Binocular summation at contrast threshold:a new look

Contrast sensitivity is better with two eyes than one. The standard view is that thresholds are about 1.4 (v2) times better with two eyes, and that this arises from monocular responses that, near threshold, are proportional to the square of contrast, followed by binocular summation of the two monocular signals. However, estimates of the threshold ratio in the literature vary from about 1.2 to 1.9, and many early studies had methodological weaknesses. We collected extensive new data, and applied a general model of binocular summation to interpret the threshold ratio. We used horizontal gratings (0.25 - 4 cycles deg-1) flickering sinusoidally (1 - 16 Hz), presented to one or both eyes through frame-alternating ferroelectric goggles with negligible cross-talk, and used a 2AFC staircase method to estimate contrast thresholds and psychometric slopes. Four naive observers completed 20 000 trials each, and their mean threshold ratios were 1.63, 1.69, 1.71, 1.81 - grand mean 1.71 - well above the classical v2. Mean ratios tended to be slightly lower (~1.60) at low spatial or high temporal frequencies. We modelled contrast detection very simply by assuming a single binocular mechanism whose response is proportional to (Lm + Rm) p, followed by fixed additive noise, where L,R are contrasts in the left and right eyes, and m, p are constants. Contrast-gain-control effects were assumed to be negligible near threshold. On this model the threshold ratio is 2(?1/m), implying that m=1.3 on average, while the Weibull psychometric slope (median 3.28) equals 1.247mp, yielding p=2.0. Together, the model and data suggest that, at low contrasts across a wide spatiotemporal frequency range, monocular pathways are nearly linear in their contrast response (m close to 1), while a strongly accelerating nonlinearity (p=2, a 'soft threshold') occurs after binocular summation. [Supported by EPSRC project grant GR/S74515/01]

Area summation in human vision at and above detection threshold

The initial image-processing stages of visual cortex are well suited to a local (patchwise) analysis of the viewed scene. But the world's structures extend over space as textures and surfaces, suggesting the need for spatial integration. Most models of contrast vision fall shy of this process because (i) the weak area summation at detection threshold is attributed to probability summation (PS) and (ii) there is little or no advantage of area well above threshold. Both of these views are challenged here. First, it is shown that results at threshold are consistent with linear summation of contrast following retinal inhomogeneity, spatial filtering, nonlinear contrast transduction and multiple sources of additive Gaussian noise. We suggest that the suprathreshold loss of the area advantage in previous studies is due to a concomitant increase in suppression from the pedestal. To overcome this confound, a novel stimulus class is designed where: (i) the observer operates on a constant retinal area, (ii) the target area is controlled within this summation field, and (iii) the pedestal is fixed in size. Using this arrangement, substantial summation is found along the entire masking function, including the region of facilitation. Our analysis shows that PS and uncertainty cannot account for the results, and that suprathreshold summation of contrast extends over at least seven target cycles of grating. © 2007 The Royal Society.

Excess leverage and productivity growth in emerging economies:is there a threshold effect?

This paper studies the relationship between leverage and growth, focusing on a large sample of firms in emerging economies of central and eastern Europe (CEE). Contrary to the general wisdom, we find that deviation from optimal leverage, especially, excess leverage is common among firms in many CEE countries. Using firm-level panel data from a group of transition countries, the paper provides support to the hypothesis that leverage positively affects productivity growth but only below an endogenously determined threshold level.

Estimating ECAP threshold from the variability of the response

Electrical compound action potentials (ECAPs) of the cochlear nerve are used clinically for quick and efficient cochlear implant parameter setting. The ECAP is the aggregate response of nerve fibres at various distances from the recording electrode, and the magnitude of the ECAP is therefore related to the number of fibres excited by a particular stimulus. Current methods, such as the masker-probe or alternating polarity methods, use the ECAP magnitude at various stimulus levels to estimate the neural threshold, from which the parameters are calculated. However, the correlation between ECAP threshold and perceptual threshold is not always good, with ECAP threshold typically being much higher than perceptual threshold. The lower correlation is partly due to the very different pulse rates used for ECAPs (below 100 Hz) and clinical programs (hundreds of Hz up to several kHz). Here we introduce a new method of estimating ECAP threshold for cochlear implants based upon the variability of the response. At neural threshold, where some but not all fibers respond, there is a different response each trial. This inter-trial variability can be detected overlaying the constant variability of the system noise. The large stimulus artefact, which requires additional trials for artefact rejection in the standard ECAP magnitude methods, is not consequential, as it has little variability. The variability method therefore consists of simply presenting a pulse and recording the ECAP, and as such is quicker than other methods. It also has the potential to be run at high rates like clinical programs, potentially improving the correlation with behavioural threshold. Preliminary data is presented that shows a detectable variability increase shortly after probe offset, at probe levels much lower than those producing a detectable ECAP magnitude. Care must be taken, however, to avoid saturation of the recording amplifier saturation; in our experiments we found a gain of 300 to be optimal.

