15,805 research outputs found

    Model Diagnostics meets Forecast Evaluation: Goodness-of-Fit, Calibration, and Related Topics

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    Principled forecast evaluation and model diagnostics are vital in fitting probabilistic models and forecasting outcomes of interest. A common principle is that fitted or predicted distributions ought to be calibrated, ideally in the sense that the outcome is indistinguishable from a random draw from the posited distribution. Much of this thesis is centered on calibration properties of various types of forecasts. In the first part of the thesis, a simple algorithm for exact multinomial goodness-of-fit tests is proposed. The algorithm computes exact pp-values based on various test statistics, such as the log-likelihood ratio and Pearson\u27s chi-square. A thorough analysis shows improvement on extant methods. However, the runtime of the algorithm grows exponentially in the number of categories and hence its use is limited. In the second part, a framework rooted in probability theory is developed, which gives rise to hierarchies of calibration, and applies to both predictive distributions and stand-alone point forecasts. Based on a general notion of conditional T-calibration, the thesis introduces population versions of T-reliability diagrams and revisits a score decomposition into measures of miscalibration, discrimination, and uncertainty. Stable and efficient estimators of T-reliability diagrams and score components arise via nonparametric isotonic regression and the pool-adjacent-violators algorithm. For in-sample model diagnostics, a universal coefficient of determination is introduced that nests and reinterprets the classical R2R^2 in least squares regression. In the third part, probabilistic top lists are proposed as a novel type of prediction in classification, which bridges the gap between single-class predictions and predictive distributions. The probabilistic top list functional is elicited by strictly consistent evaluation metrics, based on symmetric proper scoring rules, which admit comparison of various types of predictions

    3d mirror symmetry of braided tensor categories

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    We study the braided tensor structure of line operators in the topological A and B twists of abelian 3d N=4\mathcal{N}=4 gauge theories, as accessed via boundary vertex operator algebras (VOA's). We focus exclusively on abelian theories. We first find a non-perturbative completion of boundary VOA's in the B twist, which start out as certain affine Lie superalebras; and we construct free-field realizations of both A and B-twist VOA's, finding an interesting interplay with the symmetry fractionalization group of bulk theories. We use the free-field realizations to establish an isomorphism between A and B VOA's related by 3d mirror symmetry. Turning to line operators, we extend previous physical classifications of line operators to include new monodromy defects and bound states. We also outline a mechanism by which continuous global symmetries in a physical theory are promoted to higher symmetries in a topological twist -- in our case, these are infinite one-form symmetries, related to boundary spectral flow, which structure the categories of lines and control abelian gauging. Finally, we establish the existence of braided tensor structure on categories of line operators, viewed as non-semisimple categories of modules for boundary VOA's. In the A twist, we obtain the categories by extending modules of symplectic boson VOA's, corresponding to gauging free hypermultiplets; in the B twist, we instead extend Kazhdan-Lusztig categories for affine Lie superalgebras. We prove braided tensor equivalences among the categories of 3d-mirror theories. All results on VOA's and their module categories are mathematically rigorous; they rely strongly on recently developed techniques to access non-semisimple extensions.Comment: 158 pages, comments welcome

    Applications of higher-form symmetries at strong and weak coupling

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    In this thesis we consider two distinct applications of higher-form symmetries in quantum field theory. First we explore the spontaneous breaking of higher-form symmetry in a holographic quantum field theory containing matter fields in the fundamental representation of the gauge group U(N). At strong coupling, we numerically solve the bulk equations of motion to compute the current-current Green’s function and demonstrate the existence of a goldstone mode. We then compare to direct analytic perturbative results obtained at weak coupling. In the second half of the thesis we work with a hydrodynamic effective field theory which possesses a higher-form symmetry. In particular, we consider a natural higher-derivative correction to force-free electrodynamics and compute a hydrodynamic transport coefficient from microscopics. Concretely, this is a perturbative QED calculation in a background magnetic field. Finally we compare our findings to astrophysical observations

    Exploring the Structure of Scattering Amplitudes in Quantum Field Theory: Scattering Equations, On-Shell Diagrams and Ambitwistor String Models in Gauge Theory and Gravity

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    In this thesis I analyse the structure of scattering amplitudes in super-symmetric gauge and gravitational theories in four dimensional spacetime, starting with a detailed review of background material accessible to a non-expert. I then analyse the 4D scattering equations, developing the theory of how they can be used to express scattering amplitudes at tree level. I go on to explain how the equations can be solved numerically using a Monte Carlo algorithm, and introduce my Mathematica package treeamps4dJAF which performs these calculations. Next I analyse the relation between the 4D scattering equations and on-shell diagrams in N = 4 super Yang-Mills, which provides a new perspective on the tree level amplitudes of the theory. I apply a similar analysis to N = 8 supergravity, developing the theory of on-shell diagrams to derive new Grassmannian integral formulae for the amplitudes of the theory. In both theories I derive a new worldsheet expression for the 4 point one loop amplitude supported on 4D scattering equations. Finally I use 4D ambitwistor string theory to analyse scattering amplitudes in N = 4 conformal supergravity, deriving new worldsheet formulae for both plane wave and non-plane wave amplitudes supported on 4D scattering equations. I introduce a new prescription to calculate the derivatives of on-shell variables with respect to momenta, and I use this to show that certain non-plane wave amplitudes can be calculated as momentum derivatives of amplitudes with plane wave states

    Annals [...].

