Tuning for speed is one key feature of motion-selective neurons in the middle temporal visual area of the macaque cortex (MT, or V5). The present paper asks whether speed is coded in a way that is invariant to the shape of the moving stimulus, and if so, how. When tested with single sine-wave gratings of different spatial and temporal frequencies, MT neurons show a continuum in the degree to which preferred speed depends on spatial frequency. There is some dependence in 75% of MT neurons, and the other 25% maintain speed tuning despite changes in spatial frequency. When tested with stimuli constructed by adding two superimposed sine-wave gratings, the preferred speed of MT neurons becomes less dependent on spatial frequency. Analysis of these responses reveals a speed-tuning nonlinearity that selectively enhances the responses of the neuron when multiple spatial frequencies are present and moving at the same speed. Consistent with the presence of the nonlinearity, MT neurons show speed tuning that is close to form-invariant when the moving stimuli comprise square-wave gratings, which contain multiple spatial frequencies moving at the same speed. We conclude that the neural circuitry in and before MT makes no explicit attempt to render MT neurons speed-tuned for sine-wave gratings, which do not occur in natural scenes. Instead, MT neurons derive form-invariant speed tuning in a way that takes advantage of the multiple spatial frequencies that comprise moving objects in natural scenes.
We consider a band of fermions in two space dimensions with a flux phase (relativistic) dispersion relation coupled to a local magnetic impurity via an $ s-d$ interaction. This model describes spinons of a flux phase and it is also a qualitative model of the quasiparticles in a $d_{x^2-y^2}$ superconductor. We find a zero-temperature phase transition at a finite coupling constant between a weak coupling unscreened impurity state and a strong coupling regime with a Kondo effect. We use large-$N$ methods to study the phase transition in this Kondo system away from marginality. The Kondo energy scales linearly with the distance to the transition . The zero-field magnetic suceptibility at zero temperature diverges linearly. Similar behavior is found in the $T$-matrix which shows a resonance at the Kondo scale. However, in addition to this simple scaling, we always find the presence of logarithmic corrections-to-scaling. Such behavior is typical of systems at an upper critical dimension. We derive an effective fermion model in one space dimension for this problem. Unlike the usual Kondo problem, this system has an intrinsic multichannel nature which follows from the spinor structure of $2+1$-dimensional relativistic fermions.Comment: 41 pages, Latex(RevTex), 1 figure in file figure.ps.gz; three ref. and one acknowledgement added, suceptibility formula and minor typos corrected, discussion adde
We study the diffusive motion of low-energy normal quasiparticles along the core of a single vortex in a dirty, type-II, s-wave superconductor. The physics of this system is argued to be described by a one-dimensional supersymmetric nonlinear σ model, which differs from the σ models known for disordered metallic wires. For an isolated vortex and quasiparticle energies less than the Thouless energy E Th , we recover the spectral correlations that are predicted by random matrix theory for the universality class C. We then consider the transport problem of transmission of quasiparticles through a vortex connected to particle reservoirs at both ends. The transmittance at zero energy exhibits a weak localization correction reminiscent of quasi-one-dimensional metallic systems with symmetry index β = 1. Weak localization disappears with increasing energy over a scale set by E Th . This crossover should be observable in measurements of the longitudinal heat conductivity of an ensemble of vortices under mesoscopic conditions. In the regime of strong localization, the localization length is shown to decrease by a factor of 8 as the quasiparticle energy goes to zero.
We consider the screening of a magnetic impurity in a d x 2 −y 2 wave superconductor. The properties of the d x 2 −y 2 state lead to an unusual behavior in the impurity magnetic susceptibility, the impurity specific heat and in the quasiparticle phase shift which can be used to diagnose the nature of the condensed state. We construct an effective theory for this problem and show that it is equivalent to a multichannel (one per node) non-marginal Kondo problem with linear density of states and coupling constant J. There is a quantum phase transition from an unscreened impurity state to an overscreened Kondo state at a critical value J c which varies with ∆ 0 , the superconducting gap away from the nodes. In the overscreened phase, the impurity Fermi level ǫ f and the amplitude ∆ of the ground state singlet vanish at J c like ∆ 0 exp(−const. /∆) and J − J c respectively. We derive the scaling laws for the susceptibility and specific heat in the overscreened phase at low fields and temperatures.
Starting from a random matrix model, we construct the low-energy effective field theory for the noninteracting gas of quasiparticles of a disordered superconductor in the mixed state. The theory is a nonlinear σ model, with the order parameter field being a supermatrix whose form is determined solely on symmetry grounds. The weak localization correction to the field-axis thermal conductivity is computed for a dilute array of s-wave vortices near the lower critical field Hc1. We propose that weak localization effects, cut off at low temperatures by the Zeeman splitting, are responsible for the field dependence of the thermal conductivity seen in recent high-Tc experiments by Aubin et al.
Repeated exposure to a consistent trans-saccadic step in the position of the saccadic target reliably produces a change of saccadic gain, a well-established trans-saccadic motor learning phenomenon known as saccadic adaptation. Trans-saccadic changes can also produce perceptual effects. Specifically, a systematic increase or decrease in the size of the object that is being foveated changes the perceptually equivalent size between fovea and periphery. Previous studies have shown that this recalibration of perceived size can be established within a few dozen trials, persists overnight, and generalizes across hemifields. In the current study, we use a novel adjustment paradigm to characterize both temporally and spatially the learning process that subtends this form of recalibration, and directly compare its properties to those of saccadic adaptation. We observed that sinusoidal oscillations in the amplitude of the trans-saccadic change produce sinusoidal oscillations in the reported peripheral size, with a lag of under 10 trials. This is qualitatively similar to what has been observed in the case of saccadic adaptation. We also tested whether learning is generalized to the mirror location on the opposite hemifield for both size recalibration and saccade adaptation. Here the results were markedly different, showing almost complete generalization for recalibration and no generalization for saccadic adaptation. We conclude that perceptual and visuomotor consequences of trans-saccadic changes rely on learning mechanisms that are distinct but develop on similar time scales.
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