Theoretical study of Talbot-like bands observed using a laser diode below threshold

We report on a theoretical study of an interferometric system in which half of a collimated beam from a broadband optical source is intercepted by a glass slide, the whole beam subsequently being incident on a diffraction grating and the resulting spectrum being viewed using a linear CCD array. Using Fourier theory, we derive the expression of the intensity distribution across the CCD array. This expression is then examined for non-cavity and cavity sources for different cases determined by the direction from which the slide is inserted into the beam and the source bandwidth. The theoretical model shows that the narrower the source linewidth, the higher the deviation of the Talbot bands' visibility (as it is dependent on the path imbalance) from the previously known triangular shape. When the source is a laser diode below threshold, the structure of the CCD signal spectrum is very complex. The number of components present simultaneously increases with the number of grating lines and decreases with the laser cavity length. The model also predicts the appearance of bands in situations not usually associated with Talbot bands.

Talbot-like bands for a laser diode below threshold

We report on the problems encountered when replacing a tungsten filament lamp with a laser diode in a set-up for displaying Talbot bands using a diffraction grating. It is shown that the band pattern is rather complex and strong interference signals may exist in situations where Talbot bands are not normally expected to appear. In these situations, the period of the bands increases with the optical path difference (OPD). The visibility of bands as dependence on path imbalance is obtained by suitably obstructing halfway into the arms of a Michelson interferometer using opaque screens.

Distributed temperature sensor based on Brillouin loss in an optical fibre for transient threshold monitoring

A distributed temperature sensor for transient threshold monitoring with a 22 km sensing length, based on the Brillouin loss in standard communications fibre, is demonstrated. The system can be used for real-time monitoring of a preset temperature threshold. Good S/N ratios were achieved with only 8–16 sample averages giving a response time of 2 to 4 s with a temperature uncertainty of ±1 °C.

Evolution of competing strategies in a threshold model for task allocation

A nature inspired decentralised multi-agent algorithm is proposed to solve a problem of distributed task allocation in which cities produce and store batches of different mail types. Agents must collect and process the mail batches, without global knowledge of their environment or communication between agents. The problem is constrained so that agents are penalised for switching mail types. When an agent process a mail batch of different type to the previous one, it must undergo a change-over, with repeated change-overs rendering the agent inactive. The efficiency (average amount of mail retrieved), and the flexibility (ability of the agents to react to changes in the environment) are investigated both in static and dynamic environments and with respect to sudden changes. New rules for mail selection and specialisation are proposed and are shown to exhibit improved efficiency and flexibility compared to existing ones. We employ a evolutionary algorithm which allows the various rules to evolve and compete. Apart from obtaining optimised parameters for the various rules for any environment, we also observe extinction and speciation.

The influence of memory in a threshold model for distributed task assignment

A nature inspired decentralised multi-agent algorithm is proposed to solve a problem of distributed task selection in which cities produce and store batches of different mail types. Agents must collect and process the mail batches, without a priori knowledge of the available mail at the cities or inter-agent communication. In order to process a different mail type than the previous one, agents must undergo a change-over during which it remains inactive. We propose a threshold based algorithm in order to maximise the overall efficiency (the average amount of mail collected). We show that memory, i.e. the possibility for agents to develop preferences for certain cities, not only leads to emergent cooperation between agents, but also to a significant increase in efficiency (above the theoretical upper limit for any memoryless algorithm), and we systematically investigate the influence of the various model parameters. Finally, we demonstrate the flexibility of the algorithm to changes in circumstances, and its excellent scalability.

Distributed temperature sensor based on Brillouin loss in an optical fibre for transient threshold monitoring

A distributed temperature sensor for transient threshold monitoring with a 22 km sensing length, based on the Brillouin loss in standard communications fibre, is demonstrated. The system can be used for real-time monitoring of a preset temperature threshold. Good S/N ratios were achieved with only 8–16 sample averages giving a response time of 2 to 4 s with a temperature uncertainty of ±1 °C.

Theoretical study of Talbot-like bands observed using a laser diode below threshold

We report on a theoretical study of an interferometric system in which half of a collimated beam from a broadband optical source is intercepted by a glass slide, the whole beam subsequently being incident on a diffraction grating and the resulting spectrum being viewed using a linear CCD array. Using Fourier theory, we derive the expression of the intensity distribution across the CCD array. This expression is then examined for non-cavity and cavity sources for different cases determined by the direction from which the slide is inserted into the beam and the source bandwidth. The theoretical model shows that the narrower the source linewidth, the higher the deviation of the Talbot bands' visibility (as it is dependent on the path imbalance) from the previously known triangular shape. When the source is a laser diode below threshold, the structure of the CCD signal spectrum is very complex. The number of components present simultaneously increases with the number of grating lines and decreases with the laser cavity length. The model also predicts the appearance of bands in situations not usually associated with Talbot bands.

Talbot-like bands for a laser diode below threshold

We report on the problems encountered when replacing a tungsten filament lamp with a laser diode in a set-up for displaying Talbot bands using a diffraction grating. It is shown that the band pattern is rather complex and strong interference signals may exist in situations where Talbot bands are not normally expected to appear. In these situations, the period of the bands increases with the optical path difference (OPD). The visibility of bands as dependence on path imbalance is obtained by suitably obstructing halfway into the arms of a Michelson interferometer using opaque screens.