All-optical interrogation of neural circuits during behaviour

This thesis explores the fundamental question of how patterns of neural activity encode information and guide behaviour. To address this, one needs three things: a way to record neural activity so that one can correlate neuronal responses with environmental variables; a flexible and specific way to influence neural activity so that one can modulate the variables that may underlie how information is encoded; a robust behavioural paradigm that allows one to assess how modulation of both environmental and neural variables modify behaviour. Techniques combining all three would be transformative for investigating which features of neural activity, and which neurons, most influence behavioural output. Previous electrical and optogenetic microstimulation studies have told us much about the impact of spatially or genetically defined groups of neurons, however they lack the flexibility to probe the contribution of specific, functionally defined subsets. In this thesis I leverage a combination of existing technologies to approach this goal. I combine two-photon calcium imaging with two-photon optogenetics and digital holography to generate an “all-optical” method for simultaneous reading and writing of neural activity in vivo with high spatio-temporal resolution. Calcium imaging allows for cellular resolution recordings from neural populations. Two-photon optogenetics allows for targeted activation of individual cells. Digital holography, using spatial light modulators (SLMs), allows for simultaneous photostimulation of tens to hundreds of neurons in arbitrary spatial locations. Taken together, I demonstrate that this method allows one to map the functional signature of neurons in superficial mouse barrel cortex and to target photostimulation to functionally-defined subsets of cells. I develop a suite of software that allows for quick, intuitive execution of such experiments and I combine this with a behavioural paradigm testing the effect of targeted perturbations on behaviour. In doing so, I demonstrate that animals are able to reliably detect the targeted activation of tens of neurons, with some sensitive to as few as five cortical cells. I demonstrate that such learning can be specific to targeted cells, and that the lower bound of perception shifts with training. The temporal structure of such perturbations had little impact on behaviour, however different groups of neurons drive behaviour to different extents. In order to probe which characteristics underly such variation, I tested whether the sensory response strength or correlation structure of targeted ensembles influenced their behavioural salience. Whilst these final experiments were inconclusive, they demonstrate their feasibility and provide us with some key actionable improvements that could further strengthen the all-optical approach. This thesis therefore represents a significant step forward towards the goal of combining high resolution readout and perturbation of neural activity with behaviour in order to investigate which features of the neural code are behaviourally relevant

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described