899 research outputs found

    Undergraduate Catalog of Studies, 2023-2024

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    Undergraduate Catalog of Studies, 2023-2024

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    Undergraduate Catalog of Studies, 2022-2023

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    Analog Photonics Computing for Information Processing, Inference and Optimisation

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    This review presents an overview of the current state-of-the-art in photonics computing, which leverages photons, photons coupled with matter, and optics-related technologies for effective and efficient computational purposes. It covers the history and development of photonics computing and modern analogue computing platforms and architectures, focusing on optimization tasks and neural network implementations. The authors examine special-purpose optimizers, mathematical descriptions of photonics optimizers, and their various interconnections. Disparate applications are discussed, including direct encoding, logistics, finance, phase retrieval, machine learning, neural networks, probabilistic graphical models, and image processing, among many others. The main directions of technological advancement and associated challenges in photonics computing are explored, along with an assessment of its efficiency. Finally, the paper discusses prospects and the field of optical quantum computing, providing insights into the potential applications of this technology.Comment: Invited submission by Journal of Advanced Quantum Technologies; accepted version 5/06/202

    Computational and experimental studies of selected magnesium and ferrous sulfate hydrates: implications for the characterisation of extreme and extraterrestrial environments

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    Magnesium sulfate hydrates are considered important rock-forming minerals on the outer three Galilean moons of Jupiter (i.e., Europa, Ganymede, Callisto) and, alongside ferrous sulfate hydrates, are promising candidate minerals for the widespread sulfate deposits that occur in the equatorial region of Mars. In such extraterrestrial environments, these minerals experience extreme high-pressure conditions in the interiour of the Galilean moons and low temperature conditions on the surface of these moons and Mars. The aim of this thesis is to understand the structural stability, compressibility, and thermal expansion of these compounds in such extreme environments and aid their identification in ongoing and future space missions. Most magnesium sulfate hydrates lack accurate reference elastic tensors, which hinders their seismological identification in lander missions on the icy moons of the outer solar system, as envisioned for the near future. In this thesis, the accuracy of recent advancements in density functional theory to predict the compressibility and elastic constants of icy satellite candidate minerals (i.e., epsomite (MgSO₄·7H₂O), gypsum (CaSO₄·2H₂O), carbon dioxide (CO₂), and benzene (C₆H₆)) was assessed by benchmarking them against experimental reference data from the literature. Key findings are that density functional theory calculations do not yield elastic constants accurate enough to be used as a reference for the seismic exploration of icy moons. However, the bulk compressibility of such materials is very accurately reproduced by density functional theory, which was therefore used to predict the compressibility of the icy satellite candidate minerals starkeyite (MgSO₄·4H₂O) and cranswickite (MgSO₄·4H₂O). Knowledge of the compressibility of such minerals is critical to model mantle processes (e.g., salt diaprisim, plate tectonics, subduction) and the density structure of the outer three Galilean moons. The thermal expansion and structural stability of three sulfate minerals (i.e., rozenite (FeSO₄·4H₂O), starkeyite, and cranswickite) was characterised for the first time using neutron diffraction. Cranswickite transforms to starkeyite at 330 K, well above the maximum surface temperature of 308 K hitherto reported on Mars. Starkeyite likely undergoes a structural phase transition at around 245 K. The structure of this proposed low-temperature polymorph could not be determined but would be of great interest since the temperature drops below 245 K on equatorial Mars at night-time. Starkeyite was also studied by means of synchrotron X-ray diffraction but suffered radiation damage. No phase transition was observed in rozenite from 290 – 21 K, which contrasts with Raman data reported in the literature, where sharpening of vibrational modes upon cooling was misinterpreted as mode splitting and evidence for two phase transitions at temperatures relevant to the Martian surface. First-principles phonon frequency calculations provide evidence supporting the absence of vibrational mode splitting. A workflow to obtain reliable reference Raman spectra for space exploration was proposed and an optical centre stick for the simultaneous acquisition of neutron diffraction and Raman spectroscopy data at the HRPD instrument was commissioned. Lastly, the structure of a polymorph of hexahydrite (MgSO₄·6H₂O), most recently proposed in the literature, was shown to be unambiguously wrong

