Hierarchical topological clustering learns stock market sectors

The breakdown of financial markets into sectors provides an intuitive classification for groups of companies. The allocation of a company to a sector is an expert task, in which the company is classified by the activity that most closely describes the nature of the company's business. Individual share price movement is dependent upon many factors, but there is an expectation for shares within a market sector to move broadly together. We are interested in discovering if share closing prices do move together, and whether groups of shares that do move together are identifiable in terms of industrial activity. Using TreeGNG, a hierarchical clustering algorithm, on a time series of share closing prices, we have identified groups of companies that cluster into clearly identifiable groups. These clusters compare favourably to a globally accepted sector classification scheme, and in our opinion, our method identifies sector structure clearer than a statistical agglomerative hierarchical clustering metho

Adaptive homodyne measurement of optical phase

We present an experimental demonstration of the power of real-time feedback in quantum metrology, confirming a theoretical prediction by Wiseman regarding the superior performance of an adaptive homodyne technique for single-shot measurement of optical phase. For phase measurements performed on weak coherent states with no prior knowledge of the signal phase, we show that the variance of adaptive homodyne estimation approaches closer to the fundamental quantum uncertainty limit than any previously demonstrated technique. Our results underscore the importance of real-time feedback for reaching quantum performance limits in coherent telecommunication, precision measurement and information processing.Comment: RevTex4, color PDF figures (separate files), submitted to PR

Robust quantum parameter estimation: coherent magnetometry with feedback

We describe the formalism for optimally estimating and controlling both the state of a spin ensemble and a scalar magnetic field with information obtained from a continuous quantum limited measurement of the spin precession due to the field. The full quantum parameter estimation model is reduced to a simplified equivalent representation to which classical estimation and control theory is applied. We consider both the tracking of static and fluctuating fields in the transient and steady state regimes. By using feedback control, the field estimation can be made robust to uncertainty about the total spin number

Sunday to Friday: Investigating Masculinity using Pornography Traffic During Two Major Events

This paper is an investigation into how Masculinity Theory can explain a shift in Pornhub traffic when specific major events take place. The paper examines two events, the recent Super Bowls and the early months of the COVID-19 pandemic framed against Pornhub traffic data at the same time. It finds that masculinity theory when combined with motivation for pornography viewing, can serve as one plausible explanation behind a shift in traffic

Choice of Measurement Sets in Qubit Tomography

Optimal generalized measurements for state estimation are well understood. However, practical quantum state tomography is typically performed using a fixed set of projective measurements and the question of how to choose these measurements has been largely unexplored in the literature. In this work we develop theoretical asymptotic bounds for the average fidelity of pure qubit tomography using measurement sets whose axes correspond to vertices of Platonic solids. We also present complete simulations of maximum likelihood tomography for mixed qubit states using the Platonic solid measurements. We show that overcomplete measurement sets can be used to improve the accuracy of tomographic reconstructions.Comment: 13 Pages, 6 figure

First order phase transition in the anisotropic quantum orbital compass model

We investigate the anisotropic quantum orbital compass model on an infinite square lattice by means of the infinite projected entangled-pair state algorithm. For varying values of the $J_x$ and $J_z$ coupling constants of the model, we approximate the ground state and evaluate quantities such as its expected energy and local order parameters. We also compute adiabatic time evolutions of the ground state, and show that several ground states with different local properties coexist at $J_x = J_z$. All our calculations are fully consistent with a first order quantum phase transition at this point, thus corroborating previous numerical evidence. Our results also suggest that tensor network algorithms are particularly fitted to characterize first order quantum phase transitions.Comment: 4 pages, 3 figures, major revision with new result