Measuring output gap uncertainty

We propose a methodology for producing density forecasts for the output gap in real time using a large number of vector autoregessions in inflation and output gap measures. Density combination utilizes a linear mixture of experts framework to produce potentially non-Gaussian ensemble densities for the unobserved output gap. In our application, we show that data revisions alter substantially our probabilistic assessments of the output gap using a variety of output gap measures derived from univariate detrending filters. The resulting ensemble produces well-calibrated forecast densities for US inflation in real time, in contrast to those from simple univariate autoregressions which ignore the contribution of the output gap. Combining evidence from both linear trends and more flexible univariate detrending filters induces strong multi-modality in the predictive densities for the unobserved output gap. The peaks associated with these two detrending methodologies indicate output gaps of opposite sign for some observations, reflecting the pervasive nature of model uncertainty in our US data

Real-time inflation forecast densities from ensemble phillips curves

A popular macroeconomic forecasting strategy takes combinations across many models to hedge against model instabilities of unknown timing; see (among others) Stock andWatson (2004) and Clark and McCracken (2009). In this paper, we examine the effectiveness of recursive-weight and equal-weight combination strategies for density forecasting using a time-varying Phillips curve relationship between inflation and the output gap. The densities reflect the uncertainty across a large number of models using many statistical measures of the output gap, allowing for a single structural break of unknown timing. We use real-time data for the US, Australia, New Zealand and Norway. Our main finding is that the recursive-weight strategy performs well across the real-time data sets, consistently giving well-calibrated forecast densities. The equal-weight strategy generates poorly-calibrated forecast densities for the US and Australian samples. There is little difference between the two strategies for our New Zealand and Norwegian data. We also find that the ensemble modeling approach performs more consistently with real-time data than with revised data in all four countries

Some Considerations of the Ultimate Spatial Resolution Achievable in Scanning Transmission Electron Microscopy

The fundamental limitations on spatial resolution of X-ray microanalysis in the scanning transmission electron microscope are set by the interrelationships between the gun brightness, operating voltage, probe convergence angle, size and current, specimen thickness, beam broadening, the probability of characteristic and Bremsstrahlung X-ray production and the statistics of the X-ray spectrum. Manipulation of expressions describing these interrelationships leads to equations predicting the optimum probe size and specimen thickness for the best achievable spatial resolution (defined as the diameter of a cylinder containing 90% of the X-ray production) in microscopes fitted with different electron sources and operating at different voltages in foils of various elements. Application of these calculations to the special case of detecting monolayer segregation at grain boundaries results in predictions of the minimum amounts of such segregation that would be observable. It is found, for example, that in a microscope with a field-emission source operating at 500 keV, resolution of \u3c 1nm is obtainable in an iron foil 20nm thick, and in this case about 0.001 monolayer of chromium is detectable segregated at grain boundaries. The calculations do not take into account instrumental or experimental problems such as specimen drift, specimen preparation, etc., and represent the basic physical limits of performance of a perfect analytical microscope

Impact of the UK general elections on total government expenditure cycles: theory and evidence

This paper presents a testable theoretical framework that extends the standard demand-side approach to modeling government expenditure on goods and services. The focus is on the adjustment of expenditure to disequilibria: we investigate whether the adjustment of UK exhaustive government expenditure between 1966 and 2002 to its long-run equilibrium path is symmetric. The evidence points to asymmetric adjustment to the demands of a representative voter over the election cycle but not between Labour and Conservative governments. Convergence to equilibrium is found to be faster during the later stages of each election cycle

Homelessness in Oxford : risks and opportunities across housing and homeless transitions

This report presents initial findings from CSI’s Homelessness in Oxford project. The project was designed by Dr. Garratt and Dr. Flaherty to be the first systematic attempt to track and understand people’s transitions into and out of different experiences of homelessness in Oxford. The project also explored the roles played by statutory and non-statutory homelessness prevention and relief services in Oxford

Probing Postmeasurement Entanglement without Postselection

We study the problem of observing quantum collective phenomena emerging from large numbers of measurements. These phenomena are difficult to observe in conventional experiments because, in order to distinguish the effects of measurement from dephasing, it is necessary to postselect on sets of measurement outcomes with Born probabilities that are exponentially small in the number of measurements performed. An unconventional approach, which avoids this exponential “postselection problem”, is to construct cross-correlations between experimental data and the results of simulations on classical computers. However, these cross-correlations generally have no definite relation to physical quantities. We first show how to incorporate classical shadows into this framework, thereby allowing for the construction of quantum information-theoretic cross-correlations. We then identify cross-correlations that both upper and lower bound the measurement-averaged von Neumann entanglement entropy, as well as cross-correlations that lower bound the measurement-averaged purity and entanglement negativity. These bounds show that experiments can be performed to constrain postmeasurement entanglement without the need for postselection. To illustrate our technique, we consider how it could be used to observe the measurement-induced entanglement transition in Haar-random quantum circuits. We use exact numerical calculations as proxies for quantum simulations and, to highlight the fundamental limitations of classical memory, we construct cross-correlations with tensor-network calculations at finite bond dimension. Our results reveal a signature of measurement-induced criticality that can be observed using a quantum simulator in polynomial time and with polynomial classical memory. Published by the American Physical Society 202

