The Equity Premium

Recent research on the equity risk premium has questioned the ability of historical estimates of the risk premium to provide reliable estimates of the expected risk premium. We calculate the equity risk premium for a number of countries over longer horizons than has been attempted to date. We show that the realised US equity premium is consistent with the premia obtained elsewhere. Furthermore, using well over a century of data, we find that current estimates of the equity premia are close to those observed during the pre-1914 era. This is of particular relevance given the argument that the financial environment during that period bears a closer resemblance to today than the 1914-1945 period, and possibly also the 1945-1971 period. This points to a current equity risk premium that is considerably lower than consensus forecasts (Welch 2001)

Universal Charge-Radius Relation for Subatomic and Astrophysical Compact Objects

Electron-positron pair creation in supercritical electric fields limits the net charge of any static, spherical object, such as superheavy nuclei, strangelets, and Q-balls, or compact stars like neutron stars, quark stars, and black holes. For radii between $4\times10^2$ fm and $10^4$ fm the upper bound on the net charge is given by the universal relation $Z=0.71R_{fm}$, and for larger radii (measured in fm or km) $Z = 7 \times 10^{-5} R_{fm}^2 = 7 \times 10^{31} R_{km}^2$. For objects with nuclear density the relation corresponds to $Z \approx 0.7 A^{1/3}$ ($10^{8} < A < 10^{12}$) and $Z \approx 7\times10^{-5} A^{2/3}$ ($A > 10^{12}$), where $A$ is the baryon number. For some systems this universal upper bound improves existing charge limits in the literature

Deep Convolutional Neural Networks for Interpretable Analysis of EEG Sleep Stage Scoring

Sleep studies are important for diagnosing sleep disorders such as insomnia, narcolepsy or sleep apnea. They rely on manual scoring of sleep stages from raw polisomnography signals, which is a tedious visual task requiring the workload of highly trained professionals. Consequently, research efforts to purse for an automatic stage scoring based on machine learning techniques have been carried out over the last years. In this work, we resort to multitaper spectral analysis to create visually interpretable images of sleep patterns from EEG signals as inputs to a deep convolutional network trained to solve visual recognition tasks. As a working example of transfer learning, a system able to accurately classify sleep stages in new unseen patients is presented. Evaluations in a widely-used publicly available dataset favourably compare to state-of-the-art results, while providing a framework for visual interpretation of outcomes.Comment: 8 pages, 1 figure, 2 tables, IEEE 2017 International Workshop on Machine Learning for Signal Processin

Extended Superconformal Algebras from Classical and Quantum Hamiltonian Reduction

We consider the extended superconformal algebras of the Knizhnik-Bershadsky type with $W$-algebra like composite operators occurring in the commutation relations, but with generators of conformal dimension 1,$\frac{3}{2}$ and 2, only. These have recently been neatly classified by several groups, and we emphasize the classification based on hamiltonian reduction of affine Lie superalgebras with even subalgebras $G\oplus sl(2)$. We reveiw the situation and improve on previous formulations by presenting generic and very compact expressions valid for all algebras, classical and quantum. Similarly generic and compact free field realizations are presented as are corresponding screening charges. Based on these a discussion of singular vectors is presented. (Based on talk by J.L. Petersen at the Int. Workshop on "String Theory, Quantum Gravity and the Unification of the Fundamental Interactions", Rome Sep. 21-26, 1992)Comment: 30 pages, NBI-HE-92-8