Relative Quantum Time

The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global invariance with the perception of change, locally. By introducing relative time observables, we are able to make rigorous the Page-Wootters conditional probability formalism to show how local Heisenberg evolution is compatible with global invariance

Time Dependent Relative Risk Aversion

Risk management and the thorough understanding of the relations between financial markets and the standard theory of macroeconomics have always been among the topics most addressed by researchers, both financial mathematicians and economists. This work aims at explaining investors’ behavior from a macroeconomic aspect (modeled by the investors’ pricing kernel and their relative risk aversion) using stocks and options data. Daily estimates of investors’ pricing kernel and relative risk aversion are obtained and used to construct and analyze a three-year long time-series. The first four moments of these time-series as well as their values at the money are the starting point of a principal component analysis. The relation between changes in a major index level and implied volatility at the money and between the principal components of the changes in relative risk aversion is found to be linear. The relation of the same explanatory variables to the principal components of the changes in pricing kernels is found to be log-linear, although this relation is not significant for all of the examined maturities.risk aversion, pricing kernels, time dependent preferences

Crossover Time in Relative Fluctuations Characterizes the Longest Relaxation Time of Entangled Polymers

In entangled polymer systems, there are several characteristic time scales, such as the entanglement time and the disengagement time. In molecular simulations, the longest relaxation time (the disengagement time) can be determined by the mean square displacement (MSD) of a segment or by the shear relaxation modulus. Here, we propose the relative fluctuation analysis method, which is originally developed for characterizing large fluctuations, to determine the longest relaxation time from the center of mass trajectories of polymer chains (the time-averaged MSDs). Applying the method to simulation data of entangled polymers (by the slip-spring model and the simple reptation model), we provide a clear evidence that the longest relaxation time is estimated as the crossover time in the relative fluctuations.Comment: 17 pages, 9 figures, to appear in J. Chem. Phy

RELATIVE AGRICULTURAL PRICE CHANGES IN DIFFERENT TIME HORIZONS

Using a monthly data covering from 1974:1 to 2002:12, this paper explores the linkage between changes in macroeconomic variables (real exchange rate and inflation rate) and changes in relative agricultural prices in different time horizons (1, 12, 24, 36, 48, and 60 months). Controlling for factors likely to determine the long run trend of relative agricultural prices, the results show that long-term changes in real exchange rate has had a significant negative correlation with the long-term changes in relative agricultural prices. Conversely, changes of the general price have a role in explaining short-term changes in relative agricultural price at best.Demand and Price Analysis,

Relative entropy and waiting times for continuous-time Markov processes

For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one does need a reference measure and so the natural object is relative entropy rather than entropy. In this paper we elaborate on this in the case of continuous-time Markov processes with finite state space. A reference measure of special interest is the one associated to the time-reversed process. In that case relative entropy is interpreted as the entropy production rate. The main results of this paper are: almost-sure convergence to relative entropy of suitable waiting-times and their fluctuation properties (central limit theorem and large deviation principle).Comment: 17 page

All-sky Relative Opacity Mapping Using Night Time Panoramic Images

An all-sky cloud monitoring system that generates relative opacity maps over many of the world's premier astronomical observatories is described. Photometric measurements of numerous background stars are combined with simultaneous sky brightness measurements to differentiate thin clouds from sky glow sources such as air glow and zodiacal light. The system takes a continuous pipeline of all-sky images, and compares them to canonical images taken on other nights at the same sidereal time. Data interpolation then yields transmission maps covering almost the entire sky. An implementation of this system is currently operating through the Night Sky Live network of CONCAM3s located at Cerro Pachon (Chile), Mauna Kea (Hawaii), Haleakala (Hawaii), SALT (South Africa) and the Canary Islands (Northwestern Africa).Comment: Accepted for publication in PAS