Many-body delocalisation as symmetry breaking

We present a framework in which the transition between a many-body localised (MBL) phase and an ergodic one is symmetry breaking. We consider random Floquet spin chains, expressing their averaged spectral form factor (SFF) as a function of time in terms of a transfer matrix that acts in the space direction. The SFF is determined by the leading eigenvalues of this transfer matrix. In the MBL phase the leading eigenvalue is unique, as in a symmetry-unbroken phase, while in the ergodic phase and at late times the leading eigenvalues are asymptotically degenerate, as in a system with degenerate symmetry-breaking phases. We identify the broken symmetry of the transfer matrix, introduce a local order parameter for the transition, and show that the associated correlation functions are long-ranged only in the ergodic phase.Comment: 5+5 page

Goldstone modes in the emergent gauge fields of a frustrated magnet

We consider magnon excitations in the spin-glass phase of geometrically frustrated antiferromagnets with weak exchange disorder, focussing on the nearest-neighbour pyrochlore-lattice Heisenberg model at large spin. The low-energy degrees of freedom in this system are represented by three copies of a U(1) emergent gauge field, related by global spin-rotation symmetry. We show that the Goldstone modes associated with spin-glass order are excitations of these gauge fields, and that the standard theory of Goldstone modes in Heisenberg spin glasses (due to Halperin and Saslow) must be modified in this setting.Comment: 6 pages, 2 figures, published in Phys. Rev.

Local pairing of Feynman histories in many-body Floquet models

We study many-body quantum dynamics using Floquet quantum circuits in one space dimension as simple examples of systems with local interactions that support ergodic phases. Physical properties can be expressed in terms of multiple sums over Feynman histories, which for these models are paths or many-body orbits in Fock space. A natural simplification of such sums is the diagonal approximation, where the only terms that are retained are ones in which each path is paired with a partner that carries the complex conjugate weight. We identify the regime in which the diagonal approximation holds, and the nature of the leading corrections to it. We focus on the behaviour of the spectral form factor (SFF) and of matrix elements of local operators, averaged over an ensemble of random circuits, making comparisons with the predictions of random matrix theory (RMT) and the eigenstate thermalisation hypothesis (ETH). We show that properties are dominated at long times by contributions to orbit sums in which each orbit is paired locally with a conjugate, as in the diagonal approximation, but that in large systems these contributions consist of many spatial domains, with distinct local pairings in neighbouring domains. The existence of these domains is reflected in deviations of the SFF from RMT predictions, and of matrix element correlations from ETH predictions; deviations of both kinds diverge with system size. We demonstrate that our physical picture of orbit-pairing domains has a precise correspondence in the spectral properties of a transfer matrix that acts in the space direction to generate the ensemble-averaged SFF. In addition, we find that domains of a second type control non-Gaussian fluctuations of the SFF. These domains are separated by walls which are related to the entanglement membrane, known to characterise the scrambling of quantum information.Comment: 22+7 page

Probing post-measurement entanglement without post-selection

We study the problem of observing quantum collective phenomena emerging from large numbers of measurements. These phenomena are difficult to observe in conventional experiments because, in order to distinguish the effects of measurement from dephasing, it is necessary to post-select on sets of measurement outcomes whose Born probabilities are exponentially small in the number of measurements performed. An unconventional approach, which avoids this exponential `post-selection problem', is to construct cross-correlations between experimental data and the results of simulations on classical computers. However, these cross-correlations generally have no definite relation to physical quantities. We first show how to incorporate shadow tomography into this framework, thereby allowing for the construction of quantum information-theoretic cross-correlations. We then identify cross-correlations which both upper and lower bound the measurement-averaged von Neumann entanglement entropy. These bounds show that experiments can be performed to constrain post-measurement entanglement without the need for post-selection. To illustrate our technique we consider how it could be used to observe the measurement-induced entanglement transition in Haar-random quantum circuits. We use exact numerical calculations as proxies for quantum simulations and, to highlight the fundamental limitations of classical memory, we construct cross-correlations with tensor-network calculations at finite bond dimension. Our results reveal a signature of measurement-induced criticality that can be observed using a quantum simulator in polynomial time and with polynomial classical memory.Comment: 13 page