Precision modulation in predictive coding hierarchies: theoretical, behavioural and neuroimaging investigations

Estimation of uncertainty is an important aspect of perception and a prerequisite for effective action. This thesis explores the implementation of uncertainty estimation as precision modulation within a predictive coding hierarchy, optimised within a neurbiologically-plausible message-passing scheme via the minimisation of free-energy. This thesis consists of six chapters. The first presents a new model of a classic visual illusion, the Cornsweet illusion, which demonstrates that the Cornsweet illusion is a natural consequence of Bayes-optimal perception under the free-energy principle, and demonstrates that increasing contrast can be modelled by increasing signal-to-noise ratio. The second chapter describes dynamic causal modelling of EEG data collected from participants viewing the Cornsweet illusion, demonstrating that a reduction in precision, or superficial pyramidal cell gain, in lower visual hierarchical levels, is sufficient to explain contrast-dependent changes in ERPs. The third describes a model of a simple attentional paradigm – the Posner paradigm – recasting attention as the optimal modulation of precision in sensory channels. The fourth describes an MEG study of the Posner paradigm, using Bayesian model selection to explore the role of changes in backwards and modulatory connections and changes in local superficial pyramidal cell gain in producing the electrophysiological and behavioural correlates of the Posner paradigm. The fifth chapter recasts the Posner paradigm in the motor domain to investigate the level (intrinsic vs. extrinsic) of precision modulation by motor cues. The sixth describes a new model of sensory attenuation based on using precision modulation to balance the imperatives to act and perceive. I hope to demonstrate that precision modulation within predictive coding hierarchies, under the free-energy principle, is a flexible and powerful way of describing and explaining both behavioural and neuroimaging data

A geometric characterization of toric varieties

We prove a conjecture of Shokurov which characterises toric varieties using log pairs

Revealed cardinal preference

I prove that as long as we allow the marginal utility for money (lambda) to vary between purchases (similarly to the budget) then the quasi-linear and the ordinal budget-constrained models rationalize the same data. However, we know that lambda is approximately constant. I provide a simple constructive proof for the necessary and sufficient condition for the constant lambda rationalization, which I argue should replace the Generalized Axiom of Revealed Preference in empirical studies of consumer behavior. 'Go Cardinals!' It is the minimal requirement of any scientifi c theory that it is consistent with the data it is trying to explain. In the case of (Hicksian) consumer theory it was revealed preference -introduced by Samuelson (1938,1948) - that provided an empirical test to satisfy this need. At that time most of economic reasoning was done in terms of a competitive general equilibrium, a concept abstract enough so that it can be built on the ordinal preferences over baskets of goods - even if the extremely specialized ones of Arrow and Debreu. However, starting in the sixties, economics has moved beyond the 'invisible hand' explanation of how -even competitive- markets operate. A seemingly unavoidable step of this 'revolution' was that ever since, most economic research has been carried out in a partial equilibrium context. Now, the partial equilibrium approach does not mean that the rest of the markets are ignored, rather that they are held constant. In other words, there is a special commodity -call it money - that reflects the trade-offs of moving purchasing power across markets. As a result, the basic building block of consumer behavior in partial equilibrium is no longer the consumer's preferences over goods, rather her valuation of them, in terms of money. This new paradigm necessitates a new theory of revealed preference

Insolubility Theorems and EPR Argument

I wish to thank in particular Arthur Fine for very perceptive comments on a previous draft of this paper. Many thanks also to Theo Nieuwenhuizen for inspiration, to Max Schlosshauer for correspondence, to two anonymous referees for shrewd observations, and to audiences at Aberdeen, Cagliari and Oxford (in particular to Harvey Brown, Elise Crull, Simon Saunders, Chris Timpson and David Wallace) for stimulating questions. This paper was written during my tenure of a Leverhulme Grant on ‘The Einstein Paradox’: The Debate on Nonlocality and Incompleteness in 1935 (Project Grant nr. F/00 152/AN), and it was revised for publication during my tenure of a Visiting Professorship in the Doctoral School of Philosophy and Epistemology, University of Cagliari (Contract nr. 268/21647).Peer reviewedPostprin

Arterial Spin Labeling MRI in Carotid Stenosis: Arterial Transit Artifacts May Predict Symptoms

