13,379 research outputs found
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 , 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
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