3,217 research outputs found

    Computational techniques to interpret the neural code underlying complex cognitive processes

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    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

    Complexity & wormholes in holography

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    Holography has proven to be a highly successful approach in studying quantum gravity, where a non-gravitational quantum field theory is dual to a quantum gravity theory in one higher dimension. This doctoral thesis delves into two key aspects within the context of holography: complexity and wormholes. In Part I of the thesis, the focus is on holographic complexity. Beginning with a brief review of quantum complexity and its significance in holography, the subsequent two chapters proceed to explore this topic in detail. We study several proposals to quantify the costs of holographic path integrals. We then show how such costs can be optimized and match them to bulk complexity proposals already existing in the literature. In Part II of the thesis, we shift our attention to the study of spacetime wormholes in AdS/CFT. These are bulk spacetime geometries having two or more disconnected boundaries. In recent years, such wormholes have received a lot of attention as they lead to interesting implications and raise important puzzles. We study the construction of several simple examples of such wormholes in general dimensions in the presence of a bulk scalar field and explore their implications in the boundary theory

    Deep Learning Techniques for Electroencephalography Analysis

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    In this thesis we design deep learning techniques for training deep neural networks on electroencephalography (EEG) data and in particular on two problems, namely EEG-based motor imagery decoding and EEG-based affect recognition, addressing challenges associated with them. Regarding the problem of motor imagery (MI) decoding, we first consider the various kinds of domain shifts in the EEG signals, caused by inter-individual differences (e.g. brain anatomy, personality and cognitive profile). These domain shifts render multi-subject training a challenging task and impede robust cross-subject generalization. We build a two-stage model ensemble architecture and propose two objectives to train it, combining the strengths of curriculum learning and collaborative training. Our subject-independent experiments on the large datasets of Physionet and OpenBMI, verify the effectiveness of our approach. Next, we explore the utilization of the spatial covariance of EEG signals through alignment techniques, with the goal of learning domain-invariant representations. We introduce a Riemannian framework that concurrently performs covariance-based signal alignment and data augmentation, while training a convolutional neural network (CNN) on EEG time-series. Experiments on the BCI IV-2a dataset show that our method performs superiorly over traditional alignment, by inducing regularization to the weights of the CNN. We also study the problem of EEG-based affect recognition, inspired by works suggesting that emotions can be expressed in relative terms, i.e. through ordinal comparisons between different affective state levels. We propose treating data samples in a pairwise manner to infer the ordinal relation between their corresponding affective state labels, as an auxiliary training objective. We incorporate our objective in a deep network architecture which we jointly train on the tasks of sample-wise classification and pairwise ordinal ranking. We evaluate our method on the affective datasets of DEAP and SEED and obtain performance improvements over deep networks trained without the additional ranking objective

    Classical and quantum algorithms for scaling problems

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    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

    Optimal decay for solutions of the Teukolsky equation on the Kerr metric for the full subextremal range |a| < M

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    We derive the large time asymptotics of initially regular and localized solutions of the Teukolsky equation on the exterior of a subextremal Kerr black hole for any half integer spin. More precisely, we obtain the leading order term (predicted by Price's law) in the large time regime assuming that the initial data have compact support and have enough (but finite) Sobolev regularity. For initial data with less spatial decay (typically decaying like r^{--1--α\alpha} with α\alpha ∈\in (0, 1)), we prove that the solution has a pointwise decay of order t^{--1--α\alpha--s--|s|+} on spatially compact regions. In the proof, we adopt the spectral point of view and make use of recent advances in microlocal analysis and non elliptic Fredholm theory which provide a robust framework to study linear operators on black hole type spacetimes

