387 research outputs found

    Asymptotics of stochastic learning in structured networks

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    Asymptotics of stochastic learning in structured networks

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    Atomistic Study of Irradiation-Induced Plastic and Lattice Strain in Tungsten

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    We demonstrate a practical way to perform decomposition of the elasto-plastic deformation directly from atomistic simulation snapshots. Through molecular dynamics simulations on a large single crystal, we elucidate the intricate process of converting plastic strain, atomic strain, and rigid rotation during irradiation. Our study highlights how prismatic dislocation loops act as initiators of plastic strain effects in heavily irradiated metals, resulting in experimentally measurable alterations in lattice strain. We show the onset of plastic strain starts to emerge at high dose, leading to the spontaneous emergence of dislocation creep and irradiation-induced lattice swelling. This phenomenon arises from the agglomeration of dislocation loops into a dislocation network. Furthermore, our numerical framework enables us to categorize the plastic transformation into two distinct types: pure slip events and slip events accompanied by lattice swelling. The latter type is particularly responsible for the observed divergence in interstitial and vacancy counts, and also impacts the behavior of dislocations, potentially activating non-conventional slip systems

    The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

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    The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations

    Exclusive QCD Factorization and Single Transverse Polarization Phenomena at High-Energy Colliders

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    This Ph.D.~thesis is divided into two distinct parts. The first part focuses on hard exclusive scattering processes in Quantum Chromodynamics (QCD) at high energies, while the second part delves into spin phenomena at the Large Hadron Collider (LHC). Hard exclusive scattering processes play a crucial role in QCD at high energies, providing unique insights into the confined partonic dynamics within hadrons, complementing inclusive processes. Studying these processes within the QCD factorization approach yields the generalized parton distribution (GPD), a nonperturbative parton correlation function that offers a three-dimensional tomographic parton image within a hadron. However, the experimental measurement of these processes poses significant challenges. This thesis will review the factorization formalism for related processes, examine the limitations of some widely used processes, and introduce two novel processes that enhance the sensitivity to GPD, particularly its dependence on the parton momentum fraction xx. The second part of the thesis centers on spin phenomena, specifically single spin production, at the LHC. Noting that a single transverse polarization can be generated even in an unpolarized collision, this research proposes two new jet substructure observables: one for boosted top quark jets and another for high-energy gluon jets. The observation of these phenomena paves the way for innovative tools in LHC phenomenology, enabling both precision measurements and the search for new physics.Comment: Ph.D. thesis. 417 page

    High-order renormalization of scalar quantum fields

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    Thema dieser Dissertation ist die Renormierung von perturbativer skalarer Quantenfeldtheorie bei großer Schleifenzahl. Der Hauptteil der Arbeit ist dem Einfluss von Renormierungsbedingungen auf renormierte Greenfunktionen gewidmet. Zunächst studieren wir Dyson-Schwinger-Gleichungen und die Renormierungsgruppe, inklusive der Gegenterme in dimensionaler Regularisierung. Anhand zahlreicher Beispiele illustrieren wir die verschiedenen Größen. Alsdann diskutieren wir, welche Freiheitsgrade ein Renormierungsschema hat und wie diese mit den Gegentermen und den renormierten Greenfunktionen zusammenhängen. Für ungekoppelte Dyson-Schwinger-Gleichungen stellen wir fest, dass alle Renormierungsschemata bis auf eine Verschiebung des Renormierungspunktes äquivalent sind. Die Verschiebung zwischen kinematischer Renormierung und Minimaler Subtraktion ist eine Funktion der Kopplung und des Regularisierungsparameters. Wir leiten eine neuartige Formel für den Fall einer linearen Dyson-Schwinger Gleichung vom Propagatortyp her, um die Verschiebung direkt aus der Mellintransformation des Integrationskerns zu berechnen. Schließlich berechnen wir obige Verschiebung störungstheoretisch für drei beispielhafte nichtlineare Dyson-Schwinger-Gleichungen und untersuchen das asymptotische Verhalten der Reihenkoeffizienten. Ein zweites Thema der vorliegenden Arbeit sind Diffeomorphismen der Feldvariable in einer Quantenfeldtheorie. Wir präsentieren eine Störungstheorie des Diffeomorphismusfeldes im Impulsraum und verifizieren, dass der Diffeomorphismus keinen Einfluss auf messbare Größen hat. Weiterhin untersuchen wir die Divergenzen des Diffeomorphismusfeldes und stellen fest, dass die Divergenzen Wardidentitäten erfüllen, die die Abwesenheit dieser Terme von der S-Matrix ausdrücken. Trotz der Wardidentitäten bleiben unendlich viele Divergenzen unbestimmt. Den Abschluss bildet ein Kommentar über die numerische Quadratur von Periodenintegralen.This thesis concerns the renormalization of perturbative quantum field theory. More precisely, we examine scalar quantum fields at high loop order. The bulk of the thesis is devoted to the influence of renormalization conditions on the renormalized Green functions. Firstly, we perform a detailed review of Dyson-Schwinger equations and the renormalization group, including the counterterms in dimensional regularization. Using numerous examples, we illustrate how the various quantities are computable in a concrete case and which relations they satisfy. Secondly, we discuss which degrees of freedom are present in a renormalization scheme, and how they are related to counterterms and renormalized Green functions. We establish that, in the case of an un-coupled Dyson-Schwinger equation, all renormalization schemes are equivalent up to a shift in the renormalization point. The shift between kinematic renormalization and Minimal Subtraction is a function of the coupling and the regularization parameter. We derive a novel formula for the case of a linear propagator-type Dyson-Schwinger equation to compute the shift directly from the Mellin transform of the kernel. Thirdly, we compute the shift perturbatively for three examples of non-linear Dyson-Schwinger equations and examine the asymptotic growth of series coefficients. A second, smaller topic of the present thesis are diffeomorphisms of the field variable in a quantum field theory. We present the perturbation theory of the diffeomorphism field in momentum space and find that the diffeomorphism has no influence on measurable quantities. Moreover, we study the divergences in the diffeomorphism field and establish that they satisfy Ward identities, which ensure their absence from the S-matrix. Nevertheless, the Ward identities leave infinitely many divergences unspecified and the diffeomorphism theory is perturbatively unrenormalizable. Finally, we remark on a third topic, the numerical quadrature of Feynman periods

