3,948 research outputs found

    Analogue event horizons in dielectric medium

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    In this thesis I numerically study an optical pulse travelling in a dielectric medium as an analogue event horizon. A novel numerical method is developed to study the scattering properties of this optical system. Numerical solutions of scattering problems often exhibit instabilities. The staircase approximation, in addition, can cause slow convergence. We present a differential equation for the scattering matrix which solves both of these problems. The new algorithm inherits the numerical stability of the S matrix algorithm and converges faster for a smoothly varying potential than the S matrix algorithm with the staircase approximation. We apply our equation to solve a 1D stationary scattering of plane waves from a non-periodic smoothly varying pulse/scatterer travelling with a constant velocity in a lossless medium. The properties of stability and the convergence of the Riccati matrix equation are demonstrated. Furthermore, we include a relative velocity between the scatterer and the wave medium to generalise the algorithm further where the number of right and left going modes are not equal. The algorithm is applicable for stationary scattering process from arbitrarily shaped smooth scatterers, periodic or non-periodic, even when the scatterer is varying at the scale of wavelengths. This method is used to present numerical results for a sub-femtoseconds optical pulse travelling in bulk silica. We calculate the analogue hawking radiation from the analogue system. The temperature of the hawking radiation is studied systematically with many different profiles of pulses. We find out steepness, intensity and duration of the pulse are most important in producing analogue hawking radiation in these systems. A better numerical and theoretical understanding will make the experiments better suited to detect hawking radiation

    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 animalā€™s own behaviour and/or the competitorā€™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 animalā€™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

    Colossal Trajectory Mining: A unifying approach to mine behavioral mobility patterns

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    Spatio-temporal mobility patterns are at the core of strategic applications such as urban planning and monitoring. Depending on the strength of spatio-temporal constraints, different mobility patterns can be defined. While existing approaches work well in the extraction of groups of objects sharing fine-grained paths, the huge volume of large-scale data asks for coarse-grained solutions. In this paper, we introduce Colossal Trajectory Mining (CTM) to efficiently extract heterogeneous mobility patterns out of a multidimensional space that, along with space and time dimensions, can consider additional trajectory features (e.g., means of transport or activity) to characterize behavioral mobility patterns. The algorithm is natively designed in a distributed fashion, and the experimental evaluation shows its scalability with respect to the involved features and the cardinality of the trajectory dataset

    Development and assessment of learning-based vessel biomarkers from CTA in ischemic stroke

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    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

    Development and assessment of learning-based vessel biomarkers from CTA in ischemic stroke

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    Analysis and Modelling of TTL ice crystals based on in-situ light scattering patterns

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    Even though there are numerous studies on cirrus clouds and its influence on climate, lack of detailed information on its microphysical properties like ice crystal geometry, still exists. Challenges like instrumental limitations and scarcity of observational data could be the reasons behind it. But this knowledge gap has only heightened the error in climate model predictions. Therefore, this study is focused on the Tropical Tropopause Layer (TTL), where cirrus clouds can be seen, and the temperature bias is higher. Since the shape and surface geometry of ice crystals greatly influence the temperature, a detailed understanding of these ice crystals is necessary. So, this paper will look in-depth on finding the morphology of different types of ice crystals in the TTL. The primary objective of this research is to analyse the scattering patterns of ice crystals in the TTL cirrus and find their characteristics like shape and size distributions. As cirrus is a high cloud, it plays a crucial role in the Earth-atmosphere radiation balance and by knowing the scattering properties of ice crystals, their impact on the radiative balance can be estimated. This research further helps to broaden the understanding of the general scattering properties of TTL ice crystals, to support climate modelling and contribute towards more accurate climate prediction. An investigation into the light scattering data is presented. The data consist of 2D scattering patterns of ice crystals of size 1-100Ī¼m captured by the Aerosol Ice Interface Transition Spectrometer (AIITS) between the scattering angles 6Ā° and 25Ā° at the wavelength of 532nm. The images were taken during the NERC and NASA Co-ordinated Airborne Studies in the Tropics and Airborne Tropical Tropopause Experiment (known as the CAST-ATTREX campaign) on 5th March 2015 at an altitude between 15-16km over the Eastern Pacific. The features in the scattering patterns are analysed to identify the crystal habit, as they vary with the geometry of the crystal. After the analysis phase, the model crystals of specific types and sizes are generated using an appropriate computer program. The scattering data of the model crystals are then simulated using a Beam Tracing Model (BTM) based on physical optics, as geometric optics doesnā€™t produce the required information and exact methods (like T-matrix or Discrete Dipole Approximation) are either unsuitable for large size parameters or time-consuming. The simulated scattering pattern of a model crystal is then compared against that of the AIITS to find the characteristics like shape, surface texture and size of the ice crystals. By successive testing and further analysis, the crystal sizes are estimated. Since the manual analysis of scattering patterns is time-consuming, a pilot study on Deep Learning Network has been undertaken to classify the scattering patterns. Previous studies have shown that there are high concentrations of small ice crystals in TTL cirrus. However, these crystals, especially <30Ī¼m, are often misclassified due to the limited resolution of the imaging instruments, or even considered as shattered ice. Through this research it was possible to explore both the crystal habit and its surface texture with greater accuracy as the scattering patterns captured by the AIITS are analysed instead of crystal images. It was found that most of the crystals are quasi-spheroidal in shape and that there is indeed an abundance of smaller crystals <30Ī¼m. It was also found that over a quarter of the crystal population has rough surfaces

    The Generation of 3D Surface Meshes for NURBS-Enhanced FEM

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    This work presents the first method for generating triangular surface meshes in three dimensions for the NURBS-enhanced finite element method. The generated meshes may contain triangular elements that span across multiple NURBS surfaces, whilst maintaining the exact representation of the CAD geometry. This strategy completely eliminates the need for de-featuring complex watertight CAD models and, at the same time, eliminates any uncertainty associated with the simplification of CAD models. In addition, the ability to create elements that span across multiple surfaces ensures that the generated meshes are highly compliant with the requirements of the user-specified spacing function, even if the CAD model contains very small geometric features. To demonstrate the capability, the proposed strategy is applied to a variety of CAD geometries, taken from areas such as solid/structural mechanics, fluid dynamics and wave propagation

    Dynamic data structures for k-nearest neighbor queries

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    Our aim is to develop dynamic data structures that support k-nearest neighbors (k-NN) queries for a set of n point sites in the plane in O(f(n)+k) time, where f(n) is some polylogarithmic function of n. The key component is a general query algorithm that allows us to find the k-NN spread over t substructures simultaneously, thus reducing an O(tk) term in the query time to O(k). Combining this technique with the logarithmic method allows us to turn any static k-NN data structure into a data structure supporting both efficient insertions and queries. For the fully dynamic case, this technique allows us to recover the deterministic, worst-case, O(log2ā”n/logā”logā”n+k) query time for the Euclidean distance claimed before, while preserving the polylogarithmic update times. We adapt this data structure to also support fully dynamic geodesic k-NN queries among a set of sites in a simple polygon. For this purpose, we design a shallow cutting based, deletion-only k-NN data structure. More generally, we obtain a dynamic planar k-NN data structure for any type of distance functions for which we can build vertical shallow cuttings. We apply all of our methods in the plane for the Euclidean distance, the geodesic distance, and general, constant-complexity, algebraic distance functions
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