We explore a synaptic plasticity model that incorporates recent findings that potentiation and depression can be induced by precisely timed pairs of synaptic events and postsynaptic spikes. In addition we include the observation that strong synapses undergo relatively less potentiation than weak synapses, whereas depression is independent of synaptic strength. After random stimulation, the synaptic weights reach an equilibrium distribution which is stable, unimodal, and has positive skew. This weight distribution compares favorably to the distributions of quantal amplitudes and of receptor number observed experimentally in central neurons and contrasts to the distribution found in plasticity models without size-dependent potentiation. Also in contrast to those models, which show strong competition between the synapses, stable plasticity is achieved with little competition. Instead, competition can be introduced by including a separate mechanism that scales synaptic strengths multiplicatively as a function of postsynaptic activity. In this model, synaptic weights change in proportion to how correlated they are with other inputs onto the same postsynaptic neuron. These results indicate that stable correlation-based plasticity can be achieved without introducing competition, suggesting that plasticity and competition need not coexist in all circuits or at all developmental stages.

CONTENTS I. Introduction A. Length scales B. Weak localization, closed paths and the backscatter cone. C. Anderson localization D. Correlation of different diffusons II. Macroscopics: the diffusion approximation A. Transmission through a slab and Ohm's law B. Diffusion propagator for slabs III. Mesoscopics: the radiative transfer equation A. Specific intensity B. Slab geometry 1. Isotropic scattering 2. Anisotropic scattering and Rayleigh scattering 3. The transport mean free path and the absorption length C. Injection depth and the improved diffusion approximation IV. Microscopics: wave equations, t matrix, and cross sections A. Schrödinger and scalar wave equations B. The t matrix and resonant point scatterers C. The t matrix as a series of returns D. Point scatterer in three dimensions 1. Second-order Born approximation 2. Regularization of the return Green's function 3. Resonances 4. Comparison with Mie scattering for scalar waves E. Cross sections and the albedo V. Green's functions in disordered systems A. Diagrammatic expansion of the self-energy B. Self-consistency VI. Transport in infinite media: isotropic scattering A. Ladder approximation to the Bethe-Salpeter equation B. Diffusion from the stationary ladder equation C. Diffusion coefficient and the speed of transport VII. Transport in a semi-infinite medium A. Plane wave incident on a semi-infinite medium B. Air-glass-medium interface C. Solutions of the Schwarzschild-Milne equation VIII. Transport through a slab A. Diffuse transmission B. Electrical conductance and contact resistance IX. The enhanced backscatter cone A. Milne kernel at nonzero transverse momentum B. Shape of the backscatter cone C. Decay at large angles D. Behavior at small angles X. Exact solution of the Schwarzschild-Milne equation A. The homogeneous Milne equation B. The inhomogeneous Milne equation C. Enhanced backscatter cone D. Exact solution for internal reflections in diffusive media E. Exact solution for very anisotropic scattering XI. Large index mismatch A. Diffuse reflected intensity B. Limit intensity and injection depth C. Comparison with the improved diffusion approximation D. Backscatter cone XII. Semiballistic transport XIII. Imaging of objects immersed in opaque media A. Spheres B. Cylinders XIV. Interference of diffusons: Hikami vertices A. Calculation of the Hikami four-point vertex B. Six-point vertex: H 6 50 C. Beyond the second-order Born approximation 51 D. Corrections to the conductivity 51 XV. Short range, long range, and conductance correlations: C 1 , C 2 , and C 3 51 A. Angular resolved transmission: the speckle pattern 52 B. Total transmission correlation: C 2 52 C. Conductance correlation: C 3 53 XVI. Calculation of correlation functions 53 A. Summary of diffuse intensities 54 B. Calculation of the C 1 correlation 55 C. Calculation of the C 2 correlation 55 1. Influence of incoming beam profile 56 2. Reflection correlations 57 D. Conductance Fluctuations: C 3 57 E. Calculation of the C 3 correlation function 58 XVII. Third cumulant of the total transmis...

Cortical circuits are thought to multiplex firing rate codes with temporal codes that rely on oscillatory network activity, but the circuit mechanisms that combine these coding schemes are unclear. We establish with optogenetic activation of layer II of the medial entorhinal cortex that theta frequency drive to this circuit is sufficient to generate nested gamma frequency oscillations in synaptic activity. These nested gamma oscillations closely resemble activity during spatial exploration, are generated by local feedback inhibition without recurrent excitation, and have clock-like features suitable as reference signals for multiplexing temporal codes within rate-coded grid firing fields. In network models deduced from our data, feedback inhibition supports coexistence of theta-nested gamma oscillations with attractor states that generate grid firing fields. These results indicate that grid cells communicate primarily via inhibitory interneurons. This circuit mechanism enables multiplexing of oscillation-based temporal codes with rate-coded attractor states.

The discrimination between two spike trains is a fundamental problem for both experimentalists and the nervous system itself. We introduce a measure for the distance between two spike trains. The distance has a time constant as a parameter. Depending on this parameter, the distance interpolates between a coincidence detector and a rate difference counter. The dependence of the distance on noise is studied with an integrate-andfire model. For an intermediate range of the time constants, the distance depends linearly on the noise. This property can be used to determine the intrinsic noise of a neuron.

Maintaining the proper balance between excitation and inhibition is necessary to prevent cortical circuits from either falling silent or generating epileptiform activity. One mechanism through which cortical networks maintain this balance is through the activity-dependent regulation of inhibition, but whether this is achieved primarily through changes in synapse number or synaptic strength is not clear. Previously, we found that 2 d of activity deprivation increased the amplitude of miniature EPSCs (mEPSCs) onto cultured visual cortical pyramidal neurons. Here we find that this same manipulation decreases the amplitude of mIPSCs. This occurs with no change in single-channel conductance but is accompanied by a reduction in the average number of channels open during the mIPSC peak and a reduction in the intensity of staining for GABA(A) receptors (GABA(A)Rs) at postsynaptic sites. In addition, the number of synaptic sites that express detectable levels of GABA(A)Rs was decreased by approximately 50% after activity blockade, although there was no reduction in the total number of presynaptic contacts. These data suggest that activity deprivation reduces cortical inhibition by reducing both the number of GABA(A)Rs clustered at synaptic sites and the number of functional inhibitory synapses. Because excitatory and inhibitory synaptic currents are regulated in opposite directions by activity blockade, these data suggest that the balance between excitation and inhibition is dynamically regulated by ongoing activity.