Binocular contrast discrimination needs monocular multiplicative noise.

The effects of signal and noise on contrast discrimination are difficult to separate because of a singularity in the signal-detection-theory model of two-alternative forced-choice contrast discrimination (Katkov, Tsodyks, & Sagi, 2006). In this article, we show that it is possible to eliminate the singularity by combining that model with a binocular combination model to fit monocular, dichoptic, and binocular contrast discrimination. We performed three experiments using identical stimuli to measure the perceived phase, perceived contrast, and contrast discrimination of a cyclopean sine wave. In the absence of a fixation point, we found a binocular advantage in contrast discrimination both at low contrasts (<4%), consistent with previous studies, and at high contrasts (≥34%), which has not been previously reported. However, control experiments showed no binocular advantage at high contrasts in the presence of a fixation point or for observers without accommodation. We evaluated two putative contrast-discrimination mechanisms: a nonlinear contrast transducer and multiplicative noise (MN). A binocular combination model (the DSKL model; Ding, Klein, & Levi, 2013b) was first fitted to both the perceived-phase and the perceived-contrast data sets, then combined with either the nonlinear contrast transducer or the MN mechanism to fit the contrast-discrimination data. We found that the best model combined the DSKL model with early MN. Model simulations showed that, after going through interocular suppression, the uncorrelated noise in the two eyes became anticorrelated, resulting in less binocular noise and therefore a binocular advantage in the discrimination task. Combining a nonlinear contrast transducer or MN with a binocular combination model (DSKL) provides a powerful method for evaluating the two putative contrast-discrimination mechanisms

λ\lambda-symmetries for discrete equations

Following the usual definition of $\lambda$-symmetries of differential equations, we introduce the analogous concept for difference equations and apply it to some examples.Comment: 10 page

Attractive forces in microporous carbon electrodes for capacitive deionization

The recently developed modified Donnan (mD) model provides a simple and useful description of the electrical double layer in microporous carbon electrodes, suitable for incorporation in porous electrode theory. By postulating an attractive excess chemical potential for each ion in the micropores that is inversely proportional to the total ion concentration, we show that experimental data for capacitive deionization (CDI) can be accurately predicted over a wide range of applied voltages and salt concentrations. Since the ion spacing and Bjerrum length are each comparable to the micropore size (few nm), we postulate that the attraction results from fluctuating bare Coulomb interactions between individual ions and the metallic pore surfaces (image forces) that are not captured by meanfield theories, such as the Poisson-Boltzmann-Stern model or its mathematical limit for overlapping double layers, the Donnan model. Using reasonable estimates of the micropore permittivity and mean size (and no other fitting parameters), we propose a simple theory that predicts the attractive chemical potential inferred from experiments. As additional evidence for attractive forces, we present data for salt adsorption in uncharged microporous carbons, also predicted by the theory.Comment: 19 page

Lie discrete symmetries of lattice equations

We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the discrete symmetries of the discrete Painlev\'e I equation and of the Toda lattice equation

Fixing Food Safety: Protecting America's Food Supply From Farm-to-Fork

Provides an overview of the major concerns regarding U.S. food safety, including an ineffective regulatory system, and of food-borne disease threats. Includes lists of recent outbreaks, major causes of food-borne illnesses, and recommended solutions

Pandemic Flu and the Potential for U.S. Economic Recession: A State-by-State Analysis

Considers how a severe health pandemic outbreak could impact the United States economy and delineates the potential financial loss each state could face