Nonlinear Hebbian learning as a unifying principle in receptive field formation

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely Nonlinear Hebbian Learning. When Nonlinear Hebbian Learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities

Energy and volume of vector fields on spherical domains

We present in this paper a \boundary version" for theorems about minimality of volume and energy functionals on a spherical domain of threedimensional Euclidean sphere

Structure and dynamics in glass-formers: predictability at large length scales

Dynamic heterogeneity in glass-formers has been related to their static structure using the concept of dynamic propensity. We re-examine this relationship by analyzing dynamical fluctuations in two atomistic glass-formers and two theoretical models. We introduce quantitative statistical indicators which show that the dynamics of individual particles cannot be predicted on the basis of the propensity, nor by any structural indicator. However, the spatial structure of the propensity field does have predictive power for the spatial correlations associated with dynamic heterogeneity. Our results suggest that the quest for a connection between static and dynamic properties of glass-formers at the particle level is vain, but they demonstrate that such connection does exist on larger length scales.Comment: 7 pages; 4 figs - Extended, clarified versio

Non-Markovian incoherent quantum dynamics of a two-state system

We present a detailed study of the non-Markovian two-state system dynamics for the regime of incoherent quantum tunneling. Using perturbation theory in the system tunneling amplitude $\Delta$, and in the limit of strong system-bath coupling, we determine the short time evolution of the reduced density matrix and thereby find a general equation of motion for the non-Markovian evolution at longer times. We relate the nonlocality in time due to the non-Markovian effects with the environment characteristic response time. In addition, we study the incoherent evolution of a system with a double-well potential, where each well consists several quantized energy levels. We determine the crossover temperature to a regime where many energy levels in the wells participate in the tunneling process, and observe that the required temperature can be much smaller than the one associated with the system plasma frequency. We also discuss experimental implications of our theoretical analysis.Comment: 10 pages, published versio