We make hundreds of decisions every day, many of them extremely quickly and without much explicit deliberation. This motivates two important open questions: What is the minimum time required to make choices with above chance accuracy? What is the impact of additional decision-making time on choice accuracy? We investigated these questions in four experiments in which subjects made binary food choices using saccadic or manual responses, under either “speed” or “accuracy” instructions. Subjects were able to make above chance decisions in as little as 313 ms, and choose their preferred food item in over 70% of trials at average speeds of 404 ms. Further, slowing down their responses by either asking them explicitly to be confident about their choices, or to respond with hand movements, generated about a 10% increase in accuracy. Together, these results suggest that consumers can make accurate every-day choices, akin to those made in a grocery store, at significantly faster speeds than previously reported.

An important open problem is how values are compared to make simple choices. A natural hypothesis is that the brain carries out the computations associated with the value comparisons in a manner consistent with the Drift Diffusion Model (DDM), since this model has been able to account for a large amount of data in other domains. We investigated the ability of four different versions of the DDM to explain the data in a real binary food choice task under conditions of high and low time pressure. We found that a seven-parameter version of the DDM can account for the choice and reaction time data with high-accuracy, in both the high and low time pressure conditions. The changes associated with the introduction of time pressure could be traced to changes in two key model parameters: the barrier height and the noise in the slope of the drift process.

The target article misrepresents the foundations of integrated information theory (IIT) and ignores many essential publications. It, thus, falls to this lead commentary to outline the axioms and postulates of IIT and correct major misconceptions. The commentary also explains why IIT starts from phenomenology and why it predicts that only select physical substrates can support consciousness. Finally, it highlights that IIT's account of experience – a cause–effect structure quantified by integrated information – has nothing to do with “information transfer.”

In this work, the error behaviour of high-order exponential operator splitting methods for the time integration of nonlinear evolutionary Schrödinger equations is investigated. The theoretical analysis utilises the framework of abstract evolution equations on Banach spaces and the formal calculus of Lie derivatives. The general approach is substantiated on the basis of a convergence result for exponential operator splitting methods of (nonstiff) order p applied to the multi-configuration time-dependent Hartree–Fock (MCTDHF) equations, which are associated with a model reduction for high-dimensional linear Schrödinger equations describing free electrons that interact by Coulomb force. Provided that the analytical solution of the MCTDHF equations constituting a system of coupled linear ordinary differential equations and low-dimensional nonlinear partial differential equations satisfies suitable regularity requirements, convergence of order p − 1 in the H1 Sobolev norm and convergence of order p in the L2 norm is proven. An analogous result follows for the cubic nonlinear Schrödinger equation, which is also illustrated by a numerical experiment.

We agree with Block's basic hypothesis postulating the existence of phenomenal consciousness without cognitive access. We explain such states in terms of consciousness without top-down, endogenous attention and speculate that their correlates may be a coalition of neurons that are consigned to the back of cortex, without access to working memory and planning in frontal cortex.