spatial frequency of the two-dimensional Gabor function and characterized by a nonuniform probability distribution with heavy tails. All three parameters are found to be strongly correlated, resulting in a basis of multiscale Gabor functions with similar aspect ratios and size-dependent spatial frequencies. A key finding is that the distribution of receptive-field sizes is scale invariant over a wide range of values, so there is no characteristic receptive field size selected by natural image statistics. The Gabor function aspect ratio is found to be approximately conserved by the learning rules and is therefore not well determined by natural image statistics. This allows for three distinct solutions: a basis of Gabor functions with sharp orientation resolution at the expense of spatial-frequency resolution, a basis of Gabor functions with sharp spatial-frequency resolution at the expense of orientation resolution, or a basis with unit aspect ratio. Arbitrary mixtures of all three cases are also possible. Two parameters controlling the shape of the marginal distributions in a probabilistic generative model fully account for all three solutions. The best-performing probabilistic generative model for sparse coding applications is found to be a gaussian copula with Pareto marginal probability density functions.
Theory of Domain Wall Nucleation in a Two Section Magnetic Wire
The energy barrier for thermally driven magnetization reversal in a two section nanowire was calculated, based on a mechanism for domain wall nucleation at the interface between sections. The wire was assumed to be cylindrical, uniform in diameter, and consisting of two different types of ferromagnetic material. It was found that the wall either overcomes the barrier and continues through the wire or falls back to its equilibrium position centered in the local minimum.
Ultra-fast detection of salient contours through horizontal connections in the primary visual cortex
Salient features instantly attract visual attention to their location and are crucial for object recognition. Experiments in ultra-fast visual perception have shown that object recognition can be surprisingly accurate given only ~20 ms of observation. Such short times exclude neural dynamics of top-down feedback and require fast mechanisms of low-level feature detection. We derive a neural model of the primary visual cortex with physiologically parameterized horizontal connections that reinforce salient features, and apply it to detect salient contours on ultra-fast time scales. Model performance qualitatively matches experimental results for human perception of contours, suggesting rapid neural mechanisms involving feedforward horizontal connections can be used to distinguish low-level objects.
A Dynamic Programming Algorithm for Finding an Optimal Sequence of Informative Measurements
An informative measurement is the most efficient way to gain information about an unknown state. We present a first-principles derivation of a general-purpose dynamic programming algorithm that returns an optimal sequence of informative measurements by sequentially maximizing the entropy of possible measurement outcomes. This algorithm can be used by an autonomous agent or robot to decide where best to measure next, planning a path corresponding to an optimal sequence of informative measurements. The algorithm is applicable to states and controls that are either continuous or discrete, and agent dynamics that is either stochastic or deterministic; including Markov decision processes and Gaussian processes. Recent results from the fields of approximate dynamic programming and reinforcement learning, including on-line approximations such as rollout and Monte Carlo tree search, allow the measurement task to be solved in real time. The resulting solutions include non-myopic paths and measurement sequences that can generally outperform, sometimes substantially, commonly used greedy approaches. This is demonstrated for a global search task, where on-line planning for a sequence of local searches is found to reduce the number of measurements in the search by approximately half. A variant of the algorithm is derived for Gaussian processes for active sensing.
A graphical technique for finding equilibrium magnetic domain walls in multilayer nanowires
A graphical technique for finding equilibrium magnetic configurations in exchange coupled multilayer magnetic nanowires is presented. For the case of a two layer wire this technique is used to find two domain wall configurations localized near the interface between the layers. Both configurations are demonstrated to satisfy some important requirements for use in a calculation of the rate of magnetization reversal due to thermal activation. It is described how the graphical technique can be used for other types of multilayer nanowires.
Rate of magnetization reversal due to nucleation of soliton-antisoliton pairs at point-like defects
The rate of magnetization reversal due to the nucleation of soliton-antisoliton pairs at point-like defects is found for a uniaxial ferromagnet in an applied magnetic field. Point-like defects are considered as local variations in the magnetic anisotropy over a length scale smaller than the domain-wall width. A weak magnetic field applied along the easy axis causes the magnetization to become metastable, and the lowest activation barrier for reversal involves the nucleation of a soliton-antisoliton pair pinned to a point-like defect. Formulas are derived for the activation energy and field of reversal, and the reversal-rate prefactor is calculated using Langer's theory for the decay of a metastable state. As the applied field tends to zero, the lowest activation energy is found to be exactly half that of an unpinned soliton-antisoliton pair, and results from the formation of a spatially nonuniform metastable state when the defect strength become large. The smallest field of reversal is exactly half of the anisotropy field. The reversal-rate prefactor is found to increase with the number of point-like defects but decreases with increase in the defect strength due to a decrease in the activation entropy when translational symmetry is broken by the point-like defects, and soliton-antisoliton pairs become more strongly localized to the pinning sites.
Competitive reinforcement learning in Atari games
This research describes a study into the ability of a state of the art reinforcement learning algorithm to learn to perform multiple tasks. We demonstrate that the limitation of learning to performing two tasks can be mitigated with a competitive training method. We show that this approach results in improved generalization of the system when performing unforeseen tasks. The learning agent assessed is an altered version of the DeepMind deep Q–learner network (DQN), which has been demonstrated to outperform human players for a number of Atari 2600 games. The key findings of this paper is that there were significant degradations in performance when learning more than one game, and how this varies depends on both similarity and the comparative complexity of the two games.
Modal analysis of corticothalamic dynamics, electroencephalographic spectra, and evoked potentials
The effects of cortical boundary conditions and resulting modal aspects of continuum corticothalamic electrodynamics are explored, including feedbacks. Dispersion relations, electroencephalographic spectra, and stimulus response functions are calculated from the underlying physiology, and the effects of discrete mode structure are determined. Conditions under which modal effects are important are obtained, along with estimates of the point at which modal series can be truncated, and the limit in which only a single globally uniform mode need be retained. It is found that for physiologically plausible parameters only the lowest cortical spatial eigenmode together with the set of next-lowest modes can produce distinct modal structure in spectra and response functions, and then only at frequencies where corticothalamic resonances reduce dissipation to the point where the spatial eigenmodes are weakly damped. The continuum limit is found to be a good approximation, except at very low frequencies and, under some circumstances, near the alpha resonance. It is argued that the major electroencephalographic rhythms result from corticothalamic feedback resonances, but that cortical modal effects can contribute to weak substructure in the alpha resonance. This mechanism is compared and contrasted with purely cortical and pacemaker-based alternatives and testable predictions are formulated to enable experimental discrimination between these possibilities.