The Global Equity Market Reactions of the Oil & Gas Midstream and Marine Shipping Industries to COVID-19: An Entropy Analysis

This article quantifies the information flow between major equities in the Oil & Gas Midstream and Marine Shipping industries, on the basis of the effective transfer entropy methodology. In addition, the article provides the first analysis of the investors` fear and market expectations in these sectors, according to Rényi entropy approach. The period of study was extended over five years, to fully capture the pre/post-COVID situations. The entropy results reveal a major change in the underlying information flow pattern among equities in the Oil & Gas Midstream and Marine Shipping sectors, in the aftermath of COVID-19. According to the new (post-COVID) paradigm, the stocks in the Oil & Gas Midstream and Integrated Freight & Logistics industries have gained momentum in occupying six of the ten positions within the list of most-influencing equities in the market, in terms of information transmission. The disorder and randomness has decreased for over 89% of the studied equities, after virus outbreak. For the equities detected with high information-transmission standing, the Rényi entropy results indicate that investors more likely showed higher level of future expectations and lower level of fear regarding frequent market events, within the post-COVID timeline. Doi: 10.28991/HIJ-2021-02-04-07 Full Text: PDF

A Generalization of the Concavity of Rényi Entropy Power

Recently, Savaré-Toscani proved that the Rényi entropy power of general probability densities solving the p-nonlinear heat equation in Rn is a concave function of time under certain conditions of three parameters n,p,μ, which extends Costa’s concavity inequality for Shannon’s entropy power to the Rényi entropy power. In this paper, we give a condition Φ(n,p,μ) of n,p,μ under which the concavity of the Rényi entropy power is valid. The condition Φ(n,p,μ) contains Savaré-Toscani’s condition as a special case and much more cases. Precisely, the points (n,p,μ) satisfying Savaré-Toscani’s condition consist of a two-dimensional subset of R3, and the points satisfying the condition Φ(n,p,μ) consist a three-dimensional subset of R3. Furthermore, Φ(n,p,μ) gives the necessary and sufficient condition in a certain sense. Finally, the conditions are obtained with a systematic approach.

Rényi and von Neumann entropies of thermal state in Generalized Uncertainty Principle-corrected harmonic oscillator

The Rényi and von Neumann entropies of thermal state in generalized uncertainty principle (GUP)-corrected single harmonic oscillator system are explicitly computed within the first order of GUP parameter [Formula: see text]. While the von Neumann entropy with [Formula: see text] exhibits a monotonically increasing behavior in external temperature, the nonzero GUP parameter makes a decreasing behavior at large temperature region. As a result, for the case of [Formula: see text], the von Neumann entropy is maximized at the finite temperature [Formula: see text]. The Rényi entropy [Formula: see text] with nonzero [Formula: see text] also exhibits similar behavior at large temperature region. In this region, the Rényi entropy exhibits a decreasing behavior with increasing temperature. The decreasing rate becomes larger when the order of the Rényi entropy is smaller.

Objective Assessments of Mental Fatigue During a Continuous Long-Term Stress Condition

Prolonged periods of cognitive workload will cause mental fatigue, but objective, quantitative, and sensitive measurements that reflect long-term, stress-induced mental fatigue have yet to be elucidated. This study aims to apply a potential marker of Rényi entropy to investigate the mental fatigue changes in a long-term, high-level stress condition and compare three different instruments for assessment of mental fatigue: EEG, the oddball task, and self-scoring. We recruited nine individuals who participated in a 5-day intellectually challenging competition. The participants were assessed for mental fatigue each day of the competition using prefrontal cortex electroencephalogram (EEG). Reaction time in an oddball task and self-rated scoring were used comparatively to evaluate the performance of the EEG. Repeated measures ANOVA was utilized to analyze the differences among score, reaction time, and wavelet Rényi entropy. The results demonstrated that both wavelet Rényi entropy extracted from EEG and self-rated scoring revealed significant increases in mental fatigue during the 5 days of competition (P < 0.001). The reaction time of the oddball task did not show significant changes during the five-day competition (P = 0.066). Moreover, the wavelet Rényi entropy analysis of EEG showed greater sensitivity than the self-rated scoring and reaction time of the oddball task for measuring mental fatigue changes. In conclusion, this study shows that mental fatigue accumulates during long-term, high-level stress situations. The study also indicates that EEG wavelet Rényi entropy is an efficient metric to reflect the change of mental fatigue under a long-term stress condition and that EEG is a better method to assess long-term mental fatigue.

Indicators of wavefunction (de)localisation for avoided crossing in a quadrupole quantum billiard

The relationship between wavefunction (de)localisation and avoided crossing in a quadrupole billiard is analysed. The following three-types of measures are employed for wavefunction (de)localisation: inverse participation ratio, inverse of Rényi entropy, and root-mean-square (RMS) image contrast. All these measures exhibit minimal values at the centre of the avoided crossing, where the wavefunction is maximally delocalised. Our results indicate that these quantities can be sufficient for the indication of wavefunction (de)localisation.