Moment bounds for the corrector in stochastic homogenization of a percolation model

We study the corrector equation in stochastic homogenization for a simplified Bernoulli percolation model on $\mathbb{Z}^d$, $d>2$. The model is obtained from the classical $\{0,1\}$-Bernoulli bond percolation by conditioning all bonds parallel to the first coordinate direction to be open. As a main result we prove (in fact for a slightly more general model) that stationary correctors exist and that all finite moments of the corrector are bounded. This extends a previous result in [GO1], where uniformly elliptic conductances are treated, to the degenerate case. With regard to the associated random conductance model, we obtain as a side result that the corrector not only grows sublinearly, but slower than any polynomial rate. Our argument combines a quantification of ergodicity by means of a Spectral Gap on Glauber dynamics with regularity estimates on the gradient of the elliptic Green's function

Visual associative learning in wood ants

Wood ants are a model system for studying visual learning and navigation. They can forage for food and navigate to their nests effectively by forming memories of visual features in their surrounding environment. Previous studies of freely behaving ants have revealed many of the behavioural strategies and environmental features necessary for successful navigation. However, little is known about the exact visual properties of the environment that animals learn or the neural mechanisms that allow them to achieve this. As a first step towards addressing this, we developed a classical conditioning paradigm for visual learning in harnessed wood ants that allows us to control precisely the learned visual cues. In this paradigm, ants are fixed and presented with a visual cue paired with an appetitive sugar reward. Using this paradigm, we found that visual cues learnt by wood ants through Pavlovian conditioning are retained for at least one hour. Furthermore, we found that memory retention is dependent upon the ants’ performance during training. Our study provides the first evidence that wood ants can form visual associative memories when restrained. This classical conditioning paradigm has the potential to permit detailed analysis of the dynamics of memory formation and retention, and the neural basis of learning in wood ants

Interaction between Purkinje Cells and Inhibitory Interneurons May Create Adjustable Output Waveforms to Generate Timed Cerebellar Output

We develop a new model that explains how the cerebellum may generate the timing in classical delay eyeblink conditioning. Recent studies show that both Purkinje cells (PCs) and inhibitory interneurons (INs) have parallel signal processing streams with two time scales: an AMPA receptor-mediated fast process and a metabotropic glutamate receptor (mGluR)-mediated slow process. Moreover, one consistent finding is an increased excitability of PC dendrites (in Larsell's lobule HVI) in animals when they acquire the classical delay eyeblink conditioning naturally, in contrast to in vitro studies, where learning involves long-term depression (LTD). Our model proposes that the delayed response comes from the slow dynamics of mGluR-mediated IP3 activation, and the ensuing calcium concentration change, and not from LTP/LTD. The conditioned stimulus (tone), arriving on the parallel fibers, triggers this slow activation in INs and PC spines. These excitatory (from PC spines) and inhibitory (from INs) signals then interact at the PC dendrites to generate variable waveforms of PC activation. When the unconditioned stimulus (puff), arriving on the climbing fibers, is coupled frequently with this slow activation the waveform is amplified (due to an increased excitability) and leads to a timed pause in the PC population. The disinhibition of deep cerebellar nuclei by this timed pause causes the delayed conditioned response. This suggested PC-IN interaction emphasizes a richer role of the INs in learning and also conforms to the recent evidence that mGluR in the cerebellar cortex may participate in slow motor execution. We show that the suggested mechanism can endow the cerebellar cortex with the versatility to learn almost any temporal pattern, in addition to those that arise in classical conditioning

A neural network model of adaptively timed reinforcement learning and hippocampal dynamics