    Mesoscopic Physics of Quantum Systems and Neural Networks

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    We study three different kinds of mesoscopic systems – in the intermediate region between macroscopic and microscopic scales consisting of many interacting constituents: We consider particle entanglement in one-dimensional chains of interacting fermions. By employing a field theoretical bosonization calculation, we obtain the one-particle entanglement entropy in the ground state and its time evolution after an interaction quantum quench which causes relaxation towards non-equilibrium steady states. By pushing the boundaries of the numerical exact diagonalization and density matrix renormalization group computations, we are able to accurately scale to the thermodynamic limit where we make contact to the analytic field theory model. This allows to fix an interaction cutoff required in the continuum bosonization calculation to account for the short range interaction of the lattice model, such that the bosonization result provides accurate predictions for the one-body reduced density matrix in the Luttinger liquid phase. Establishing a better understanding of how to control entanglement in mesoscopic systems is also crucial for building qubits for a quantum computer. We further study a popular scalable qubit architecture that is based on Majorana zero modes in topological superconductors. The two major challenges with realizing Majorana qubits currently lie in trivial pseudo-Majorana states that mimic signatures of the topological bound states and in strong disorder in the proposed topological hybrid systems that destroys the topological phase. We study coherent transport through interferometers with a Majorana wire embedded into one arm. By combining analytical and numerical considerations, we explain the occurrence of an amplitude maximum as a function of the Zeeman field at the onset of the topological phase – a signature unique to MZMs – which has recently been measured experimentally [Whiticar et al., Nature Communications, 11(1):3212, 2020]. By placing an array of gates in proximity to the nanowire, we made a fruitful connection to the field of Machine Learning by using the CMA-ES algorithm to tune the gate voltages in order to maximize the amplitude of coherent transmission. We find that the algorithm is capable of learning disorder profiles and even to restore Majorana modes that were fully destroyed by strong disorder by optimizing a feasible number of gates. Deep neural networks are another popular machine learning approach which not only has many direct applications to physical systems but which also behaves similarly to physical mesoscopic systems. In order to comprehend the effects of the complex dynamics from the training, we employ Random Matrix Theory (RMT) as a zero-information hypothesis: before training, the weights are randomly initialized and therefore are perfectly described by RMT. After training, we attribute deviations from these predictions to learned information in the weight matrices. Conducting a careful numerical analysis, we verify that the spectra of weight matrices consists of a random bulk and a few important large singular values and corresponding vectors that carry almost all learned information. By further adding label noise to the training data, we find that more singular values in intermediate parts of the spectrum contribute by fitting the randomly labeled images. Based on these observations, we propose a noise filtering algorithm that both removes the singular values storing the noise and reverts the level repulsion of the large singular values due to the random bulk

    Quantum Computing for Airline Planning and Operations

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    Classical algorithms and mathematical optimization techniques have beenused extensively by airlines to optimize their profit and ensure that regulationsare followed. In this thesis, we explore which role quantum algorithmscan have for airlines. Specifically, we have considered the two quantum optimizationalgorithms; the Quantum Approximate Optimization Algorithm(QAOA) and Quantum Annealing (QA). We present a heuristic that integratesthese quantum algorithms into the existing classical algorithm, whichis currently employed to solve airline planning problems in a state-of-the-artcommercial solver. We perform numerical simulations of QAOA circuits andfind that linear and quadratic algorithm depth in the input size can be requiredto obtain a one-shot success probability of 0.5. Unfortunately, we areunable to find performance guarantees. Finally, we perform experiments withD-wave’s newly released QA machine and find that it outperforms 2000Q formost instances

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Elastic shape analysis of geometric objects with complex structures and partial correspondences

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    In this dissertation, we address the development of elastic shape analysis frameworks for the registration, comparison and statistical shape analysis of geometric objects with complex topological structures and partial correspondences. In particular, we introduce a variational framework and several numerical algorithms for the estimation of geodesics and distances induced by higher-order elastic Sobolev metrics on the space of parametrized and unparametrized curves and surfaces. We extend our framework to the setting of shape graphs (i.e., geometric objects with branching structures where each branch is a curve) and surfaces with complex topological structures and partial correspondences. To do so, we leverage the flexibility of varifold fidelity metrics in order to augment our geometric objects with a spatially-varying weight function, which in turn enables us to indirectly model topological changes and handle partial matching constraints via the estimation of vanishing weights within the registration process. In the setting of shape graphs, we prove the existence of solutions to the relaxed registration problem with weights, which is the main theoretical contribution of this thesis. In the setting of surfaces, we leverage our surface matching algorithms to develop a comprehensive collection of numerical routines for the statistical shape analysis of sets of 3D surfaces, which includes algorithms to compute Karcher means, perform dimensionality reduction via multidimensional scaling and tangent principal component analysis, and estimate parallel transport across surfaces (possibly with partial matching constraints). Moreover, we also address the development of numerical shape analysis pipelines for large-scale data-driven applications with geometric objects. Towards this end, we introduce a supervised deep learning framework to compute the square-root velocity (SRV) distance for curves. Our trained network provides fast and accurate estimates of the SRV distance between pairs of geometric curves, without the need to find optimal reparametrizations. As a proof of concept for the suitability of such approaches in practical contexts, we use it to perform optical character recognition (OCR), achieving comparable performance in terms of computational speed and accuracy to other existing OCR methods. Lastly, we address the difficulty of extracting high quality shape structures from imaging data in the field of astronomy. To do so, we present a state-of-the-art expectation-maximization approach for the challenging task of multi-frame astronomical image deconvolution and super-resolution. We leverage our approach to obtain a high-fidelity reconstruction of the night sky, from which high quality shape data can be extracted using appropriate segmentation and photometric techniques

    Undergraduate and Graduate Course Descriptions, 2023 Spring

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    Wright State University undergraduate and graduate course descriptions from Spring 2023
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