A fundamental task of the visual system is to infer depth by using binocular disparity. To encode binocular disparity, the visual cortex performs two distinct computations: one detects matched patterns in paired images (matching computation); the other constructs the cross-correlation between the images (correlation computation). How the two computations are used in stereoscopic perception is unclear. We dissociated their contributions in near/far discrimination by varying the magnitude of the disparity across separate sessions. For small disparity (0.03°), subjects performed at chance level to a binocularly opposite-contrast (anti-correlated) random-dot stereogram (RDS) but improved their performance with the proportion of contrast-matched (correlated) dots. For large disparity (0.48°), the direction of perceived depth reversed with an anti-correlated RDS relative to that for a correlated one. Neither reversed nor normal depth was perceived when anti-correlation was applied to half of the dots. We explain the decision process as a weighted average of the two computations, with the relative weight of the correlation computation increasing with the disparity magnitude. We conclude that matching computation dominates fine depth perception, while both computations contribute to coarser depth perception. Thus, stereoscopic depth perception recruits different computations depending on the disparity magnitude.
In the lattice QCD formalism, we investigate the relation between confinement and chiral symmetry breaking. A gauge-invariant analytical relation connecting the Polyakov loop and the Dirac modes is derived on a temporally odd-number lattice, where the temporal lattice size is odd, with the normal (nontwisted) periodic boundary condition for link-variables. This analytical relation indicates that low-lying Dirac modes have little contribution to the Polyakov loop, and it is numerically confirmed at the quenched level in both confinement and deconfinement phases. This fact indicates no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD. Using the relation, we also investigate the contribution from each Dirac mode to the Polyakov loop. In the confinement phase, we find a new "positive/negative symmetry" of the Dirac-mode matrix element of the link-variable operator, and this symmetry leads to the zero value of the Polyakov loop. In the deconfinement phase, there is no such symmetry and the Polyakov loop is nonzero. Also, we develop a new method for spin-diagonalizing the Dirac operator on the temporally odd-number lattice modifying the Kogut-Susskind formalism.
Stereoscopic depth perception is supported by a combination of correlation-based and match-based representations of binocular disparity. It also relies on both transient and sustained temporal channels of the visual system. Previous studies suggest that the relative contribution of the correlation-based representation (over the match-based representation) and the transient channel (over the sustained channel) to depth perception increases with the disparity magnitude. The mechanisms of the correlation-based and match-based representations may receive preferential inputs from the transient and sustained channels, respectively. We examined near/far discrimination by observers using random-dot stereograms refreshed at various rates. The relative contribution of the two representations was inferred by changing the fraction of dots that were contrast reversed between the two eyes. Both representations contributed to depth discrimination over the tested range of refresh rates. As the rate increased, the correlation-based representation increased its contribution to near/far discrimination. Another experiment revealed that the match-based representation was constructed by exploiting the variability in correlation-based disparity signals. Thus, the relative weight of the transient over sustained channel differs between the two representations. The correlation-based representation dominates depth perception with dynamic inputs. The match-based representation, which may be a nonlinear refinement of the correlation-based representation, exerts more influence on depth perception with slower inputs.
Primates are capable of discriminating depth with remarkable precision using binocular disparity. Neurons in area V4 are selective for relative disparity, which is the crucial visual cue for discrimination of fine disparity. Here, we investigated the contribution of V4 neurons to fine disparity discrimination. Monkeys discriminated whether the center disk of a dynamic random-dot stereogram was in front of or behind its surrounding annulus. We first behaviorally tested the reference frame of the disparity representation used for performing this task. After learning the task with a set of surround disparities, the monkey generalized its responses to untrained surround disparities, indicating that the perceptual decisions were generated from a disparity representation in a relative frame of reference. We then recorded single-unit responses from V4 while the monkeys performed the task. On average, neuronal thresholds were higher than the behavioral thresholds. The most sensitive neurons reached thresholds as low as the psychophysical thresholds. For subthreshold disparities, the monkeys made frequent errors. The variable decisions were predictable from the fluctuation in the neuronal responses. The predictions were based on a decision model in which each V4 neuron transmits the evidence for the disparity it prefers. We finally altered the disparity representation artificially by means of microstimulation to V4. The decisions were systematically biased when microstimulation boosted the V4 responses. The bias was toward the direction predicted from the decision model. We suggest that disparity signals carried by V4 neurons underlie precise discrimination of fine stereoscopic depth.
We present a calculation of the strangeness and charmness contents N |ss|N and N |cc|N of the nucleon from dynamical lattice QCD with 2 + 1 flavors. The calculation is performed with overlap valence quarks on 2+1-flavor domain-wall fermion gauge configurations. The configurations are generated by the RBC collaboration on a 24 3 × 64 lattice with sea quark mass am l = 0.005, am s = 0.04, and inverse lattice spacing a −1 = 1.73 GeV. Both actions have chiral symmetry which is essential in avoiding contamination due to the operator mixing with other flavors. Nucleon propagator and the quark loops are both computed with stochastic grid sources, while low-mode substitution and low-mode averaging methods are used respectively which substantially improve the signal to noise ratio. We obtain the strangeness matrix element f Ts = m s N |ss|N /M N = 0.0334(62), and the charmness content f Tc = m c N |cc|N /M N = 0.094(31) which is resolved from zero by 3 σ precision for the first time.
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