    Data-assisted modeling of complex chemical and biological systems

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    Complex systems are abundant in chemistry and biology; they can be multiscale, possibly high-dimensional or stochastic, with nonlinear dynamics and interacting components. It is often nontrivial (and sometimes impossible), to determine and study the macroscopic quantities of interest and the equations they obey. One can only (judiciously or randomly) probe the system, gather observations and study trends. In this thesis, Machine Learning is used as a complement to traditional modeling and numerical methods to enable data-assisted (or data-driven) dynamical systems. As case studies, three complex systems are sourced from diverse fields: The first one is a high-dimensional computational neuroscience model of the Suprachiasmatic Nucleus of the human brain, where bifurcation analysis is performed by simply probing the system. Then, manifold learning is employed to discover a latent space of neuronal heterogeneity. Second, Machine Learning surrogate models are used to optimize dynamically operated catalytic reactors. An algorithmic pipeline is presented through which it is possible to program catalysts with active learning. Third, Machine Learning is employed to extract laws of Partial Differential Equations describing bacterial Chemotaxis. It is demonstrated how Machine Learning manages to capture the rules of bacterial motility in the macroscopic level, starting from diverse data sources (including real-world experimental data). More importantly, a framework is constructed though which already existing, partial knowledge of the system can be exploited. These applications showcase how Machine Learning can be used synergistically with traditional simulations in different scenarios: (i) Equations are available but the overall system is so high-dimensional that efficiency and explainability suffer, (ii) Equations are available but lead to highly nonlinear black-box responses, (iii) Only data are available (of varying source and quality) and equations need to be discovered. For such data-assisted dynamical systems, we can perform fundamental tasks, such as integration, steady-state location, continuation and optimization. This work aims to unify traditional scientific computing and Machine Learning, in an efficient, data-economical, generalizable way, where both the physical system and the algorithm matter

    Hyperbolic Image-Text Representations

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    Visual and linguistic concepts naturally organize themselves in a hierarchy, where a textual concept ``dog'' entails all images that contain dogs. Despite being intuitive, current large-scale vision and language models such as CLIP do not explicitly capture such hierarchy. We propose MERU, a contrastive model that yields hyperbolic representations of images and text. Hyperbolic spaces have suitable geometric properties to embed tree-like data, so MERU can better capture the underlying hierarchy in image-text data. Our results show that MERU learns a highly interpretable representation space while being competitive with CLIP's performance on multi-modal tasks like image classification and image-text retrieval.Comment: Technical repor

    Robust Estimation of Surface Curvature Information from Point Cloud Data

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    This paper surveys and evaluates some popular state of the art methods for algorithmic curvature and normal estimation. In addition to surveying existing methods we also propose a new method for robust curvature estimation and evaluate it against existing methods thus demonstrating its superiority to existing methods in the case of significant data noise. Throughout this paper we are concerned with computation in low dimensional spaces (N < 10) and primarily focus on the computation of the Weingarten map and quantities that may be derived from this; however, the algorithms discussed are theoretically applicable in any dimension. One thing that is common to all these methods is their basis in an estimated graph structure. For any of these methods to work the local geometry of the manifold must be exploited; however, in the case of point cloud data it is often difficult to discover a robust manifold structure underlying the data, even in simple cases, which can greatly influence the results of these algorithms. We hope that in pushing these algorithms to their limits we are able to discover, and perhaps resolve, many major pitfalls that may affect potential users and future researchers hoping to improve these methodsComment: 16 pages, 13 figure

    FibeRed: Fiberwise Dimensionality Reduction of Topologically Complex Data with Vector Bundles

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    Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way that the base space accounts for the large scale topology, while the fibers account for the local geometry. This allows one to reduce the dimensionality of the fibers, while preserving the large scale topology. We formalize this point of view and, as an application, we describe a dimensionality reduction algorithm based on topological inference for vector bundles. The algorithm takes as input a dataset together with an initial representation in Euclidean space, assumed to recover part of its large scale topology, and outputs a new representation that integrates local representations obtained through local linear dimensionality reduction. We demonstrate this algorithm on examples coming from dynamical systems and chemistry. In these examples, our algorithm is able to learn topologically faithful embeddings of the data in lower target dimension than various well known metric-based dimensionality reduction algorithms
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