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]

The Sarkozy effect: France’s new presidential dynamic

The election on 6 May 2007 of Nicolas Sarkozy as President of the Republic ushered in the promise of a new era in France. Sarkozy’s presidency follows those of the Socialist François Mitterrand (1981-95) and the neo-Gaullist Jacques Chirac (1995-2007), who together occupied France’s highest political office for more than a quarter-century. From the outset, Sarkozy’s presidential campaign was predicated on the need for change in France, for a “rupture” with the past; and his emphatic victory against the Socialist Ségolène Royal gave him a mandate to effect this. The legislative elections of June 2007, by assuring a strong majority in the National Assembly for Sarkozy’s centre-right Union pour un Mouvement Populaire (UMP), left the way clear for implementing the new President’s reform agenda over the next five years. This article examines the political context within which Sarkozy was elected to power, the main proposals of his presidential program, the challenges he faces, and his prospects for bringing real change to France.