Parkinson’s disease is a frequent and disabling neurological disorder, which heavily impairs patients’ ability to perform and control movements. Electrical stimulation of a deep-seated brain region, the subthalamic nucleus (STN), has been shown to significantly improve patients’ motor function and quality of life. Recent technological advances in deep brain stimulation (DBS) render it possible to adjust electrical stimulation of the STN to ongoing brain activity, referred to as closed-loop DBS. Here, the implanted electrodes do not only send signals to the brain but also read out neural signals generated by the brain. Closed-loop DBS offers the intriguing possibility to specifically suppress pathological brain activity while leaving physiological activity unaltered. We propose an innovative and ambitious project, which the researcher will conduct in the Experimental Neurology group headed by Prof. Peter Brown at the University of Oxford, a world-leading laboratory in closed-loop stimulation. In this project we aim to test the hypothesis that closed-loop DBS that selectively targets pathological synchronous firing of neurons at 13 – 30 Hz, the so-called beta-rhythm, will interrupt neural activity related to motor impairment, but not normal functions of the brain. To this end, Parkinson patients with implanted electrodes in the STN will perform two tasks probing different aspects of motor control whilst receiving closed loop stimulation. We will simultaneously record activity from the STN and areas localized on the surface of the brain. This will allow us to assess how suppression of the beta-rhythm affects motor-related activity and connectivity in the human brain revealing it’s causal effects on motor function. Selective suppression of abnormal brain function and preservation of physiological brain mechanisms could be the key to obtain the best possible clinical benefit, whilst avoiding unwanted side effects in the treatment of Parkinson’s disease.

The aim of this project is to develop a new synergy between climate and computer science to increase the accuracy and hence reliability of comprehensive weather and climate models. The scientific basis for this project lies in the PI’s pioneering research on stochastic sub-grid parametrisations for climate models. These parametrisations provide estimates of irreducible uncertainty in weather and climate models, and will be used to determine where numerical precision for model variables can be reduced without degradation. By identifying those bits that carry negligible information – typically in high-wavenumber components of the dynamical core and within parametrisation and Earth-System modules – computational resources can be reinvested into areas (resolution, process representation, ensemble size) where they are sorely needed. This project will determine scale-dependent estimates of information content as rigorously as possible based on a variety of new tools, which include information-theoretic diagnostics and emulators of imprecision, and in a variety of models, from idealised to comprehensive. The project will contribute significantly to the development of next-generation weather and climate models and is well timed for the advent of exascale supercomputing where energy efficiency is paramount and where movement of bits, being the single biggest determinant of power consumption, must be minimised. The ideas will be tested on emerging hardware capable of exploiting the benefits of mixed-precision arithmetic. A testable scientific hypothesis is presented: a proposed increase in forecast reliability arising from an increase in the forecast model’s vertical resolution, the cost being paid for by a reduction in precision of small-scale variables. This project can be expected to provide new scientific understanding of how different scales interact in the nonlinear climate system, for example in maintaining persistent atmospheric flow regimes.

Questions about prime numbers make up several of the oldest and most important open problems in mathematics. Unfortunately our techniques for solving these problems are very limited; even some of the most basic and simple to state questions about primes are well beyond current techniques. This project studies several different questions related to the distribution of the primes, with the aim of developing new flexible techniques for studying the primes in general. Such new techniques would then give insight to the fundamental problems at the heart of the subject. The only general approach we have to counting primes is via variants of ‘Type I’ and ‘Type II’ arithmetic information. There have been several remarkable developments in sieve methods in recent years, which have greatly enhanced the utility of Type I information. Without establishing some sort of Type II information, however, it seems unlikely that one can fully solve the most important problems in the subject. This proposal seeks to develop both our Type I techniques and our Type II techniques, as well as the interactions between them. A common theme throughout the proposal is to identify and classify potential obstructions to traditional methods, and then overcome these obstructions using a combinations of new ideas. Often these new ideas will come from other areas of mathematics, such as combinatorics, geometry, probability, automorphic forms or harmonic analysis. This approach has already led to significant advances in our understanding of primes in recent years, most notably in the gaps between primes. The proposal is based around several intermediate problems for developing these connections further, giving opportunities for proof-of-concept results of such new ideas overcoming old barriers.

Sleep is vital and universal, but its biological function remains unknown. This project will seek to understand why we need to sleep by studying how the brain responds to sleep loss. My previous work in Drosophila showed that rising sleep pressure activates two dozen sleep-inducing neurons in the dorsal fan-shaped body (dFB) of the central complex. Sleep need is encoded in the electrical excitability of these neurons, which fluctuates because two potassium conductances, voltage-gated Shaker and the leak channel Sandman, are modulated antagonistically. As a consequence, dFB neurons are electrically silent during waking and persistently active during sleep. The key open question addressed in this project is the nature of the molecular changes that drive dFB neurons into the electrically active state. My preliminary data point to two dFB-intrinsic transducers of sleep pressure. First, the Shaker β subunit Hyperkinetic responds via a bound nicotinamide cofactor to oxidative by-products of mitochondrial electron transport, revealing a potential connection between energy metabolism, oxidative stress, and sleep, three processes implicated independently in lifespan, aging, and disease. To strengthen this connection, we will monitor sleep and the biophysics of dFB neurons after perturbing mitochondrial respiration or cellular redox chemistry and vice versa. Second, Rho GTPases relay currently unknown signals to the machinery responsible for the regulated endocytosis of Sandman, whose extraction from the plasma membrane is a prerequisite for switching the sleep-promoting activity of dFB neurons on. To identify these signals, we will investigate cell-autonomous, synaptic, and non-synaptic mechanisms of GTPase control. Because clear parallels exist between dFB neurons and sleep-active neurons in the mammalian hypothalamus, mechanistic insights that can currently be gained only in Drosophila are expected to have broad validity for understanding sleep and its disruptions.