7,770 research outputs found
Computational techniques to interpret the neural code underlying complex cognitive processes
Advances in large-scale neural recording technology have significantly improved the
capacity to further elucidate the neural code underlying complex cognitive processes.
This thesis aimed to investigate two research questions in rodent models. First, what
is the role of the hippocampus in memory and specifically what is the underlying
neural code that contributes to spatial memory and navigational decision-making.
Second, how is social cognition represented in the medial prefrontal cortex at the
level of individual neurons. To start, the thesis begins by investigating memory and
social cognition in the context of healthy and diseased states that use non-invasive
methods (i.e. fMRI and animal behavioural studies). The main body of the thesis
then shifts to developing our fundamental understanding of the neural mechanisms
underpinning these cognitive processes by applying computational techniques to ana lyse stable large-scale neural recordings. To achieve this, tailored calcium imaging
and behaviour preprocessing computational pipelines were developed and optimised
for use in social interaction and spatial navigation experimental analysis. In parallel,
a review was conducted on methods for multivariate/neural population analysis. A
comparison of multiple neural manifold learning (NML) algorithms identified that non linear algorithms such as UMAP are more adaptable across datasets of varying noise
and behavioural complexity. Furthermore, the review visualises how NML can be
applied to disease states in the brain and introduces the secondary analyses that
can be used to enhance or characterise a neural manifold. Lastly, the preprocessing
and analytical pipelines were combined to investigate the neural mechanisms in volved in social cognition and spatial memory. The social cognition study explored
how neural firing in the medial Prefrontal cortex changed as a function of the social
dominance paradigm, the "Tube Test". The univariate analysis identified an ensemble
of behavioural-tuned neurons that fire preferentially during specific behaviours such
as "pushing" or "retreating" for the animal’s own behaviour and/or the competitor’s
behaviour. Furthermore, in dominant animals, the neural population exhibited greater
average firing than that of subordinate animals. Next, to investigate spatial memory,
a spatial recency task was used, where rats learnt to navigate towards one of three
reward locations and then recall the rewarded location of the session. During the
task, over 1000 neurons were recorded from the hippocampal CA1 region for five rats
over multiple sessions. Multivariate analysis revealed that the sequence of neurons encoding an animal’s spatial position leading up to a rewarded location was also active
in the decision period before the animal navigates to the rewarded location. The result
posits that prospective replay of neural sequences in the hippocampal CA1 region
could provide a mechanism by which decision-making is supported
Applications of Deep Learning Models in Financial Forecasting
In financial markets, deep learning techniques sparked a revolution, reshaping conventional approaches and amplifying predictive capabilities. This thesis explored the applications of deep learning models to unravel insights and methodologies aimed at advancing financial forecasting.
The crux of the research problem lies in the applications of predictive models within financial domains, characterised by high volatility and uncertainty. This thesis investigated the application of advanced deep-learning methodologies in the context of financial forecasting, addressing the challenges posed by the dynamic nature of financial markets. These challenges were tackled by exploring a range of techniques, including convolutional neural networks (CNNs), long short-term memory networks (LSTMs), autoencoders (AEs), and variational autoencoders (VAEs), along with
approaches such as encoding financial time series into images. Through analysis, methodologies such as transfer learning, convolutional neural networks, long short-term memory networks, generative modelling, and image encoding of time series data were examined. These methodologies collectively offered a comprehensive toolkit for extracting meaningful insights from financial data.
The present work investigated the practicality of a deep learning CNN-LSTM model within the Directional Change framework to predict significant DC events—a task crucial for timely decisionmaking in financial markets. Furthermore, the potential of autoencoders and variational autoencoders to enhance financial forecasting accuracy and remove noise from financial time series data was explored. Leveraging their capacity within financial time series, these models offered promising avenues for improved data representation and subsequent forecasting. To further contribute to
financial prediction capabilities, a deep multi-model was developed that harnessed the power of pre-trained computer vision models. This innovative approach aimed to predict the VVIX, utilising the cross-disciplinary synergy between computer vision and financial forecasting. By integrating knowledge from these domains, novel insights into the prediction of market volatility were provided
Symmetries of Riemann surfaces and magnetic monopoles
This thesis studies, broadly, the role of symmetry in elucidating structure. In particular, I investigate the role that automorphisms of algebraic curves play in three specific contexts; determining the orbits of theta characteristics, influencing the geometry of the highly-symmetric Bring’s curve, and in constructing magnetic monopole solutions. On theta characteristics, I show how to turn questions on the existence of invariant characteristics into questions of group cohomology, compute comprehensive tables of orbit decompositions for curves of genus 9 or less, and prove results on the existence of infinite families of curves with invariant characteristics. On Bring’s curve, I identify key points with geometric significance on the curve, completely determine the structure of the quotients by subgroups of automorphisms, finding new elliptic curves in the process, and identify the unique invariant theta characteristic on the curve. With respect to monopoles, I elucidate the role that the Hitchin conditions play in determining monopole spectral curves, the relation between these conditions and the automorphism group of the curve, and I develop the theory of computing Nahm data of symmetric monopoles. As such I classify all 3-monopoles whose Nahm data may be solved for in terms of elliptic functions
En Route to Reduction: Lorentzian Manifolds and Causal Sets
I present aspects of causal set theory (a research programme in quantum gravity) as being en route to achieving a reduction of Lorentzian geometry to causal sets. I take reduction in philosophers' sense; and I argue that the prospects are good for there being a reduction of the type envisaged by Nagel. (I also discuss the prospects for the stronger functionalist variant of Nagelian reduction, that was formulated by Lewis.)
One main theme will be causal set theory's use of a physical scale (viz. the Planck scale) to formulate how it recovers a Lorentzian manifold. This use illustrates various philosophical topics relevant to reduction, such as limiting relations between theories, and the role of analogy. I also emphasise causal set theory's probabilistic method, viz. Poisson sprinkling: which is used both for formulating the reduction and for exploring its prospects
Classical and quantum algorithms for scaling problems
This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size
On the Global Topology of Moduli Spaces of Riemannian Metrics with Holonomy
We discuss aspects of the global topology of moduli spaces of hyperkähler metrics.
If the second Betti number is larger than , we show that each connected component of these moduli spaces is not contractible. Moreover, in certain cases, we show that the components are simply connected and determine the second rational homotopy group. By that, we prove that the rank of the second homotopy group is bounded from below by the number of orbits of MBM-classes in the integral cohomology. \\
An explicit description of the moduli space of these hyperkähler metrics in terms of Torelli theorems will be given. We also provide such a description for the moduli space of Einstein metrics on the Enriques manifold. For the Enriques manifold, we also give an example of a desingularization process similar to the Kummer construction of Ricci-flat metrics on a Kummer surface.\\
We will use these theorems to provide topological statements for moduli spaces of Ricci-flat and Einstein metrics in any dimension larger than . For a compact simply connected manifold we show that the moduli space of Ricci flat metrics on splits homeomorphically into a product of the moduli space of Ricci flat metrics on and the moduli of sectional curvature flat metrics on the torus
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