Short-Term Load Forecasting of Natural Gas with Deep Neural Network Regression

Deep neural networks are proposed for short-term natural gas load forecasting. Deep learning has proven to be a powerful tool for many classification problems seeing significant use in machine learning fields such as image recognition and speech processing. We provide an overview of natural gas forecasting. Next, the deep learning method, contrastive divergence is explained. We compare our proposed deep neural network method to a linear regression model and a traditional artificial neural network on 62 operating areas, each of which has at least 10 years of data. The proposed deep network outperforms traditional artificial neural networks by 9.83% weighted mean absolute percent error (WMAPE)

Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors

We provide an alternative proof of Wallman's [Quantum 2, 47 (2018)] and Proctor's [Phys. Rev. Lett. 119, 130502 (2017)] bounds on the effect of gate-dependent noise on randomized benchmarking (RB). Our primary insight is that a RB sequence is a convolution amenable to Fourier space analysis, and we adopt the mathematical framework of Fourier transforms of matrix-valued functions on groups established in recent work from Gowers and Hatami [Sbornik: Mathematics 208, 1784 (2017)]. We show explicitly that as long as our faulty gate-set is close to some representation of the Clifford group, an RB sequence is described by the exponential decay of a process that has exactly two eigenvalues close to one and the rest close to zero. This framework also allows us to construct a gauge in which the average gate-set error is a depolarizing channel parameterized by the RB decay rates, as well as a gauge which maximizes the fidelity with respect to the ideal gate-set

Thermal Stratification in Small Lakes with TELEMAC-3D: Showcase “Lake Monsterloch”

Hydrodynamic

Control of inhomogeneous atomic ensembles of hyperfine qudits

We study the ability to control d-dimensional quantum systems (qudits) encoded in the hyperfine spin of alkali-metal atoms through the application of radio- and microwave-frequency magnetic fields in the presence of inhomogeneities in amplitude and detuning. Such a capability is essential to the design of robust pulses that mitigate the effects of experimental uncertainty and also for application to tomographic addressing of particular members of an extended ensemble. We study the problem of preparing an arbitrary state in the Hilbert space from an initial fiducial state. We prove that inhomogeneous control of qudit ensembles is possible based on a semi-analytic protocol that synthesizes the target through a sequence of alternating rf and microwave-driven SU(2) rotations in overlapping irreducible subspaces. Several examples of robust control are studied, and the semi-analytic protocol is compared to a brute force, full numerical search. For small inhomogeneities, < 1%, both approaches achieve average fidelities greater than 0.99, but the brute force approach performs superiorly, reaching high fidelities in shorter times and capable of handling inhomogeneities well beyond experimental uncertainty. The full numerical search is also applied to tomographic addressing whereby two different nonclassical states of the spin are produced in two halves of the ensemble

The Second Amendment in Context: The Case of the Vanishing Predicate

Uviller and Merkel argue that the Second Amendment right to keep and bear arms was intended by the framers (and, perhaps more importantly, understood by the ratifiers) to be intimately bound up in the ideal of service in the lawfully established militia-for many eighteenth-century Americans, the preferred alternative to that bane of liberty, the standing army. But as Uviller and Merkel set out to show, the historic common militia celebrated in the republican ideology of eighteenth-century Whigs was already on the road to obsolescence when the Second Amendment became law. By the middle of the nineteenth century, few citizens mustered on militia days, those who did arrived unarmed, and state after state simply chose to let the founders\u27 militia wither away. As a result, Congress established the National Guard in 1903 to replace the long defunct militia-of-the-whole. This statutory militia of today is federally armed and manned by trained volunteers who in large measure are paid and drilled by the U.S. Army. Not even a shadow of the eighteenth century\u27s self-armed, universal militia remains. Uviller and Merkel conclude that in this critically changed context, the Second Amendment right cannot be meaningfully applied