Extendable self-avoiding walks

The connective constant mu of a graph is the exponential growth rate of the number of n-step self-avoiding walks starting at a given vertex. A self-avoiding walk is said to be forward (respectively, backward) extendable if it may be extended forwards (respectively, backwards) to a singly infinite self-avoiding walk. It is called doubly extendable if it may be extended in both directions simultaneously to a doubly infinite self-avoiding walk. We prove that the connective constants for forward, backward, and doubly extendable self-avoiding walks, denoted respectively by mu^F, mu^B, mu^FB, exist and satisfy mu = mu^F = mu^B = mu^FB for every infinite, locally finite, strongly connected, quasi-transitive directed graph. The proofs rely on a 1967 result of Furstenberg on dimension, and involve two different arguments depending on whether or not the graph is unimodular.Comment: Accepted versio

Wearing a bike helmet leads to less cognitive control, revealed by lower frontal midline theta power and risk indifference

A recent study claims that participants wearing a bike helmet behave riskier in a computer-based risk task compared to control participants without a bike helmet. We hypothesized that wearing a bike helmet reduces cognitive control over risky behavior. To test our hypothesis, we recorded participants' EEG brain responses while they played a risk game developed in our laboratory. Previously, we found that, in this risk game, anxious participants showed greater levels of cognitive control as revealed by greater frontal midline theta power, which was associated with less risky decisions. Here, we predicted that cognitive control would be reduced in the helmet group, indicated by reduced frontal midline theta power, and that this group would prefer riskier options in the risk game. In line with our hypothesis, we found that participants in the helmet group showed significantly lower frontal midline theta power than participants in the control group, indicating less cognitive control. We did not replicate the finding of generally riskier behavior in the helmet group. Instead, we found that participants chose the riskier option in about half of trials, no matter how risky the other option was. Our results suggest that wearing a bike helmet reduces cognitive control, as revealed by reduced frontal midline theta power, leading to risk indifference when evaluating potential behaviors

When is an error not a prediction error? An electrophysiological investigation

A recent theory holds that the anterior cingulate cortex (ACC) uses reinforcement learning signals conveyed by the midbrain dopamine system to facilitate flexible action selection. According to this position, the impact of reward prediction error signals on ACC modulates the amplitude of a component of the event-related brain potential called the error-related negativity (ERN). The theory predicts that ERN amplitude is monotonically related to the expectedness of the event: It is larger for unexpected outcomes than for expected outcomes. However, a recent failure to confirm this prediction has called the theory into question. In the present article, we investigated this discrepancy in three trial-and-error learning experiments. All three experiments provided support for the theory, but the effect sizes were largest when an optimal response strategy could actually be learned. This observation suggests that ACC utilizes dopamine reward prediction error signals for adaptive decision making when the optimal behavior is, in fact, learnable

Stability of Service under Time-of-Use Pricing

We consider "time-of-use" pricing as a technique for matching supply and demand of temporal resources with the goal of maximizing social welfare. Relevant examples include energy, computing resources on a cloud computing platform, and charging stations for electric vehicles, among many others. A client/job in this setting has a window of time during which he needs service, and a particular value for obtaining it. We assume a stochastic model for demand, where each job materializes with some probability via an independent Bernoulli trial. Given a per-time-unit pricing of resources, any realized job will first try to get served by the cheapest available resource in its window and, failing that, will try to find service at the next cheapest available resource, and so on. Thus, the natural stochastic fluctuations in demand have the potential to lead to cascading overload events. Our main result shows that setting prices so as to optimally handle the {\em expected} demand works well: with high probability, when the actual demand is instantiated, the system is stable and the expected value of the jobs served is very close to that of the optimal offline algorithm.Comment: To appear in STOC'1

What you give is what you get : payment of one randomly selected trial induces risk-aversion and decreases brain responses to monetary feedback

In economic studies, it is standard practice to pay out the reward of only one randomly selected trial (pay-one) instead of the total reward accumulated across trials (pay-all), assuming that both methods are equivalent. We tested this assumption by recording electrophysiological activity to reward feedback from participants engaged in a decision-making task under both a pay-one and a pay-all condition. We show that participants are approximately 12% more risk averse in the pay-one condition than in the pay-all condition. Furthermore, we observed that the electrophysiological response to monetary rewards, the reward positivity, is significantly reduced in the pay-one condition relative to the pay-all condition. The difference of brain responses is associated with the difference in risky behavior across conditions. We concluded that the two payment methods lead to significantly different results and are therefore not equivalent