Spectral estimation for detecting low-dimensional structure in networks using arbitrary null models.

Discovering low-dimensional structure in real-world networks requires a suitable null model that defines the absence of meaningful structure. Here we introduce a spectral approach for detecting a network's low-dimensional structure, and the nodes that participate in it, using any null model. We use generative models to estimate the expected eigenvalue distribution under a specified null model, and then detect where the data network's eigenspectra exceed the estimated bounds. On synthetic networks, this spectral estimation approach cleanly detects transitions between random and community structure, recovers the number and membership of communities, and removes noise nodes. On real networks spectral estimation finds either a significant fraction of noise nodes or no departure from a null model, in stark contrast to traditional community detection methods. Across all analyses, we find the choice of null model can strongly alter conclusions about the presence of network structure. Our spectral estimation approach is therefore a promising basis for detecting low-dimensional structure in real-world networks, or lack thereof.

Engagement, not personal characteristics, was associated with the seriousness of regulatory adjudication decisions about physicians: a cross-sectional study.

BACKGROUND: Outcomes of processes questioning a physician's ability to practise -e.g. disciplinary or regulatory- may strongly impact their career and provided care. However, it is unclear what factors relate systematically to such outcomes. METHODS: In this cross-sectional study, we investigate this via multivariate, step-wise, statistical modelling of all 1049 physicians referred for regulatory adjudication at the UK medical tribunal, from June 2012 to May 2017, within a population of 310,659. In order of increasing seriousness, outcomes were: no impairment (of ability to practise), impairment, suspension (of right to practise), or erasure (its loss). This gave adjusted odds ratios (OR) for: age, race, sex, whether physicians first qualified domestically or internationally, area of practice (e.g. GP, specialist), source of initial referral, allegation type, whether physicians attended their outcome hearing, and whether they were legally represented for it. RESULTS: There was no systematic association between the seriousness of outcomes and the age, race, sex, domestic/international qualification, or the area of practice of physicians (ORs p≥0.05), except for specialists who tended to receive outcomes milder than suspension or erasure. Crucially, an apparent relationship of outcomes to age (Kruskal-Wallis, p=0.009) or domestic/international qualification (χ2,p=0.014) disappeared once controlling for hearing attendance (ORs p≥0.05). Both non-attendance and lack of legal representation were consistently related to more serious outcomes (ORs [95% confidence intervals], 5.28 [3.89, 7.18] and 1.87 [1.34, 2.60], respectively, p<0.001). CONCLUSIONS: All else equal, personal characteristics or first qualification place were unrelated to the seriousness of regulatory outcomes in the UK. Instead, engagement (attendance and legal representation), allegation type, and referral source were importantly associated to outcomes. All this may generalize to other countries and professions.

A probabilistic, distributed, recursive mechanism for decision-making in the brain.

Decision formation recruits many brain regions, but the procedure they jointly execute is unknown. Here we characterize its essential composition, using as a framework a novel recursive Bayesian algorithm that makes decisions based on spike-trains with the statistics of those in sensory cortex (MT). Using it to simulate the random-dot-motion task, we demonstrate it quantitatively replicates the choice behaviour of monkeys, whilst predicting losses of otherwise usable information from MT. Its architecture maps to the recurrent cortico-basal-ganglia-thalamo-cortical loops, whose components are all implicated in decision-making. We show that the dynamics of its mapped computations match those of neural activity in the sensorimotor cortex and striatum during decisions, and forecast those of basal ganglia output and thalamus. This also predicts which aspects of neural dynamics are and are not part of inference. Our single-equation algorithm is probabilistic, distributed, recursive, and parallel. Its success at capturing anatomy, behaviour, and electrophysiology suggests that the mechanism implemented by the brain has these same characteristics.

Probabilistic Decision Making with Spikes: From ISI Distributions to Behaviour via Information Gain.

Computational theories of decision making in the brain usually assume that sensory 'evidence' is accumulated supporting a number of hypotheses, and that the first accumulator to reach threshold triggers a decision in favour of its associated hypothesis. However, the evidence is often assumed to occur as a continuous process whose origins are somewhat abstract, with no direct link to the neural signals - action potentials or 'spikes' - that must ultimately form the substrate for decision making in the brain. Here we introduce a new variant of the well-known multi-hypothesis sequential probability ratio test (MSPRT) for decision making whose evidence observations consist of the basic unit of neural signalling - the inter-spike interval (ISI) - and which is based on a new form of the likelihood function. We dub this mechanism s-MSPRT and show its precise form for a range of realistic ISI distributions with positive support. In this way we show that, at the level of spikes, the refractory period may actually facilitate shorter decision times, and that the mechanism is robust against poor choice of the hypothesized data distribution. We show that s-MSPRT performance is related to the Kullback-Leibler divergence (KLD) or information gain between ISI distributions, through which we are able to link neural signalling to psychophysical observation at the behavioural level. Thus, we find the mean information needed for a decision is constant, thereby offering an account of Hick's law (relating decision time to the number of choices). Further, the mean decision time of s-MSPRT shows a power law dependence on the KLD offering an account of Piéron's law (relating reaction time to stimulus intensity). These results show the foundations for a research programme in which spike train analysis can be made the basis for predictions about behavior in multi-alternative choice tasks.