Background: Stenosis of the internal carotid artery has a higher risk for stroke. Many investigations have focused on structure and plaque composition as signs of plaque vulnerability, but few studies have analyzed hemodynamic changes in the brain as a risk factor. Purpose: To use 3-T MRI methods including contrast material–enhanced MR angiography, carotid plaque imaging, and arterial spin labeling (ASL) to identify imaging parameters that best help distinguish between asymptomatic and symptomatic participants with carotid stenosis. Materials and Methods: Participants with carotid stenosis from two ongoing prospective studies who underwent ASL and carotid plaque imaging with use of 3-T MRI in the same setting from 2014 to 2018 were studied. Participants were assessed clinically for recent symptoms (transient ischemic attack or stroke) and divided equally into symptomatic and nonsymptomatic groups. Reviewers were blinded to the symptomatic status and MRI scans were analyzed for the degree of stenosis, plaque surface structure, presence of intraplaque hemorrhage (IPH), circle of Willis collaterals, and the presence and severity of arterial transit artifacts (ATAs) at ASL imaging. MRI findings were correlated with symptomatic status by using t tests and the Fisher exact test. Results: A total of 44 participants (mean age, 71 years 6 10 [standard deviation]; 31 men) were evaluated. ATAs were seen only in participants with greater than 70% stenosis (16 of 28 patients; P , .001) and were associated with absence of anterior communicating artery (13 of 16 patients; P = .003). There was no association between history of symptoms and degree of stenosis (27 patients with 70% stenosis and 17 patients with ,70%; P = .54), IPH (12 patients with IPH and 32 patients without IPH; P = .31), and plaque surface structure (17 patients with irregular or ulcerated plaque and 27 with smooth plaque; P = .54). Participants with ATAs (n = 16) were more likely to be symptomatic than were those without ATAs (n = 28) (P = .004). Symptomatic status also was associated with the severity of ATAs (P = .002). Conclusion: Arterial transit artifacts were the only factor associated with recent ischemic symptoms in participants with carotid stenosis. The degree of stenosis, plaque ulceration, and intraplaque hemorrhage were not associated with symptomatic statu

Analyticity, Unitarity and One-loop Graviton Corrections to Compton Scattering

We compute spin-flip cross section for graviton photoproduction on a spin-1/2 target of finite mass. Using this tree-level result, we find one-loop graviton correction to the spin-flip low-energy forward Compton scattering amplitude by using Gerasimov-Drell-Hearn sum rule. We show that this result agrees with the corresponding perturbative computations, implying the validity of the sum rule at one-loop level, contrary to the previous claims. We discuss possible effects from the black hole production and string Regge trajectory exchange at very high energies. These effects seem to soften the UV divergence present at one-loop graviton level. Finally, we discuss the relation of these observations with the models that involve extra dimensions.Comment: 15 pages, 3 figure

The computational anatomy of psychosis.

This paper considers psychotic symptoms in terms of false inferences or beliefs. It is based on the notion that the brain is an inference machine that actively constructs hypotheses to explain or predict its sensations. This perspective provides a normative (Bayes-optimal) account of action and perception that emphasizes probabilistic representations; in particular, the confidence or precision of beliefs about the world. We will consider hallucinosis, abnormal eye movements, sensory attenuation deficits, catatonia, and delusions as various expressions of the same core pathology: namely, an aberrant encoding of precision. From a cognitive perspective, this represents a pernicious failure of metacognition (beliefs about beliefs) that can confound perceptual inference. In the embodied setting of active (Bayesian) inference, it can lead to behaviors that are paradoxically more accurate than Bayes-optimal behavior. Crucially, this normative account is accompanied by a neuronally plausible process theory based upon hierarchical predictive coding. In predictive coding, precision is thought to be encoded by the post-synaptic gain of neurons reporting prediction error. This suggests that both pervasive trait abnormalities and florid failures of inference in the psychotic state can be linked to factors controlling post-synaptic gain - such as NMDA receptor function and (dopaminergic) neuromodulation. We illustrate these points using biologically plausible simulations of perceptual synthesis, smooth pursuit eye movements and attribution of agency - that all use the same predictive coding scheme and pathology: namely, a reduction in the precision of prior beliefs, relative to sensory evidence