Threshold games and cooperation on multiplayer graphs

Objective: The study investigates the effect on cooperation in multiplayer games, when the population from which all individuals are drawn is structured - i.e. when a given individual is only competing with a small subset of the entire population. Method: To optimize the focus on multiplayer effects, a class of games were chosen for which the payoff depends nonlinearly on the number of cooperators - this ensures that the game cannot be represented as a sum of pair-wise interactions, and increases the likelihood of observing behaviour different from that seen in two-player games. The chosen class of games are named "threshold games", and are defined by a threshold, $M > 0$, which describes the minimal number of cooperators in a given match required for all the participants to receive a benefit. The model was studied primarily through numerical simulations of large populations of individuals, each with interaction neighbourhoods described by various classes of networks. Results: When comparing the level of cooperation in a structured population to the mean-field model, we find that most types of structure lead to a decrease in cooperation. This is both interesting and novel, simply due to the generality and breadth of relevance of the model - it is likely that any model with similar payoff structure exhibits related behaviour. More importantly, we find that the details of the behaviour depends to a large extent on the size of the immediate neighbourhoods of the individuals, as dictated by the network structure. In effect, the players behave as if they are part of a much smaller, fully mixed, population, which we suggest an expression for.Comment: in PLOS ONE, 4th Feb 201

Discrete Optimization for Interpretable Study Populations and Randomization Inference in an Observational Study of Severe Sepsis Mortality

Motivated by an observational study of the effect of hospital ward versus intensive care unit admission on severe sepsis mortality, we develop methods to address two common problems in observational studies: (1) when there is a lack of covariate overlap between the treated and control groups, how to define an interpretable study population wherein inference can be conducted without extrapolating with respect to important variables; and (2) how to use randomization inference to form confidence intervals for the average treatment effect with binary outcomes. Our solution to problem (1) incorporates existing suggestions in the literature while yielding a study population that is easily understood in terms of the covariates themselves, and can be solved using an efficient branch-and-bound algorithm. We address problem (2) by solving a linear integer program to utilize the worst case variance of the average treatment effect among values for unobserved potential outcomes that are compatible with the null hypothesis. Our analysis finds no evidence for a difference between the sixty day mortality rates if all individuals were admitted to the ICU and if all patients were admitted to the hospital ward among less severely ill patients and among patients with cryptic septic shock. We implement our methodology in R, providing scripts in the supplementary material

On the Keyhole Hypothesis:High Mutual Information between Ear and Scalp EEG

We propose and test the keyhole hypothesis—that measurements from low dimensional EEG, such as ear-EEG reflect a broadly distributed set of neural processes. We formulate the keyhole hypothesis in information theoretical terms. The experimental investigation is based on legacy data consisting of 10 subjects exposed to a battery of stimuli, including alpha-attenuation, auditory onset, and mismatch-negativity responses and a new medium-long EEG experiment involving data acquisition during 13 h. Linear models were estimated to lower bound the scalp-to-ear capacity, i.e., predicting ear-EEG data from simultaneously recorded scalp EEG. A cross-validation procedure was employed to ensure unbiased estimates. We present several pieces of evidence in support of the keyhole hypothesis: There is a high mutual information between data acquired at scalp electrodes and through the ear-EEG “keyhole,” furthermore we show that the view—represented as a linear mapping—is stable across both time and mental states. Specifically, we find that ear-EEG data can be predicted reliably from scalp EEG. We also address the reverse view, and demonstrate that large portions of the scalp EEG can be predicted from ear-EEG, with the highest predictability achieved in the temporal regions and when using ear-EEG electrodes with a common reference electrode