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    Pedometrics: innovation in tropics; Legacy data: how turn it useful?; Advances in soil sensing; Pedometric guidelines to systematic soil surveys.Evento online. Coordenado por: Waldir de Carvalho Junior, Helena Saraiva Koenow Pinheiro, Ricardo Simão Diniz Dalmolin

    Foundations for programming and implementing effect handlers

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    First-class control operators provide programmers with an expressive and efficient means for manipulating control through reification of the current control state as a first-class object, enabling programmers to implement their own computational effects and control idioms as shareable libraries. Effect handlers provide a particularly structured approach to programming with first-class control by naming control reifying operations and separating from their handling. This thesis is composed of three strands of work in which I develop operational foundations for programming and implementing effect handlers as well as exploring the expressive power of effect handlers. The first strand develops a fine-grain call-by-value core calculus of a statically typed programming language with a structural notion of effect types, as opposed to the nominal notion of effect types that dominates the literature. With the structural approach, effects need not be declared before use. The usual safety properties of statically typed programming are retained by making crucial use of row polymorphism to build and track effect signatures. The calculus features three forms of handlers: deep, shallow, and parameterised. They each offer a different approach to manipulate the control state of programs. Traditional deep handlers are defined by folds over computation trees, and are the original con-struct proposed by Plotkin and Pretnar. Shallow handlers are defined by case splits (rather than folds) over computation trees. Parameterised handlers are deep handlers extended with a state value that is threaded through the folds over computation trees. To demonstrate the usefulness of effects and handlers as a practical programming abstraction I implement the essence of a small UNIX-style operating system complete with multi-user environment, time-sharing, and file I/O. The second strand studies continuation passing style (CPS) and abstract machine semantics, which are foundational techniques that admit a unified basis for implementing deep, shallow, and parameterised effect handlers in the same environment. The CPS translation is obtained through a series of refinements of a basic first-order CPS translation for a fine-grain call-by-value language into an untyped language. Each refinement moves toward a more intensional representation of continuations eventually arriving at the notion of generalised continuation, which admit simultaneous support for deep, shallow, and parameterised handlers. The initial refinement adds support for deep handlers by representing stacks of continuations and handlers as a curried sequence of arguments. The image of the resulting translation is not properly tail-recursive, meaning some function application terms do not appear in tail position. To rectify this the CPS translation is refined once more to obtain an uncurried representation of stacks of continuations and handlers. Finally, the translation is made higher-order in order to contract administrative redexes at translation time. The generalised continuation representation is used to construct an abstract machine that provide simultaneous support for deep, shallow, and parameterised effect handlers. kinds of effect handlers. The third strand explores the expressiveness of effect handlers. First, I show that deep, shallow, and parameterised notions of handlers are interdefinable by way of typed macro-expressiveness, which provides a syntactic notion of expressiveness that affirms the existence of encodings between handlers, but it provides no information about the computational content of the encodings. Second, using the semantic notion of expressiveness I show that for a class of programs a programming language with first-class control (e.g. effect handlers) admits asymptotically faster implementations than possible in a language without first-class control

    Full stack development toward a trapped ion logical qubit

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    Quantum error correction is a key step toward the construction of a large-scale quantum computer, by preventing small infidelities in quantum gates from accumulating over the course of an algorithm. Detecting and correcting errors is achieved by using multiple physical qubits to form a smaller number of robust logical qubits. The physical implementation of a logical qubit requires multiple qubits, on which high fidelity gates can be performed. The project aims to realize a logical qubit based on ions confined on a microfabricated surface trap. Each physical qubit will be a microwave dressed state qubit based on 171Yb+ ions. Gates are intended to be realized through RF and microwave radiation in combination with magnetic field gradients. The project vertically integrates software down to hardware compilation layers in order to deliver, in the near future, a fully functional small device demonstrator. This thesis presents novel results on multiple layers of a full stack quantum computer model. On the hardware level a robust quantum gate is studied and ion displacement over the X-junction geometry is demonstrated. The experimental organization is optimized through automation and compressed waveform data transmission. A new quantum assembly language purely dedicated to trapped ion quantum computers is introduced. The demonstrator is aimed at testing implementation of quantum error correction codes while preparing for larger scale iterations.Open Acces

    New Techniques for High Orders in Scattering Amplitudes

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    This thesis uses four-dimensional unitarity and augmented recursion to calculate a selection of Yang-Mills amplitudes. This selection consists of the full-colour, two-loop, all-plus helicity amplitudes for five- and six-points; a conjecture for an n-point sub-subleading in colour two-loop amplitude; calculation of the cut-constructible piece of the full-colour, two-loop, all-plus helicity n-point amplitude. A new technique for calculating the cut constructible part of the leading in colour two-loop, five-point, single-minus helicity amplitude is presented. The correct infrared divergent piece of this single-minus amplitude was calculated, as well as the correct transcendental two pieces at finite order. Logarithms containing Mandelstam variables including only positive helicity legs were unable to be correctly calculated, but the calculation of this final amplitude uncovered many new relations involving generalised hypergeometric functions such as the Appell functions
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