    Algorithms for Near-Term and Noisy Quantum Devices

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    Quantum computing promises to revolutionise many fields, including chemical simulations and machine learning. At the present moment those promises have not been realised, due to the large resource requirements of fault tolerant quantum computers, not excepting the scientific and engineering challenges to building a fault tolerant quantum computer. Instead, we currently have access to quantum devices that are both limited in qubit number, and have noisy qubits. This thesis deals with the challenges that these devices present, by investigating applications in quantum simulation for molecules and solid state systems, quantum machine learning, and by presenting a detailed simulation of a real ion trap device. We firstly build on a previous algorithm for state discrimination using a quantum machine learning model, and we show how to adapt the algorithm to work on a noisy device. This algorithm outperforms the analytical best POVM if ran on a noisy device. We then discuss how to build a quantum perceptron - the building block of a quantum neural network. We also present an algorithm for simulating the Dynamical Mean Field Theory (DMFT) using a quantum device, for two sites. We also discuss some of the difficul- ties found in scaling up that system, and present an algorithm for building the DMFT ansatz using the quantum device. We also discuss modifications to the algorithm that make it more ‘device-aware’. Finally we present a pule-level simulation of the noise in an ion trap device, designed to match the specifications of a device at the National Physical Laboratory (NPL), which we can use to direct future experimental focus. Each of these sections is preceded by a review of the relevant literature

    Asymptotics and Statistical Inference in High-Dimensional Low-Rank Matrix Models

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    High-dimensional matrix and tensor data is ubiquitous in machine learning and statistics and often exhibits low-dimensional structure. With the rise of these types of data is the need to develop statistical inference procedures that adequately address the low-dimensional structure in a principled manner. In this dissertation we study asymptotic theory and statistical inference in structured low-rank matrix models in high-dimensional regimes where the column and row dimensions of the matrix are allowed to grow, and we consider a variety of settings for which structured low-rank matrix models manifest. Chapter 1 establishes the general framework for statistical analysis in high-dimensional low-rank matrix models, including introducing entrywise perturbation bounds, asymptotic theory, distributional theory, and statistical inference, illustrated throughout via the matrix denoising model. In Chapter 2, Chapter 3, and Chapter 4 we study the entrywise estimation of singular vectors and eigenvectors in different structured settings, with Chapter 2 considering heteroskedastic and dependent noise, Chapter 3 sparsity, and Chapter 4 additional tensor structure. In Chapter 5 we apply previous asymptotic theory to study a two-sample test for equality of distribution in network analysis, and in Chapter 6 we study a model for shared community memberships across multiple networks, and we propose and analyze a joint spectral clustering algorithm that leverages newly developed asymptotic theory for this setting. Throughout this dissertation we emphasize tools and techniques that are data-driven, nonparametric, and adaptive to signal strength, and, where applicable, noise distribution. The contents of Chapters 2-6 are based on the papers Agterberg et al. (2022b); Agterberg and Sulam (2022); Agterberg and Zhang (2022); Agterberg et al. (2020a) and Agterberg et al. (2022a) respectively, and Chapter 1 contains several novel results
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