L. F. Abbott

Competitive Hebbian learning through spike-timing-dependent synaptic plasticity

Hebbian models of development and learning require both activity-dependent synaptic plasticity and a mechanism that induces competition between different synapses. One form of experimentally observed long-term synaptic plasticity, which we call spike-timing-dependent plasticity (STDP), depends on the relative timing of pre- and postsynaptic action potentials. In modeling studies, we find that this form of synaptic modification can automatically balance synaptic strengths to make postsynaptic firing irregular but more sensitive to presynaptic spike timing. It has been argued that neurons in vivo operate in such a balanced regime. Synapses modifiable by STDP compete for control of the timing of postsynaptic action potentials. Inputs that fire the postsynaptic neuron with short latency or that act in correlated groups are able to compete most successfully and develop strong synapses, while synapses of longer-latency or less-effective inputs are weakened.

Synaptic plasticity: taming the beast.

Synaptic plasticity provides the basis for most models of learning, memory and development in neural circuits. To generate realistic results, synapse-specific Hebbian forms of plasticity, such as long-term potentiation and depression, must be augmented by global processes that regulate overall levels of neuronal and network activity. Regulatory processes are often as important as the more intensively studied Hebbian processes in determining the consequences of synaptic plasticity for network function. Recent experimental results suggest several novel mechanisms for regulating levels of activity in conjunction with Hebbian synaptic modification. We review three of them—synaptic scaling, spike-timing dependent plasticity and synaptic redistribution—and discuss their functional implications.

When inhibition not excitation synchronizes neural firing

Excitatory and inhibitory synaptic coupling can have counter-intuitive effects on the synchronization of neuronal firing. While it might appear that excitatory coupling would lead to synchronization, we show that frequently inhibition rather than excitation synchronizes firing. We study two identical neurons described by integrate-and-fire models, general phase-coupled models or the Hodgkin-Huxley model with mutual, non-instantaneous excitatory or inhibitory synapses between them. We find that if the rise time of the synapse is longer than the duration of an action potential, inhibition not excitation leads to synchronized firing.

The Background Field Method Beyond One Loop

The background field approach to multi-loop calculations in gauge field theories is presented. A relation between the gauge-invariant effective action computed using this method and the effective action of the conventional functional approach is derived. Feynman rules are given and renormalization is discussed. It is shown that the renormalization programme can be carried out without any reference to fields appearing inside loops. Finally, as an explicit example, the two-loop contribution to the β function of pure Yang-Mills theory is calculated using the background field method.

Stability of gravity with a cosmological constant

The stability properties of Einstein theory with a cosmological constant Λ are investigated. For Λ > 0, stability is established for small fluctuations, about the de Sitter background, occurring inside the event horizon and semiclassical stability is analyzed. For Λ < 0, stability is demonstrated for all asymptotically anti-de Sitter metrics. The analysis is based on the general construction of conserved flux-integral expressions associated with the symmetries of a chosen background. The effects of an event horizon, which lead to Hawking radiation, are expressedfor general field hamiltonians. Stability for Λ < 0 is proved, using supergravity techniques, in terms of the graded anti-de Sitter algebra with spinorial charges also expressed as flux integrals.

The effect of correlated variability on the accuracy of a population code

We study the impact of correlated neuronal firing rate variability on the accuracy with which an encoded quantity can be extracted from a population of neurons. Contrary to widespread belief, correlations in the variabilities of neuronal firing rates do not, in general, limit the increase in coding accuracy provided by using large populations of encoding neurons. Furthermore, in some cases, but not all, correlations improve the accuracy of a population code.

A Cosmological Bound on the Invisible Axion

Abstract The production of axions in the early universe is studied. Axion models which break the U(1)PQ symmetry above 1012 GeV are found to produce an unacceptably large axion energy density.

Cortical Development and Remapping through Spike Timing-Dependent Plasticity

Long-term modification of synaptic efficacy can depend on the timing of pre- and postsynaptic action potentials. In model studies, such spike timing-dependent plasticity (STDP) introduces the desirable features of competition among synapses and regulation of postsynaptic firing characteristics. STDP strengthens synapses that receive correlated input, which can lead to the formation of stimulus-selective columns and the development, refinement, and maintenance of selectivity maps in network models. The temporal asymmetry of STDP suppresses strong destabilizing self-excitatory loops and allows a group of neurons that become selective early in development to direct other neurons to become similarly selective. STDP, acting alone without further hypothetical global constraints or additional forms of plasticity, can also reproduce the remapping seen in adult cortex following afferent lesions.

Vector reconstruction from firing rates

In a number of systems including wind detection in the cricket, visual motion perception and coding of arm movement direction in the monkey and place cell response to position in the rat hippocampus, firing rates in a population of tuned neurons are correlated with a vector quantity. We examine and compare several methods that allow the coded vector to be reconstructed from measured firing rates. In cases where the neuronal tuning curves resemble cosines, linear reconstruction methods work as well as more complex statistical methods requiring more detailed information about the responses of the coding neurons. We present a new linear method, the optimal linear estimator (OLE), that on average provides the best possible linear reconstruction. This method is compared with the more familiar vector method and shown to produce more accurate reconstructions using far fewer recorded neurons.

Cascade models of synaptically stored memories.

Storing memories of ongoing, everyday experiences requires a high degree of plasticity, but retaining these memories demands protection against changes induced by further activity and experience. Models in which memories are stored through switch-like transitions in synaptic efficacy are good at storing but bad at retaining memories if these transitions are likely, and they are poor at storage but good at retention if they are unlikely. We construct and study a model in which each synapse has a cascade of states with different levels of plasticity, connected by metaplastic transitions. This cascade model combines high levels of memory storage with long retention times and significantly outperforms alternative models. As a result, we suggest that memory storage requires synapses with multiple states exhibiting dynamics over a wide range of timescales, and we suggest experimental tests of this hypothesis.