A neural model is described of how adaptively timed reinforcement learning occurs. The adaptive timing circuit is suggested to exist in the hippocampus, and to involve convergence of dentate granule cells on CA3 pyramidal cells, and NMDA receptors. This circuit forms part of a model neural system for the coordinated control of recognition learning, reinforcement learning, and motor learning, whose properties clarify how an animal can learn to acquire a delayed reward. Behavioral and neural data are summarized in support of each processing stage of the system. The relevant anatomical sites are in thalamus, neocortex, hippocampus, hypothalamus, amygdala, and cerebellum. Cerebellar influences on motor learning are distinguished from hippocampal influences on adaptive timing of reinforcement learning. The model simulates how damage to the hippocampal formation disrupts adaptive timing, eliminates attentional blocking, and causes symptoms of medial temporal amnesia. It suggests how normal acquisition of subcortical emotional conditioning can occur after cortical ablation, even though extinction of emotional conditioning is retarded by cortical ablation. The model simulates how increasing the duration of an unconditioned stimulus increases the amplitude of emotional conditioning, but does not change adaptive timing; and how an increase in the intensity of a conditioned stimulus "speeds up the clock", but an increase in the intensity of an unconditioned stimulus does not. Computer simulations of the model fit parametric conditioning data, including a Weber law property and an inverted U property. Both primary and secondary adaptively timed conditioning are simulated, as are data concerning conditioning using multiple interstimulus intervals (ISIs), gradually or abruptly changing ISis, partial reinforcement, and multiple stimuli that lead to time-averaging of responses. Neurobiologically testable predictions are made to facilitate further tests of the model.Air Force Office of Scientific Research (90-0175, 90-0128); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI-87-16960); Office of Naval Research (N00014-91-J-4100

Application of Biological Learning Theories to Mobile Robot Avoidance and Approach Behaviors

We present a neural network that learns to control approach and avoidance behaviors in a mobile robot using the mechanisms of classical and operant conditioning. Learning, which requires no supervision, takes place as the robot moves around an environment cluttered with obstacles and light sources. The neural network requires no knowledge of the geometry of the robot or of the quality, number or configuration of the robot's sensors. In this article we provide a detailed presentation of the model, and show our results with the Khepera and Pioneer 1 mobile robots.Office of Naval Research (N00014-96-1-0772, N00014-95-1-0409

Modelling and feedback control design for quantum state preparation

The goal of this article is to provide a largely self-contained introduction to the modelling of controlled quantum systems under continuous observation, and to the design of feedback controls that prepare particular quantum states. We describe a bottom-up approach, where a field-theoretic model is subjected to statistical inference and is ultimately controlled. As an example, the formalism is applied to a highly idealized interaction of an atomic ensemble with an optical field. Our aim is to provide a unified outline for the modelling, from first principles, of realistic experiments in quantum control

A Neural Model of Timed Response Learning in the Cerebellum

A spectral timing model is developed to explain how the cerebellum learns adaptively timed responses during the rabbit's conditioned nictitating membrane response (NMR). The model posits two learning sites that respectively enable conditioned excitation and timed disinhibition of the response. Long-term potentiation of mossy fiber pathways projecting to interpositus nucleus cells allows conditioned excitation of the response's adaptive gain. Long-term depression of parallel fiber- Purkinje cell synapses in the cerebellar cortex allows learning of an adaptively timed reduction in Purkinje cell inhibition of the same nuclear cells. A spectrum of partially timed responses summate to generate an accurately timed population response. In agreement with physiological data, the model Purkinje cell activity decreases in the interval following the onset of the conditioned stimulus, and nuclear cell responses match conditioned response (CR) topography. The model reproduces key behavioral features of the NMR, including the properties that CR peak amplitude occurs at the unconditioned stimulus (US) onset, a discrete CR peak shift occurs with a change in interstimulus interval (ISI) between conditioned stim- ulus (CS) and US, mixed training at two different ISis produces a double-peaked CR, CR acquisition and rate of responding depend unimodally on the lSI, CR onset latency decreases during training, and maladaptively-timed, small-amplitude CRs result from ablation of cerebellar cortex.National Science Foundation (IRI-90-24877); Office of Naval Research (N00014-92-J-1309); Air Force Office of Scientific Research (F49620-92-J-0225